Theory Of Viscoelastic Solids With Voids And Quasi-Static And Dynamical Analysis For Structures

In this dissertation, according to the theory of viscoelastic materials and the micro- structure theory for linear elastic materials with damage, theoretical analyses of viscoelastic materials with damage and numerical simulations of quasi-static and dynamical analysis for viscoelastic structures with damage are systematically studied. New theoretical and numerical results are obtained. The main results contain as follows:1 .Applying the micro-structure theory for linear elastic materials with voids and the constitutive laws of viscoelastic materials, two kinds of linear constitutive equations of viscoelastic solids with damage are given by the differential-type and integral-type constitutive laws of linear viscoelastic materials.2.From the Boltzmann's constitutive law of viscoelastic materials and the linear theory of elastic material with voids, a constitutive model of generalized force fields for viscoelastic solids with voids is given. The convolution-type functional ispresented, the generalized variational principles and potential energy principle of viscoelastic solids with voids are presented by using the variational integral method.3.Under the case of small deflections, the generalized differential equations of motion for Timoshenko beams with damage are derived. By using the variational integral method, the generalized variational principle of viscoelastic Timoshenko beams with damage is presented. The quasi-static behaviors of the viscoelastic Timoshenko beam with two sides of the beam are simply supported, and under step loading are analyzed by using Laplace transformation and the numerical inverse Laplace transform. The influences of material parameters and damage on the quasi-static behavior of the beam are considered in detail.4.From convolution-type constitutive equations for linear viscoelastic materials with damage and the hypotheses of Timoshenko beams with large deflections, the differential equations of motion governing nonlinear dynamical behavior of Timoshenko beams with damage on viscoelastic foundation are given. The dynamic behaviors of viscoelastic Timoshenko beams with damage on viscoelastic foundation are numerically analyzed. At the same time, the influence of the foundation on the dynamic behaviors of beam is also studied.5.From the constitutive model expressed by convolution method for viscoelastic solids with damage, initial-boundary-value problems analyzing static-dynamic behaviors of viscoelastic thin plates with damage are all formulated under the case of small and finite deflections. Under the case of small deflections, the generalized variational principle of viscoelastic thin plates with damage is established. The quasi-static behaviors of the viscoelastic rectangular thin plate with damage under step loading are analyzed when the boundary of plate is simply supported. At the same time, the dynamical response of the viscoelastic thin plate with damage subjected to a periodic excitation is studied.6.Based on Timoshenko geometry deformation hypotheses of thick plates and the integral-type contitutive model of viscoelastic solids with damage, the nonlinear governing equations are derived for dynamic analysis of viscoelastic thick plates with damage. The generalized variational principle of viscoelastic thick plates with damage is presented. Applying the Galerkin method and numerical methods in nonlinear dynamics, the dynamical behaviors of viscoelastic plates with simply supported edges are discussed in detail. The influences of the load, geometry and materialparameters on the dynamical behaviors of the viscoelastic plate with damage are considered. The dynamical behavior of viscoelastic plates with damage under small deformations is also analyzed. To consider the effect of damage on the dynamical behavior of plate, we compare dynamical properties of plates with damage and without damage.7.According to the constitutive model expressed by convolution method for viscoelastic solids with damage, the differential equations of motion governing dynamical behaviors...