Multiscale isogeometric topology optimization for lattice materials

This paper presents isogeometric topology optimization (ITO) for periodic lattice materials, where non-uniform rational B-spline (NURBS) basis functions of CAD models are directly used in the finite element analysis to improve computational accuracy and efficiency. Two TO schemes that use asymptotic homogenization (AH) for the calculation of the mechanical properties are proposed for lattice materials with uniform and graded relative density respectively. To accelerate ITO for graded lattice materials, the mechanical properties are expressed as a function of the relative density of the unit cell, a step that avoids their iterative calculations during ITO. Three benchmark examples are presented to validate the proposed scheme with results that show tangible advantages, such as reduced computational time and faster convergence, of ITO over conventional TO.

GPU parallel strategy for parameterized LSM-based topology optimization using isogeometric analysis

This paper proposes a new level set-based topology optimization (TO) method using a parallel strategy of Graphics Processing Units (GPUs) and the isogeometric analysis (IGA). The strategy consists of parallel implementations for initial design domain, IGA, sensitivity analysis and design variable update, and the key issues in the parallel implementation, e.g., the parallel assembly race condition, are discussed in detail. The computational complexity and parallelization of the different steps in the TO are also analyzed in this paper. To better demonstrate the advantages of the proposed strategy, we compare efficiency of serial CPU, multi-thread parallel CPU and GPU by benchmark examples, and the speedups achieve two orders of magnitude.