Zeitschriftenartikel: „DIMENSION SHEET“

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Burton, D. A., und R. W. Tucker. „Geometry and dynamics of vortex sheets in 3 dimension“. Theoretical and Applied Mechanics, Nr. 28-29 (2002): 55–76. http://dx.doi.org/10.2298/tam0229055b.

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We consider the properties and dynamics of vortex sheets from a geometrical, coordinate-free, perspective. Distribution-valued forms (de Rham currents) are used to represent the fluid velocity and vorticity due to the vortex sheets. The smooth velocities on either side of the sheets are solved in terms of the sheet strengths using the language of double forms. The classical results regarding the continuity of the sheet normal component of the velocity and the conservation of vorticity are exposed in this setting. The formalism is then applied to the case of the self-induced velocity of an isolated vortex sheet. We develop a simplified expression for the sheet velocity in terms of representative curves. Its relevance to the classical Localized Induction Approximation (LIA) to vortex filament dynamics is discussed. .

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Safronov, Evgeniy, und Andrey Nosko. „Analysis of Linear Dimension Accuracy of Sheet Metal Bending“. MATEC Web of Conferences 346 (2021): 01007. http://dx.doi.org/10.1051/matecconf/202134601007.

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Working on the design of the products obtained by the V-bending, the engineer uses the nominal thickness of the material. In this case, the problem is to evaluate the accuracy of the linear dimensions of the resulting products due to deviations in the thickness of the material and the manufacturing technology of the steel sheets. Article presents analysis of linear dimension accuracy for V-bending for the metal cold-rolled and hot-rolled sheets with thickness 1.0…8.0 mm and width from 1000…1500mm. Proposed method is based on the calculation of difference between nominal flat length and flat lengths corresponding maximum and minimum thickness of the metal sheet.

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Hwang, Y.-M., und D.-C. Chen. „Finite element simulations on void closure behaviour inside the sheet during sheet rolling processes“. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 216, Nr. 9 (01.09.2002): 1227–37. http://dx.doi.org/10.1243/095440502760291781.

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The purpose of this paper is to explore the deformation mechanism of voids and stress-strain distributions around internal voids inside the sheet during sheet rolling processes. The plastic deformation and flow pattern of sheets during sheet rolling were simulated by the finite element method. The influences of various rolling conditions, such as the thickness reduction, the dimension of the internal void, friction factor, cross-sectional area of the void, etc., on the dimension of the void at the exit are discussed. The critical thickness reductions, over which the void would close completely, were also investigated. Furthermore, experiments on sheet rolling with an internal void inside the sheet were conducted. Theoretical predictions of the dimension of voids after rolling were compared with experimental results and relatively good agreement between them was found. Clearly, these analytical results can provide useful knowledge for designing the pass-schedule of sheet rolling processes for eliminating internal voids.

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He, Song, Heyun Liu, Yuan Zhang, Haili Liu und Wang Chen. „Investigation of the Interface Effects and Frosting Mechanism of Nanoporous Alumina Sheets“. Processes 11, Nr. 7 (06.07.2023): 2019. http://dx.doi.org/10.3390/pr11072019.

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Nanoporous alumina sheets can inhibit the growth of the frost layer in a low-temperature environment, which has been widely used in air-conditioning heat exchangers. In this study, nanoporous alumina sheets with pore diameters of 30 nm, 100 nm, 200 nm, 300 nm, and 400 nm were prepared by using the anodic oxidation method with the conventional polished aluminum sheet as the reference. A comprehensive and in-depth analysis of the frosting mechanism has been proposed based on the contact angle, specific surface area, and fractal dimension. It was found that compared with the polished aluminum sheet, the nanoporous alumina sheets had good anti-frost properties. Due to its special interface effects, the porous alumina sheet with a 100 nm pore diameter had strong anti-frost performance under low temperatures and high humidity. In an environment with low surface temperature and high relative humidity, it is recommended to use hydrophilic aluminum fins with large specific areas and small fractal dimensions for the heat exchange fins of air source heat pump air conditioning systems.

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Wang, Xiao Xiong, Jing Liu, Jing Tao Han und Qian Liu. „Numerical Simulation of Polyurethane Pad Punching Process“. Advanced Materials Research 941-944 (Juni 2014): 1817–21. http://dx.doi.org/10.4028/www.scientific.net/amr.941-944.1817.

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A numerical simulation was conducted to investigate the effect of the punching clearance, the thickness of sheet, and the hardness of polyurethane pad on the process of punching by finite element program ABAQUS which based on shear failure criterion and arbitrary Lagrangian-Eulerian adaptive meshing method. And the collapse height dimension and width dimension tendency of the sheet under different control parameters was analyzed after punching process according to this simulation result. The results show that the collapse height dimension and width dimension decreased with the increase of the polyurethane hardness, it means the cross section quality perspicuously has been increased; the collapse height dimension and width dimension decreased with the increasing of the sheet thickness; while the influence of the punching gap is indistinctive.

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Napolitano, F., G. De Rosa, G. Caporale, A. Carlucci, F. Grasso und E. Monteleone. „Bridging consumer perception and on-farm assessment of animal welfare“. Animal Welfare 16, Nr. 2 (Mai 2007): 249–53. http://dx.doi.org/10.1017/s0962728600031456.

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AbstractThe present study aims to assess the relationship between consumer perception and on-farm assessment of animal welfare performed using the Animal Needs Index 35L (ANI). Two tie-stall, 2 straw yard and 2 cubicle farms were scored by trained assessors using the ANI and filmed to produce six 3.5 min videos. Each of them contained 4 clips: barn overall view, feeding, milking and individual animals. Ten untrained observers were asked to elicit terms describing how they perceived the observed farming systems to affect animal welfare using Free Choice Profiling (FCP). Data from FCP were subjected to Generalised Procrustes Analysis (GPA). GPA showed a significant consensus among observers. Observers characterised the first dimension with terms ranging from constrictive to comfortable conditions and the second one in terms of cleanliness/dirtiness. Principal Component Analysis (PCA) was conducted using the scores of the farms on the first two dimensions of GPA and the data gathered through the ANI. The first dimension of GPA (Comfortable), ANI's sheet 1 (Locomotion), sheet 2 (Social interaction) and sheet 6 (Total score) showed high loadings on the first component of PCA, whereas the second dimension of GPA (Clean), sheet 3 (Flooring) and sheet 4 (Stockmanship) were correlated with the second component of PCA. We concluded that FCP may be used to elicit lay person perception of welfare-related characteristics of dairy cattle farming systems, thus providing a tool to study the relationships between consumer perception and on-farm assessment of animal welfare.

