Topology optimization for the elastic field using the lattice Boltzmann method

The lattice Boltzmann method (LBM) has often been employed for numerical analysis of fluid dynamics problems and is described as an algorithm based on a simple fully explicit method. When LBM can be applied to structural mechanics problems, there is a possibility that topology optimization can be performed efficiently for non-linear elastic fields and the topology optimization of fluid-structure interaction problems can be performed easily with the single calculation method. We propose a topology optimization method for isotropic linear elastic body problems using LBM in this paper, as a first step to realize this. First, the analysis approach of the isotropic linear elastic field using LBM is constructed with incorporating the expansion technique of the governing equations for applying to a topology optimization framework. Next, based on the density approach, the optimization problem is formulated, and by using the adjoint lattice Boltzmann method (ALBM), the design sensitivity is derived. Finally, the validity of the proposed method is demonstrated with several numerical examples.