Topology optimization of multimaterial distribution based on isogeometric boundary element and piecewise constant level set method

Based on isogeometric boundary element method (IGA BEM) and piecewise constant level set (PCLS) method, a new topology optimization approach is proposed to design the distribution of sound absorbing materials (SAMs) on structural surfaces. First, an efficient IGA BEM is developed with the combination of multipatch discretization and parallel CPU design. A complex submarine model comprising multiple non-uniform rational B-spline surfaces is built for engineering optimization design. Second, the PCLS method is applied to represent the multiple SAM domains without gray elements, and the sensitivities of the objective function with respect to PCLS functions are obtained using the adjoint variable method. Finally, the optimization algorithm based on PCLS method is improved by a novel penalty coefficient formulation and ordered volume constraints. The improved optimization algorithm can realize the control of multimaterial volume fractions and make the objective function steadily converge for different volume structures without the need to change any parameters. The accuracy, efficiency, and applicability of the proposed approach in engineering are demonstrated by several numerical examples.