Topology optimization design of frame structures based on the Direct FE2 method

In the existing design methodology studies, the topology optimization of the engineering structures suffers from the heavy computational burden during the solution process. To handle this issue, a novel topology optimization method is proposed by using Direct FE² with shear-flexible beam elements. In this proposed method, the solid isotropic material with penalization (SIMP) topology optimization method is incorporated with the Direct FE² method for beam elements, allowing topology optimization to be performed based on the Direct FE² homogenization framework instead of establishing complex mapping relationships between macro and micro structures. This unique characteristic enables the microscopic RVE morphology to be optimized according to the macroscopic beam deformation. Consequently, the enhanced multiscale connection improves computational efficiency over direct numerical simulation (DNS). The effectiveness and applicability of this proposed Direct FE² topology optimization method is well validated by several numerical examples, the optimization results of the microscopic RVE exhibits rational morphology and geometric configuration that can provide a superior mechanical performance on the macroscopic structure. The proposed topology optimization method provides an efficient and effective way to conduct the design and improvement for slender structures.