Theoretical model of displacement response of circular plate under multiple explosive loads

The response of plate structures under multiple explosive loads has important engineering significance. Currently, there are many experimental and numerical studies on this issue, but research based on theoretical methods is still lacking. This article focuses on the theoretical model of displacement response of a circular plate under multiple explosive loads. The energy equation based on membrane theory is used to describe the motion of the circular plate. Multiple explosive loads are simplified into multiple linear decay pulses. The displacement field caused by the first loading is approximated by a linear function, and the displacement field after the second loading is approximated by a quadratic function. The effects of strain rate strengthening and multiple loading hardening on material flow stress are considered, and the theoretical solution of displacement response of the circular plate under multiple explosive loads is given. Simulations of dynamic response of the circular plate under two and three explosive loads are conducted by LS-Dyna. It is found that the error between the theoretical and numerical values of the midpoint displacement of the circular plate is mainly of the rage 20% -30% for the two explosive load conditions, and below 20% for the three explosive load conditions. Theoretical formulas indicate that the midpoint displacement of a circular plate under multiple explosive loads can be expressed as a function of the displacement caused solely by the last loading and the cumulative displacement of previous loads, which is the square root of the weighted sum of squares of the two, and the weighting coefficient depends on the form of the assumed displacement field. The displacement increment caused by the subsequent loading is smaller than the displacement caused by it alone, and the magnitude of this increment is related to the cumulative displacement of the previous loadings. The larger the cumulative displacement of the previous loadings, the smaller the displacement increment caused by the subsequent loading.