Abstract: As a conceptual design of product structure, continuum structural topology optimization can provide presumption for innovation of product. The nodal relative density is chosen as the design variable, and a novel model of continuum structural topology optimization based on element-free Galerkin method under multiple loading conditions is presented, in which the model proposed takes the weighted mean of structure compliance under every loading condition as the objective function. The essential boundary conditions are imposed by Lagrange multipliers. Its sensitivity algorithm is deduced. Integrating with SIMP interpolation model, the two examples of topology optimization under multi-load cases are solved successfully by programming. The optimal results of multi-load cases and single loading condition are investigated. The results obtained show that a multi-case result is not assembled simply by optimal ones under single loading. The uppermost advantage of using nodal density is that the displacement and density in influence domain have the same approximation scheme, and the continuity of density fields is improved. The checkerboard phenomenon occurred frequently in topology optimization can be effectively eliminated in the optimal model proposed. The results of example also validate the effectiveness of the model.

Key words: Element-free Galerkin method, Multi-load cases, Sensitivity analysis, Topology optimization