Isogeometric Level Set-Based Topology Optimization for Geometrically Nonlinear Plane Stress Problems

Abstract

This paper addresses geometrically nonlinear topology optimization using IsoGeometric Analysis (IGA) and Level Set Method (LSM) under plane stress assumptions. The IGA is employed to solve governing equations and accurately describe geometric modeling. The pointwise gradient-based sensitivity analysis is applied to derive the normal velocity of the Reaction–Diffusion Equation (RDE) to update the control net of the Level Set Function (LSF). The Generalized Displacement Control Method (GDCM) is used to obtain the equilibrium path based on the Total Lagrange (TL) formulation. A pointwise energy interpolation strategy is employed to avoid low-density instabilities. The exact Heaviside function is also applied to obtain a 0/1 manufacturable design. The objective is to maximize the total strain energy of structure, which is defined as the total external work within a specified displacement, while a certain volume of the design domain is considered. To demonstrate the ability and efficiency of the proposed method, several numerical examples are presented. By making comparisons, the results of both optimization algorithm and nonlinear analysis are shown to be in good agreement with the literature. Also, it is shown that obtained layouts are different from those in the linear behavior modeling due to considering buckling effects. In addition, linear and nonlinear final layouts are analyzed under large deformation assumption and the load–displacement curves are compared to illustrate the improvement of the objective function and final load. • Optimized topologies are parameterized using NURBS. • A pointwise energy interpolation strategy is employed to avoid low-density instabilities. • The control net of the design domain is updated by the reaction–diffusion equation. • Pointwise sensitivity analysis of the optimization problem is analytically derived. • 0/1 manufacturable design was performed using an exact (binary) Heaviside step function.