Topology Optimization Using Parabolic Aggregation Function with Independent-Continuous-Mapping Method

This paper concentrates on finding the optimal distribution for continuum structure such that the structural weight with stress constraints is minimized where the physical design domain is discretized by finite elements. A novel Independent-Continuous-Mapping (ICM) method is proposed to convert equivalently the binary design variables which is used to indicate material or void in the various elements to independent continuous design variables. Moreover, three smooth mappings about weight, stiffness, and stress of the structural elements are introduced to formulate the objective function based on the so-called concepts of polish function and weighting filter function. A new general continuous approach for topology optimization is given which can eliminate the stress singularity phenomena more efficiently than the traditional -relaxation method, and an alternative strain energy method for the stress constraints is proposed to overcome the difficulty in stress sensitivity analyses. Mathematically, by means of a generalized aggregation KS-like function defined as the parabolic aggregation function, a topology optimization model is formulated with the weight objective and single parabolic global strain energy constraints. The numerical examples demonstrate that the proposed methods effectively remove the stress concentrations and generate black-and-white designs for practically sized problems.