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1
Abusabir, Ahmed, Muhammad A. Khan, Muhammad Asif, and Kamran A. Khan. "Effect of Architected Structural Members on the Viscoelastic Response of 3D Printed Simple Cubic Lattice Structures." Polymers 14, no. 3 (February 5, 2022): 618. http://dx.doi.org/10.3390/polym14030618.
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Three-dimensional printed polymeric lattice structures have recently gained interests in several engineering applications owing to their excellent properties such as low-density, energy absorption, strength-to-weight ratio, and damping performance. Three-dimensional (3D) lattice structure properties are governed by the topology of the microstructure and the base material that can be tailored to meet the application requirement. In this study, the effect of architected structural member geometry and base material on the viscoelastic response of 3D printed lattice structure has been investigated. The simple cubic lattice structures based on plate-, truss-, and shell-type structural members were used to describe the topology of the cellular solid. The proposed lattice structures were fabricated with two materials, i.e., PLA and ABS using the material extrusion (MEX) process. The quasi-static compression response of lattice structures was investigated, and mechanical properties were obtained. Then, the creep, relaxation and cyclic viscoelastic response of the lattice structure were characterized. Both material and topologies were observed to affect the mechanical properties and time-dependent behavior of lattice structure. Plate-based lattices were found to possess highest stiffness, while the highest viscoelastic behavior belongs to shell-based lattices. Among the studied lattice structures, we found that the plate-lattice is the best candidate to use as a creep-resistant LS and shell-based lattice is ideal for damping applications under quasi-static loading conditions. The proposed analysis approach is a step forward toward understanding the viscoelastic tolerance design of lattice structures.
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Li, He, Lingjie Li, Haozhang Zhong, Hanxuan Mo, and Mengyuan Gu. "Hierarchical lattice: Design strategy and topology characterization." Advances in Mechanical Engineering 15, no. 6 (June 2023): 168781322311796. http://dx.doi.org/10.1177/16878132231179623.
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The structure-material integrated design is an art-of-state concept and be enabled by additive manufacturing. The lattice material is classified into structure as well as material because mechanical properties are determined by its topology. However, the lack of a flexible design strategy hinders the lattice achieve the structure-material integrated material candidate. This work suggests the strut-nested based strategies to effectively conduct the hierarchical lattice design. The strut in the larger-scale lattice can be replaced by the smaller-scale lattice structure through the rotation, stretching, and translation operations combining the local and global numbering, thereby complete the multi-scale lattice design. The design skills are well elucidated with custom-developed algorithm; a serious of complex lattices achieve multi-scale design. The influence of hierarchical structures in lattices on a significant parameter, strut length-to-diameter, is identified. Our work offers the alternative strategy to realize the hierarchical lattice design.
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Li, Yuhua, Deyu Jiang, Rong Zhao, Xin Wang, Liqiang Wang, and Lai-Chang Zhang. "High Mechanical Performance of Lattice Structures Fabricated by Additive Manufacturing." Metals 14, no. 10 (October 12, 2024): 1165. http://dx.doi.org/10.3390/met14101165.
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Lattice structures show advantages in mechanical properties and energy absorption efficiency owing to their lightweight, high strength and adjustable geometry. This article reviews lattice structure classification, design and applications, especially those based on additive manufacturing (AM) technology. This article first introduces the basic concepts and classification of lattice structures, including the classification based on topological shapes, such as strut, surface, shell, hollow-strut, and so on, and the classification based on the deformation mechanism. Then, the design methods of lattice structure are analyzed in detail, including the design based on basic unit, mathematical algorithm and gradient structure. Next, the effects of different lattice elements, relative density, material system, load direction and fabrication methods on the mechanical performance of AM-produced lattice structures are discussed. Finally, the advantages of lattice structures in energy absorption performance are summarized, aiming at providing theoretical guidance for further optimizing and expanding the engineering application potential of lattices.
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Dong, Wei, Yang Li, Kehao Xin, Dezheng Yin, Longlong Song, and Tong Gao. "A method of designing plate structure consisting of lattices and stiffeners based on topology optimization." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 39, no. 6 (December 2021): 1233–39. http://dx.doi.org/10.1051/jnwpu/20213961233.
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In order to satisfy the lightweight design requirements of the equipment mounting plate in the hypersonic vehicle instrument cabin and improve its static/dynamic performance, a novel structure consisting of both lattices and stiffeners are studied and topology optimization method is proposed in this paper. This structure combines the advantages of lattice structures and conventional stiffened structures. First, the lattice structure is regarded as a kind of virtual material, and its equivalent mechanical properties are calculated by the homogenization method. Then, a marerial interpolation model of the virtual and solid materials are established. A topology optimization problem to minimize the mean compliance under the mass constraint is proposed to realize the layout optimization design of stiffened structure with lattices. Taking an equipment mounting plate as an example, the optimization design of the traditional stiffened structure and the novel stiffened structure with lattices is completed, respectively. Numerical analysis indicates that the lattice stiffened plate structure provides advantageous mechanical performation in the condition of the same weight. The maximum deformation under inertial force is reduced by 11.17% and the peak displacement response under harmonic excitation is reduced by 73.81% by using the stiffened structure with lattices.
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Khan, Numan, Valerio Acanfora, and Aniello Riccio. "Non-Conventional Wing Structure Design with Lattice Infilled through Design for Additive Manufacturing." Materials 17, no. 7 (March 23, 2024): 1470. http://dx.doi.org/10.3390/ma17071470.
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Lightweight structures with a high stiffness-to-weight ratio always play a significant role in weight reduction in the aerospace sector. The exploration of non-conventional structures for aerospace applications has been a point of interest over the past few decades. The adaptation of lattice structure and additive manufacturing in the design can lead to improvement in mechanical properties and significant weight reduction. The practicality of the non-conventional wing structure with lattices infilled as a replacement for the conventional spar–ribs wing is determined through finite element analysis. The optimal lattice-infilled wing structures are obtained via an automated iterative method using the commercial implicit modeling tool nTop and an ANSYS workbench. Among five different types of optimized lattice-infilled structures, the Kelvin lattice structure is considered the best choice for current applications, with comparatively minimal wing-tip deflection, weight, and stress. Furthermore, the stress distribution dependency on the lattice-unit cell type and arrangement is also established. Conclusively, the lattice-infilled structures have shown an alternative innovative design approach for lightweight wing structures.
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Li, You Tong, and Hui Wang. "The Influence of Rapid Prototyping Technology on Optimization of Automobile Energy-Absorbing Box." Key Engineering Materials 871 (January 2021): 153–58. http://dx.doi.org/10.4028/www.scientific.net/kem.871.153.
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To optimize the structure of the automobile energy-absorbing box and obtain the energy-absorbing box structure with improved impact energy absorption property, and apply it to the structure of automobile energy absorption box, test piece of crystal lattice structure and polycrystalline structure of energy-absorbing box are designed via rapid prototyping technology in this study Four different crystal lattice structures of triangle, quadrangle, hexagon, and hollow lattice structure are designed respectively. And their mechanical properties, impact energy absorption properties, and impact properties are tested. The results show that the wall thickness of the four lattices differs greatly when the quality of all crystal lattice structures is 17.8g. The compressive strength and yield strength of the hollow crystal lattice structure test piece are the largest, reaching 51.1Mpa and 69.2Mpa respectively. The maximum compression modulus of the hexagonal lattice test piece is 1462.1, followed by the hollow crystal lattice structure test piece, whose compression modulus value is 1341. The minimum absorption energy of the hollow lattice structure energy-absorbing box test piece is 2847.99J. The minimum impact value of the hollow lattice structure energy-absorbing box test piece is 69.251KN, and the impact value of triangle structure energy-absorbing box test piece is 118.11 KN. The effective impact time of the drop weight test of the hollow lattice structure energy-absorbing box test piece is only 0.08s, the peak value of the impact acceleration is 28.96g, and the maximum load of the test piece is 26.95KN. According to the comprehensive indicators, the hollow lattice structure energy-absorbing box test piece designed based on rapid prototyping technology has improved the impact energy absorption property of the automobile energy-absorbing box.
