Anti-impact topology optimization for 2D and shell-based structures based on velocity field level set method with response spectrum analysis

Abstract

Anti-impact design is of significant importance in various areas, particularly in the naval equipment and architecture. Advanced structural optimization techniques can offer powerful and efficient tools to achieve innovative configurations with extraordinary performances. This paper proposes a velocity field level set topology optimization method for anti-impact structural design using the response spectrum analysis. A multi-objective optimization formulation combined with the structural compliance and the spectrum compliance is presented, which effectively balances load-bearing capacity and impact resistance enhancement. Here the response spectrum analysis is used to evaluate the anti-impact performances efficiently while avoiding the complexity and high cost of time-domain integration. In the sensitivity analysis, the optimization problem is reformulated into a self-adjoint form through modal superposition, which eliminates the need to solve additional adjoint equations and significantly reduces computational complexity. The optimization is performed in the velocity field level set framework, which allows using a general optimizer (such as the MMA algorithm) to handling constraints steadily and efficiently. Meanwhile, the clear and smooth boundary representation is combined with the body-fitted mesh technology, which enhances the accuracy of the mechanical response calculation and facilitate the manufacturability of the optimization results.