Sensitivity Analysis of Structural Dynamic Behavior Based on the Sparse Polynomial Chaos Expansion and Material Point Method

This paper presents a framework for constructing surrogate models for sensitivity analysis of structural dynamics behavior. Physical models involving deformation, such as collisions, vibrations, and penetration, are developed using the material point method. To reduce the computational cost of Monte Carlo simulations, response surface models are created as surrogate models for the material point system to approximate its dynamic behavior. An adaptive randomized greedy algorithm is employed to construct a sparse polynomial chaos expansion model with a fixed order, effectively balancing the accuracy and computational efficiency of the surrogate model. Based on the sparse polynomial chaos expansion, sensitivity analysis is conducted using the global finite difference and Sobol methods. Several examples of structural dynamics are provided to demonstrate the effectiveness of the proposed method in addressing structural dynamics problems.