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Shatabda, Swakkhar, M. A. Hakim Newton, Mahmood A. Rashid, Duc Nghia Pham, and Abdul Sattar. "How Good Are Simplified Models for Protein Structure Prediction?" Advances in Bioinformatics 2014 (April 29, 2014): 1–9. http://dx.doi.org/10.1155/2014/867179.
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Protein structure prediction (PSP) has been one of the most challenging problems in computational biology for several decades. The challenge is largely due to the complexity of the all-atomic details and the unknown nature of the energy function. Researchers have therefore used simplified energy models that consider interaction potentials only between the amino acid monomers in contact on discrete lattices. The restricted nature of the lattices and the energy models poses a twofold concern regarding the assessment of the models. Can a native or a very close structure be obtained when structures are mapped to lattices? Can the contact based energy models on discrete lattices guide the search towards the native structures? In this paper, we use the protein chain lattice fitting (PCLF) problem to address the first concern; we developed a constraint-based local search algorithm for the PCLF problem for cubic and face-centered cubic lattices and found very close lattice fits for the native structures. For the second concern, we use a number of techniques to sample the conformation space and find correlations between energy functions and root mean square deviation (RMSD) distance of the lattice-based structures with the native structures. Our analysis reveals weakness of several contact based energy models used that are popular in PSP.
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Liu, Tinghao, and Guangbo Hao. "Design of Deployable Structures by Using Bistable Compliant Mechanisms." Micromachines 13, no. 5 (April 19, 2022): 651. http://dx.doi.org/10.3390/mi13050651.
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A deployable structure can significantly change its geometric shape by switching lattice configurations. Using compliant mechanisms as the lattice units can prevent wear and friction among multi-part mechanisms. This work presents two distinctive deployable structures based on a programmable compliant bistable lattice. Several novel parameters are introduced into the bistable mechanism to better control the behaviour of bistable mechanisms. By adjusting the defined geometry parameters, the programmable bistable lattices can be optimized for specific targets such as a larger deformation range or higher stability. The first structure is designed to perform 1D deployable movement. This structure consists of multi-series-connected bistable lattices. In order to explore the 3D bistable characteristic, a cylindrical deployable mechanism is designed based on the curved double tensural bistable lattice. The investigation of bistable lattices mainly involves four types of bistable mechanisms. These bistable mechanisms are obtained by dividing the long segment of traditional compliant bistable mechanisms into two equal parts and setting a series of angle data to them, respectively. The experiment and FEA simulation results confirm the feasibility of the compliant deployable structures.
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Rachůnek, Jiří. "Structure spaces of lattice ordered groups." Czechoslovak Mathematical Journal 39, no. 4 (1989): 686–91. http://dx.doi.org/10.21136/cmj.1989.102345.
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Jiang, Cho-Pei, Alvian Toto Wibisono, and Tim Pasang. "Selective Laser Melting of Stainless Steel 316L with Face-Centered-Cubic-Based Lattice Structures to Produce Rib Implants." Materials 14, no. 20 (October 11, 2021): 5962. http://dx.doi.org/10.3390/ma14205962.
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Selective laser melting has a great potential to manufacture biocompatible metal alloy scaffolds or implants with a regulated porosity structure. This study uses five face-centered cubic (FCC) lattice structures, including FCC, FCC-Z, S-FCC, S-FCC-Z, and FCC-XYZ. Specimens with different lattice structures are fabricated using two laser energy densities, 71 J/mm3 and 125 J/mm3. Density, tensile, compressive and flexural test results exhibit the effect of laser parameters and lattice structure geometries on mechanical properties. The higher laser energy density of 125 J/mm3 results in higher properties such as density, strength, and Young’s modulus than the laser energy density of 71 J/mm3. The S-FCC lattice has the lowest density among all lattices. The mechanical tests result show specimen with FCC-XYZ lattice structures fabricated using a laser energy density of 125 J/mm3 meet the tensile properties requirement for human ribs. This structure also meets the requirement in flexural strength performance, but its stiffness is over that of human ribs. The compression test results of lattices are still incomparable due to unavailable compression data of the human ribs. In short, The FCC-XYZ lattice design fabricated by the 125 J/mm3 laser energy density parameter can be used to manufacture customized rib implants.
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Wang, Xinglong, Cheng Wang, Xin Zhou, Di Wang, Mingkang Zhang, Yun Gao, Lei Wang, and Peiyu Zhang. "Evaluating Lattice Mechanical Properties for Lightweight Heat-Resistant Load-Bearing Structure Design." Materials 13, no. 21 (October 27, 2020): 4786. http://dx.doi.org/10.3390/ma13214786.
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Heat-resistant, load-bearing components are common in aircraft, and they have high requirements for lightweight and mechanical performance. Lattice topology optimization can achieve high mechanical properties and obtain lightweight designs. Appropriate lattice selection is crucial when employing the lattice topology optimization method. The mechanical properties of a structure can be optimized by choosing lattice structures suitable for the specific stress environment being endured by the structural components. Metal lattice structures exhibit excellent unidirectional load-bearing performance and the triply periodic minimal surface (TPMS) porous structure can satisfy multi-scale free designs. Both lattice types can provide unique advantages; therefore, we designed three types of metal lattices (body-centered cubic (BCC), BCC with Z-struts (BCCZ), and honeycomb) and three types of TPMS lattices (gyroid, primitive, and I-Wrapped Package (I-WP)) combined with the solid shell. Each was designed with high level of relative density (40%, 50%, 60%, 70%, and 80%), which can be directly used in engineering practice. All test specimens were manufactured by selective laser melting (SLM) technology using Inconel 718 superalloy as the material and underwent static tensile testing. We found that the honeycomb test specimen exhibits the best strength, toughness, and stiffness properties among all structures evaluated, which is especially suitable for the lattice topology optimization design of heat-resistant, unidirectional load-bearing structures within aircraft. Furthermore, we also found an interesting phenomenon that the toughness of the primitive and honeycomb porous test specimens exhibited sudden increases from 70% to 80% and from 50% to 60% relative density, respectively, due to their structural characteristics. According to the range of the exponent value n and the deformation laws of porous structures, we also concluded that a porous structure would exhibit a stretching-dominated deformation behavior when exponent value n < 0.3, a bending-dominated deformation behavior when n > 0.55, and a stretching-bending-dominated deformation behavior when 0.3 < n < 0.55. This study can provide a design basis for selecting an appropriate lattice in lattice topology optimization design.
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FELSNER, STEFAN, and KOLJA B. KNAUER. "ULD-Lattices and Δ-Bonds." Combinatorics, Probability and Computing 18, no. 5 (September 2009): 707–24. http://dx.doi.org/10.1017/s0963548309010001.
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We provide a characterization of upper locally distributive lattices (ULD-lattices) in terms of edge colourings of their cover graphs. In many instances where a set of combinatorial objects carries the order structure of a lattice, this characterization yields a slick proof of distributivity or UL-distributivity. This is exemplified by proving a distributive lattice structure on Δ-bonds with invariant circular flow-difference. This instance generalizes several previously studied lattice structures, in particular,c-orientations (Propp), α-orientations of planar graphs (Felsner, resp. de Mendez) and planar flows (Khuller, Naor and Klein). The characterization also applies to other instances,e.g., to chip-firing games.
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Terwijn, Sebastiaan A. "On the structure of the Medvedev lattice." Journal of Symbolic Logic 73, no. 2 (June 2008): 543–58. http://dx.doi.org/10.2178/jsl/1208359059.