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BRAUNE, S. „GEOMETRICAL PROPERTIES OF CONFORMAL FIELD THEORIES COUPLED TO TWO-DIMENSIONAL QUANTUM GRAVITY“. International Journal of Modern Physics A 11, Nr. 11 (30.04.1996): 1913–28. http://dx.doi.org/10.1142/s0217751x96000997.

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In this work we discuss an approach due to F. David to the geometry of world sheets of noncritical strings in quasiclassical approximation. The gravitational dressed conformal dimension is related to the scaling behavior of the two-point function with respect to a distance variable. We show how this approach can reproduce the standard gravitational dressing in the next order of perturbation theory. Furthermore, we try to find this scaling dimension by studying the functional integral. With the same technique we calculate the intrinsic Hausdorff dimension of a world sheet.

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BEZEMER, DIRK J. „THE ECONOMY AS A COMPLEX SYSTEM: THE BALANCE SHEET DIMENSION“. Advances in Complex Systems 15, supp02 (September 2012): 1250047. http://dx.doi.org/10.1142/s0219525912500476.

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Given the economy's complex behavior and sudden transitions as evidenced in the 2007–2008 crisis, agent-based models are widely considered a promising alternative to current macroeconomic research dominated by DSGE models. Their failure is commonly interpreted as a failure to incorporate heterogeneous interacting agents. This paper explains that complex behavior and sudden transitions also arise from the economy's financial structure as reflected in its balance sheets, not just from heterogeneous interacting agents. It introduces "flow-of-funds" or "accounting" models, which were pre eminent in successful anticipations of the recent crisis. In illustration, a simple balance sheet model of the economy is developed to demonstrate that non-linear behavior and sudden transition may arise from the economy's balance sheet structure, even without any micro-foundations. The paper concludes by discussing one recent example of combining flow-of-funds and agent-based models. This appears a promising avenue for future research.

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Yang, Xiaoyong, und Tan Jin. „Fractal calculation method of friction parameters: Surface morphology and load of galvanized sheet“. Open Physics 19, Nr. 1 (01.01.2021): 375–82. http://dx.doi.org/10.1515/phys-2021-0042.

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Abstract In the forming process of galvanized sheet, the friction between the die and the blank often causes the zinc coating of galvanized sheet to peel off, scratch, and crack. The aim of this study is to evaluate and calculate the fractal characteristics of the surface morphology of galvanized sheet and the effect of pressure on the interfacial friction behavior. Two steel plates, GA and GI, produced by Shanghai Baosteel Company, were used as materials to conduct tribological experiments, measure the surface profile and three-dimensional shape of the galvanized sheet, and calculate the fractal dimension and fractal roughness parameters. According to the analysis results of friction surface damage of galvanized sheet, the damage failure parameters of galvanized sheet are calculated. On this basis, according to the adhesive friction theory, the total surface friction value of galvanized sheet is obtained, and the fractal calculation model of galvanized sheet friction is established. The simulation results show that the galvanized sheet has fractal characteristics. The average values of fractal dimension and scale factor of SP781BQ alloy hot-dip galvanized sheet are 1.52 and 0.23 µm, respectively. The average fractal dimension and scale coefficient of HC420/780DPD + Z hot-dip galvanized sheet are 1.60 and 0.11 µm, respectively. The friction coefficient calculated by the proposed method is consistent with the theoretical value, and the error is less than 10%, which proves the accuracy and feasibility of the friction fractal calculation method.

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ELLIS, JOHN, N. E. MAVROMATOS und D. V. NANOPOULOS. „WORLD SHEET FORMULATION OF M THEORY“. International Journal of Modern Physics A 13, Nr. 29 (20.11.1998): 5093–112. http://dx.doi.org/10.1142/s0217751x98002377.

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We first review the interpretation of world sheet defects as D branes described by a critical theory in 11 dimensions, that we interpret as M theory. We then show that D-brane recoil induces dynamically an anti-de Sitter (AdS) space–time background, with criticality restored by a twelfth timelike dimension described by a Liouville field. Local physics in the bulk of this AdS11 may be described by an Osp (1|32, R) ⊗ Osp (1|32, R) topological gauge theory (TGT), with nonlocal boundary states in doubleton representations. We draw analogies with structures previously exhibited in two-dimensional black hole models. Wilson loops of "matter" in the TGT may be described by an effective string action, and defect condensation may yield string tension and cause a space–time metric to appear.

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Yu, De Zhong, und Xiang Hong Xu. „Dimension Error Analysis and Simulation of Sheet Metal Multistage Assemblies“. Applied Mechanics and Materials 201-202 (Oktober 2012): 208–12. http://dx.doi.org/10.4028/www.scientific.net/amm.201-202.208.

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The dimension quality of sheet metal subassembly（SMS）, which is usually assembled in the multistage process, has serious effect on its performance. Based on the multistage transmitting model of dimension errors of SMS, this paper detailedly analyzed the dimension errors of SMS in locating phase, over-locating phase and springback phase, and also simulated their dimension errors by Matlab and FEM, and finally predicted the assembly dimension errors of aeroplane wainscot subassembly sample.

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12

Mountford, T. S. „Uniform Dimension Results for the Brownian Sheet“. Annals of Probability 17, Nr. 4 (Oktober 1989): 1454–62. http://dx.doi.org/10.1214/aop/1176991165.

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13

Depauw, Jérôme. „Degree two Brownian Sheet in Dimension three“. Probability Theory and Related Fields 135, Nr. 3 (17.08.2005): 457–69. http://dx.doi.org/10.1007/s00440-005-0463-2.

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14

Chen, Zhenlong, und Sanyang Liu. „DIMENSION OF POLAR SETS FOR BROWNIAN SHEET“. Acta Mathematica Scientia 23, Nr. 4 (Oktober 2003): 549–60. http://dx.doi.org/10.1016/s0252-9602(17)30499-x.

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15

Bao, Yufang, und Xingwu Zhuang. „The uniform dimension of Generalized Brownian Sheet“. Acta Mathematica Sinica 11, Nr. 3 (September 1995): 278–90. http://dx.doi.org/10.1007/bf02265393.

