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Three-dimensional shape optimization with variational geometry

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Abstract

The unification of computer aided design (CAD) and the finite element method (FEM) has greatly enhanced the engineer's ability to evaluate potential designs (Finniganet al. 1989). However, analysis alone is not the answer to design, and thus shape optimization methods have become increasingly popular, particularly for structural problems (Yanget al. 1992; Botkin 1992). However, for shape optimization methods to be fully accepted by the engineering community they must first be integrated with CAD systems. To date, the difficulty of integrating CAD and shape optimization is the inability to relate the finite element nodal coordinates to the CAD solid model dimensions. Here, the critical link between these CAD and FEM data is developed within an industry standard feature-based modelling environment. A three-dimensional connecting rod model is optimized to exemplify the method.

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References

  • Aldefeld, B. 1988: Variation of geometries based on a geometric-reasoning method.Computer Aided Design 20, 117–126

    Google Scholar 

  • Atiqullah, M.M.; Rao, S.S. 1995: Parallel processing in optimal structural design using simulated annealing.AIAA J. 33, 2386–2392

    Google Scholar 

  • Belegundu, A.D.; Rajan, S.D. 1988: A shape optimization approach based on natural design variables and shape functions.Comp. Meth. Appl. Mech. Eng. 66, 87–106

    Google Scholar 

  • Bendsøe, M.P. 1995:Optimization of structural topology, shape, and material. Berlin, Heidelberg, New York. Springer

    Google Scholar 

  • Botkin, M.E. 1992: Three-dimensional shape optimization using fully automatic mesh generation.AIAA J. 30, 1932–1934

    Google Scholar 

  • Braibant, V.; Fleury, C. 1984: Shape optimal design using bsplines.Comp. Meth. Appl. Mech. Eng. 44, 247–267

    Google Scholar 

  • Chang, K.H.; Choi, K.K. 1992: A geometry-based parameterization method for shape design of elastic solids.Mech. Struct. & Mach. 20, 215–252

    Google Scholar 

  • Chen, S. 1996:Three-dimensional shape optimization with variational geometry. Master's Thesis, University of Illinois at Urbana-Champaign

  • Chen, J.L.; Ho, J.S. 1994: A comparative study of design sensitivity analysis by using commercial finite element programs.Finite Elements in Analysis and Design 15, 189–200

    Google Scholar 

  • Choi, K.K.; Twu, S.L. 1989: Equivalence of continuum and discrete methods of shape design sensitivity analysis.AIAA J. 27, 1418–1424

    Google Scholar 

  • El-Sayed, M.E.M.; Zumwalt, K.W. 1991: Comparison of two different approaches for making design sensitivity analysis an integrated part of finite element analysis.Struct. Optim. 3, 149–156

    Google Scholar 

  • Farin, G. 1988:Curves and surfaces for computer aided geometric design: a practical guide. New York: Academic Press

    Google Scholar 

  • Fianigan, F.M.; Keia, A.; Davis, J.E., 1989: Geometry as a basis for finite element automation.Eng. with Comp. 5, 147–160

    Google Scholar 

  • Foley, J.D.; van Dam, A.; Feiner, S.K.; Hughes, J.F. 1989:Computer graphics-principle and practice. Massachusetts: Addison-Wesley

    Google Scholar 

  • Haftka, R.T.; Barthelemy, B. 1991: On the accuracy of shape sensitivity.Struct. Optim. 3, 1–6

    Google Scholar 

  • Hoffmann, C.M. 1989:Geometric and solid modeling: an introduction. San Mateo, CA: Morgan Kaufmann

    Google Scholar 

  • Kodiyalam, S.; Kumar, V.; Finnigan, P.M. 1992: Constructive solid geometry approach to three-dimensional structural shape optimization.AIAA J. 30, 1408–1415

    Google Scholar 

  • Lee, K. 1983: Shape optimization of assemblies using geometric properties. Ph.D. Thesis, Massachusetts Institute of Technology

  • Lee, T.H.; Arora, J.S. 1993: Shape design sensitivity analysis of viscoplastic structures.Comp. Meth. Appl. Mech. Eng. 108, 237–259

    Google Scholar 

  • Lee, K., Tortorelli, D.A. 1986: Computer-aided design of robotic manipulators.Computer Aided Design 18, 139–146

    Google Scholar 

  • Light, R.A.; Gossard, D. 1982: Modification of geometric models through variational geometry.Computer Aided Design 14, 209–214

    Google Scholar 

  • Light, R.A.; Gossard, D. 1983: Variational geometry: a new method for modifying part geometry for finite element analysis.Comp. & Struct. 17, 903–909

    Google Scholar 

  • Lin, V.C.; Gossard, D.C.; Light, R.A. 1981: Variational geometry in computer-aided design.Computer Grafics 15, 171–177