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AbstractWe investigate the structure of the Medvedev lattice as a partial order. We prove that every interval in the lattice is either finite, in which case it is isomorphic to a finite Boolean algebra, or contains an antichain of size . the size of the lattice itself. We also prove that it is consistent with ZFC that the lattice has chains of size . and in fact that these big chains occur in every infinite interval. We also study embeddings of lattices and algebras. We show that large Boolean algebras can be embedded into the Medvedev lattice as upper semilattices, but that a Boolean algebra can be embedded as a lattice only if it is countable. Finally we discuss which of these results hold for the closely related Muchnik lattice.
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Kitano, Yasuyuki, and Masaki Takata. "Coincidence-site-lattice-pattern (CSL-pattern) of 70.5°/[110] boundary of the 6H-type layer structure." Proceedings, annual meeting, Electron Microscopy Society of America 48, no. 4 (August 1990): 356–57. http://dx.doi.org/10.1017/s0424820100174916.
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The most useful and intuitive model may be a CSL-model to analyze boundary structures. In order to apply the CSL-model to layer structures, we have proposed to use ‘lattice point’ in a wide sence and to add extra lattice points to the Bravais lattice points when interpenetrating(IP)-lattices are drawn. These lattice points will be called ‘extended lattice points’. It is well known that a layer structure is built up with (almost) identical layers stacking on the top of the others with a cirtain amount of shift in a direction perpendicular to the stacking. Each layer consists of one or more atomic planes and has almost (or exactly) the same atomic configuration. The extended lattice points can be defined as the origins in each layer in crystal. The number of such points depends upon the number of layers in a unit cell.To draw IP-lattices we have adopted all the extended lattice points in addition to the Bravais lattice points. There are three important advantages of doing this extension. First is that the Coincidence-Sites in the IP-lattices drawn do not scatter homogeneously, but gather in a region and make a cluster. They exibit a characteristic pattern of Coincidence-Sites. This pattern is called a CSL-pattern. Second is that the DSC-lattice (Displacement Shift Complete Lattice) provides a set of basic vectors smaller than predicted before extention.
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Kitano, Yasuyuki, and Masaki Takata. "Coincidence-Site-Lattice Pattern (Csl Pattern) of 70.5°/[110] Boundary of the 6H-Type Layer Structure." Proceedings, annual meeting, Electron Microscopy Society of America 48, no. 1 (August 12, 1990): 576–77. http://dx.doi.org/10.1017/s0424820100181646.
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The most useful and intuitive model may be a CSL-model to analyze boundary structures. In order to apply the CSL-model to layer structures, we have proposed to use ‘lattice point’ in a wide sence and to add extra lattice points to the Bravais lattice points when interpenetrating(IP)-lattices are drawn. These lattice points will be called ‘extended lattice points‘. It is well known that a layer structure is built up with (almost) identical layers stacking on the top of the others with a cirtain amount of shift in a direction perpendicular to the stacking. Each layer consists of one or more atomic planes and has almost (or exactly) the same atomic configuration. The extended lattice points can be defined as the origins in each layer in crystal. The number of such points depends upon the number of layers in a unitcell.To draw IP-lattices we have adopted all the extended lattice points in addition to the Bravais lattice points. There are three important advantages of doing this extension[ 1,2,3]. First is that the Coincidence-Sites in the IP-lattices drawn do not scatter homogeneously, but gather in a region and make a cluster. They exibit a characteristic pattern of Coincidence-Sites. This pattern is called a CSL-pattern. Second is that the DSC-lattice (Displacement Shift Complete Lattice) provides a set of basic vectors smaller than predicted before extention. Third is that reasonable models of boundaries are able to be made between two different layer structures. This is because the crystal volume attributed to one extended lattice point is exactly the same for the both adjacent crystals.
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Kirihara, Soshu, and Yoshinari Miyamoto. "Selective Transmission of Electromagnetic Wave by Using Diamond Photonic Crystals with Graded Lattice Spacing." Advances in Science and Technology 45 (October 2006): 1139–44. http://dx.doi.org/10.4028/www.scientific.net/ast.45.1139.
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Three-dimensional electromagnetic or photonic crystals with periodic variations of the dielectric constants were fabricated by using a rapid prototyping method called stereolithography. Millimeter-order epoxy lattices with a diamond structure were designed to reflect electromagnetic waves by forming an electromagnetic band gap in GHz range. Titania based ceramic particles were dispersed into the lattice to control the dielectric constant. The diamond lattice structures formed the perfect band gap reflecting electromagnetic waves for all directions. The location of the band gap agreed with the band calculation using the plane wave propagation method. The diamond structures with graded lattice spacing were successfully fabricated as well, resulting in the directional transmission of microwaves. The stretching ratio of the lattice spacing in the crystal structure was changed according to the electromagnetic band calculation. A microwave antenna head composed of the diamond structure with graded lattice spacing was fabricated which achieved the unidirectional transmission.
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Huang, Aiping, and William Zhu. "Geometric Lattice Structure of Covering-Based Rough Sets through Matroids." Journal of Applied Mathematics 2012 (2012): 1–25. http://dx.doi.org/10.1155/2012/236307.
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Covering-based rough set theory is a useful tool to deal with inexact, uncertain, or vague knowledge in information systems. Geometric lattice has been widely used in diverse fields, especially search algorithm design, which plays an important role in covering reductions. In this paper, we construct three geometric lattice structures of covering-based rough sets through matroids and study the relationship among them. First, a geometric lattice structure of covering-based rough sets is established through the transversal matroid induced by a covering. Then its characteristics, such as atoms, modular elements, and modular pairs, are studied. We also construct a one-to-one correspondence between this type of geometric lattices and transversal matroids in the context of covering-based rough sets. Second, we present three sufficient and necessary conditions for two types of covering upper approximation operators to be closure operators of matroids. We also represent two types of matroids through closure axioms and then obtain two geometric lattice structures of covering-based rough sets. Third, we study the relationship among these three geometric lattice structures. Some core concepts such as reducible elements in covering-based rough sets are investigated with geometric lattices. In a word, this work points out an interesting view, namely, geometric lattice, to study covering-based rough sets.
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Sorbi, Andrea. "Some remarks on the algebraic structure of the Medvedev Lattice." Journal of Symbolic Logic 55, no. 2 (June 1990): 831–53. http://dx.doi.org/10.2307/2274668.
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AbstractThis paper investigates the algebraic structure of the Medvedev lattice . We prove that is not a Heyting algebra. We point out some relations between and the Dyment lattice and the Mučnik lattice. Some properties of the degrees of enumerability are considered. We give also a result on embedding countable distributive lattices in the Medvedev lattice.
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Semenov, Alexei, and Sergei Soprunov. "Automorphisms and Definability (of Reducts) for Upward Complete Structures." Mathematics 10, no. 20 (October 12, 2022): 3748. http://dx.doi.org/10.3390/math10203748.
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The Svenonius theorem establishes the correspondence between definability of relations in a countable structure and automorphism groups of these relations in extensions of the structure. This may help in finding a description of the lattice constituted by all definability spaces (reducts) of the original structure. Results on definability lattices were previously obtained only for ω-categorical structures with finite signature. In our work, we introduce the concept of an upward complete structure and define the upward completion of a structure. For upward complete structures, the Galois correspondence between definability lattice and the lattice of closed supergroups of the automorphism group of the structure is an anti-isomorphism. We describe the natural class of structures which have upward completion, we call them discretely homogeneous graphs, present the explicit construction of their completion and automorphism groups of completions. We establish the general localness property of discretely homogeneous graphs and present examples of completable structures and their completions.
