Topology optimization using immersed isogeometric analysis and its software implementation

Abstract

This work integrates the immersed isogeometric analysis (IGA) with topology optimization (IITO), which paves the way of seamless integration between CAD and CAE as well as topology optimization for complex engineering structures. A truncated hierarchical B-spline (THB) based local adaptivity strategy is proposed to improve the integral accuracy of trimmed elements for immersed IGA, and an adaptive IITO framework is established in terms of the explicit elemental stiffness representation using multi-level Bézier extraction operator and tensor product decomposed implicit filter, as well as the suitably graded THB constraint. Numerical examples indicates that the proposed adaptive IITO method is superior to both traditional IITOs with adaptive Gaussian quadrature rule and successive global refinement, and achieves a sound balance between optimization accuracy and computation efficiency, irrespectively of the physical dimension and boundary conditions as well as geometry shape of design domain. Moreover, an object-oriented IITO engineering software is developed by C++ language and can be applied in engineering topology optimization design problems effectively, which show the superiorities of our IITO system. Therefore, the proposed IITO framework is a very promising way of implementing the seamless integration between CAD and CAE as well as topology optimization for complex engineering problems.