Shape Optimization of 2D Structures using Parametric Integral Equations System and Genetic Algorithms

E. Zieniuk, K. Szerszeń, and A. Bołtuć (Poland)


Shape optimization, genetic algorithms, linear elasticity, parametric integral equation system (PIES), Bezier curves


This paper proposes the use of parametric integral equation system (PIES) in procedure of 2D shape optimization for problems governed by the Navier-Lame equation. The declaration of boundary geometry in PIES on the basis of parametric curves allows for easy modification of initial geometry with help of a limited number of control points. In order to use genetic algorithms (GA) to shape optimization, control points of parametric curves which describe geometry are chosen as design variables. Therefore, we can greatly reduce the number of optimized unknowns to minimum with significant possibilities of geometry modification. The effectiveness of the proposed approach is illustrated by two test problems.

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