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Ma, Songyang, Wenzhen Chen, and Hongguang Xiao. "Influence of Micro Ribs Segment on Quasi-periodic Large-scale Vortex Structure in 4 Rod Bundle Lattices." Journal of Physics: Conference Series 2584, no. 1 (September 1, 2023): 012056. http://dx.doi.org/10.1088/1742-6596/2584/1/012056.
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Abstract Rod bundle lattices play a crucial role in nuclear reactors, steam generators, and heat exchangers. The inclusion of quasi-periodic large-scale vortex structures (QLVS) can enhance flow mixing between the channels of the rod bundle and improve the lattice’s heat transfer capability. To study the impact of micro-rib segments on flow and heat transfer in the lattice, the Reynolds stress model (RSM) is utilized. Results reveal that the arrangement of micro-ribs on the rod bundle surface promotes the generation of QLVSs. These micro-rib segments modify the flow field within the lattice, thereby influencing the QLVS. The drag coefficient and heat transfer coefficient of the rod bundle lattice with micro-rib segments show a positive correlation with the length of these segments compared with the standard rod bundle lattice.
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Guo, Zhengmiao, Fan Yang, Lingbo Li, and Jiacheng Wu. "Bio-Inspired Curved-Elliptical Lattice Structures for Enhanced Mechanical Performance and Deformation Stability." Materials 17, no. 17 (August 24, 2024): 4191. http://dx.doi.org/10.3390/ma17174191.
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Lattice structures, characterized by their lightweight nature, high specific mechanical properties, and high design flexibility, have found widespread applications in fields such as aerospace and automotive engineering. However, the lightweight design of lattice structures often presents a trade-off between strength and stiffness. To tackle this issue, a bio-inspired curved-elliptical (BCE) lattice is proposed to enhance the mechanical performance and deformation stability of three-dimensional lattice structures. BCE lattice specimens with different parameters were fabricated using selective laser melting (SLM) technology, followed by quasi-static compression tests. Finite element (FE) numerical simulations were also carried out for validation. The results demonstrate that the proposed BCE lattice structures exhibit stronger mechanical performance and more stable deformation modes that can be adjusted through parameter tuning. Specifically, by adjusting the design parameters, the BCE lattice structure can exhibit a bending-dominated delocalized deformation mode, avoiding catastrophic collapse during deformation. The specific energy absorption (SEA) can reach 24.6 J/g at a relative density of only 8%, with enhancements of 48.5% and 297.6% compared with the traditional energy-absorbing lattices Octet and body-center cubic (BCC), respectively. Moreover, the crushing force efficiency (CFE) of the BCE lattice structure surpasses those of Octet and BCC by 34.9% and 15.8%, respectively. Through a parametric study of the influence of the number of peaks N and the curve amplitude A on the compression performance of the BCE lattice structure, the compression deformation mechanism is further analyzed. The results indicate that the curve amplitude A and the number of peaks N have significant impacts on the deformation mode of the BCE lattice. By adjusting the parameters N and A, a structure with a combination of high energy absorption, high stiffness, and strong fracture resistance can be obtained, integrating the advantages of tensile-dominated and bending-dominated lattice structures.
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HART, JAMES B., LORI RAFTER, and CONSTANTINE TSINAKIS. "THE STRUCTURE OF COMMUTATIVE RESIDUATED LATTICES." International Journal of Algebra and Computation 12, no. 04 (August 2002): 509–24. http://dx.doi.org/10.1142/s0218196702001048.
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A commutative residuated lattice, is an ordered algebraic structure [Formula: see text], where (L, ·, e) is a commutative monoid, (L, ∧, ∨) is a lattice, and the operation → satisfies the equivalences [Formula: see text] for a, b, c ∊ L. The class of all commutative residuated lattices, denoted by [Formula: see text], is a finitely based variety of algebras. Historically speaking, our study draws primary inspiration from the work of M. Ward and R. P. Dilworth appearing in a series of important papers [9, 10, 19–22]. In the ensuing decades special examples of commutative, residuated lattices have received considerable attention, but we believe that this is the first time that a comprehensive theory on the structure of residuated lattices has been presented from the viewpoint of universal algebra. In particular, we show that [Formula: see text] is an "ideal variety" in the sense that its congruences correspond to order-convex subalgebras. As a consequence of the general theory, we present an equational basis for the subvariety [Formula: see text] generated by all commutative, residuated chains. We conclude the paper by proving that the congruence lattice of each member of [Formula: see text] is an algebraic, distributive lattice whose meet-prime elements form a root-system (dual tree). This result, together with the main results in [12, 18], will be used in a future publication to analyze the structure of finite members of [Formula: see text]. A comprehensive study of, not necessarily commutative, residuated lattices is presented in [4].
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Салахутдинов, Марат Айдарович, Иван Леонидович Кузнецов, and Адель Эдуардович Фахрутдинов. "LATTICE STRUCTURE." Академический вестник УралНИИпроект РААСН, no. 2(41) (July 1, 2019): 86–90. http://dx.doi.org/10.25628/uniip.2019.41.2.016.
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Использование уголковых профилей в качестве элементов решетки в решетчатых конструкциях приводит к увеличению расхода стали при их креплении болтами. Предлагается сплющивание полок уголка в месте его крепления к поясам и разрез обушка для симметричного крепления к стенкам поясов. Для обеспечения симметричности и равноустойчивости предлагается оптимальный угол раскрытия полок уголков. На примере решетчатой конструкции показано достижение экономии по расходу стали. The use of angular profiles as lattice elements in lattice structures results in an increase in the consumption of steel when they are fastened with bolts. The flattening of the angle’s flanges in the place of its attachment to the chords and the cut of the heel for symmetrical fastening to the web of the chords are proposed. To ensure symmetry and bistable, an optimum angle between legs of angle section is proposed. On the example of the lattice construction, it is shown that the economy of steel consumption is achieved.
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AKBAY, Özgün Ceren, Burak Özdemir, Erkan Bahçe, and Ender Emir. "Deformation Behaviors Investigation of CoCr Alloy Lattice Structures under Compression Test." Journal of Manufacturing Engineering 18, no. 1 (March 1, 2023): 001–10. http://dx.doi.org/10.37255/jme.v18i1pp001-010.
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ith the development of the additive manufacturing method, the production of lattice structures with complex geometries attracts increasing attention. These lattice structures can be designed with the desired properties, and they are encountered in many areas such as automotive, aerospace and aviation, and manufacturing industries, as they offer the freedom to control their physical, mechanical and geometric properties. The high strength characteristic of lattice structures that can be designed at any scale makes these structures useful for producing different designs. Since the mechanical responses of the lattice structures depend on the lattice design parameters, such as the large number of independent struts forming the lattice, cell size and cell geometry, the mechanical behaviour of these structures should be examined. In this study, a porous lattice structure with four different cell models, namely Dode Medium, Diamond, Rhombic Dodecahedron, and Dode Thin, was produced by Selective Laser Melting (SLM) method. In order to reveal the mechanical properties and deformation responses of the porous lattice structures, they were analyzed under compression test and by the finite element method, and experimental and numerical procedures were compared. The effect of the compression test on the lattice properties and how the deformation is distributed throughout the lattice structure were investigated. The finite Element Analysis and Digital Image Processing (DIP) method was used to determine how the lattices deform. The results obtained will be useful for designing new metallic lattice structures with more excellent deformation resistance in future studies.
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NURAKUNOV, A. M. "UNREASONABLE LATTICES OF QUASIVARIETIES." International Journal of Algebra and Computation 22, no. 03 (May 2012): 1250006. http://dx.doi.org/10.1142/s0218196711006728.
