To explore the cushioning properties of expanded polystyrene (EPS), a novel two‐degree‐of‐freedom mathematical model is proposed with a dynamic nonlinear system and successfully implemented it. The maximum response acceleration of the product was first determined in the novel dynamic mathematical model and used as a parameter for evaluating product damage. Furthermore, a drop test was carried out to verify the theoretical model and showed good consistency. Based on the correct theoretical model, a number of simulations with different drop heights and thicknesses of the cushion were done to investigate cushioning properties of EPS. The results show that EPS can reduce the maximum response acceleration of the product by more than 20% of the excitation acceleration. Thus, EPS has good cushioning ability and can be used as packaging material to protect products. Finally, the theoretical model was applied to an example application. A new method for constructing the cushioning curve is recommended, which could replace the traditional ASTM D 1596 drop test method.

This paper is aimed at proposing a new approach to Reliability-based Design Optimization (RBDO) and applying it to cushioning packaging design with a highly nonlinear system. The problem is formulated as an RBDO problem, which is included a minimizing cost function and probabilistic constraints. Here, the thickness of the cushion material is dealt with uncertainty and uncontrolled parameters. The traditional reliability index approach (RIA) has evolved as a powerful tool to solve the RBDO problem; however, due to its convergence problem, the modified reliability index approach (MRIA) is proposed. Although the MRIA method solves the problems of the traditional RIA, it inherits the low efficiency of searching for the most probability point (MPP). Thus, we developed a novel RIA based on MRIA to improve the efficiency and robustness during the RBDO process. The innovation active set strategy is developed in reliability assessment, which is a strict inequality to determine whether the current constraint is active or inactive. An application example is presented, and the results are compared with MRIA to assess cost-effectiveness and efficiency. Results indicate the proposed method is feasible to solve the uncertainty problem of packaging materials in the processing process and is also an efficient RBDO method.