Synthesis of Optimal Shape and Topology of Structures

Abstract

In this paper, a method is proposed for the design optimization of structural components where both shape and topology are optimized. The boundaries of the shape of the structure are represented using contours of a “shape density” function. The contour of the density function corresponding to a threshold value is defined as the boundary of the shape. The shape density function is defined over a feasible domain and is represented by a continuous piece-wise interpolation over the finite elements used for structural analysis. The values of the density function at the nodes serve as the design variables of the optimization problem. The advantage of this shape representation is that both shape and topology of the structure can be modified and optimized by the optimization algorithm. Unlike previous methods for shape and topology optimization, the material is not modeled as porous or composite using the homogenization method. Instead the material properties of the structure are assumed to depend on the density function and many approximate material property-density relations have been studied. The shape and topology of structural components are optimized with the objective of minimizing the compliance subject to a constraint on the total mass of the structure.