Artykuły w czasopismach: „Meshfree methods (Numerical analysis) Simulation methods”

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Gu, Yuan Tong. "An Adaptive Local Meshfree Updated Lagrangian Approach for Large Deformation Analysis of Metal Forming". Advanced Materials Research 97-101 (marzec 2010): 2664–67. http://dx.doi.org/10.4028/www.scientific.net/amr.97-101.2664.

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The large deformation analysis is one of major challenges in numerical modelling and simulation of metal forming. Because no mesh is used, the meshfree methods show good potential for the large deformation analysis. In this paper, a local meshfree formulation, based on the local weak-forms and the updated Lagrangian (UL) approach, is developed for the large deformation analysis. To fully employ the advantages of meshfree methods, a simple and effective adaptive technique is proposed, and this procedure is much easier than the re-meshing in FEM. Numerical examples of large deformation analysis are presented to demonstrate the effectiveness of the newly developed nonlinear meshfree approach. It has been found that the developed meshfree technique provides a superior performance to the conventional FEM in dealing with large deformation problems for metal forming.

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Song, Nan, Dong Qian, Jian Cao, Wing Kam Liu i Shaofan Li. "Effective Models for Prediction of Springback In Flanging". Journal of Engineering Materials and Technology 123, nr 4 (25.07.2000): 456–61. http://dx.doi.org/10.1115/1.1395019.

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A study on the prediction of springback angle is presented, with focus on the straight flanging operation. The objective of this work is to evaluate the reliability of different methods of prediction. An experiment of straight flanging operation is conducted. Major prediction approaches such as analytical model, numerical simulation using the Finite Element Method (FEM) and the Meshfree Method using the Reproducing Kernel Particle Methods (RKPM) are discussed. A set of sample problems is computed and comparisons are made with the experiment. The numerical analysis shows that the prediction from the 3D meshfree contact code matches well with the data from the FEM 2D solid model. A material property described by the kinematic hardening law provides a better prediction of springback than the isotropic hardening law.

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Li, Dong Feng, i Jian Tong Zhang. "A Review of Numerical Study of Micro-Scale Modeling for Asphalt Mixture". Applied Mechanics and Materials 716-717 (grudzień 2014): 332–37. http://dx.doi.org/10.4028/www.scientific.net/amm.716-717.332.

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Combining with digital image processing and numerical simulation technology, X-ray computerized tomography (CT) was used to study the microstructure of asphalt mixture for analyzing internal structure of asphalt mixture. The microstructure modeling methods of asphalt mixture can be classified as continuum-based numerical method and discontinuum-based numerical method. This paper described a review of the work done by many researchers on the modeling of asphalt mixture. The simulation methods are included finite element network model (FENM), a micromechanical finite element model (FEM), a clustered discrete element model (DEM), disturbed state concept (DSC), DDA (Discontinuous Displacement Analysis), numerical manifold method (NMM) and meshfree manifold method (MMM) that were used in micromechanical modeling of asphalt mixture.

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Hesar, Goudarz Ghanizadeh, Yeliz Pekbey, Hasan Yildiz i Farshid Khosravi Maleiki. "A mesh-free simulation of mode I delamination of composite structures". Science and Engineering of Composite Materials 21, nr 1 (1.01.2014): 137–49. http://dx.doi.org/10.1515/secm-2013-0019.

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AbstractA numerical and experimental investigation for the analysis of delamination problem under mode I loading in composite material is presented. Firstly, the simulation of the delamination under mode I loading and failure of composite materials based on the cohesive segments model is investigated by using the meshfree method. With the partition of unity of moving least-squares shape functions, the discontinuities at the cohesive segments are approximated with additional degrees of freedom at the nodes. An iterative solution scheme between the continuous and discontinuous fields is presented to solve mode I delamination growth. Secondly, to verify the meshfree method’s results, an experimental investigation and the finite element method were used for the simulation of delamination. The experimental study used a double-cantilever beam made of carbon/epoxy laminate (AS4/3501-6) which consists of 10 plies in [0]10 and [0/90/0/90/0]s layup with delamination inserted in the middle of the laminate. The critical fracture force, which can be experimentally measured, was used to calculate the mode I delamination fracture toughness of the carbon/epoxy laminate. Results obtained from the meshfree method showed very good agreement with experimental data for single-mode delamination under mode I loading. The meshfree method could also be used effectively to produce delamination growth in composite laminates and is especially suitable for the simulation of complex delamination patterns that are difficult to model using traditional numerical methods.

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HASEGAWA, KYOKO, SUSUMU NAKATA i SATOSHI TANAKA. "MESHFREE ELASTODYNAMIC ANALYSIS OF THREE-DIMENSIONAL SOLIDS USING RADIAL POINT INTERPOLATION METHOD". International Journal of Modeling, Simulation, and Scientific Computing 02, nr 01 (marzec 2011): 83–95. http://dx.doi.org/10.1142/s1793962311000372.

