Topology Optimization of Freeform Shells by Employing Isogeometric Analysis

Abstract

Topology optimization has attracted significant attention for creating efficient structures in shells. One of the prominent methods in the field is the Solid Isotropic Materials with Penalization (SIMP) approach which is typically employed alongside finite element method (FEM). However in classical FEM, achieving a smooth shell surface, necessitates a considerable number of elements, leading to high computational cost. In this article an Isogeometric Analysis (IGA) based technique is utilized to determine the optimum topology of freeform shell structures. The proposed approach follows the methodology of SIMP by defining a density function over a design domain to parametrize the optimization problem so that zero value represents void areas and one denotes solid parts. Non-Uniform Rational B-splines (NURBS) are employed for structural analysis as well as for interpolating density function for topology optimization (TO). Two models are employed: one with coarse mesh for defining the geometry and another with a fine mesh for analysis and optimization. The Method of Moving Asymptotes (MMA) is employed to solve the optimization problem. A few examples are presented, and the results are discussed and compared with literature in one case to verify the proposed method. It is demonstrated that the proposed approach is efficient in finding the optimum topology of shell structures. The findings show that finer control nets results in clearer boundaries. It was observed that the penalty exponent is essential for obtaining an acceptable solution. It was also noted that the influence of the NURBS degree on optimal topology is trivial.