Static and dynamic multi-objective topological optimization of continuum structure

A multi-objective programming scheme for continuum topology optimization is proposed, in which both compliance, displacement of nodes and eigenfrequency are regarded as static and dynamic optimization objectives, respectively. Node-based independent variables which ensure continuity in design domain are taken as design variables. The method is immune to checkerboard instabilities that are a concern with element-based design variables. Modeling of stiffness matrix, mass matrix and volume of element are more flexible due to independence of the design variables. To improve the smoothness of the objective function and avoid the singularity of numerical computation, the weighted objection function is normalized. Image-filtering method is adopted to overcome checkerboard and mesh-dependence instabilities. Several numerical applications are used to prove the validity of the model and method proposed in this paper.