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Meshfree methods are effective tools for solving partial differential equations. The radial point interpolation method, a partial differential equation solver based on a meshfree approach, enables accurate imposition of displacement boundary conditions and has been successfully applied to elastostatic analysis of various kinds of three-dimensional solids. In this method, stiffness matrix construction accounts for the majority of CPU time required for the entire process, resulting in high computational costs, especially when higher-order numerical integration is applied for accurate matrix construction. An alternative method, modified radial point interpolation, was proposed to overcome this shortcoming and has accomplished fast computation of elastostatic solid analysis. The purpose of this study is to develop an algorithm for time-dependent simulation of three-dimensional elastic solids. We show that the modified radial point interpolation method also accelerates the construction of the mass matrix required for time-dependent analysis in addition to that of the stiffness matrix. In our approach, the problem domain is assumed to have an implicit function representation that can be constructed from a set of surface points measured using a three-dimensional scanning system. Several numerical tests for elastodynamic analysis of complex shape models are presented.

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Yoon, Sangpil, Cheng-Tang Wu, Hui-Ping Wang i Jiun-Shyan Chen. "Efficient Meshfree Formulation for Metal Forming Simulations". Journal of Engineering Materials and Technology 123, nr 4 (24.07.2000): 462–67. http://dx.doi.org/10.1115/1.1396349.

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A stabilized conforming (SC) nodal integration method is developed for elastoplastic contact analysis of metal forming processes. In this approach, strain smoothing stabilization is introduced to eliminate spatial instability in collocation meshfree methods. The gradient matrix associated with strain smoothing satisfies the integration constraint (IC) of linear exactness in the Galerkin approximation. Strain smoothing formulation and numerical procedures for history-dependent problems are introduced. Applications to metal forming analysis are presented, with the results demonstrating a significant improvement in computational efficiency without loss of accuracy.

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Zakrzewski, Nadia, Majidreza Nazem, Scott William Sloan i Mark Cassidy. "On Application of the Maximum Entropy Meshless Method for Large Deformation Analysis of Geotechnical Problems". Applied Mechanics and Materials 846 (lipiec 2016): 331–35. http://dx.doi.org/10.4028/www.scientific.net/amm.846.331.

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Traditional grid-based numerical techniques such as the Finite Element Method (FEM) are known to suffer when large deformations of the continuum are encountered. As such, there has been limited success using this class of methods to solve many of the complex problems encountered in computational geomechanics. The potential of Meshfree techniques for addressing this perceived deficiency has been recognised. This study presents a robust Maximum Entropy Meshless (MEM) method for the analysis of problems involving geometrical nonlinearity in computational geomechanics. The method is validated via simulation of an undrained layer of soil under a rigid and rough strip footing undergoing large deformations and its merit is demonstrated through a comparison of the results with those obtained via the FEM.

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Wu, C. T., W. Hu i M. Koishi. "A Smoothed Particle Galerkin Formulation for Extreme Material Flow Analysis in Bulk Forming Applications". International Journal of Computational Methods 13, nr 03 (31.05.2016): 1650019. http://dx.doi.org/10.1142/s0219876216500195.

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This paper presents a new particle formulation for extreme material flow analyses in the bulk forming applications. The new formulation is first established by an introduction of a smoothed displacement field to the standard Galerkin formulation to eliminate zero-energy modes in conventional particle methods. The discretized system of linear equations is consistently derived and integrated using a direct nodal integration scheme. The linear formulation is next extended to the large deformation quasi-static analysis of inelastic materials. As quasi-static Lagrangian simulation proceeds in the severe deformation range, the analysis method is switched to explicit dynamics formulation and an adaptive Lagrangian kernel approach is preformed to reset the reference configuration and maintain the injective deformation mapping at the particles. Both nonconvex and convex meshfree approximations are investigated in this study. Several numerical benchmarks are provided to demonstrate the effectiveness and accuracy of the proposed method.

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Ju, J. W., K. Y. Yuan, A. W. Kuo i J. S. Chen. "Novel Strain Energy Based Coupled Elastoplastic Damage and Healing Models for Geomaterials – Part II: Computational Aspects". International Journal of Damage Mechanics 21, nr 4 (17.08.2011): 551–76. http://dx.doi.org/10.1177/1056789511407360.

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In Part I of this sequel (Ju, J.W., Yuan, K.Y. and Kuo, A.W. (2010). Novel Strain Energy Based Coupled Elastoplastic Damage and Healing Models for Geomaterials – Part I: Formulations, International Journal of Damage Mechanics, DOI: 10.1177/1056789511407359), we have developed innovative strain energy based coupled elastoplastic hybrid isotropic and anisotropic damage-healing formulations for geomaterials under complex 2D earth-moving processes. Emanating from a micromechanics-based brittle (tensile) damage characterization (P+) and a ductile (mixed tension–compression) damage-healing characterization ([Formula: see text]), the proposed hybrid isotropic and anisotropic damage-healing models for soils are implemented. Entirely new computational algorithms are systematically developed based on the two-step operator splitting methodology. The elastic damage-healing predictor and the plastic corrector are consistently implemented within the existing Nonlinear Meshfree Analysis Program at University of California, Los Angeles ( Chen, J.S., Wu, C.T., Yoon, S. and You, Y. (2001) . A Stabilized Conforming Nodal Integration for Galerkin Meshfree Methods, International Journal for Numerical Methods in Engineering, 50: 435–466). Several numerical simulations featuring sophisticated earth excavation, transport, compaction, and a numerical notched soil bar under cyclic tension–compression loading are presented to illustrate the salient elastoplastic damage and healing features of soils, such as shear band and partial recovery of soil stiffness due to compression (compaction) by the proposed innovative damage-healing models and step-by-step computational algorithms.