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16

Han, Zhi Ren, Xu Geng, Ze Bing Yuan und Guan Long Wang. „The Research on the Algorithm of Rubber Parts Forming Die Dimension Based on Mid-Difference Value Method“. Advanced Materials Research 418-420 (Dezember 2011): 1188–93. http://dx.doi.org/10.4028/www.scientific.net/amr.418-420.1188.

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It mainly focuses on the research of the occurred problems and the suggested solutions when the dimension of the injection part die is calculated. The algorithm we usually use in enterprises is mid-value difference method, but it often appears parts working dimensions out of tolerance; So a compensatory algorithm based on mid-value difference method was developed, and the compensation algorithm and modified formula used in the thickness direction are put forward for sheet part. A series of sheet part are analyzed by ANSYS thermal transient analysis module, and the parameters in the compensation algorithm in the thickness direction are determined. The compensation results show that parts working dimensions in the thickness direction is in tolerance.

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ELLIS, JOHN, und N. E. MAVROMATOS. „CONFINEMENT IN GAUGE THEORIES FROM THE CONDENSATION OF WORLD SHEET DEFECTS IN LIOUVILLE STRING“. International Journal of Modern Physics A 14, Nr. 24 (30.09.1999): 3761–88. http://dx.doi.org/10.1142/s0217751x99001743.

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We present a Liouville-string approach to confinement in four-dimensional gauge theories, which extends previous approaches to include nonconformal theories. We consider Liouville field theory on world sheets whose boundaries are the Wilson loops of gauge theory, which exhibit vortex and spike defects. We show that world sheet vortex condensation occurs when the Wilson loop is embedded in four target–space–time dimensions, and show that this corresponds to the condensation of gauge magnetic monopoles in target–space. We also show that vortex condensation generates an effective string tension corresponding to the confinement of electric degrees of freedom. The tension is independent of the string length in a gauge theory whose electric coupling varies logarithmically with the length scale. The Liouville field is naturally interpreted as an extra target dimension, with an anti-de-Sitter (AdS) structure induced by recoil effects on the gauge monopoles, interpreted as D branes of the effective string theory. Black holes in the bulk AdS space correspond to world sheet defects, so that phases of the bulk gravitational system correspond to the different world sheet phases, and hence to different phases of the four-dimensional gauge theory. Deconfinement is associated with a Berezinskii–Kosterlitz–Thouless transition of vortices on the Wilson-loop world sheet, corresponding in turn to a phase transition of the black holes in the bulk AdS space.

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Dgheim, J., A. Chahine, M. Ghazeleh und M. Abdallah. „Numerical computation of thermoelectric effiency of graphite sheet optimal dimension“. Lebanese Science Journal 20, Nr. 1 (27.04.2019): 122–33. http://dx.doi.org/10.22453/lsj-020.1.122-133.

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Thermoelectric Graphite sheet has been studied numerically due to their ability to convert directly heat to electricity. Electro-thermal heat transfer equations coupling to initial and boundary conditions, are solved using finite difference and finite element schemes. The obtained results of both numerical techniques show good qualitative and quantitative agreements. In addition, the results of our numerical models present good conformity with the experimental result of Luo et al.. The voltage difference, the temperature variation, the Seebeck coefficient, the figure of merit and the maximum efficiency of graphite sheet are determined numerically. The ZT of the graphite sheet is calculated to be 1.27 at a temperature of 850 K for a graphite sheet surface of 0.26×0.25 cm2.

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Sreenu, Pothala, und Ravi Kumar Gupta. „Extraction of Process Parameters from a Sheet Metal Part Model“. Applied Mechanics and Materials 592-594 (Juli 2014): 888–93. http://dx.doi.org/10.4028/www.scientific.net/amm.592-594.888.

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Process planning in a computer integrated manufacturing (CIM) requires integrated system for design and manufacturing activities. For sheet metal part, feature recognition and feature reasoning of a product model for process planning is an essential component of CIM environment. Research work for feature recognition and reasoning has been addressed in literature, which is limited to the geometric and topological information but actual process parameters requited for manufacturing operation is still an open issue. Our research is for extraction of process parameters from a sheet metal part model which is in STEP Format. These process parameters can be used in sheet metal manufacturing to control the operations. This paper presents extraction of process parameters for a sheet metal feature from a sheet metal part model (STEP Format). This work then formulates the feature processes in terms of extracted process parameters, material properties, sheet metal dimension and feature dimension. The actual operation in real manufacturing environment is identified as extension of the proposed work. The extraction of process parameters for sheet metal operation is demonstrated with case studies.

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Hsu, Quang Cherng. „Size Effects on Sheet-Metal Formability for Miniature Parts“. Materials Science Forum 505-507 (Januar 2006): 721–26. http://dx.doi.org/10.4028/www.scientific.net/msf.505-507.721.

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Due to the rapid progress of industrial development, the formation of lightweight and small-size parts is becoming increasingly important. Especially in the IC and 3C industry, the sheet metal forming of miniature parts is especially interesting. Size effects such as specimen dimension, blank thickness, punch corner dimension, grain size, and grid dimension (for strain measurement), as well as the microstructure of material and surface condition all seriously influence the forming of miniature parts. In this paper, systematic experiments including Erichsen stretch forming and hydraulic bulge, and strain analyzers including for circular and rectangular grids are described for establishing the relationships of sheet metal formability to process parameters. The details of the experimental procedures and results are presented and discussed.

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Sugandini, Wayan, Wayan Dewi Tarini, Ketut Espana Giri und Luh Nik Armini. „EVALUASI PROGRAM PENILAIAN PENCAPAIAN KOMPETENSI I (PPK I) DENGAN MODEL CONTENT, INPUT, PROSES, DAN PRODUCT (CIPP)“. Jurnal Imiah Pendidikan dan Pembelajaran 2, Nr. 3 (10.12.2018): 305. http://dx.doi.org/10.23887/jipp.v2i3.16228.

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The purpose of this study was to evaluate the PPK I program in order to identify its effectiveness. The method used in this study was the Context, Input, Process, and Product (CIPP) model of Stufflebeam. This research was conducted in the Midwifery 3 diploma program. Research subjects included 13 lecturers, and 2 education staff. Data collection was done by filling out questionnaires by the subject, as well as filling out the interview sheet. The data obtained were analyzed by percentile quantitative analysis. The results showed that: 1) 78.21% of the Context dimension supported the PPK I program, 2) 74.8%, the Input dimension supported the PPK I program, 3) 82%, of the Process dimension supported PPK I and 4 programs) 78%. Product dimensions support the PPK program I. From the results of the above research, it can be concluded that the Context dimension of the category of effectiveness is sufficient, the dimensions of the input category of effectiveness are sufficient, the dimensions of the Process category are high, and the dimensions of the category of effectiveness are sufficient. Keywords: Evaluation, CIPP, PPK I

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Geiger, Manfred, Marion Merklein und Massimo Cojutti. „Integrated Tube and Double Sheet Hydroforming Technology - Optimised Process for the Production of a Complex Part“. Key Engineering Materials 344 (Juli 2007): 477–84. http://dx.doi.org/10.4028/www.scientific.net/kem.344.477.

