Bending and buckling solution of composite viscoelastic plate using the generalized exponential basis function method

In this study, we employ first-order shear deformation theory to calculate maximum deformation and critical buckling load of moderately thick viscoelastic composite plates. These quantities are calculated over time under in-plane and out of plane loadings. The mechanical properties of the viscoelastic material are assumed linearly by expressing the modulus of relaxation in the form of the Prony series. Constitutive equations are expressed as polynomials in the Laplace-Carson domain. Also, the Illyushin’s approximation and inverse Laplace-Carson methods have been used for calculating the response of these relations in the time domain. Finally, the method of generalized exponential basis functions is used to solve the governing equations for different values of time. Finally, the method of generalized exponential basis functions is used to solve the governing equations for different time values. The time-history of maximum deflection and critical buckling load are presented for the plates with different boundary conditions. The results of bending and buckling of the simply-supported plates are compared with the existing literature. Plates with two edges simply-supported and other edges fixed as well as those with all edges fixed are considered under transverse and in-plane loading, to investigate the effect of changing boundary conditions. Several problems with different boundary conditions are considered which many other analytical and semi analytical methods are unable to handle. In all cases the proposed method has been able to outperform the other methods.