Topological optimization of the stiffness of an irregular structure based on an element size independent filter

Abstract

Because of the overly averaged element sensitivity in the topological optimization of an irregular structure with a grid independent filter, a topological optimization model was built for the structural domain. The maximization of stiffness was first taken as the goal for the topological optimization of irregular structure stiffness. Subsequently, an element size filter was proposed to address the overly averaged local element sensitivity with the grid independent filter when the designed domain element size varied dramatically. Finally, the element sensitivity of the objective function was derived under the given constraints. A case study was then conducted on a naval gun mount with the maximization of structural flexibility as the objective function and the volume of structural material as a constraint. A stiffness optimization model based on the bi-directional evolutionary structural optimization algorithm was adopted for the topological optimization of the gun mount. Structural optimization was conducted for the gun mount with different shooting angles to realize its optimal stiffness and strength under the constraint of consistent material volume. The optimization results proved that the element independent filter proposed in this paper could be effectively applied in the topological optimization of an irregular structure and used to explore the topological optimization of the supporting structure under impact.