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The possibility to produce lightweight components with a complex geometry enhanced, in the last decades, the industrial application of the tube hydroforming and, more recently and restricted to specific industrial fields, of the sheet hydroforming technology. The integration in one tool of a tube and a double sheet hydroforming process represents an innovative technology which further emphasises the advantages offered by hydroforming in terms of costs reduction and complexity of the manufactured part. This paper describes the design and the construction of a complex hollow part resulting from the simultaneous hydroforming of two sheets and a tubular component in one tool. The focus is set in particular on the optimisation of the joining zone between tube and sheet pair, whose geometry allows a “metallic” sealing of the gap between the sheets and the tube, i.e. without using sealing components. The contact between tube and sheet pair allows the transmission of the axial force used to support the bulging of the tube to the sheet blanks, thus increasing their draw-in in the die and, consequently, avoiding the occurrence of tearing on the part. The paper describes the optimisation of different process parameters like the shape and the dimension of the blanks, their initial positioning in the tool, the value of the axial force applied to the tubular component and the blankholder force during the preforming and the calibrating stages.

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Nakamura, T. K. M., W. L. Teh, S. Zenitani, T. Umeda, M. Oka, H. Hasegawa, A. M. Veronig und R. Nakamura. „Spatial and time scaling of coalescing multiple magnetic islands“. Physics of Plasmas 30, Nr. 2 (Februar 2023): 022902. http://dx.doi.org/10.1063/5.0127107.

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Magnetic reconnection is a key fundamental process in collisionless plasmas, which converts magnetic energy to plasma kinetic energy. Past observation and simulation studies suggested that this process causes an efficient energy conversion through the formation and coalescence of multiple magnetic islands. In this study, based on a large-scale two-dimensional fully kinetic simulations of coalescing multiple islands with a moderate guide magnetic field, we first examined the spatial dimensions of the internal structures of the coalescing islands. The results show that the dimensions of the structures in the directions normal to and along the initial current sheet depend on the initial thickness of the current sheet and the number of coalescing islands. We then found that the horizontal dimension of the structures controls the evolution time scale of the island coalescence process. We further found that when the vertical dimension of the structures, which corresponds to the length of the reconnection X-line in the reconnection outflow direction at the merging point between the two coalescing islands, is sufficiently longer than the ion inertial length, reconnection in the merging current sheet can well mature and both ions and electrons can be effectively heated around the merging X-line. The obtained scaling predicts that such a strong heating by well-matured reconnection in the island coalescence process would be seen in various plasma environments, such as the Earth's magnetotail and solar flares.

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Nguyen, Nam Thanh, Cuong Van Vo, Dien Khanh Le und Sy Van Le. „A CALCULATION FOR COMPENSATING THE ERRORS DUE TO SPRINGBACK WHEN FORMING METAL SHEET BY SINGLE POINT INCREMENTAL FORMING (SPIF)“. Science and Technology Development Journal 13, Nr. 3 (30.09.2010): 14–24. http://dx.doi.org/10.32508/stdj.v13i3.2131.

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The question of compensating for the error of dimension due to springback phenomenon when forming metal sheet by SPIF method is being one of the challenges that the researchers of SPIF in the world trying to solve. This paper is only a recommendation that is based on the macro analysis of a sheet metal forming model when machining by SPIF method for calculating a reasonable recompensated feeding that almost all researchers have not been interested in yet: - Considering the metal sheet workpiece is elasto-plastic and the sphere tool tip is elastic, the authors attempt to calculate for compensating the error of dimension due to elastic deforming of the tool tip. - The metal sheet is clamped by a cantilever joint that has an evident sinking at the machiningarea that is also calculated to add to the compensating feeding value. The paper also studies the limited force for ensuring the elastic deforming at these working area of the sheet to eliminate all theunexpected plastic deforming of the sheet. With two small but novel contributions, this study can help to take theoretical model for elastic forming of metal sheet closer to real situation.

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Zhang, Peng, und Hong Wei Liu. „Simulation and Control Models of Laser Bending Angle of Sheet Metals“. Key Engineering Materials 431-432 (März 2010): 118–21. http://dx.doi.org/10.4028/www.scientific.net/kem.431-432.118.

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Laser bending process of sheet metals is a highly flexible forming technique. Simulate model of laser bending process was established by dimension analysis, and the control model of laser bending was achieved with the regression of swatch datum. It was shown that dimension analysis was an effective method in simulating the complex laser bending process, and the control model, which came from non-dimension group datum, was a high-accuracy model in predictive analysis of bending angle.

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Jung, Dong Won. „A New Engineering Technique in Roller Design to Prevent Thinning of Sheet in Roll Forming Process“. Applied Mechanics and Materials 873 (November 2017): 42–47. http://dx.doi.org/10.4028/www.scientific.net/amm.873.42.

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These days sheet metal forming is a widely used in different industrial fields with large production volumes. Formability of metal sheets is limited by localized necking and plastic instability. In sheet metal forming processes like drawing and stamping the main challenge is thinning of the metal sheet in some regions. To reduce thinning of the sheet product, roll forming has been suggested instead of stamping process. Thinning strain can cause necking, tearing or wrinkling which are failure of the metal sheet. In this study a new engineering technique is proposed in order to prevent thinning of the steel galvanized hot coil commercial (SGHC) in roll forming process. An explicit finite element code, ABAQUS software, was used to simulate the roll forming process. The results show that the proposed technique has an important effect on thinning of the sheet and can reduce it significantly. Investigation on the second and third and fourth rollers show the effect of modified roller dimension as on reducing the thickness. These reductions in second, third and fourth rollers are from 4 percent to 0.5 percent, 2.8 to 1.4 percent and from 1.4 to 0.7 percent respectively. The reasons of the new techniques effect were also discussed.

