Topology Optimization for Complex 3D Structures and Loading Conditions

Abstract Existing topology optimization methods are predominantly developed based on structured meshes and static loading assumptions, which result in insufficient geometric adaptability for complex three-dimensional structures and difficulties in accurately capturing transient dynamic responses encountered in practical engineering applications. To address these limitations, this study proposes a topology optimization method for complex three-dimensional structures based on hybrid-mesh discretization and transient dynamic response analysis. For mesh discretization, a hybrid mesh generation strategy combining tetrahedral and hexahedral elements is developed, with pentahedral pyramid elements employed as transition elements to ensure conformal connectivity and geometric compatibility between different mesh types, thereby enhancing the adaptability of the proposed method to complex geometries. In addition, a volume-weighted density filtering scheme is introduced to account for differences in element size during the smoothing of design variables, effectively suppressing the nonphysical influence of small-volume elements in transition regions on the density field. For topology optimization problems under time-varying loads, a transient topology optimization model is established based on transient adjoint sensitivity analysis, so as to make the optimization results of structural responses closer to the requirements of actual engineering conditions. Finally, several representative numerical examples are presented to demonstrate the effectiveness, numerical stability, and general applicability of the proposed method. The proposed approach provides an effective framework for high-accuracy topology optimization for complex 3D structures subjected to time-varying loads, offering both strong geometric adaptability and accurate transient dynamic analysis.