Level Set Topology Optimization for Design Dependent Hydrostatic Loading Using the Reproducing Kernel Particle Method

Abstract

Level set topology optimization for the design of structures subjected to design dependent hydrostatic loads is considered in this paper. Problems involving design-dependent loads remain a challenge in the field of topology optimization. In this class of problems, the applied loads depend on the structure itself. The direction, location and magnitude of the loads may change as the shape of the structure changes throughout optimization. The main challenge lies in determining the surface on which the load will act. In this work, the reproducing kernel particle method (RKPM) is used in combination with the level set method to handle the dependence of loading by moving the particles on the structural boundary throughout the optimization process. This allows for the hydrostatic pressure loads to be applied directly on the evolving boundary. One-way fluid-structure coupling is considered here. A hydrostatic pressure field governed by Laplace’s equation is employed to compute the pressure acting on linear elastic structures. The objective in this optimization problem is to minimize compliance of these structures. Numerical results show good agreement with those in the literature.