A review of structural shape optimization

Abstract Shape optimization attempts to integrate geometrical modeling, structural analysis, and optimization into one complete and automated computer-aided design process. It determines the shape of the boundary of a two- or three-dimensional structural component of minimum mass under constraints on geometry and structural responses such as stress, displacements and natural frequencies. This paper presents a general review of structural shape optimization, with emphasis on the recent developments in this field. First the general concepts are introduced. Different approaches of the process of shape optimization, which consists of geometrical representation, structural analysis, sensitivity analysis, and optimization algorithms, are reviewed. Then the difficulties in expanding from two-to three-dimensional shape optimization are discussed. Finally the paper concludes that more attention should be paid to research of zero-order optimization algorithms which are better suitable for shape optimization problems, and mechanical design optimization problems in general.

[1]  E. J. Haug,et al.  Numerical Considerations in Structural Component Shape Optimization , 1985 .

[2]  Shyue-Jian Wu,et al.  Shape optimization using the boundary element method with substructuring , 1988 .

[3]  Eisuke Kita,et al.  Boundary element method for quasi-harmonic differential equation with application to stress analysis and shape optimization of helical spring , 1990 .

[4]  V. Braibant,et al.  Shape optimal design using B-splines , 1984 .

[5]  A. J. Durelli,et al.  OPTIMUM HOLE SHAPES IN FINITE PLATES UNDER UNIAXIAL LOAD , 1979 .

[6]  Subrata Mukherjee,et al.  Shape design sensitivity analysis for geometrically and materially nonlinear problems by the boundary element method , 1992 .

[7]  Ren-Jye Yang,et al.  Component shape optimization using bem , 1990 .

[8]  C. Fleury,et al.  Shape optimal design using high-order elements , 1988 .

[9]  Tsu-Chien Cheu.  Procedures for shape optimization of gas turbine disks , 1990 .

[10]  R. Haftka,et al.  Elements of Structural Optimization , 1984 .

[11]  M. E. Botkin,et al.  Shape Optimization of Plate and Shell Structures , 1981 .

[12]  Ibrahim Zeid,et al.  CAD/CAM theory and practice , 1991 .

[13]  Kyung K. Choi,et al.  Accuracy of Finite Element Based Shape Design Sensitivity Analysis , 1985 .

[14]  A. D. Drozdov,et al.  Optimization problems in the mechanics of growing solids , 1988 .

[15]  Noboru Kikuchi,et al.  Adaptive finite element methods for shape optimization of linearly elastic structures , 1986 .

[16]  Garret N. Vanderplaats,et al.  CONMIN: A FORTRAN program for constrained function minimization: User's manual , 1973 .

[17]  Walter D. Pilkey,et al.  The coupling of geometric descriptions and finite elements using NURBs: a study in shape optimization , 1993 .

[18]  C. Mattheck,et al.  Three-dimensional shape optimization of a bar with a rectangular hole , 1992 .

[19]  Ren-Jye Yang,et al.  Three-Dimensional Shape Optimization with Substructuring , 1989 .

[20]  Srinivas Kodiyalam,et al.  Constructive solid geometry approach to three-dimensional structuralshape optimization , 1992 .

[21]  S. Kodiyalam,et al.  Shape optimization of three-dimensional continuum structures via force approximation techniques , 1989 .

[22]  Carlos Alberto Brebbia,et al.  The Boundary Element Method for Engineers , 1978 .

[23]  Yunliang Ding,et al.  Shape optimization of structures: a literature survey , 1986 .

[24]  Michael E. Mortenson,et al.  Geometric Modeling , 2008, Encyclopedia of GIS.

[25]  Yisheng Li,et al.  Shape Optimization of Arch Dams for Static and Dynamic Loads , 1992 .

[26]  Paull Pedersen,et al.  Design for Minimum Stress Concentration by Finite Elements and Linear Programming , 1982 .

[27]  M. E. Botkin,et al.  Three-dimensional shape optimization using fully automatic mesh generation , 1992 .

[28]  V. Braibant,et al.  An approximation-concepts approach to shape optimal design , 1985 .

[29]  Philip E. Gill,et al.  Practical optimization , 1981 .

[30]  M. L. Luchi,et al.  An interactive optimization procedure applied to the design of gas turbine discs , 1980 .

[31]  R. T. Fenner,et al.  Design optimization using the boundary element method , 1991 .

[32]  R. Haftka,et al.  Structural shape optimization — a survey , 1986 .

[33]  M. Kitano,et al.  An efficient shape optimization technique of a two-dimensional body based on the boundary element method , 1993 .

[34]  Andrzej Służalec,et al.  Shape optimization of weld surface , 1989 .

[35]  R. J. Yang,et al.  A three-dimensional shape optimization system—shop3D , 1989 .

[36]  S. S. Bhavikatti,et al.  Optimum shape design of rotating disks , 1980 .

[37]  M. Week,et al.  An Efficient Technique in Shape Optimization , 1983 .

[38]  Erik Steen Kristensen,et al.  On the optimum shape of fillets in plates subjected to multiple in‐plane loading cases , 1976 .

[39]  Ren-Jye Yang,et al.  Comparison Between the Variational and Implicit Differentiation Approaches to Shape Design Sensitivities , 1986 .

[40]  M. Imam.  Three‐dimensional shape optimization , 1982 .

[41]  Subramaniam Rajan,et al.  Shape optimal design using fictitious loads , 1989 .

[42]  Toshiyuki Imaizumi,et al.  Shape optimization of the wire cross section of helical springs , 1992 .

[43]  A. J. Durelli,et al.  Optimization of hole shapes in circular cylindrical shells under axial tension , 1981 .

[44]  H. L. Groth,et al.  Shape optimization of bonded joints , 1991 .

[45]  C. Fleury,et al.  Shape and mesh optimization using geometric modeling methods , 1990 .

[46]  Byung Man Kwak,et al.  Shape optimization of two-dimensional thermoelastic structures using boundary integral equation formulation , 1991 .

[47]  Martin P. Bendsøe,et al.  Integrated topology and boundary shape optimization of 2-D solids , 1991 .

[48]  M. E. Botkin,et al.  Structural shape optimization with geometric description and adaptive mesh refinement , 1985 .

[49]  C. Mattheck,et al.  DESIGN AND GROWTH RULES FOR BIOLOGICAL STRUCTURES AND THEIR APPLICATION TO ENGINEERING , 1990 .