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Chen, Fuh Kuo, und Chih Kun Chang. „Warm Stamping of Cell-Phone Cases with AZ31 Magnesium-Alloy Sheets“. Advanced Materials Research 154-155 (Oktober 2010): 1826–29. http://dx.doi.org/10.4028/www.scientific.net/amr.154-155.1826.

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The stamping process for manufacturing cell phone cases with magnesium alloy AZ31 sheets was studied using both the experimental approach and the finite element analysis. The formability of AZ31 magnesium-alloy sheet at elevated temperatures was studied first. The experimental results reveal that the forming of AZ31 sheets becomes possible as long as the sheet is heated to an elevated temperature and 200oC is an optimum forming temperature to start with. An optimum stamping process, including die geometry, forming temperature, and blank dimension, for manufacturing the cell phone cases was examined by the finite element analysis. The finite element analyses performed for the cell phone were validated by the good agreement between the simulation results and the experimental data. It also confirms that the cell phone cases can be produced with AZ31 magnesium-alloy sheets at elevated temperature by the stamping process. It provides an alternative to the electronics industry in the application of magnesium alloys.

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Omran, Isam I., Nabeel H. Al-Saati, Hyam H. Al-Saati, Khalid S. Hashim und Zainab N. Al-Saati. „Sustainability assessment of wastewater treatment techniques in urban areas of Iraq using multi-criteria decision analysis (MCDA)“. Water Practice and Technology 16, Nr. 2 (18.02.2021): 648–60. http://dx.doi.org/10.2166/wpt.2021.013.

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Abstract Sustainable development is based on environmental, social, economic, and technical dimensions. In this study, the sustainability of wastewater treatment techniques in urban areas of Iraq was assessed using a multi-criteria decision analysis (MCDA)/the weighted sum model (WSM). The analysis was performed on 13 operating wastewater treatment plants in 10 provinces, Iraq, using a questionnaire sheet with the assistance of 52 specialists in the Ministry of Municipalities and Public Works, Iraq. Four types of wastewater treatment techniques (Conventional Treatment, Oxidation Ditches, Aeration Lagoons, and membrane bio-reactor (MBR)) were assessed. The environmental, social, economic, and technical dimensions were represented by 11, 5, 7, and 4 indicators, respectively. The main results of this study indicate that the sustainability of MBR recorded the highest total importance; the order of the total importance from the highest to the lowest was: MBR > Oxidation Ditches > Aeration Lagoons > Conventional Treatment. The environmental dimension proved its dominance in the four studied treatment techniques' sustainability as it recorded the maximum contribution to sustainability. While the technical dimension recorded the least contribution to sustainability, the order from the highest to the lowest was: Environmental Dimension > Economic Dimension > Social Dimension > Technical Dimension.

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Chen, Jenn-Yeu. „Stroop Interference is the Result of Comparable, Not of Differential Processing Speeds of Two Stimulus Dimensions“. Perceptual and Motor Skills 87, Nr. 1 (August 1998): 375–80. http://dx.doi.org/10.2466/pms.1998.87.1.375.

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On a digit-counting Stroop task, processing of the slower, nonverbal, i.e., number, dimension was slowed further by a large-number set (6 to 9), as compared with a small-number set (1 to 4). In the task, neutral symbols or conflicting digits were arranged on a horizontal line (e.g., @@@, 444) and on two separate sheets. Each sheet contained 120 stimulus arrays. Subjects counted out loud the number of symbols or digits in each array, and their counting times for each sheet were recorded. 23 subjects received the small-number set while 21 received the large-number set. It was found that counting a large number of symbols took significantly longer time (by 162 sec. per 120 stimulus arrays) than counting a small number of symbols. Moreover, interference was nonexistent (2 msec. per stimulus array) when a large number of conflicting digits were counted but was of a typical magnitude (110 msec. per stimulus array) when a small number of conflicting digits were counted. This suggests that Stroop interference is better explained as the result of comparable, not of differential, processing speeds of the two stimulus dimensions. Implications for the cause and the locus of Stroop interference are discussed.

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Velho, J., und N. F. Santos. „Fractal Analysis of Coated Papers“. Materials Science Forum 730-732 (November 2012): 209–14. http://dx.doi.org/10.4028/www.scientific.net/msf.730-732.209.

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The main goal of this research is to apply AFM to the analysis of coated paper topography in order to find out relationships between sheet gloss and some parameters obtained from AFM, such as roughness and fractal dimension (D). Flooding technique was also developed using appropriated software. Number of hills/flooding volume for 25%, 50% and 75% flooded volume was applied in this research. Ground calcium carbonate and precipitated calcium carbonate were applied in coating colour formulations, alone and blended in three formulations, 75:25, 50:50 and 25:75. The results obtained showed high correlations between sheet gloss with fractal dimension (D) parameter. Finally, flooding technique showed to be very interesting, all of them gave useful information in interpreting the influence of topography on sheet gloss.

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Boschetto, Alberto, Armando Ruggiero und Francesco Veniali. „Deburring of Sheet Metal by Barrel Finishing“. Key Engineering Materials 344 (Juli 2007): 193–200. http://dx.doi.org/10.4028/www.scientific.net/kem.344.193.

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In sheet metal processes the burrs cannot be completely eliminated during the process but can be minimized by optimization of the process parameters. Hence the deburring often becomes an essential secondary operation. Most of the deburring operations are hand-made and therefore several manufacturers tend to eliminate these tedious and labor-intensive operations due to time and cost issues. Moreover, clamping problems can arise which, together with the deburring forces, can induce dimension alterations and local deformations, particularly for thin sheets. Barrel finishing is an old technique commonly used to improve the surface roughness of complicated parts, but can find interesting applications also in the deburring. Aim of this work is to present an experimental investigation on the deburring of sheet metal performed by barreling. A technological model has been developed in order to assess the height of the burr as a function of the initial burr and of the working time.

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Li, Hui-qiong, und Zhen-long Chen. „Polar Sets and Relative Dimension for Generalized Brownian Sheet“. Acta Mathematicae Applicatae Sinica, English Series 23, Nr. 4 (Oktober 2007): 579–92. http://dx.doi.org/10.1007/s10255-007-0397.

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Feli, Saeed, und Maziar M Jalilian. „Theoretical model of low-velocity impact on foam-core sandwich panels using finite difference method“. Journal of Sandwich Structures & Materials 19, Nr. 3 (29.12.2016): 261–90. http://dx.doi.org/10.1177/1099636216685316.