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A quasivariety is a universal Horn class of algebraic structures containing the trivial structure. The set [Formula: see text] of all subquasivarieties of a quasivariety [Formula: see text] forms a complete lattice under inclusion. A lattice isomorphic to [Formula: see text] for some quasivariety [Formula: see text] is called a lattice of quasivarieties or a quasivariety lattice. The Birkhoff–Maltsev Problem asks which lattices are isomorphic to lattices of quasivarieties. A lattice L is called unreasonable if the set of all finite sublattices of L is not computable, that is, there is no algorithm for deciding whether a finite lattice is a sublattice of L. The main result of this paper states that for any signature σ containing at least one non-constant operation, there is a quasivariety [Formula: see text] of signature σ such that the quasivariety lattice [Formula: see text] is unreasonable. Moreover, there are uncountable unreasonable lattices of quasivarieties. We also present some corollaries of the main result.
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Jin, Xin, Guo Xi Li, and Meng Zhang. "Optimal design of three-dimensional non-uniform nylon lattice structures for selective laser sintering manufacturing." Advances in Mechanical Engineering 10, no. 7 (July 2018): 168781401879083. http://dx.doi.org/10.1177/1687814018790833.
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As a kind of novel multifunctional structure with three-dimensional pores characterized by low relative density, lattice structures can attain a lightweight design while maintaining high specific mechanical properties in three-dimensional solid structures. Focusing on the challenge of finding the optimal design of lattice structures in the design object, a design and modeling method of non-uniform three-dimensional lattice structures is proposed while ensuring the selective laser sintering manufacturability. Optimization for cell type, cell size, and strut size distribution of lattices is specified with the mechanical properties analyzed and the material model calculated beforehand. The manufacturing constraints are analyzed and expressed in topology optimization and the optimal distribution of topology optimization results is mapped to the strut size distribution of lattice cells. The rapid and automatic computer-aided design modeling of optimized structures is realized by the parametric definition and assembling of lattice components. Finally, the non-uniform structures are successfully manufactured by selective laser sintering and it is shown by means of finite element analysis and experiments that the proposed design approach can improve the mechanical performance compared to the uniform lattice structure under the same weight reduction. And for the design object in this study, body-centered structure with cell size [Formula: see text]mm is chosen as the optimal cell type and cell size under the given selective laser sintering manufacturing constraints.
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Yu, Guoji, Cheng Miao, Hailing Wu, and Jiayi Liang. "Mechanical performance of heterogeneous lattice structure." Vibroengineering Procedia 50 (September 21, 2023): 206–12. http://dx.doi.org/10.21595/vp.2023.23454.
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Heterogeneous lattice structure was constructed with rhombic dodecahedron and octet-truss lattice structures. The rhombic dodecahedron lattice was bending-dominated, while octet-truss lattice was stretching-dominated. The rhombic dodecahedron lattice fabricated by selective laser melting (SLM) was compressed by a universal testing machine, which was also investigated by finite element model. Afterwards, the validated numerical model was used to study the designed heterogeneous lattice. Calculations indicates that heterogeneous lattice structures outperform the rhombic dodecahedron lattice structure. The introduction of octet-truss unit cell enhances the mechanical behavior of the heterogeneous lattice structure in terms of Young’s modulus and stress magnitude, which depends on the pattern of octet-truss cells.
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Wang, Peng, Fan Yang, and Jinfeng Zhao. "Compression Behaviors and Mechanical Properties of Modified Face-Centered Cubic Lattice Structures under Quasi-Static and High-Speed Loading." Materials 15, no. 5 (March 6, 2022): 1949. http://dx.doi.org/10.3390/ma15051949.
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Our previous work reported a novel lattice structure composed of modified face-centered cubic (modified FCC) cells with crossing rods introduced at the center of each cell. In this work, the proposed modified FCC lattice is further investigated to ascertain its compression behaviors under different loading rates. For this purpose, numerical simulations were carried out for compressing the two-dimensional and three-dimensional modified FCC lattice structures with different loading rates, and to compare their deformation modes and energy absorption capacity under different loading rates. In addition, lattice specimens were fabricated using selective laser melting technology and quasi-static compression experiments were performed to validate the finite element simulations. The results indicate that the proposed modified FCC lattices exhibit better load-bearing capacity and energy absorption than the traditional FCC lattices under different loading rates. Under high-speed loading, the modified FCC structure is less susceptible to buckling, and the length ratio of the central cross-rod corresponding to maximum energy absorption capacity is larger.
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Flaut, Cristina, and Dana Piciu. "Commutative Rings Behind Divisible Residuated Lattices." Mathematics 12, no. 23 (December 9, 2024): 3867. https://doi.org/10.3390/math12233867.
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Divisible residuated lattices are algebraic structures corresponding to a more comprehensive logic than Hajek’s basic logic with an important significance in the study of fuzzy logic. The purpose of this paper is to investigate commutative rings whose lattice of ideals can be equipped with a structure of divisible residuated lattice. We show that these rings are multiplication rings. A characterization, additional examples, and their connections to other classes of rings are established. Furthermore, we analyze the structure of divisible residuated lattices using finite commutative rings. From computational considerations, we present an explicit construction of isomorphism classes of divisible residuated lattices (that are not BL-algebras) of small size n (2≤n≤6), and we give summarizing statistics.
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Martínez-Moro, Edgar, and Roberto Canogar-Mckenzie. "On the structure of multipliers ofℤ2." International Journal of Mathematics and Mathematical Sciences 2003, no. 15 (2003): 935–46. http://dx.doi.org/10.1155/s0161171203203124.
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We show the combinatorial structure ofℤ2modulo sublattices similar toℤ2. The tool we use for dealing with this purpose is the notion of association scheme. We classify when the scheme defined by the lattice is imprimitive and characterize its decomposition in terms of the decomposition of the Gaussian integer defining the lattice. This arises in the classification of different forms of tilingℤ2by lattices of this type. The main application of these structures is that they are closely related to two-dimensional signal constellations with a Mannheim metric in the coding theory.
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Emamy, Hamed, Oleg Gang, and Francis W. Starr. "The Stability of a Nanoparticle Diamond Lattice Linked by DNA." Nanomaterials 9, no. 5 (April 26, 2019): 661. http://dx.doi.org/10.3390/nano9050661.
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The functionalization of nanoparticles (NPs) with DNA has proven to be an effective strategy for self-assembly of NPs into superlattices with a broad range of lattice symmetries. By combining this strategy with the DNA origami approach, the possible lattice structures have been expanded to include the cubic diamond lattice. This symmetry is of particular interest, both due to the inherent synthesis challenges, as well as the potential valuable optical properties, including a complete band-gap. Using these lattices in functional devices requires a robust and stable lattice. Here, we use molecular simulations to investigate how NP size and DNA stiffness affect the structure, stability, and crystallite shape of NP superlattices with diamond symmetry. We use the Wulff construction method to predict the equilibrium crystallite shape of the cubic diamond lattice. We find that, due to reorientation of surface particles, it is possible to create bonds at the surface with dangling DNA links on the interior, thereby reducing surface energy. Consequently, the crystallite shape depends on the degree to which such surface reorientation is possible, which is sensitive to DNA stiffness. Further, we determine dependence of the lattice stability on NP size and DNA stiffness by evaluating relative Gibbs free energy. We find that the free energy is dominated by the entropic component. Increasing NP size or DNA stiffness increases free energy, and thus decreases the relative stability of lattices. On the other hand, increasing DNA stiffness results in a more precisely defined lattice structure. Thus, there is a trade off between structure and stability of the lattice. Our findings should assist experimental design for controlling lattice stability and crystallite shape.
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Eljihad, A., M. Nassraoui, and O. Bouksour. "Experimental investigation of mechanical stiffness in lattice structures fabricated with PLA using fused deposition modelling." Journal of Achievements in Materials and Manufacturing Engineering 119, no. 2 extended (August 1, 2023): 60–71. http://dx.doi.org/10.5604/01.3001.0053.9491.
