An isogeometrical approach to structural level set topology optimization

Abstract

This paper aims to utilize the Isogeometric Analysis (IGA) for the level set structural topology optimization. The level set function is parametrized using the Non-Uniform Rational B-Spline (NURBS) basis functions in a higher dimension. The same basis functions are employed for approximating the unknown deformations, geometry modeling of the design domain and the level set function. In this research, three optimization problems including minimization of the mean compliance considering a certain amount of material, minimization of weight with avoiding local stress concentration as well as minimization of weight and strain energy under local stress constraints are dealt with. The sensitivity analyses for the optimization problems are carried out to obtain velocity functions on the boundaries. In order to move the boundaries towards optimum the Hamilton–Jacobi (H–J) equation is solved using the forward Euler scheme. In order to illustrate the performance of the method to obtain reasonable results with smooth boundaries, several numerical examples are presented and compared with well-known problems in literature.