Theory And Static-Dynamical Analysis For Elastic And Viscoelastic Plates With Higher-Order Shear Deformation

In this dissertation, nonlinear mathematical models of visco-elastic plates with finite deformations and the effect of higher-order shear deformations are established. At the same time, an extended differential quadrature method is formulated. The static and dynamical problems of visco-elastic plates and the corresponding degenerate models are systematically studied in theoretical and in numerical. The main results contain as follows:1.Based on the Boltzmann superposition principles and the Reddy's theory of plates with the of effect of higher-order shear deformations, the nonlinear governing equations are established for static and dynamic analyses of visco-elastic plates with finite deformations and taking account of shear effects by the Laplace transformation and its inverse transformation. The governing equations are a set of coupled nonlinear integro-partial-differential equations. The differential quadrature method (DQM) is extended to analyze the nonlinear behaviors of such systems. The differential quadrature approach suggested by Wang and Bert is extended to handle the high-order moment boundary conditions of plates, too.2.Based on the above nonlinear model of visco-elastic plates with the effect of higher-order shear deformations, the coupled nonlinear governing equations for laminated plates with finite deformations are presented. The differential quadrature method presented in this dissertation is applied to discretize the nonlinear model and the corresponding DQ form is obtained. By extending the special matrix product and decoupled technique, the coupled nonlinear equations are decoupled and the simplified iterative formulae of DQ are presented for the static problem, and hence it is able to avoid the ill-conditioning matrix and greatly reduce nonlinear computation. For the dynamic problem, the harmonic balance method of DQ is presented. The static bending, free and force vibrations of the system with different parameters and grid spacing are simulated numerically. The numerical convergence and comparison studies are carried out to validate the validity of the present method. The influence of grid spacing on the convergence rate is discussed. The results show that the presented differential quadrature method is more accurate and efficient than traditional one. Influences of geometric and material parameters, transverse shear deformations and rotation inertia as well as vibration amplitudes on nonlinear characteristics of laminated plates are studied in detail.3.In the case of small deflections, the convolution-type functional and the corresponding Gurtin-type variational principle are all presented for the static- and dynamic analysis of visco-elastic plates with higher-order shear deformations and arbitrary boundary. By the extended differential quadrature method in spatial domain, the original integro-partial-differential equations are transformed into a set of integro-ordinary equations. The latter may reduced to a set of ordinary differential equations in time domain. The approximate analytical solutions are proposed for the quasi-static bending of visco-elastic plates subjected to step loads. The dynamic response of the visco-elastic plate with simply supported is obtained. The convergence and comparison of solutions are studied. The numerical results proves that the DQ method presented in this paper is very a reliable and available computational method with higher precision. Moreover, the influences of geometric and material parameters as well as the transverse shear deformations on dynamic behaviors are studied.4. The nonlinear dynamic stability of visco-elastic plates with finite deformations and takingaccount of higher-order shear deformation effects is discussed. By the Galerkin method, a system of integro-partial differential equations with infinite dimension is transformed into a set of nonlinear autonomous ordinary differential equations with higher-dimension via introducing new variables. The numerical methods in nonlinear dynamics, such as, time history, phase plane portrait...