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PEKEDIS, MAHMUT, i HASAN YILDIZ. "NUMERICAL ANALYSIS OF A PROJECTILE PENETRATION INTO THE HUMAN HEAD VIA MESHLESS METHOD". Journal of Mechanics in Medicine and Biology 14, nr 04 (3.07.2014): 1450059. http://dx.doi.org/10.1142/s0219519414500596.

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In recent years, physicists, engineers and medical scientists have tried to demonstrate the biomechanics of gunshot wounds with numerical methods and experimental observations. Currently, the finite element method (FEM) is the most widely used numerical method among the studies related to ballistic wound injuries. However, when the FEM is used for the penetration analysis, the path of the projectile in the skull is subjected to extremely large deformations which will introduce errors due to distortion of elements. To overcome this error, the meshfree technique was established to simulate the gunshot wound as a preliminary study in which the skull was modeled by smoothed particle hydrodynamics (SPH) and the projectile was modeled by nondeformable rigid elements. In order to simulate a realistic penetration phenomenon, orthotropic material properties were defined for different regions (forehead, zygomatic and mandible) with material principal axis along the surface of the bones. Human response to the ballistics impacts were determined in terms of force occurring along the pathway of the bullet in the skull, residual velocity of the projectile and penetration depth. The obtained results were compared with the data reported in literature. As a result, mechanical behavior of the head under ballistic impacts simulated by the SPH, compared well with the results determined by the data given in literature, which indicates the applicability of the SPH method as a powerful technique in simulating different gunshot wound mechanisms.

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Liu, Wing Kam, Sergio R. Idelsohn i Eugenio O�ate. "Announcement ?Meshfree Methods?" International Journal for Numerical Methods in Engineering 49, nr 5 (2000): 721–23. http://dx.doi.org/10.1002/1097-0207(20001020)49:5<721::aid-nme92>3.0.co;2-4.

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Dumont, Serge, Olivier Goubet, Tuong Ha-Duong i Pierre Villon. "Meshfree methods and boundary conditions". International Journal for Numerical Methods in Engineering 67, nr 7 (2006): 989–1011. http://dx.doi.org/10.1002/nme.1659.

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Oliveira, Tiago, Wilber Vélez i Artur Portela. "Formulation of local numerical methods in linear elasticity". Multidiscipline Modeling in Materials and Structures 16, nr 5 (4.06.2020): 853–86. http://dx.doi.org/10.1108/mmms-05-2018-0094.

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PurposeThis paper is concerned with new formulations of local meshfree and finite element numerical methods, for the solution of two-dimensional problems in linear elasticity.Design/methodology/approachIn the local domain, assigned to each node of a discretization, the work theorem establishes an energy relationship between a statically admissible stress field and an independent kinematically admissible strain field. This relationship, derived as a weighted residual weak form, is expressed as an integral local form. Based on the independence of the stress and strain fields, this local form of the work theorem is kinematically formulated with a simple rigid-body displacement to be applied by local meshfree and finite element numerical methods. The main feature of this paper is the use of a linearly integrated local form that implements a quite simple algorithm with no further integration required.FindingsThe reduced integration, performed by this linearly integrated formulation, plays a key role in the behavior of local numerical methods, since it implies a reduction of the nodal stiffness which, in turn, leads to an increase of the solution accuracy and, which is most important, presents no instabilities, unlike nodal integration methods without stabilization. As a consequence of using such a convenient linearly integrated local form, the derived meshfree and finite element numerical methods become fast and accurate, which is a feature of paramount importance, as far as computational efficiency of numerical methods is concerned. Three benchmark problems were analyzed with these techniques, in order to assess the accuracy and efficiency of the new integrated local formulations of meshfree and finite element numerical methods. The results obtained in this work are in perfect agreement with those of the available analytical solutions and, furthermore, outperform the computational efficiency of other methods. Thus, the accuracy and efficiency of the local numerical methods presented in this paper make this a very reliable and robust formulation.Originality/valuePresentation of a new local mesh-free numerical method. The method, linearly integrated along the boundary of the local domain, implements an algorithm with no further integration required. The method is absolutely reliable, with remarkably-accurate results. The method is quite robust, with extremely-fast computations.

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Garg, Sahil, i Mohit Pant. "Meshfree Methods: A Comprehensive Review of Applications". International Journal of Computational Methods 15, nr 04 (24.05.2018): 1830001. http://dx.doi.org/10.1142/s0219876218300015.

