A continuous field adaptive mesh refinement algorithm for isogeometric topology optimization using PHT-Splines

Abstract

This study proposes a continuous density-field based isogeometric topology optimization (ITO) using Polynomial splines over Hierarchical T-meshes (PHT-Splines). Taking the benefit of isogeometric methods, the design density values for the mesh are defined using spline basis functions as a continuous density function (CDF) through the control points. The material density at the control points will then appear as a facade over the domain, which is further employed to generate a very smooth topology and also to propose a marking criterion for an adaptive mesh refinement (AMR) strategy during the optimization process. During this adaptive meshing, the isogeometric domain mesh is refined during each adaptive step, properly tracking the density variation over the elements and sharpening the boundaries of the optimized topologies. By utilizing the rationale of the Geometry Independent Field approximaTion (GIFT) framework, any complex multi-patch geometry constructed in an industry-standard CAD package using Non-Uniform Rational B-Splines (NURBS) may be imported and discretized using PHT-Splines, including higher dimensions. This helps to maintain the geometrical accuracy through an initial coarse mesh and computational accuracy of the optimization iterations through the local refinement feature of the PHT-Splines. An adaptive first-neighbourhood smoothening algorithm based on the Shepard function is also proposed to obtain manufacturable topologies and to circumvent post-processing stages. The proposed method was observed to provide remarkably smooth topologies with an initial coarse mesh, thereby obtaining a computationally efficient domain to be solved. Compared to existing element density based methods, the proposed method demonstrates a substantial minimization in Degree’s-of-Freedom (DoF) requirement to arrive at clear and realistic solutions. Also, when compared to globally refined solutions, a 50%–90% reduction in DoF is achieved using the adaptive refinement strategy.