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In this article, a three-dimensional solution based on the Fourier’s series and finite difference method has been presented to study the low-velocity impact on sandwich panels with foam core and composite face sheets. The Navier’s equations are derived and displacements are substituted by their corresponding Fourier’s series and three partial differential equations with coefficients of Fourier’s series are obtained. The contact force has been considered as a Fourier’s series of impactor displacement and deflection of top face sheet. Also, the model is verified by experiments performed on sandwich panel with epoxy/woven-fiberglass composites, face sheets and polyurethane foam core, and other researchers’ works. The history of contact forces and lateral displacement of contact point has been obtained experimentally and compared with theoretical model. Finally, the effects of impact energy and geometrical parameters including in-plane dimension ratio, core thickness, and face sheet thickness on contact force and lateral deflection histories have been investigated.

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Wu, Ji Gang, Kuan Fang He und Bin Qin. „Research on Edge Detection of Thin Sheet Part Dimension Inspection System Based on Machine Vision“. Applied Mechanics and Materials 103 (September 2011): 194–98. http://dx.doi.org/10.4028/www.scientific.net/amm.103.194.

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Aiming at the edge detection of thin sheet part dimension inspection system based on machine vision, a contrast research on edge detection is investigated. The Gaussian blurred simulation image and thin sheet part image are took as evaluation images, and the edge detection are done with Roberts operator, Sobel operator, Prewitt operator, Kirsch operator, Laplacian operator, LOG operator and mathematical morphology edge detection method. The results of edge detection are analyzed deeply, and the edge location accuracy, noise resisting ability and calculation time of each algorithm are compared. The single-pixel width connected contour is acquired with mathematical morphology edge detection method, the detection time are 0.0521 second and 0.457 second respectively. It is appropriate that taking the mathematical morphology edge detection method as the edge detection method of thin sheet part dimension inspection system based on machine vision.

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Kistanov, Andrey A., Devesh R. Kripalani, Yongqing Cai, Sergey V. Dmitriev, Kun Zhou und Yong-Wei Zhang. „Ultrafast diffusive cross-sheet motion of lithium through antimonene with 2 + 1 dimensional kinetics“. Journal of Materials Chemistry A 7, Nr. 6 (2019): 2901–7. http://dx.doi.org/10.1039/c8ta11503f.

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Cai, Wayne W., Ching-Chieh Hsieh, Yufeng Long, Samuel P. Marin und Kong P. Oh. „Digital Panel Assembly Methodologies and Applications for Compliant Sheet Components“. Journal of Manufacturing Science and Engineering 128, Nr. 1 (04.05.2005): 270–79. http://dx.doi.org/10.1115/1.2112967.

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This paper presents digital panel assembly (DPA) methodologies and applications for sheet component assembly in automotive body manufacturing processes. Core to DPA is the customized finite element analysis formulas we have developed, which simulates assembly processes and predicts assembly dimensions by taking into consideration the panel compliances. Two key analysis types of the DPA are presented, the deterministic analysis and variation analysis. We present a methodology to utilize the quadratic form of Taylor series expansion to approximate the assembly dimensions efficiently in variation simulation, and discuss its pros and cons versus the traditional Monte Carlo method under different modeling conditions. For either the deterministic or variation analysis, linear models (without contact, efficient but less accurate), and nonlinear models (with contact, less efficient but accurate) can be established. It is shown that the linear models are only valid when panels do not penetrate, and that the nonlinear models should generally be used for accurate assembly dimension prediction. Based on the DPA methodologies, a software tool called Elastic Assembly Variation Simulation (EAVS) is presented, followed by application case studies. The confidence intervals for variation analysis are also discussed.

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Chen, Xinya, Zhen Chen und Yang Zhao. „Analysis of Sheet Fracture Failure Based on XFEM“. Open Mechanical Engineering Journal 9, Nr. 1 (07.10.2015): 887–91. http://dx.doi.org/10.2174/1874155x01509010887.

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Extended finite element method (XFEM) is the most effective numerical method to solve discrete mechanical problem. Crack growth problem of two-dimension finite length rectangle panel is researched based on Abaqus XFEM frame. Stress intensity factor is obtained respectively by theoretical calculation and XFEM simulation, which proves reliability of XFEM and the software.

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Ma, Xin Wu, Guo Qun Zhao und Wen Juan Li. „A Method for Determination of Friction Coefficient in Sheet Metal Forming of Magnesium Alloy“. Applied Mechanics and Materials 268-270 (Dezember 2012): 430–35. http://dx.doi.org/10.4028/www.scientific.net/amm.268-270.430.

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A new method for determination of friction coefficient in sheet metal forming of Mg alloy AZ31B is presented in this paper. The method is based on the bulging test of sheet metal in which the specimen is processed with a hole at the center. The diameter of the hole will increase along the stroke of the punch and the dimensional change of the hole has a certain relationship with the friction coefficient at the punch/specimen interface. Thus, the friction coefficient can be determined indirectly according to the dimension of the hole in the bulging process. The bulging process of the sheet is simulated using FE code DEFORM-2D. The analysis model is set up according to the experiment of the bulging and the friction calibration curves are generated from the simulations of the bulging by setting different coefficients of friction. The friction coefficient can be determined by measuring the hole dimension during the bulging process and comparing it with the friction calibration curves.

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Baudin, Thierry, Sandrine Bozzi, François Brisset und Hiba Azzeddine. „Local Microstructure and Texture Development during Friction Stir Spot of 5182 Aluminum Alloy“. Crystals 13, Nr. 3 (21.03.2023): 540. http://dx.doi.org/10.3390/cryst13030540.

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The local microstructure, texture gradient and mechanical properties through the shoulder dimension (10 mm) of upper and lower AA5182 aluminum sheets were investigated using electron backscatter diffraction (EBSD) and Vickers microhardness after friction stir spot welding (FSSW). Based on the microstructural features (mean grain size, grain boundary type and dynamic recrystallization (DRX)), the upper sheet was found to be mainly composed of the stir zone (SZ) and thermomechanically affected zone (TMAZ) due to the high deformation induced simultaneously by the tool rotation and the shoulder download force, while the SZ, TMAZ, heat-affected zone (HAZ) and base metal (BM) were detected in the lower sheet due to the limited effect of the shoulder on the lower sheet. The texture changes, due to the nature of the deformation, demonstrated a shear-type texture at the SZ to a plane strain compression deformation type texture at the TMAZ and then a recrystallization texture at the HAZ and BM. The microhardness gradually decreased with the increasing distance from the keyhole along the SZ, TMAZ and HAZ regions. Eventually, the microstructure and microhardness evolutions were correlated based on the Hall–Petch relationship.

