Based on the weighted residual integration of the non-linear dynamic equilibrium equation of a plate, an energy conservation is established when the plate is subjected to impulsive loads. The constitutive relation of the plate material is described by a rigid perfect plastic material model which is sufficiently accurate for large plastic deformation when the elastic deformation becomes negligible. Thus acquired non-homogenous yield surface is replaced, in the present study, by a circumscribing and an inscribing surface given by homogenous functions and results, respectively, in a lower and an upper bound solution of the displacement. Roof-shaped and sinusoidal deformation patterns have been used to find the permanent plastic deformation of quadrangular plates subjected to impulsive loads. The results show that, when a roof shaped deformation pattern is utilized, the present theoretical model agrees with the experimental data and numerical simulations very well regarding the central deflection of the plate. For the convenience in engineering application, some approximate integral formulas are adopted so that all the results are given in analytical expressions.
Research on the behavior of quadrangular plates subjected to explosive loads can be dated back to 1950 (Taylor, 1950). Since then, increasing attention has been paid to this topic. However, literature review has shown that, as compared to that on circular plates, research on quadrangular plates is much less (Nurick and Martin, 1989a, 1989b; Chen, 1992). This is probably due to the difficulties caused by the loss of axial symmetry in the structure and stress distribution. Nevertheless, significant achievement has been obtained referring to the published work. Experimental studies on the dynamic behavior of quadrangular plates were carried out by Johnson et al (1964), Duncan (1968), Jones et al (1970, 1971, 1972) and Nurick et al (1986, 1987).