SIMP-Based Topology Optimization of Lightweight Cantilever Beam Structures under Nonlinear Dynamic Impact Loading

This paper decisively addresses the topology optimization of lightweight cantilever beam structures subjected to nonlinear dynamic impact loading. We implemented a simplified one-dimensional finite element model in MATLAB, integrating it with the Solid Isotropic Material with Penalization (SIMP) method to identify optimal material distributions under transient impulsive forces. Our objective was clear: minimize the tip displacement while strictly adhering to a 50% volume constraint. The governing dynamic equilibrium equations were effectively solved using an explicit central difference integration scheme, and we systematically updated the design variables through finite-difference sensitivities. The results demonstrate that the optimized topologies effectively concentrate material in high-stress regions, leading to a significant reduction in peak displacements compared to the baseline design. This finding emphasizes the capability of SIMP-based topology optimization to enhance structural stiffness and energy dissipation under impact conditions, even within a highly simplified one-dimensional framework. The study presents a computationally efficient approach that combines dynamic finite element analysis with topology optimization, offering valuable insights for the early-stage design of crashworthy lightweight components. Future work will extend the framework to two- and three-dimensional geometries, incorporate nonlinear and inelastic material behavior, and integrate contact and damage models for more realistic predictions. Additional enhancements will include adjoint-based sensitivity analysis to reduce computational cost and multi-objective optimization strategies that consider energy absorption, robustness, and reliability. These improvements aim to advance the proposed method into a powerful tool for designing crashworthy, lightweight structures in aerospace, automotive, and defense applications.