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The meshfree methods in computational mechanics have been actively proposed and increasingly developed in order to overcome some drawbacks in the conventional numerical methods. Over past three decades meshfree methods have found their way into many different application areas ranging from classical astronomical problems to solid mechanics analysis, fluid flow problems, vibration analysis, heat transfer and optimization to the numerical solution of all kind of (partial) differential equation problems. The present work is an effort to provide a comprehensive review of various Meshfree methods, their classification, underlying methodology, application area along with their advantages and limitations. Key contributions of mesh free techniques to the area of fracture mechanics have been discussed with applications of element free Galerkin method (EFGM) to fracture analysis as primary concern.

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Afrasiabi, Mohamadreza, i Konrad Wegener. "3D Thermal Simulation of a Laser Drilling Process with Meshfree Methods". Journal of Manufacturing and Materials Processing 4, nr 2 (22.06.2020): 58. http://dx.doi.org/10.3390/jmmp4020058.

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Numerical simulation of laser drilling is rapidly gaining interest in academia and industry since this process remains one of the most important and widely-used technologies in modern manufacturing. Meshfree methods such as Smoothed Particle Hydrodynamics (SPH) have proven to be successful as a numerical tool for the computation of the heat transfer and material removal associated with a laser drilling problem. Nonetheless, the vast majority of recent developments incorporate an inconsistent SPH kernel into their thermal simulations. In this paper, several enhanced schemes are implemented to address this problem by solving the heat transfer more accurately. These meshfree schemes can provide a second-order accurate discretization of the Laplace operator and abolish the inconsistency issue of the standard SPH kernels. An efficient approach is additionally suggested to handle the associated boundary conditions, which relies on the idea of the color function and particle label. The implementation is initially validated by a 3D benchmark study and then applied for the first time to a laser drilling problem.

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Belytschko, T., Y. Krongauz, J. Dolbow i C. Gerlach. "On the completeness of meshfree particle methods". International Journal for Numerical Methods in Engineering 43, nr 5 (15.11.1998): 785–819. http://dx.doi.org/10.1002/(sici)1097-0207(19981115)43:5<785::aid-nme420>3.0.co;2-9.

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Wu, Junchao, i Dongdong Wang. "An accuracy analysis of Galerkin meshfree methods accounting for numerical integration". Computer Methods in Applied Mechanics and Engineering 375 (marzec 2021): 113631. http://dx.doi.org/10.1016/j.cma.2020.113631.

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Alves, Carlos J. S., i Svilen S. Valtchev. "Numerical comparison of two meshfree methods for acoustic wave scattering". Engineering Analysis with Boundary Elements 29, nr 4 (kwiecień 2005): 371–82. http://dx.doi.org/10.1016/j.enganabound.2004.09.008.

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Racz, Donat, i Tinh Quoc Bui. "Novel adaptive meshfree integration techniques in meshless methods". International Journal for Numerical Methods in Engineering 90, nr 11 (17.04.2012): 1414–34. http://dx.doi.org/10.1002/nme.4268.

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Ji, Yanju, Tingzhe Huang, Wanyu Huang i Liangliang Rong. "Meshfree Method in Geophysical Electromagnetic Prospecting: The 2D Magnetotelluric Example". International Journal of Computational Methods 15, nr 02 (28.09.2017): 1750084. http://dx.doi.org/10.1142/s0219876217500840.

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As an important supplement and development of traditional methods, the meshfree method has received a great deal of attention in the field of engineering calculation, and has been successfully used to solve many problems which traditional methods have difficulty in solving. However, the application of meshfree method is relatively less in the area of geophysics. In this paper, we apply the meshfree method to the numerical simulation of geophysical electromagnetic prospecting, taking the 2D magnetotelluric as an example and deduce the corresponding meshfree radial point interpolation method (RPIM) equivalent linear equations in detail. The high-efficiency and accurate solutions of large-scale sparse linear equations are solved by the quasi-minimal residual method based on Krylov subspace. The optimal values of the shape parameters are given by numerical experiments. The correctness of the meshfree method is verified by a layered model. The root mean square error of the calculation results is no more than 0.35%, its accuracy is superior to the finite element method. We also compare the meshfree solution with FEM solution by calculating an inclined vein body model, and the calculation results are in good agreement. A continuously changing fault model and undulating terrain model which traditional methods have difficulty in simulating are respectively calculated, the sectional profiles of the apparent resistivity accurately reflect the trend of the anomalies. The meshfree method does not require the complicated mesh generation, and the physical parameters are loaded at a series of points, thus it is especially suitable for the calculation of the complex geological models. With the rapid development of computational science, the meshfree techniques will certainly become a new robust numerical simulation method in geophysical electromagnetic prospecting.

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Daxini, S. D., i J. M. Prajapati. "A Review on Recent Contribution of Meshfree Methods to Structure and Fracture Mechanics Applications". Scientific World Journal 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/247172.

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Meshfree methods are viewed as next generation computational techniques. With evident limitations of conventional grid based methods, like FEM, in dealing with problems of fracture mechanics, large deformation, and simulation of manufacturing processes, meshfree methods have gained much attention by researchers. A number of meshfree methods have been proposed till now for analyzing complex problems in various fields of engineering. Present work attempts to review recent developments and some earlier applications of well-known meshfree methods like EFG and MLPG to various types of structure mechanics and fracture mechanics applications like bending, buckling, free vibration analysis, sensitivity analysis and topology optimization, single and mixed mode crack problems, fatigue crack growth, and dynamic crack analysis and some typical applications like vibration of cracked structures, thermoelastic crack problems, and failure transition in impact problems. Due to complex nature of meshfree shape functions and evaluation of integrals in domain, meshless methods are computationally expensive as compared to conventional mesh based methods. Some improved versions of original meshfree methods and other techniques suggested by researchers to improve computational efficiency of meshfree methods are also reviewed here.

