Nonparametric gradient-less shape optimization for real-world applications

A nonparametric gradient-less shape optimization approach for finite element stress minimization problems is presented. The shape optimization algorithm is based on optimality criteria, which leads to a robust and fast convergence independent of the number of design variables. Sensitivity information of the objective function and constraints are not required, which results in superior performance and offers the possibility to solve the structural analysis task using fast and reliable industry standard finite element solvers such as ABAQUS, ANSYS, I-DEAS, MARC, NASTRAN or PERMAS. The approach has been successfully extended to complex nonlinear problems including material, boundary and geometric nonlinear behavior. The nonparametric geometry representation creates a complete design space for the optimization problem, which includes all possible solutions for the finite element discretization. The approach is available within the optimization system TOSCA and has been used successfully for real-world optimization problems in industry for several years. The approach is compared to other approaches and the benefits and restrictions are highlighted. Several academic and real-world examples are presented.

[1]  Erik Lund,et al.  A Method of “Exact” Numerical Differentiation for Error Elimination in Finite-Element-Based Semi-Analytical Shape Sensitivity Analyses* , 1993 .

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

[3]  Jürgen Sauter,et al.  A New Approach for Sizing, Shape and Topology Optimization , 1996 .

[4]  Franz-Joseph Barthold,et al.  A hierarchical design concept for shape optimization based on the interaction of CAGD and FEM , 1999 .

[5]  T. Szabó,et al.  Optimal shape design for contact problems , 1994 .

[6]  M. Z. Cohn,et al.  Theory and practice of structural optimization , 1994 .

[7]  Ingo Rechenberg,et al.  Evolution Strategy: Nature’s Way of Optimization , 1989 .

[8]  Eckart Schnack,et al.  A mechanical dynamic programming algorithm for structure optimization , 1986 .

[9]  S. Zhang,et al.  A systematic approach for generating velocity fields in shape optimization , 1992 .

[10]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[11]  K. Schittkowski,et al.  Numerical comparison of nonlinear programming algorithms for structural optimization , 1994 .

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

[13]  Claude Fleury,et al.  A unified parametric design approach to structural shape optimization , 1995 .

[14]  J. Haslinger,et al.  Numerical comparison between two cost functions in contact shape optimization , 1995 .

[15]  P. Pedersen.  On optimal shapes in materials and structures , 2000 .

[16]  N. V. Banichuk,et al.  Mesh refinement for shape optimization , 1995 .

[17]  Grant P. Steven,et al.  Structural application of a shape optimization method based on a genetic algorithm , 2001 .

[18]  Garret N. Vanderplaats,et al.  Numerical optimization techniques for engineering design , 1999 .

[19]  Eckart Schnack,et al.  An optimization procedure for stress concentrations by the finite element technique , 1979 .

[20]  E. Ramm,et al.  Adaptive FE-procedures in shape optimization , 2000 .

[21]  G. P. Cherepanov.  Inverse problems of the plane theory of elasticity: PMM vol. 38, n≗ 6, 1974, pp. 963–979 , 1974 .

[22]  Niels Olhoff,et al.  Rigid body motion test against error in semi-analytical sensitivity analysis , 1993 .

[23]  A. Belegundu,et al.  A shape optimization approach based on natural design variables and shape functions , 1988 .

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

[25]  C. Mattheck,et al.  A new method of structural shape optimization based on biological growth , 1990 .

[26]  Uri Kirsch,et al.  Structural Optimization: Fundamentals and Applications , 1993 .

[27]  Jahau Lewis Chen,et al.  Shape Optimization by Growth Using Simulated Biological Approaches , 1993 .

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

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

[30]  J. -F. M. Barthelemy,et al.  Approximation concepts for optimum structural design — a review , 1993 .

[31]  Ekkehard Ramm,et al.  Efficient modeling in shape optimal design , 1991 .

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