Adaptive isogeometric topology optimization of shell structures based on truncated hierarchical B-splines

Abstract

We present a truncated hierarchical B-splines-oriented adaptive isogeometric topology optimization (THB-AITO) framework for shell structures. The method integrates the isogeometric analysis (IGA) approach using Kirchhoff–Love theory with THB-splines to achieve adaptive topology optimization for shell structures. IGA ensures the accuracy of displacement fields and sensitivity values during numerical analysis. Compared with non-uniform rational B-spline (NURBS) with the tensor product structure, the basis functions of THB-splines are more suitable for performing the local adaptive refinement on shell structure meshes. Specifically, intermediate density meshes near the topological boundary are refined to achieve a highly accurate topology configuration with few degrees of freedom (DOFs), facilitated by a fully adaptive marking strategy. Numerical results indicate that, compared with NURBS-based isogeometric topology optimization, THB-AITO can solve the compliance minimization shell problem with fewer DOFs and design variables. In addition, comparisons with other refined splines were conducted to demonstrate the advantages of our proposed THB-AITO approach. The THB-AITO is a promising way of optimizing thin-shell structures.

Graphical abstract

Keywords

topology optimization / isogeometric analysis / Kirchhoff–Love shell / truncated hierarchical B-splines

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