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Niemiec, Dominik, Roman Bulko i Juraj Mužík. "The Meshfree Localized Petrov-Galerkin Approach in Slope Stability Analysis". Civil and Environmental Engineering 15, nr 1 (1.06.2019): 79–84. http://dx.doi.org/10.2478/cee-2019-0011.

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Abstract The article focuses on the use of the meshfree numerical method in the field of slope stability computations. There are many meshfree implementations of numerical methods. The article shows the results obtained using the meshfree localized Petrov-Galerkin method (MLPG) – localized weak-form of the equilibrium equations with an often used elastoplastic material model based on Mohr-Coulomb (MC) yield criterion. The most important aspect of MLPG is that the discretization process uses a set of nodes instead of elements. Node position within the computational domain is not restricted by any prescribed relationship. The shape functions are constructed using just the set of nodes present in the simple shaped domain of influence. The benchmark slope stability numerical model was performed using the developed meshfree computer code and compared with conventional finite element (FEM) and limit equilibrium (LEM) codes. The results showed the ability of the implemented theoretical preliminaries to solve the geotechnical stability problems.

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Duan, Qinglin, Xikui Li, Hongwu Zhang i Ted Belytschko. "Second-order accurate derivatives and integration schemes for meshfree methods". International Journal for Numerical Methods in Engineering 92, nr 4 (5.06.2012): 399–424. http://dx.doi.org/10.1002/nme.4359.

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Chen, Jiun-Shyan, Michael Hillman i Marcus Rüter. "An arbitrary order variationally consistent integration for Galerkin meshfree methods". International Journal for Numerical Methods in Engineering 95, nr 5 (12.06.2013): 387–418. http://dx.doi.org/10.1002/nme.4512.

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Rabczuk, T., i T. Belytschko. "Adaptivity for structured meshfree particle methods in 2D and 3D". International Journal for Numerical Methods in Engineering 63, nr 11 (2005): 1559–82. http://dx.doi.org/10.1002/nme.1326.

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WANG, DONGDONG, i ZHENTING LIN. "A COMPARATIVE STUDY ON THE DISPERSION PROPERTIES OF HRK AND RK MESHFREE APPROXIMATIONS FOR KIRCHHOFF PLATE PROBLEM". International Journal of Computational Methods 09, nr 01 (marzec 2012): 1240015. http://dx.doi.org/10.1142/s0219876212400154.

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Dispersion analysis provides a rational way to examine the dynamic properties of numerical methods through comparing the numerical and continuum frequencies. In this paper a detailed comparative investigation is presented on the dispersion features of the Hermite reproducing kernel (HRK) and the conventional reproducing kernel (RK) meshfree methods for Kirchhoff plate problem with particular reference to the spatial discretizations. In the analysis the nodal variables of the semi-discretized meshfree Kirchhoff plate equations are assumed as harmonic wave functions to extract the numerical frequency. For the RK approximation, only the deflectional nodal variables are expressed by the harmonic wave functions, while unlike RK approximation, both deflectional and rotational nodal variables should be expressed by the harmonic wave functions for the HRK approximation. The dispersion analysis results uniformly evince that the HRK meshfree discretization has much smaller dispersion errors and performs superiorly compared to the conventional RK meshfree discretization for Kirchhoff plate problem.

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LIU, S. J., H. WANG i H. ZHANG. "SMOOTHED FINITE ELEMENTS LARGE DEFORMATION ANALYSIS". International Journal of Computational Methods 07, nr 03 (wrzesień 2010): 513–24. http://dx.doi.org/10.1142/s0219876210002246.

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The smoothed finite element method (SFEM) was developed in order to eliminate certain shortcomings of the finite element method (FEM). SFEM enjoys some of the flexibilities of meshfree methods. One advantage of SFEM is its applicability to modeling large deformations. Due to the absence of volume integration and parametric mapping, issues such as negative volumes and singular Jacobi matrix do not occur. However, despite these advantages, SFEM has never been applied to problems with extreme large deformation. For the first time, we apply SFEM to extreme large deformations. For two numerical problems, we demonstrate the advantages of SFEM over FEM. We also show that SFEM can compete with the flexibility of meshfree methods.

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Talebi, Hossein, Cristóbal Samaniego, Esteban Samaniego i Timon Rabczuk. "On the numerical stability and mass-lumping schemes for explicit enriched meshfree methods". International Journal for Numerical Methods in Engineering 89, nr 8 (4.11.2011): 1009–27. http://dx.doi.org/10.1002/nme.3275.