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Traub, Tilman, und Peter Groche. „Experimental and Numerical Determination of the Required Initial Sheet Width in Die Bending“. Key Engineering Materials 639 (März 2015): 147–54. http://dx.doi.org/10.4028/www.scientific.net/kem.639.147.

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So far, determining the necessary precut dimensions of metal sheets prior to bending has been an unsolved question. During the last decades numerous calculation methods have been suggested. However, comparing these different methods indicates that different calculation methods suggest diverging precut dimensions. Especially in roll-forming, where multiple bend operations occur within the same bend part, these differences between several calculation methods can add up to some millimetres. The accuracy of presently available methods can hardly be compared. Thus an optimized method is needed. One possibility to determine the initial sheet width is identifying the position of the unlengthened layer in the bend zone. This study compares the position of the unlengthened layer determined in experiments and numerical simulations for different bend geometries and materials. The results indicate that even state of the art measuring technique is not accurate enough to determine the position of the unlengthened layer properly. Due to high measurement uncertainties, numerical simulations are required to assess the influence of geometry or material parameters on the position of the unlengthened layer. However, combining numerical and experimental results shows that the geometry of the bend part influences the position of the unlengthened layer and thus the required precut dimension. In contrast, a significant influence of material strength on the position of the unlegthened layer was not found.

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Wang, Chunju, Weiwei Zhang, Lidong Cheng, Changqiong Zhu, Xinwei Wang, Haibo Han, Haidong He und Risheng Hua. „Investigation on Microsheet Metal Deformation Behaviors in Ultrasonic-Vibration-Assisted Uniaxial Tension with Aluminum Alloy 5052“. Materials 13, Nr. 3 (31.01.2020): 637. http://dx.doi.org/10.3390/ma13030637.

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Ultrasonic vibration (UV) is widely used in the forming, joining, machining process, etc. for the acoustic softening effect. For parts with small dimensions, UV with limited output energy is very suitable for the microforming process and has been gaininf more and more attention. In this investigation, UV-assisted uniaxial tensile experiments were carried out utilizing GB 5052 thin sheets of different thicknesses and grain sizes, respectively. The coupling effects of UV and the specimen dimension on the properties of the material were analyzed from the viewpoint of acoustic energy in activating dislocations. A reduction of flow stress was found for the existing acoustic softening effects of UV. Additionally, the residual effects of UV were demonstrated when UV was turned off. The uniform deformation ability of thin sheet could be improved by increasing the hardening exponent with UV. The experimental results indicate that UV is very helpful in improving the forming limit in microsheet forming, e.g., microbulging and deep drawing processes.

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Zhu, Hu, Guixi Cheng und Dongwon Jung. „Toolpath Planning and Generation for Multi-Stage Incremental Forming Based on Stretching Angle“. Materials 14, Nr. 17 (25.08.2021): 4818. http://dx.doi.org/10.3390/ma14174818.

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To solve the problems that exist in the multi-stage forming of the straight wall parts, such as the sheet fracture, uneven thickness distribution, and the stepped feature sinking, a new forming toolpath planning and generation method for the multi-stage incremental forming was proposed based on the stretching angle. In this method, the parallel planes that were used for forming toolpath generation were constructed by using the stretching angle so that the distances between the parallel planes and the forming angles were gradually reduced. This makes the sheet material flow become changed and the thickness thinning is relieved. The software system for the toolpath generation was developed by using C++, VC++, and OpenGL library. In order to verify the feasibility of the proposed method, numerical simulation and forming experiments were carried out for the single stage forming, the traditional multi-stage forming, and multi-stage forming based on the proposed forming toolpath, using 1060 aluminum sheets. The comparative analysis of the thickness distribution, profile curve, strain curve, and sheet material flow shows that the proposed method is feasible, and the profile dimension accuracy is better, the thickness distribution is more uniform, and the sinking and bulging are significantly reduced. The formed sheet part with the stretching angle of 15° has higher dimensional accuracy, smaller bottom subsidence, and larger thickness than that of the stretching angle 5°.

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Torkhov, Nikolay Anatolyevich, Maxim Pavlovich Evstigneev, Andrey Alexandrocivh Kokolov und Leonid Ivanovich Babak. „The Fractal Geometry of TiAlNiAu Thin Film Metal System and Its Sheet Resistance (Lateral Size Effect)“. Symmetry 13, Nr. 12 (11.12.2021): 2391. http://dx.doi.org/10.3390/sym13122391.

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This paper investigates the relation between the geometry of metric space of a TiAlNiAu thin film metal system and the geometry of normed functional space of its sheet resistances (functionals), which are elements of the functional space. The investigation provides a means to describe a lateral size effect that involves a dependency in local approximation of sheet resistance Rsq of TiAlNiAu metal film on its lateral linear dimensions (in (x,y) plane). This dependency is defined by fractal geometry of dendrites, or, more specifically, it is a power-law dependency on fractal dimension Df value. The revealed relation has not only fundamental but also a great practical importance both for a precise calculation of thin film metal system Rsq values in designing discreet devices and ICs, and for controlling results at micro- and nanoscale in producing workflow for thin metal films and systems based on them.

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Pollard, David, und Eric J. Barron. „Causes of model–data discrepancies in European climate during oxygen isotope stage 3 with insights from the last glacial maximum“. Quaternary Research 59, Nr. 1 (Januar 2003): 108–13. http://dx.doi.org/10.1016/s0033-5894(02)00019-4.

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AbstractOxygen isotope stage 3 (OIS 3), encompassing the long middle section of the last glacial interval, has been the focus of an intensive high-resolution climate modeling effort for Europe. These model simulations produce substantially colder climates than modern simulations; however, the temperatures appear warmer than many proxy indicators suggest. In order to evaluate the importance of the model boundary conditions, comparable simulations are completed for the last glacial maximum (LGM). The LGM simulation produces a much colder European continent than OIS 3, despite similarities in the specification of sea-surface temperatures (SSTs). Ice-sheet dimension is evidently a key factor in explaining the difference in European climates over the past 40,000 yr. However, underestimates in specified OIS 3 ice sheets cannot be invoked to explain the discrepancies, since data strongly indicate small ice-sheet extents at that time; this leaves errors in specified OIS 3 SSTs as the most likely cause.