    Google Scholar 

  • Longo, A.; Unzueta, J.; Schaeidt, E.; Alvarez, A.; Anza, J.J. 1993: A general related variational approach to shape optimum design.Advances in Eng. Software 16, 135–142

    Google Scholar 

  • Lund, E. 1994:Finite element based design sensitivity analysis and optimization. Ph.D. Thesis, Aalborg University

  • Marsan, A.L. 1995:Construction of a surface model from 3d homogenization output. Master's Thesis, University of Michigan

  • Mortenson, M.E. 1985:Geometric modeling. New York: John Willey & Sons

    Google Scholar 

  • Olhoff, N.; Lund, E.; Rasmussen, J. 1992: Concurrent engineering design optimization in a CAD enviroment.Special Report 16, Institute of Mechanical Engineering, Aalborg University

  • Olhoff, N.; Rasmussen, J.; Lund, E. 1993: A method of “exact” numerical differentiation for error elimination in finite-element based semi-analytical shape sensitivity analyses.Mech. Struct. & Mach. 21, 1–66

    Google Scholar 

  • Parametric Technology Corporation 1995a:Pro/Engineer users guide. Waltham, MA

  • Parametric Technology Corporation 1995b:Pro/Develop users guide. Waltham, MA

  • Pedersen, P.; Hammer, V.B. 1994: On global design description for orientational strength optimization.Report 481, Institute of Mechanical Engineering, Aalborg University

  • Pilkey, W.D.; Schramm, U. 1993: The coupling geometric descriptions and finite elements using nurbs—a study in shape optimization.Finite Elements in Analysis and Design 15, 11–34

    Google Scholar 

  • Rajan, S.D. 1995: Sizing, shape, and topology design optimization of trusses using genetic algorithm,ASCE J. Struct. Eng. 121, 1480–1487

    Google Scholar 

  • Rogers, D.F.; Adams, J.A. 1976:Mathematical elements for computer graphics. New York: McGraw-Hill

    Google Scholar 

  • Shephard, M.S.; Georges, M.K. 1991: Automatic three-dimensional mesh generation by the finite octree technique.Int. J. Num. Meth. Eng. 32, 709–749

    Google Scholar 

  • Spivey, C.O.; Tortorelli, D.A. 1994: Tangent operators, sensitivity expressions, and optimal design of non-linear elastica in contact with applications to beams.Int. J. Num. Meth. Engrg. 37, 49–73

    Google Scholar 

  • Taylor, D.L. 1992:Computer-aided design. Massachusetts: Addison Wesley

    Google Scholar 

  • The MacNeal-Schwendler Corporation 1994:MSC/NASTRAN users guide. Los Angeles

  • Tortorelli, D.A. 1993: A geometric representation scheme suitable for shape optimization.Mech. Struct. & Mach. 21, 95–121

    Google Scholar 

  • Tortorelli, D.A.; Chen, S. 1996: Implementation of the semianalytical sensitivity method in commercial software for nonlinear problems. (Submitted)

  • Tortorelli, D.A.; Tomasko, J.A.; Morthland, T.E.; Dantzig, J.A. 1994. Optimal design of nonlinear parabolic systems — Part II: variable spatial domain with applications to casting optimization.Comp. Meth. Appl. Mech. Eng. 113, 157–172

    Google Scholar 

  • Tortorelli, D.A.; Wang, Z. 1993: A systematic approach to shape sensitivity analysis.Int. J. Solids Struct. 30, 1181–1212

    Google Scholar 

  • VMA Engineering 1991:Genesis user's manual. Goleta, CA

  • VMA Engineering 1993:Dot user's manual. Goleta, CA

  • Watt, A. 1993:3D computer graphics. Massachusetts: Addison-Wesley

    Google Scholar 

  • Wolfram, S. 1991:Mathematica: a system for doing mathematics by computer. Massachusetts: Addison-Wesley

    Google Scholar 

  • Yang, R.J.; Dewhirst, D.L.; Allison, J.E.; Lee, A. 1992: Shape optimization of connecting rod pin end using a generic model.Finite Elements in Analysis and Design 11, 257–264

    Google Scholar 

  • Zhang, W.; Beckers, P.; Fleury, C. 1995: A unified parametric design approach to structural shape optimization.Int. J. Num. Meth. Eng. 38, 2283–2292

    Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, 61801, Urbana, IL, USA

    S. Chen & D. A. Torterelli

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  1. S. Chen
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  2. D. A. Torterelli
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Also: Department of Theoretical and Applied Mechanics

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Chen, S., Torterelli, D.A. Three-dimensional shape optimization with variational geometry. Structural Optimization 13, 81–94 (1997). https://doi.org/10.1007/BF01199226

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