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Zhang, Hongjun, Guangsong Chen, Linfang Qian i Jia Ma. "FE-Meshfree QUAD4 Element with Modified Radial Point Interpolation Function for Structural Dynamic Analysis". Shock and Vibration 2019 (8.01.2019): 1–23. http://dx.doi.org/10.1155/2019/3269276.

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The partition-of-unity method based on FE-Meshfree QUAD4 element synthesizes the respective advantages of meshfree and finite element methods by exploiting composite shape functions to obtain high-order global approximations. This method yields high accuracy and convergence rate without necessitating extra nodes or DOFs. In this study, the FE-Meshfree method is extended to the free and forced vibration analysis of two-dimensional solids. A modified radial point interpolation function without any supporting tuning parameters is applied to construct the composite shape functions. The governing equations of elastodynamic problem are transformed into a standard weak formulation and then discretized into time-dependent equations which are solved via Bathe time integration scheme to conduct the forced vibration analysis. Several numerical test problems are solved and compared against previously published numerical solutions. Results show that the proposed FE-Meshfree QUAD4 element owns greater tolerance for mesh distortion and provides more accurate solutions.

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Quaglino, A., i R. Krause. "kFEM: Adaptive meshfree finite-element methods using local kernels on arbitrary subdomains". International Journal for Numerical Methods in Engineering 114, nr 6 (21.01.2018): 581–97. http://dx.doi.org/10.1002/nme.5755.

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Yang, Yongtao, Xuhai Tang, Hong Zheng i Quansheng Liu. "Four-Node Quadrilateral Element with Continuous Nodal Stress for Geometrical Nonlinear Analysis". International Journal of Computational Methods 15, nr 02 (28.09.2017): 1850005. http://dx.doi.org/10.1142/s0219876218500056.

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In this paper, the performance of a hybrid ‘FE-Meshfree’ quadrilateral element with continuous nodal stress (Quad4-CNS) is investigated for geometrical nonlinear solid mechanic problems. By combining finite element method (FEM) and meshfree method, this Quad4-CNS synergizes the individual strengths of these two methods, which leads to higher accuracy, better convergence rate, as well as high tolerance to mesh distortion. Therefore, Quad4-CNS is attractive for geometrical nonlinear solid mechanic problems where excessive distorted meshes occur. For geometrical nonlinear analysis, numerical results show that the results of Quad4-CNS element are much better than those of four-node isoparametric quadrilateral element (Quad4), and are comparable to quadratic quadrilateral element (Quad8) and other hybrid ‘FE- Meshfree’ elements.

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Sadono, Kresno Wikan. "Penyelesaian Numerik Advection Equation 1 Dimensi dengan EFG-DGM". MEDIA KOMUNIKASI TEKNIK SIPIL 22, nr 1 (25.10.2016): 51. http://dx.doi.org/10.14710/mkts.v22i1.12406.

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Differential equation can be used to model various phenomena in science and engineering. Numerical method is the most common method used in solving DE. Numerical methods that popular today are finite difference method (FDM), finite element method (FEM) dan discontinuous Galerkin method (DGM), which the method includes mesh based. Lately, the developing methods, that are not based on a mesh, which the nodes directly spread in domain, called meshfree or meshless. Element free Galerkin method (EFG), Petrov-Galerkin meshless (MLPG), reproducing kernel particle method (RKPM) and radial basis function (RBF) fall into the category meshless or meshfree. Time integration generally use an explicit Runge Kutta 4th order, Newmark- , HHT- , Wilson- dll. This research was carried out numerical simulations DE, by combining the EFG method to solve the domain space and time integration with DGM methods. EFG using the complete order polynomial 1, and DGM used polynomial order 1. The equation used advection equation in one dimension. EFG-DGM comparison with analytical results also performed. The simulation results show the method EFG-DGM match the one-dimensional advection equations well.

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Tootoonchi, Arash, Arman Khoshghalb i Nasser Khalili. "Meshfree Method Analysis of Biot's Consolidation Using Cell-Based Smoothed Point Interpolation Method". Applied Mechanics and Materials 846 (lipiec 2016): 409–14. http://dx.doi.org/10.4028/www.scientific.net/amm.846.409.

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A set of cell-based smoothed point interpolation methods are proposed for the numerical analysis of Biot’s formulation. In the proposed methods, the problem domain is discretized using a triangular background mesh. Shape functions are constructed using either polynomial or radial point interpolation method (PIM), leading to the delta function property of shape functions and consequently, easy implementation of essential boundary conditions. The Biot’s equations are discretised in space and time. A variety of support domain selection schemes (T-schemes) are investigated. The accuracy and convergence rate of the proposed methods are examined by comparing the numerical results with the analytical solution for the benchmark problem of one dimensional consolidation.

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HORI, Muneo, i Takanobu KOYAMA. "Numerical simulation of grouting by two grout analysis methods." Doboku Gakkai Ronbunshu, nr 624 (1999): 21–30. http://dx.doi.org/10.2208/jscej.1999.624_21.

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Ishihara, Ken, Takehiro Noda i Hiroyuki Sakurai. "Investigating Applicability of the Meshfree Method to the Structural Analysis of Tires". Tire Science and Technology 40, nr 2 (1.04.2012): 60–82. http://dx.doi.org/10.2346/1945-5852-40.2.60.

