Effect of Coupled Bending and Membrane Strains on the Large Plastic Deformations of Rectangular Plates due to Impact Loading

In this paper, the effect of coupled bending and membrane strains on the large plastic deformation of rectangular plates due to impact loading is investigated both analytically and experimentally. The energy approach based on upper bound solution has been used in order to predict the maximum permanent deflection of rectangular plates. By assuming a deformation shape function, two consecutive energy based analyses have been presented. In the first step, it has been shown that the longitudinal and transverse displacements do not affect the amount of plastic work as well as maximum permanent deflection. Hence, the analytical expressions are derived by excluding the longitudinal and transverse displacements from the analysis. Next, in the first analysis, the analytical models have been extracted for the case when membrane strain energy and bending one are considered. Thereafter, an analytical model has been presented for predicting midpoint deflection-thickness ratio of rectangular plates by incorporating the coupled interaction between membrane and bending strains. Eventually, the obtained analytical results have been compared with the experimental results and illustrate good agreement with experiments for different impact velocities, plate materials and plate thicknesses