Dynamic buckling of plate made of glass reinforced plastic under rapidly increasing shear load

Abstract

The research object of this work is a clamped rectangular plate made of glass-reinforced plastic. The dynamic problem of stability of the plate under rapidly increasing shear load is considered. Within the Kirchhoff–Love hypothesis framework, a mathematical model was built in a geometrically nonlinear formulation. By the Bubnov–Galerkin method, based on a polynomial approximation of the deflection, the problem was reduced to solving systems of nonlinear ordinary integro-differential equations. With a weakly singular Koltunov–Rzhanitsyn kernel with variable coefficients, the resulting system was solved by a numerical method based on quadrature formulas. The plate’s dynamic behavior was investigated depending on the plate’s geometric and physic parameters. The importance of considering the viscoelastic properties of the material is shown.