Bulking of physically nonlinear plates under the action of dynamic shearing loads

Abstract

The study of the stability of plates under shear under the action of dynamic loads is one of the important problems of structural mechanics. The plates are widely used in construction, mechanical engineering, shipbuilding and aircraft building. The paper presents a method for calculating plates for shear buckling, taking into account the physical nonlinearity of the material. A plate is considered under the action of a shearing dynamic load along the edges. The calculation is based on the Kirchhoff - Love hypotheses and the hypothesis of a non-linear elastic body. The plate material is assumed to be physically nonlinear. The deformation diagram is approximated as a cubic polynomial. The deflection of the plate points is determined in the form of Vlasov - Kantorovich expansions. Basic non-linear differential equations are derived using the energy method. Lagrange’s equations are used to obtain the resolving equations for plate buckling. On the basis of the developed technique, a calculation was made for the stability of a physically nonlinear square plate under the action of a shear dynamic load. The edges of the plate are hinged. The finite system of nonlinear differential equations is integrated numerically by the Runge - Kutta method. Based on the results of calculations, plots of the dependence of the relative value of the deflection of the central point of the plate on the dynamic coefficient Kd (with and without taking into account the physical nonlinearity of the material) are plotted. The influence of the degree of physical nonlinearity of the material, the parameter of the rate of change of the shear load on the criteria for the dynamic stability of a square plate is studied.