Meshless approximation combined with implicit topology description for optimization of continua

The implicit topology description function method is integrated into Reproducing Kernel Particle Method and presents a new implementation of topology optimization of continua. The structural response analysis and the sensitivity analysis are carried out by using the meshless reproducing kernel approximations. Compared with mesh-based methods, the construction of an explicit mesh and the definition of nodal connectivity are avoided. The differences between the finite element method and the meshless method for topology optimization problems are highlighted. Formulations for imposition of concentrated forces and analysis of sensitivity in meshless method are derived in details. Several two-dimensional linear elastic topology optimization problems are solved successfully by the proposed method. The method is found robust and no checkerboarding is found in our numerical examples. Without any worry of mesh-entanglement, the method is expected to be further developed for the topology optimization of nonlinear structures with large deformations.