M-VCUT level set method for the layout and shape optimization of stiffeners in plate

Abstract

Stiffened plates are widely used in engineering due to their relatively high rigidly-to-weight ratio. The stiffener layout and shape can significantly affect the mechanical properties of the plate. In this paper, a novel approach is developed in the framework of the Multiple Variable Cutting (M-VCUT) level set method for optimizing the layout and shape of stiffeners based on the Mindlin plate theory. In this approach, the layout and shape of stiffener can be controlled by adjusting the lower and upper limits of the design variables (cutting heights of the cutting surfaces at the cell nodes) conveniently. The coordinate mapping technique from the rectangular cell to the quadrilateral cell enables the shape of design domain to be arbitrary. In addition, multi-node cell with high-order polynomial interpolation technique is also applied for generating more complex geometry of stiffener. The numerical examples meshed by rectangular and quadrilateral cells are conducted for verifying the effectiveness of the proposed approach.