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.

During the underwater launch of multiple projectiles, each projectile operates within a highly complex and dynamic flow field, where its trajectory deflection is influenced by a combination of factors. These factors include initial conditions such as the projectile’s velocity and the presence of crossflow, as well as the mutual interference effects among the projectiles. To gain a deeper understanding of the cavitation evolution and trajectory interference characteristics during the underwater launch of multiple projectiles, this study develops a comprehensive numerical simulation model. The model integrates the overlapping grid technique and the finite volume method and is coupled with a six-degree-of-freedom (6-DOF) motion model. Through this model, the influence mechanisms of spatial arrangement, launch velocity, and crossflow on trajectory deflection are systematically analyzed. The results of this study reveal several important findings. First, the spatial arrangement of the projectiles has a relatively minor impact on trajectory deflection. An equilateral triangular configuration is found to be an optimal choice for practical applications, as it maximizes the efficient utilization of the launch space. Second, as the launch velocity increases, the wake interference between projectiles becomes more pronounced. This intensified interference leads to significant disturbances in the flow field and stronger mutual trajectory interference among the projectiles. Third, higher crossflow velocities exacerbate the asymmetric development of cavitation near the projectile shoulders. When the crossflow velocity exceeds 0.75 m/s, it becomes the dominant factor influencing trajectory deflection. These research findings provide a robust theoretical foundation for trajectory prediction and layout optimization in the underwater launch of multiple projectiles.