Simultaneous optimization of shape and topology for stiffener creation

Abstract

In this paper, we propose a method for designing stiffeners on thin plate structures by shape and topology optimization. The compliance is minimized under the constraints of volume and equilibrium equations. The optimal stiffeners’ shape and placement are simultaneously determined. Shape optimization and topology optimization are formulated as distributed-parameter optimization problem, in which the shape gradient function and density gradient function are derived by using the adjoint equations and the equilibrium equation. The shape optimization is performed by applying the shape gradient function to the H1 gradient method for vector variable, and the topology optimization is performed by applying the density gradient function to the H1 gradient method for scalar deign variable using the SIMP method. Several numerical examples are presented to confirm the effectiveness of the proposed method for the design of stiffeners.