Topology optimization of orthotropic multi-material structures with length-scale control based on element-free Galerkin method

The topology optimization framework based on element-free Galerkin (EFG) method for orthotropic multi-material structures with length-scale control (LSC) strategy is proposed, including maximum and minimum LSC of solid and void phase. The alternating active-phase algorithm is integrated with the meshless multi-material interpolation model, and the gradient algorithm is used to update the relative density of the meshless nodes. This method is easy to implement and can realize the LSC of single or multiple phase orthotropic materials accurately in the EFG optimal topological structure. The effects of orthotropic off-angles, LSC strategies, filtering radius, and control domain radius on EFG topological structures and minimum compliance are investigated through numerical examples. The results show that the length scale of the EFG optimal topological structure can meet the requirement of the additive manufacturing, and there will be desirable dimensional gaps between the members using the LSC strategy. The appropriate combination of orthotropic multi-material off-angles can reduce the compliance and improve mechanical performance greatly. The sizes and gaps of topological members become more uniform, and the minimum length scale and compliance of the optimal topological structure will increase with the filtering radius which should be smaller than the control domain radius of the maximum LSC.