Application of Isogeometric Analysis and Charged System Search Algorithm in Structural Shape Optimization

In this article, the Charged System Search (CSS) algorithm is utilized for structural shape optimization that aims to minimize weight of a plane structure under stress constraints. Also, the Isogeometric Analysis (IA) is employed in order to analyze the structure. In the IA method, Non Uniform Rational B-Spline (NURBS) basis functions are used for approximation and interpolation of the displacement field as well as modelling geometry of the structure. Coordinates of the NURBS control points, that construct the geometry, can be considered as the design variables of the shape optimization problem. In earlier studies in structural shape optimization using the Finite Element (FE) method, boundaries of the structure were made by NURBS and the finite element discretization changed when the boundaries were modified in every iteration of the optimization process. As it mentioned, when the IA method is used the geometry is constructed by NURBS, therefore, contrary to using the FE method, the need for remeshing of the domain is eliminated and the computational cost will be remarkably decreased. In this paper, the IA method is briefly reviewed for analysis of the plane-stress elasticity problems. Also, the CSS formulation is derived based on physics laws for shape optimization problems. A few examples are presented to demonstrate the performance of the method and the results are compared when the Sequential Quadratic Programming (SQP) is used as a mathematical based method for structural shape optimization.