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The objective of the paper is to design and characterise with polylactic acid (PLA) material three cellular structures in the form of lattices which are diagonal-octet-centred shapes for two sizes 6x6x6 and 12x12x12 with a compression test to examine their stiffness using FDM technology compared to polyjet technology.The study used two analytical approaches to investigate lattice structures: experimental analysis and theoretical analysis. Experimental methods such as compression tests were conducted to determine the characteristics of lattice structures. In addition, theoretical analysis was conducted using Hook's law and Ashby's Gibson model to predict appropriate behaviour. The combination of experimental and theoretical methods provided a comprehensive understanding of lattice structures and their properties.The experimental study examined the impact of the shape and size of a lattice structure on the stiffness and lightness of objects 3D printed with FDM technology by PLA material. The research revealed that the 6x6x6 diagonal lattice structure size provided a good balance between stiffness and lightness. While the 6x6x6 byte structure was even lighter, with a mass ratio of 2.09 compared to the diagonal structure, it was less rigid, with a ratio of 0.43, making the diagonal structure more suitable for certain applications. The study highlights the importance of considering both the shape and size of the lattice structure when designing 3D-printed objects with specific mechanical properties; the chosen structure could be a good choice for applications where stiffness and lightness are important.The limitations of the research lie in its limited scope, focusing primarily on the effect of shape (octet-diagonal centred) and unit cell size on Young's modulus of PLA material. Other aspects of 3D printing, such as material selection and thermal properties, were not considered. Furthermore, the results obtained are specific to the printing parameters and experimental conditions chosen, which limits their generalizability to other 3D printing configurations or methods. However, these results have important implications for optimising the PLA printing process. They enable the identification of optimal parameters, such as unit cell shape and size, to produce stiffer, higher-quality structures. In addition, the research is helping to improve the mechanical properties of 3D-printed lattice parts, paving the way for more efficient manufacturing methods and stronger components.Our analysis can be used as a decision aid for the design of FDM lattice parts. Indeed, we can choose the diagonal structure of 6x6x6, which would provide favourable stiffness for functional parts.The paper explores the compression test of lattice structures using FDM technology, which presents a new direction for additive manufacturing. The study takes an experimental approach to evaluate the reliability of various additive manufacturing technologies for creating lattice structures. The study results provide insight into the most reliable technology for producing lattice structures.
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Rahman, Hafizur, Ebrahim Yarali, Ali Zolfagharian, Ahmad Serjouei, and Mahdi Bodaghi. "Energy Absorption and Mechanical Performance of Functionally Graded Soft–Hard Lattice Structures." Materials 14, no. 6 (March 11, 2021): 1366. http://dx.doi.org/10.3390/ma14061366.
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Today, the rational combination of materials and design has enabled the development of bio-inspired lattice structures with unprecedented properties to mimic biological features. The present study aims to investigate the mechanical performance and energy absorption capacity of such sophisticated hybrid soft–hard structures with gradient lattices. The structures are designed based on the diversity of materials and graded size of the unit cells. By changing the unit cell size and arrangement, five different graded lattice structures with various relative densities made of soft and hard materials are numerically investigated. The simulations are implemented using ANSYS finite element modeling (FEM) (2020 R1, 2020, ANSYS Inc., Canonsburg, PA, USA) considering elastic-plastic and the hardening behavior of the materials and geometrical non-linearity. The numerical results are validated against experimental data on three-dimensional (3D)-printed lattices revealing the high accuracy of the FEM. Then, by combination of the dissimilar soft and hard polymeric materials in a homogenous hexagonal lattice structure, two dual-material mechanical lattice statures are designed, and their mechanical performance and energy absorption are studied. The results reveal that not only gradual changes in the unit cell size provide more energy absorption and improve mechanical performance, but also the rational combination of soft and hard materials make the lattice structure with the maximum energy absorption and stiffness, in comparison to those structures with a single material, interesting for multi-functional applications.
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Bathla, Pranjal, and John Kennedy. "3D Printed Structured Porous Treatments for Flow Control around a Circular Cylinder." Fluids 5, no. 3 (August 14, 2020): 136. http://dx.doi.org/10.3390/fluids5030136.
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The use of porous coatings is one of the passive flow control methods used to reduce turbulence, noise and vibrations generated due to fluid flow. Porous coatings for flow stabilization have potential for a light-weight, cost-effective, and customizable solution. The design and performance of a structured porous coating depend on multiple control parameters like lattice size, strut thickness, lattice structure/geometry, etc. This study investigated the suitability of MSLA 3D printers to manufacture porous coatings based on unit cell designs to optimize porous lattices for flow control behind a cylinder. The Reynolds number used was 6.1×104–1.5×105 and the flow measurements were taken using a hotwire probe. Different experiment sets were conducted for single cylinder with varying control parameters to achieve best performing lattice designs. It was found that lattice structures with higher porosity produced lower turbulence intensity in the wake of the cylinder. However, for constant porosity lattice structures, there was negligible difference in turbulence and mean wake velocity levels. Coating thickness did not have a linear relationship with turbulence reduction, suggesting an optimal thickness value. For constant porosity coatings, cell count in coating thickness did not influence the turbulence or mean wake velocity. Partial coating designs like helical and spaced coatings had comparable performance to that of a full coating. MSLA printers were found capable of manufacturing thin and complex porous lattices.
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Razmjooei, Nasrin, and Robert Magnusson. "Band Dynamics of Multimode Resonant Nanophotonic Lattices with Adjustable Liquid Interfaces." Nanomaterials 13, no. 16 (August 16, 2023): 2350. http://dx.doi.org/10.3390/nano13162350.
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Subwavelength resonant lattices offer a wide range of fascinating spectral phenomena under broadside illumination. The resonance mechanism relies on the generation of lateral Bloch modes that are phase matched to evanescent diffraction orders. The spectral properties and the total number of resonance states are governed by the structure of leaky modes and the mode count. This study investigates the effect of interface modifications on the band dynamics and bound-state transitions in guided-mode resonant lattices. We provide photonic lattices comprising rectangular Si3N4 rods with a liquid film with an adjustable boundary. The band structures and band flips are examined through numerical simulations using the rigorous coupled-wave analysis (RCWA) method and analyzing the zero-order spectral reflectance as a function of the incident angle. The band structures and band flips are examined through numerical simulations, and the influences of the refractive index and the thickness of the oil layer on the band dynamics are investigated. The results reveal distinct resonance linewidths corresponding to different refractive indices of the oil layer. Furthermore, the effect of the oil thickness on the band dynamics is explored, demonstrating precise control over the number of propagating modes within the lattice structure. Theoretical simulations and experimental results are presented for a subwavelength silicon-nitride lattice combined with a liquid film featuring an adjustable boundary. The presence of a relatively thick liquid waveguiding region enables the emergence of additional modes, including the first four transverse-electric (TE) leaky modes, which produce observable resonance signatures. Through experimental manipulation of the basic lattice’s duty cycle, the four bands undergo quantifiable band transitions and closures. The experimental results obtained within the 1400–1600 nm spectral range exhibit reasonable agreement with the numerical analysis. These findings underscore the significant role played by the interface in shaping the band dynamics of the lattice structure, providing valuable insights into the design and optimization of photonic lattices with adjustable interfaces.
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HENTSCHEL, MICHAEL, ALOYS KRIEG, and GABRIELE NEBE. "ON THE CLASSIFICATION OF EVEN UNIMODULAR LATTICES WITH A COMPLEX STRUCTURE." International Journal of Number Theory 08, no. 04 (May 16, 2012): 983–92. http://dx.doi.org/10.1142/s1793042112500583.
