Simultaneous shape and topology optimization method based on the H 1 gradient method for creating light weight plate and shell structures

Abstract

In this paper, we present a simultaneous optimization method of shape and topology for designing a lightweight plate and shell structure. The free-form optimization method for shells and SIMP method are respectively employed for shape and topology optimization, and combined effectively. Shape and fictitious homogenized-density variations are used as the design variables, and simultaneously determined in one iteration of the convergence process. With this method, the optimal topology is determined in the variable design surface optimized by shape optimization. Compliance is used as the objective functional, and minimized under the volume constraint. The optimal design problem is formulated as a distributed-parameter optimization problem, and the sensitivity functions with respect to shape and density variations are theoretically derived. Both the optimal shape and density variations are determined by the H 1 gradient method, where the sensitivity functions are applied as the Robin condition to the design surface. With the proposed method, the optimal lighter and stiffer shell structure with smooth surface can be obtained without any design parameterization and numerical instabilities such as checkerboard and zigzag-shape problems.