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Kanetake, Naoyuki, und Yasuhisa Tozawa. „Crystallographical Calculation of Earing in Deep Drawing under Various Conditions“. Textures and Microstructures 7, Nr. 2 (01.01.1987): 131–47. http://dx.doi.org/10.1155/tsm.7.131.

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Earing in the cup drawing of sheet metals is calculated quantitatively using a crystallographical theory with measured texture data. In the analysis a polycrystalline sheet is simplified to be an aggregate of many single crystals with various orientations, and a crystallite orientation distribution function which is calculated from the measured texture is used as a volume fraction of a certain oriented crystal. The circumferential distribution of radial strain in a flange of a blank being drawn is calculated by considering a restricted glide in a crystal, and then cup height at each peripheral position of a drawn cup is calculated from this distribution of radial strain. For an aluminium, a copper and two steel sheets the calculated cup profiles are compared with experimental ones under various drawing conditions of dimension of a punch, a die and a blank. The result shows that earing in the drawn cup can be predicted satisfactorily by the present calculation for a wide range of drawing conditions and materials.

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McCarthy, Alan. „Doughnuts and the Fourth Dimension“. Boolean: Snapshots of Doctoral Research at University College Cork, Nr. 2014 (01.01.2014): 79–83. http://dx.doi.org/10.33178/boolean.2014.15.

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Those of you with a sweet tooth are no doubt already familiar with the delicious doughnut, but did you know there is much more to that simple pastry than meets the eye? Here’s an experiment: take a sheet of A4 paper and roll it up, now try to join the two open ends without bending or making any corners on the paper, go on I’ll wait…..impossible right? Well that’s because we are stuck with only three dimensions, add in one more dimension though and you can! What’s more is that if we lived on the surface of that doughnut, the world would look a lot like the surface of the Earth does to us now-flat as far as the eye can see (but a lot sweeter if you choose to eat the soil). My research is on understanding all these ‘flat’ doughnuts (called tori in mathematics) and how to make ...

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Yang, Lian Fa, Liang Yi, Xian Chang Mao und Guo Chen. „Deformation Behaviors of AZ31B Magnesium Alloy Sheets in Hydraulic Deep Drawing“. Advanced Materials Research 139-141 (Oktober 2010): 520–23. http://dx.doi.org/10.4028/www.scientific.net/amr.139-141.520.

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Magnesium alloy sheets have poor formability at room temperature, and the hydraulic forming may be a choice to improve its formability. Experiments were conducted to investigate the deformation behaviors of AZ31B magnesium alloy sheet in radial pressure deep drawing, one of the hydraulic forming technologies. The influence of hydraulic pressure, die dimension, blank dimension on the limit drawing height (LDH) of the drawn workpieces is investigated, and the location, evolvement and pattern of the fractures are also analyzed. The research results show that the obtained LDH increases with the hydraulic pressure when the punch corner radius is large enough, the formability can be improved only under a proper moderate hydraulic pressure when the punch corner radius is small; moreover, the location of the fractures may be around the corner, on the flange and the sidewall of the drawn workpieces, which appears different evolvement directions and patterns through cross-section.

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Karagülle, Hira, Murat Akdağ und İlker Bülbül. „Design Automation of a Two Scissors Lift“. European Journal of Research and Development 2, Nr. 4 (31.12.2022): 178–91. http://dx.doi.org/10.56038/ejrnd.v2i4.192.

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In this study, the design of a two scissors greenhouse lift trolley is considered. The maximum height of the platform from the ground is 3500 mm. A program developed in Visual BASIC to automate the design is introduced. The lift is modeled in SolidWorks (SW) and the finite element (FE) modal and static analyses are performed as an initial design first by using graphical user interface (GUI). The lift contains revolute joints and slider joints. A simply supported beam which has two revolute joints and a slider joint is studied to verify how to model the joints. Pim connectors are defined for revolute joints in SW-FE analysis. Spring connectors with very large values are defined between sliding faces in the normal direction for translational joints. The results obtained with solid finite elements in SW are compared with analytical results for the natural frequency and static analyses and it was observed that the results are in good agreement for the simply supported beam. An Excel file where a main sheet contains the list of the bodies and all the geometric values is created after the initial design. The Excel file also contains sheets for each body. Body sheets have all the dimensions in the sketches and features. The dimension values in the cells of the body sheets are defined by formulas related to the geometric values given in the main sheet. Kinematic, kinetic, and revision of the SW model are performed by the design automation program. The FE analyses are done by GUI and the results are evaluated. If the results are not satisfactory, the geometric values are changed in Excel file and the analyses are repeated. The final design is obtained by the iteration easily. The automation program and the procedure developed in this work can be extended other scissors lifts.

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DELDUC, F., und E. SOKATCHEV. „SIGMA MODELS WITH (2, 2) WORLD SHEET SUPERSYMMETRY“. International Journal of Modern Physics B 08, Nr. 25n26 (November 1994): 3725–39. http://dx.doi.org/10.1142/s0217979294001615.

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We propose a new mechanism for constructing (2, 2) superspace actions for WZWN sigma models. We use the already known semi-chiral superfields, but we choose the Lagrangian in a special way, so that it has a gauge invariance capable of eliminating half of the initially propagating degrees of freedom. Thus we avoid the doubling of the target space dimension. The nonlinear differential conditions on the Lagrangian are derived and it is shown that this type of action corresponds to the general (2, 2) sigma model.

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Khalid, Usman, Othman Mohammad Ahmed Mustafa, Muhammad Ali Naeem, Mohammad Yousef Mohammad Alkhateeb und Basil Marwan Abed Eljaber Awad. „Direct Optimization of an Automotive Sheet Metal Part Using ANSYS“. International Journal of Engineering and Management Sciences 5, Nr. 3 (10.12.2020): 134–42. http://dx.doi.org/10.21791/ijems.2020.3.14.

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Optimization of automotive parts nowadays is mainly used to design lightweight and cost-effective vehicle parts in order to improve the cost and efficiency. In this research, a sheet metal part was taken into consideration and optimized using direct optimization module in ANSYS to evaluate the process. An initial Finite Element Analysis (FEA) was done on the sheet metal part by adding forces and constraints in order to initiate direct optimization. The purpose of the optimization is to minimize the mass of the sheet metal part and maintaining a certain Factor of Safety (FOS) by automatically modifying the sheet thickness and the dimension of the side holes. As a result, the best candidate point with 23% mass reduction was found which complied with FOS value was selected for optimal geometry.

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