Optimization of 2D boundary element models using β-splines and genetic algorithms

The optimization of bidimensional shapes is one of the most commonly addressed problems in engineering. This work is concerned with the use of Genetic Algorithms (GAs) and β-spline-curves modeling for the optimization of Boundary Element Models (BEM). The paper briefly summarizes the basis of the GAs formulation and describes how to use refined genetic operators. The model boundary is discretized by using the BEM, and selected parts of the boundary are modeled by using β-spline curves, in order to allow easy remeshing and adaptation of the boundary to the external actions. Two numerical examples are presented and discussed in detail, showing that the proposed combined technique is able to optimize the shape of the domains with minimum computational effort. The reduction in the model area is significant, without violating the restrictions imposed to the model.

[1]  Lawrence. Davis,et al.  Handbook Of Genetic Algorithms , 1990 .

[2]  Sunil Saigal,et al.  Design-sensitivity analysis of solids using BEM , 1988 .

[3]  M. H. Aliabadi,et al.  Flaw identification using the boundary element method , 1995 .

[4]  B. Kwak,et al.  A unified approach for adjoint and direct method in shape design sensitivity analysis using boundary integral formulation , 1990 .

[5]  Miguel Cerrolaza,et al.  A STRUCTURAL OPTIMIZATION APPROACH AND SOFTWARE BASED ON GENETIC ALGORITHMS AND FINITE ELEMENTS , 1999 .

[6]  R. T. Fenner,et al.  Shape optimisation by the boundary element method: a comparison between mathematical programming and normal movement approaches , 1997 .

[7]  Niels Olhoff,et al.  On CAD-integrated structural topology and design optimization , 1991 .

[8]  Leonard Spunt,et al.  Optimum structural design , 1971 .

[9]  M. Galante,et al.  GENETIC ALGORITHMS AS AN APPROACH TO OPTIMIZE REAL‐WORLD TRUSSES , 1996 .

[10]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[11]  R. Alsan Meric,et al.  Differential and integral sensitivity formulations and shape optimization by BEM , 1995 .

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

[13]  A. Cheng,et al.  A Laplace transform BEM for axisymmetric diffusion utilizing pre-tabulated Green's function , 1992 .

[14]  Miguel Cerrolaza,et al.  Optimization of finite element bidimensional models: an approach based on genetic algorithms , 1998 .

[15]  C. V. Ramakrishnan,et al.  Structural Shape Optimization Using Penalty Functions , 1974 .

[16]  Ren-Jye Yang,et al.  Boundary Integral Equations for Recovery of Design Sensitivities in Shape Optimization , 1988 .

[17]  Kyung K. Choi,et al.  3‐D shape optimal design and automatic finite element regridding , 1989 .

[18]  Anne Brindle,et al.  Genetic algorithms for function optimization , 1980 .

[19]  Edward J. Haug,et al.  Design Sensitivity Analysis of Structural Systems , 1986 .

[20]  Eisuke Kita,et al.  Shape optimization of continuum structures by genetic algorithm and boundary element method , 1997 .

[21]  Miguel Cerrolaza,et al.  Finite elements, genetic algorithms and b-splines: a combined technique for shape optimization , 1999 .

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