Buckling reliability evaluation of a clamped beam with random imperfections subjected to axial impact using probability density evolution method

Based on the generalized probability density evolution theory, the joint probability density function of impact responses and random factors, that is, random initial imperfection and load intensity for a clamped beam, is derived. And a Total Variation Diminishing (TVD)-based numerical scheme is employed to obtain the numerical solutions. With given threshold values, the dynamic reliability is assessed in terms of a bilateral displacement criterion. Two numerical examples are then presented to demonstrate the proposed method. One is a clamped beam with random initial perfections subjected to a deterministic impulse load, and another is a clamped beam with a deterministic initial imperfection subjected to impact loading with a random amplitude. The predicted dynamic reliability is in good agreement with the result by Monte Carlo method.