Level set-based topology optimization of thin plate structure for maximizing stiffness under out-of-plane deformation

Abstract

The topology optimization method using the level set method and incorporating a fictitious interface energy derived from the phase field method was proposed by part of the authors. The method has been applied to several structural and multidisciplinary design problems. However, the method has not been applied to the plate bending structural design problem using the two-dimensional plate bending element model yet, regardless that the thin plate structures are widely used in engineering applications that require lightweightness. This paper extends the topology optimization method to the thin plate structure for maximizing stiffness under out-of-plane deformation by using the thin plate bending elements based on Reissner-Mindlin theory. The structural design problem using the thin plate bending elements is formulated as the mean compliance minimization under volume constraint problem. Through simple numerical examples, effects of the proposed method are illustrated. At first, the method significantly reduces computational cost for the thin plate maximizing stiffness design problem in comparison with the three-dimensional solid model. The obtained optimum configuration is shown to be equivalent to that of the three-dimensional solid model. Then, it is shown that the advantages of the method such as high convergence property, low initial design dependency, and the effect of the regularization parameters on the complexity of the configuration are also held in the plate bending element model.