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

This paper investigates the topology optimization of lightweight cantilever beam structures subjected to nonlinear dynamic impact loading. A simplified one-dimensional finite element model (FEM) was developed in MATLAB and coupled with the Solid Isotropic Material with Penalization (SIMP) method to determine the optimal material distribution under transient impulsive forces. The objective of the optimization was to minimize the tip displacement of the beam while satisfying a prescribed volume constraint. Through an explicit time integration scheme, the dynamic response of the structure was evaluated iteratively. A cantilever beam was analyzed using numerical modeling and optimization to minimize tip displacement under a nonlinear dynamic impact load, while maintaining a 50% volume limit. The study utilized MATLAB with a one-dimensional finite element model and the SIMP method. The beam, fixed at one end and subjected to a short-term impact load at the free end, was divided into 15 elements. The governing dynamic equilibrium equation is solved using explicit time integration, and the squared tip displacement is minimized using a penalty factor (P) = 3. Design variables were iteratively adjusted based on finite-difference sensitivities to enhance performance during impact. The beam, modeled as a 1.0 m long rectangular cross-section bar, assumed linear stiffness with Young's modulus (E) = 210 GPa and density (ρ) = 7800 kg / m³. The results demonstrate that the optimized topologies concentrate material near high-stress regions, significantly reducing peak displacements after impact. Although this framework provides an efficient proof of concept, future enhancements are needed to capture more realistic behavior, including geometric nonlinearities, contact, and inelastic material responses. This work lays the groundwork for designing crashworthy, lightweight structures in automotive, aerospace, and defense applications.