Minimum Averaged Compliance Density Based Topology Optimization of Structures

Usually, an optimal topology is obtained by optimizing the material distribution within a prescribed domain; for example, a rectangular domain with a specified length and width for a plane problem. However, the dimensions (i.e. aspect ratio) of a rectangular design domain have significant influence on the resultant optimal topology. In this paper, a minimum Averaged Compliance Density (ACD) based method for topology optimization of structures is proposed. Unlike the conventional topology optimization method, the ACD is taken as the objective function, and the topology and domain dimensions of the structure are optimized simultaneously. As an example, the topology of a cantilever beam with large aspect ratio will be optimized, which is often difficult for traditional topology optimization algorithms. Through optimizing the topology and the dimensions of the design domain, a base structure is obtained, which is repeated to yield the whole, assembled beam. The influence of the relative values of shear force and moment is analyzed numerically. Results show that as the value of the bending moment increases relative to the shear force, the optimal topology changes from a truss‐like structure to a vertically stiffened box‐like structure.