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ABSTRACT In contrast to the finite element method (FEM), which is widely used in the tire industry nowadays, some alternative methods have been proposed by academic communities over the past decade or so. The meshfree method is one of those new methodologies. Originally intended to remove the burden of creating the mesh that is inherent in FEM, the meshfree method relies on the point data rather than the mesh, which makes it much easier to discretize the geometry. In addition to those modeling issues, it has been found that the meshfree method has several advantages over FEM in handling geometrical nonlinearities, continuities, and so forth. In accordance with those emerging possibilities, the authors have been conducting research on the matter. This article describes the results of the authors' preliminary research on the applicability of the meshfree method to tire analyses, which include the theoretical outline, the strategy of tire modeling, numerical results, comparisons with results of FEM, and conclusions.

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Silva‐Valenzuela, R., A. Ortiz‐Bernardin, N. Sukumar, E. Artioli i N. Hitschfeld‐Kahler. "A nodal integration scheme for meshfree Galerkin methods using the virtual element decomposition". International Journal for Numerical Methods in Engineering 121, nr 10 (30.05.2020): 2174–205. http://dx.doi.org/10.1002/nme.6304.

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Arroyo, M., i M. Ortiz. "Localmaximum-entropy approximation schemes: a seamless bridge between finite elements and meshfree methods". International Journal for Numerical Methods in Engineering 65, nr 13 (2006): 2167–202. http://dx.doi.org/10.1002/nme.1534.

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Dijkstra, Henk A. "Numerical bifurcation methods applied to climate models: analysis beyond simulation". Nonlinear Processes in Geophysics 26, nr 4 (8.10.2019): 359–69. http://dx.doi.org/10.5194/npg-26-359-2019.

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Abstract. In this special issue contribution, I provide a personal view on the role of bifurcation analysis of climate models in the development of a theory of climate system variability. The state of the art of the methodology is shortly outlined, and the main part of the paper deals with examples of what has been done and what has been learned. In addressing these issues, I will discuss the role of a hierarchy of climate models, concentrate on results for spatially extended (stochastic) models (having many degrees of freedom) and evaluate the importance of these results for a theory of climate system variability.

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Hauth, Michael, Olaf Etzmuss i Wolfgang Strasser. "Analysis of numerical methods for the simulation of deformable models". Visual Computer 19, nr 7-8 (grudzień 2003): 581–600. http://dx.doi.org/10.1007/s00371-003-0206-2.

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GEORGE, E., J. GLIMM, X. L. LI, A. MARCHESE, Z. L. XU, J. W. GROVE i DAVID H. SHARP. "Numerical methods for the determination of mixing". Laser and Particle Beams 21, nr 3 (lipiec 2003): 437–42. http://dx.doi.org/10.1017/s0263034603213239.

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We present a Rayleigh–Taylor mixing rate simulation with an acceleration rate falling within the range of experiments. The simulation uses front tracking to prevent interfacial mass diffusion. We present evidence to support the assertion that the lower acceleration rate found in untracked simulations is caused, at least to a large extent, by a reduced buoyancy force due to numerical interfacial mass diffusion. Quantitative evidence includes results from a time-dependent Atwood number analysis of the diffusive simulation, which yields a renormalized mixing rate coefficient for the diffusive simulation in agreement with experiment. We also present the study of Richtmyer–Meshkov mixing in cylindrical geometry using the front tracking method and compare it with the experimental results.

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Xu, Y., J. J. Zhao i Z. N. Sui. "Stability Analysis ofθ-Methods for Neutral Multidelay Integrodifferential System". Discrete Dynamics in Nature and Society 2007 (2007): 1–8. http://dx.doi.org/10.1155/2007/42540.

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This paper studies the stability of a class of neutral delay integrodifferential system. A necessary and sufficient condition of stability for its analytic solutions is considered. The improvedθ-methods are developed. Some numerical stability properties are obtained and numerical experiments are given.

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Yang, Judy P., i Jian-Yu Chen. "Strong-Form Formulated Generalized Displacement Control Method for Large Deformation Analysis". International Journal of Applied Mechanics 09, nr 07 (październik 2017): 1750101. http://dx.doi.org/10.1142/s1758825117501010.

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The traditional analysis of geometric nonlinearity is mostly based on the weak-formulated Galerkin method such as the finite element method. The element nature has limited its application as a result of numerical integration in the governing equation and quality control of deformed mesh. In the middle of 1990s, the meshfree methods have been developed and become one leading research topic in computational mechanics. Especially, the strong form collocation methods require no additional efforts to process numerical integration and impose Dirichlet boundary condition, thereby making the collocation methods computationally efficient. In the incremental–iterative process, how to accurately reflect the change in the slope of the load–deflection curve of the structure and remain numerically stable are of major concerns. Thus, we propose a strong-form formulated generalized displacement control method to analyze geometric nonlinear problems, where the radial basis collocation method is adopted. The numerical examples demonstrate the ability of the proposed method for large deformation analysis.