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This paper classifies the even unimodular lattices that have a structure as a Hermitian [Formula: see text]-lattice of rank r ≤ 12 for rings of integers in imaginary quadratic number fields K of class number 1. The Hermitian theta series of such a lattice is a Hermitian modular form of weight r for the full modular group, therefore we call them theta lattices. For arbitrary imaginary quadratic fields we derive a mass formula for the principal genus of theta lattices which is applied to show completeness of the classifications.
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Seharing, Asliah, Abdul Hadi Azman, and Shahrum Abdullah. "Finite element analysis of gradient lattice structure patterns for bone implant design." International Journal of Structural Integrity 11, no. 4 (June 11, 2020): 535–45. http://dx.doi.org/10.1108/ijsi-03-2020-0028.
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PurposeThe objective of this paper is to identify suitable lattice structure patterns for the design of porous bone implants manufactured using additive manufacturing.Design/methodology/approachThe study serves to compare and analyse the mechanical behaviours between cubic and octet-truss gradient lattice structures. The method used was uniaxial compression simulations using finite element analysis to identify the translational displacements.FindingsFrom the simulation results, in comparison to the cubic lattice structure, the octet-truss lattice structure showed a significant difference in mechanical behaviour. In the same design space, the translational displacement for both lattice structures increased as the relative density decreased. Apart from the relative density, the microarchitecture of the lattice structure also influenced the mechanical behaviour of the gradient lattice structure.Research limitations/implicationsGradient lattice structures are suitable for bone implant applications because of the variation of pore sizes that mimic the natural bone structures. The complex geometry that gradient lattice structures possess can be manufactured using additive manufacturing technology.Originality/valueThe results demonstrated that the cubic gradient lattice structure has the best mechanical behaviour for bone implants with appropriate relative density and pore size.
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Huang, Aiping, and William Zhu. "Geometric Lattice Structure of Covering and Its Application to Attribute Reduction through Matroids." Journal of Applied Mathematics 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/183621.
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The reduction of covering decision systems is an important problem in data mining, and covering-based rough sets serve as an efficient technique to process the problem. Geometric lattices have been widely used in many fields, especially greedy algorithm design which plays an important role in the reduction problems. Therefore, it is meaningful to combine coverings with geometric lattices to solve the optimization problems. In this paper, we obtain geometric lattices from coverings through matroids and then apply them to the issue of attribute reduction. First, a geometric lattice structure of a covering is constructed through transversal matroids. Then its atoms are studied and used to describe the lattice. Second, considering that all the closed sets of a finite matroid form a geometric lattice, we propose a dependence space through matroids and study the attribute reduction issues of the space, which realizes the application of geometric lattices to attribute reduction. Furthermore, a special type of information system is taken as an example to illustrate the application. In a word, this work points out an interesting view, namely, geometric lattice, to study the attribute reduction issues of information systems.
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Ye, Gaoyuan, Qingyuan Xu, Yanpeng Cheng, Zixuan Fan, Qi Li, Jiankun Qin, Shuguang Li, and Yingcheng Hu. "Compression properties of two-dimensional wood-based dowel lattice structure filled with polyurethane foam." BioResources 14, no. 4 (September 23, 2019): 8849–65. http://dx.doi.org/10.15376/biores.14.4.8849-8865.
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Foam-filled two-dimensional lattice structures were designed, and their compression performance was studied relative to corresponding structures without the foam. The experimental results showed that the compressive load of foam-filled lattice structures improved greatly compared with foam-unfilled specimens. The specific energy absorption (SEA) of foam-unfilled specimens exceeded that of the corresponding foam-filled lattice structure. The maximum energy absorption efficiency of the foam-unfilled lattice structure exceeded 1.5, while that of the foam-filled lattice structure was less than 1. The theoretically predicted compression performance was close to the experimental results. The wood-based lattice structure exhibited excellent specific strength and stiffness compared with other structures.
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KAMEI, HIROKO. "THE EXISTENCE AND CLASSIFICATION OF SYNCHRONY-BREAKING BIFURCATIONS IN REGULAR HOMOGENEOUS NETWORKS USING LATTICE STRUCTURES." International Journal of Bifurcation and Chaos 19, no. 11 (November 2009): 3707–32. http://dx.doi.org/10.1142/s0218127409025079.
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For regular homogeneous networks with simple eigenvalues (real or complex), all possible explicit forms of lattices of balanced equivalence relations can be constructed by introducing lattice generators and lattice indices [Kamei, 2009]. Balanced equivalence relations in the lattice correspond to clusters of partially synchronized cells in a network. In this paper, we restrict attention to regular homogeneous networks with simple real eigenvalues, and one-dimensional internal dynamics for each cell. We first show that lattice elements with nonzero indices indicate the existence of codimension-one synchrony-breaking steady-state bifurcations, and furthermore, the positions of such lattice elements give the number of partially synchronized clusters. Using four-cell regular homogeneous networks as an example, we then classify a large number of regular homogeneous networks into a small number of lattice structures, in which networks share an equivalent clustering type. Indeed, some of these networks even share the same generic bifurcation structure. This classification leads us to explore how regular homogeneous networks that share synchrony-breaking bifurcation structure are topologically related.
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Halaš, Radomír, Jozef Pócs, and Jana Pócsová. "On Join-Dense Subsets of Certain Families of Aggregation Functions." Mathematics 11, no. 1 (December 20, 2022): 14. http://dx.doi.org/10.3390/math11010014.
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Several important classes of aggregation functions defined on a bounded lattice form a lattice with respect to the pointwise operations of join and meet, respectively. The lattice structure of such classes is usually very complex; thus, it is very useful to characterize them by some appropriate sets of functions. In this paper, we focus on the three important classes of aggregation functions, namely the lattice of all aggregation functions, the lattice of idempotent aggregation functions, and the lattice of Sugeno integrals (defined on distributive lattices) and characterize their lattices by means of join-dense subsets. Moreover, the minimality of these sets is discussed.
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Wen, Zhou, and Ming Li. "Compressive Properties of Functionally Graded Bionic Bamboo Lattice Structures Fabricated by FDM." Materials 14, no. 16 (August 6, 2021): 4410. http://dx.doi.org/10.3390/ma14164410.
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Bionic design is considered a promising approach to improve the performance of lattice structures. In this work, bamboo-inspired cubic and honeycomb lattice structures with graded strut diameters were designed and manufactured by 3D printing. Uniform lattice structures were also designed and fabricated for comparison. Quasi-static compression tests were conducted on lattice structures, and the effects of the unit cell and structure on the mechanical properties, energy absorption and deformation mode were investigated. Results indicated that the new bionic bamboo structure showed similar mechanical properties and energy absorption capacity to the honeycomb structure but performed better than the cubic structure. Compared with the uniform lattice structures, the functionally graded lattice structures showed better performance in terms of initial peak strength, compressive modulus and energy absorption.
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Sulaiman, Mohammed Shariff Mohamed, Seong Chun Koay, Ming Yeng Chan, Hui Leng Choo, Ming Meng Pang, and Thai Kiat Ong. "Finite Element Analysis Study on Lattice Structure Fabricated Using Corn Husk Fibre Reinforced Recycled Polystyrene Composite." MATEC Web of Conferences 335 (2021): 03011. http://dx.doi.org/10.1051/matecconf/202133503011.
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This research investigated the lattice structure fabricated using corn husk fibre reinforced recycled polystyrene composite using Finite Element Analysis (FEA). The material’s properties of this composite material were obtained from previous study. Then, the lattice structure of lattice structure was created using Creo® software and the FEA simulation was done by ANSYS software. In this study, the lattice structures were created using triangular prism and hexagonal prism. The analysis was divided into two conditions: 1) lattice structure with different prism shape and similar surface area, 2) lattice structure with varies of strut thickness and 3) lattice structure with different prism shape and similar lattice parameter. The results show the lattice structure with triangular prism have more structural integrity than hexagonal prism. Then, lattice structure with triangular prism can be built with lesser material but stronger and stiffer than lattice structure with hexagonal prism.
