Free isotropic material optimization via second order cone programming

Abstract

Designing an engineered structure of optimal performance is the ultimate goal of engineering design, and various structural optimization approaches have been proposed. However, previous studies on the topic mainly rely on the single design variable of Young’s modulus or density without considering its Poisson’s ratio as another key isotropic material parameter, and thus may limit the best design ultimately reached. In the study, the problem of free isotropic material optimization (FIMO) is studied that takes as design variables both Young’s modulus and Poisson’s ratio at each point of the design domain without constraints on its manufacturability; certain necessary conditions on the material attainability are the only imposed requirements. Global optimum to the FIMO is achieved via rigorously reformulating it as a second order cone programming, to which a global optimum is theoretically verified and numerically trackable; the novel formulation also avoids the challenging singularity issue on void elements. The material dimension of the resulted design can also be reduced to any prescribed number of high fidelity via a hierarchical material clustering algorithm. The generated structure can be taken as benchmark solutions with which other optimized designs can be compared, and to propose novel new product design. Performance of the approach is tested on various 2D examples, in comparison with structures generated via classical topology optimization.