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Abdessalam, H., B. Abbès, Y. Q. Guo, E. Kwassi i J. L. Romain. "Numerical Simulation of Polyurethane Foaming Process Using Finite Point Method". Advanced Materials Research 856 (grudzień 2013): 179–83. http://dx.doi.org/10.4028/www.scientific.net/amr.856.179.

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For the numerical simulation of fluid mechanics problems in complex geometries, the use of the classical grid methods such as the finite element method and the finite volume method can give rise to several problems related to the deformation of the mesh. In this work, a meshfree Lagrangian method is used to avoid these problems. This method called Finite Point Method (FPM) has been developed by Kuhnert. It consists in representing the fluid domain by a set of particles. The efficiency of this method is pointed by studying the problem of polyurethane foaming. To do so, we have adopted a theoretical model describing the contribution of the chemical kinetics and the rheological coupling characterizing such process. This coupling is displayed through the dependency of the fluid viscosity to the evolution of the temperature and the chemical reactions present during the foaming process. The expansion of the mixture is governed by the front velocity which is calculated by solving the Navier-Stokes equations. Compared to the experimental results for polyurethane foaming process in a conical beaker, the numerical results using the FPM code are acceptable.

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Kohatsu-Higa, Arturo, i Roger Pettersson. "Variance Reduction Methods for Simulation of Densities on Wiener Space". SIAM Journal on Numerical Analysis 40, nr 2 (styczeń 2002): 431–50. http://dx.doi.org/10.1137/s0036142901385507.

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Rosolen, Adrian, Daniel Millán i Marino Arroyo. "On the optimum support size in meshfree methods: A variational adaptivity approach with maximum-entropy approximants". International Journal for Numerical Methods in Engineering 82, nr 7 (1.12.2009): 868–95. http://dx.doi.org/10.1002/nme.2793.

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Hillman, Michael, i Jiun-Shyan Chen. "An accelerated, convergent, and stable nodal integration in Galerkin meshfree methods for linear and nonlinear mechanics". International Journal for Numerical Methods in Engineering 107, nr 7 (23.12.2015): 603–30. http://dx.doi.org/10.1002/nme.5183.

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Arbogast, Todd, Mandri Obeyesekere i Mary F. Wheeler. "Numerical Methods for the Simulation of Flow in Root-Soil Systems". SIAM Journal on Numerical Analysis 30, nr 6 (grudzień 1993): 1677–702. http://dx.doi.org/10.1137/0730086.

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Martikainen, Janne. "Numerical Study of Two Sparse AMG-methods". ESAIM: Mathematical Modelling and Numerical Analysis 37, nr 1 (styczeń 2003): 133–42. http://dx.doi.org/10.1051/m2an:2003016.

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Rohit, Gaurang R., Jagdish M. Prajapati i Vikram B. Patel. "Coupling of Finite Element and Meshfree Method for Structure Mechanics Application: A Review". International Journal of Computational Methods 17, nr 04 (29.11.2019): 1850151. http://dx.doi.org/10.1142/s0219876218501517.

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In many engineering problems, the meshfree methods (MMs) have been dynamically projected and increasingly advanced in order to overwhelm some hitches in the predictable numerical methods. Over the past three decades in many different application area, MMs have found their way ranging from solid mechanics analysis, fluid problems, vibration analysis, heat transfer and optimization to numerical solutions of all kinds of (partial) differential equations. As every technique has shortcomings, the meshfree method also has drawbacks like higher computational cost and imposition of boundary condition which can be overruled by coupling it with the finite element method (FEM). In the past two decades, coupled MMs and FEM have appeared into a new session of computational methods with significant achievement. In addition, a noteworthy amount of growth has been made in addressing the major deficiencies that were present in the conventional methods and MMs at the premature phases. The objective of the present work is to provide a comprehensive review of various coupling techniques used for interface elements of MMs and FEM and general discussion on shape function formulation of FE and element free Galerkin method (EFGM). Key contribution of coupling techniques for coupled EFGM and FEM to structure mechanics application as primary concern.

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Dijkstra, Henk A., Fred W. Wubs, Andrew K. Cliffe, Eusebius Doedel, Ioana F. Dragomirescu, Bruno Eckhardt, Alexander Yu Gelfgat i in. "Numerical Bifurcation Methods and their Application to Fluid Dynamics: Analysis beyond Simulation". Communications in Computational Physics 15, nr 1 (styczeń 2014): 1–45. http://dx.doi.org/10.4208/cicp.240912.180613a.

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AbstractWe provide an overview of current techniques and typical applications of numerical bifurcation analysis in fluid dynamical problems. Many of these problems are characterized by high-dimensional dynamical systems which undergo transitions as parameters are changed. The computation of the critical conditions associated with these transitions, popularly referred to as ‘tipping points’, is important for understanding the transition mechanisms. We describe the two basic classes of methods of numerical bifurcation analysis, which differ in the explicit or implicit use of the Jacobian matrix of the dynamical system. The numerical challenges involved in both methods arementioned and possible solutions to current bottlenecks are given. To demonstrate that numerical bifurcation techniques are not restricted to relatively low-dimensional dynamical systems, we provide several examples of the application of the modern techniques to a diverse set of fluid mechanical problems.

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