Modeling of dynamic bending of a rigid-plastic reinforced layered curvilinear plate with a supported circular hole under explosive loads

A general method is developed to calculate the dynamic behavior of rigid-plastic hybrid laminated composite plates with an arbitrary piecewise-smooth free outer contour and a circular inner simply supported or clamped hole. The plates are under a uniformly distributed, short-term dynamic load of a high intensity explosive type. The plates are hybrid fibrous-laminated with the distribution of layers symmetrically relative to the middle surface. In each layer the reinforcing fibres are placed in radial, circumferential and angular directions. The structural model of the reinforced layer with one-dimensional stress states in the fibres is used. Different schemes of dynamic deformation of the plates are possible. In case when the loads slightly exceed the ultimate values, the plates are deformed in the form of ruled surfaces rotating around the supported contour. At high load amplitudes, the plastic hinge in the form of a circle can be formed in the inner region of the plates. On the basis of the virtual power principle together with the principle of d'Alembert for each of the schemes of motion, the dynamic deformation equations are obtained and the conditions for their implementation are analyzed. Analytical expressions are obtained for the evaluation of limit loads, time of deformation and final deflections of the plates. Numerical examples are given for square plates with a supported circular hole and for annular plates. It is shown that the change in the reinforcement parameters significantly affects both the carrying capacity of plates and the final deflections. The proposed solutions can be used in the design of reinforced metal-composite curvilinear flat structural elements with a supported circular hole.