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Xue, Yingying, Peixin Gao, Li Zhou, and Fusheng Han. "An Enhanced Three-Dimensional Auxetic Lattice Structure with Improved Property." Materials 13, no. 4 (February 24, 2020): 1008. http://dx.doi.org/10.3390/ma13041008.
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In order to enhance the mechanical property of auxetic lattice structures, a new enhanced auxetic lattice structure was designed by embedding narrow struts into a three-dimensional (3D) re-entrant lattice structure. A series of enhanced lattice structures with varied parameters were fabricated by 3D printing combined with the molten metal infiltration technique. Based on the method, parameter studies were performed. The enhanced auxetic lattice structure was found to exhibit superior mechanical behaviors compared to the 3D re-entrant lattice structure. An interesting phenomenon showed that increasing the diameter of connecting struts led to less auxetic and non-auxetic structures. Moreover, the compressive property of the enhanced structure also exhibited obvious dependence on the base material and compression directions. The present study can provide useful information for the design, fabrication and application of new auxetic structures with enhanced properties.
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Nestorovski, Blagoja, Elena Angeleska, and Nikola Avramov. "Load carrying capacities of gears with a lattice structure body." MATEC Web of Conferences 387 (2023): 02001. http://dx.doi.org/10.1051/matecconf/202338702001.
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Lattice structures are type of topology structures that have complex geometry, composed of multiplicated unit cells through which a pattern is generated. Lattice structures are of great interest in engineering due to their strength-to-weight ratio. There has been an increasing trend for their application as infill patterns in a variety of engineering parts and elements. However, the complexity of the lattice geometries, makes them difficult to be produced by conventional methods. Therefore, additive manufacturing technologies have been used as technologies for production of parts containing lattice structures. In this research, the focus is placed on analyzing various unit cell structures and their application in conventional gears as their structure body. One specific lattice structure is chosen and generated. Several characteristics of the lattice structure can vary, like the cell size, density, wall thickness etc. The lattice shape will remain the same for all the analysis. The lattice is optimized by weight reduction and maintaining load carrying capacity of the gears. Different samples are examined using FEM (Finite Element Method) in terms of determination the load carrying capacity. The results for the optimized gear body structures are elaborated, conclusions are drawn and recommendations for application of gears with a specific lattice structure are provided.
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Bari, Klaudio. "Design, Simulation, and Mechanical Testing of 3D-Printed Titanium Lattice Structures." Journal of Composites Science 7, no. 1 (January 11, 2023): 32. http://dx.doi.org/10.3390/jcs7010032.
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Lattice structure topology is a rapidly growing area of research facilitated by developments in additive manufacturing. These low-density structures are particularly promising for their medical applications. However, predicting their performance becomes a challenging factor in their use. In this article, four lattice topologies are explored for their suitability as implants for the replacement of segmental bone defects. The study introduces a unit-cell concept for designing and manufacturing four lattice structures, BCC, FCC, AUX, and ORG, using direct melt laser sintering (DMLS). The elastic modulus was assessed using an axial compression strength test and validated using linear static FEA simulation. The outcomes of the simulation revealed the disparity between the unit cell and the entire lattice in the cases of BCC, FCC, and AUX, while the unit-cell concept of the full lattice structure was successful in ORG. Measurements of energy absorption obtained from the compression testing revealed that the ORG lattice had the highest absorbed energy (350 J) compared with the others. The observed failure modes indicated a sudden collapsing pattern during the compression test in the cases of BCC and FCC designs, while our inspired ORG and AUX lattices outperformed the others in terms of their structural integrity under identical loading conditions.
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Air, A., and A. Wodehouse. "Deformation Taxonomy of Additively Manufactured Lattice Structures." Proceedings of the Design Society 2 (May 2022): 1361–70. http://dx.doi.org/10.1017/pds.2022.138.
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AbstractAdditive manufacturing offers opportunities for designed mechanical deformation within parts by integrating lattice structures into their designs. This work re-analyses and translates data on lattice structure deformation behaviours into a novel taxonomy, enabling their actions to be understood and controlled. Parallels between these actions and the four basic types of mechanical motion are identified. Creating a taxonomy method using these motions enables the future development of a DfAM framework that assimilates controlled anisotropy via lattices and aids the design of compliant mechanisms.
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Mostafa, Khaled G., Guilherme A. Momesso, Xiuhui Li, David S. Nobes, and Ahmed J. Qureshi. "Dual Graded Lattice Structures: Generation Framework and Mechanical Properties Characterization." Polymers 13, no. 9 (May 10, 2021): 1528. http://dx.doi.org/10.3390/polym13091528.
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Additive manufacturing (AM) enables the production of complex structured parts with tailored properties. Instead of manufacturing parts as fully solid, they can be infilled with lattice structures to optimize mechanical, thermal, and other functional properties. A lattice structure is formed by the repetition of a particular unit cell based on a defined pattern. The unit cell’s geometry, relative density, and size dictate the lattice structure’s properties. Where certain domains of the part require denser infill compared to other domains, the functionally graded lattice structure allows for further part optimization. This manuscript consists of two main sections. In the first section, we discussed the dual graded lattice structure (DGLS) generation framework. This framework can grade both the size and the relative density or porosity of standard and custom unit cells simultaneously as a function of the structure spatial coordinates. Popular benchmark parts from different fields were used to test the framework’s efficiency against different unit cell types and grading equations. In the second part, we investigated the effect of lattice structure dual grading on mechanical properties. It was found that combining both relative density and size grading fine-tunes the compressive strength, modulus of elasticity, absorbed energy, and fracture behavior of the lattice structure.
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Liu, Xiaoyang, Keito Sekizawa, Asuka Suzuki, Naoki Takata, Makoto Kobashi, and Tetsuya Yamada. "Compressive Properties of Al-Si Alloy Lattice Structures with Three Different Unit Cells Fabricated via Laser Powder Bed Fusion." Materials 13, no. 13 (June 28, 2020): 2902. http://dx.doi.org/10.3390/ma13132902.
Full textAbstract:
In the present study, in order to elucidate geometrical features dominating deformation behaviors and their associated compressive properties of lattice structures, AlSi10Mg lattice structures with three different unit cells were fabricated by laser powder bed fusion. Compressive properties were examined by compression and indentation tests, micro X-ray computed tomography (CT), together with finite element analysis. The truncated octahedron- unit cell (TO) lattice structures exhibited highest stiffness and plateau stress among the studied lattice structures. The body centered cubic-unit cell (BCC) and TO lattice structures experienced the formation of shear bands with stress drops, while the hexagon-unit cell (Hexa) lattice structure behaved in a continuous deformation and flat plateau region. The Hexa lattice structure densified at a smaller strain than the BCC and TO lattice structures, due to high density of the struts in the compressive direction. Static and high-speed indentation tests revealed that the TO and Hexa exhibited slight strain rate dependence of the compressive strength, whereas the BCC lattice structure showed a large strain rate dependence. Among the lattice structures in the present study, the TO lattice exhibited the highest energy absorption capacity comparable to previously reported titanium alloy lattice structures.
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Shinde, N. V., S. A. Tapadia, and B. N. Waphare. "Order Structure of Good Sets in Hypercube." Journal of Combinatorial Mathematics and Combinatorial Computing 117 (December 31, 2023): 47–54. http://dx.doi.org/10.61091/jcmcc117-05.
Full textAbstract:
A good set on k vertices is a vertex induced subgraph of the hypercube Qn that has the maximum number of edges. The long-lasting problem of characterizing graphs that are cover graphs of lattices is NP-complete. This paper constructs and studies lattice theoretic properties of a class of lattices whose cover graphs are isomorphic to good sets.