A theoretical model of displacement response of clamped circular plate under multiple far-field blast loads

Regarding the displacement response of clamped circular plates under multiple far-field blast loads, we proposes a novel theoretical modeling approach based on membrane theory energy equations, by simplifying multiple blast loads into linearly decaying pulse sequences, a theoretical displacement response model for clamped circular plates is established for the first time, considering both strain rate strengthening effects and cumulative hardening effects. The linear displacement field approximation is adopted for the initial loading phase, while a quadratic function displacement field assumption is introduced for subsequent loading phases, deriving recursive formulas for midpoint displacements under multiple blasts. Numerical validations were conducted using LS-DYNA for both double and triple blast scenarios. For double blast cases, theoretical predictions exhibited errors of 20%–30% compared to simulation results, while errors reduced to below 20% for triple blast conditions. The ASTM A415 steel circular plate model was used for the simulations, and the strain rate strengthening effect was described by the Cowper-Symonds model. Finite element models with quadrilateral shell elements demonstrated strong agreement with experimental data (errors<10%), confirming model reliability. The assumption of quadratic function displacement field for subsequent loading phases was verified by numerical displacement curves of the middle profiles of the plates. Further parametric analysis proved that the theoretical model is effective for different tangent modulus, which represents the strength of the strain strengthening effect. The model reveals that midpoint displacement can be characterized as a weighted square root function combining the final explosion’s individual displacement and prior cumulative displacement, with displacement increments from subsequent explosions decreasing as prior cumulative displacement increases.