Nonlinear Static/ Dynamic Mechanical Analysis Of Viscoelastic Plates With Damage Effects Under The Varied Temperature Field

By considering geometric nonlinearity, damage effects, and viscoelasticity of the material synthetically, the actual state of viscoelastic structure under the varied temperature field can be described accurately and the essential character of the nonlinear mechanical behaviors can be illustrated precisely. However, the establishment of the constitutive relations for viscoelastic material with damage under the varied temperature field and corresponding damage evolution equations are very difficult. When such factors are involved, the nonlinear governing equations become more complicated, which is quite difficult to solve. Due to the above reasons, there is only little research in this field. The problem is investigated in this thesis, and some achievements are obtained on several aspects such as the establishment of the constitutive relations with damage under the varied temperature field, the construction of the mechanical modeling and the sake of efficient computational method, etc. The research results are significant not only in theory but also in the practical engineering. And the main researches are as follows.Based on the theory of thermo viscoelasticity, Von Karman theory of plates and continuum damage mechanics, the viscoelastic constitutive equation of isotropic material with damage under the varied temperature field is derived in two-dimensional space. And the nonlinear dynamic governing equations of viscoelastic isotropic rectangular plate with damage under the varied temperature field are established. By generalizing the Ladeveze's damage model of the uni-ply for laminated plates, a constitutive relation with damage under the varied temperature field for fiber-reinforced composite laminated plates including shear viscoelasticity in plane is obtained. Moreover, the corresponding nonlinear governing equations of motion and nonlinear equilibrium equations are established, respectively. On the basis of the aforementioned research works, through applying Kachanov damage evolution equation to constitutive relations with damage as above, a model considering damage and damage evolution for viscoelastic structure under the varied temperature field is founded. By using finite difference method, Newmark method and iteration method synthetically, the nonlinear static/dynamic analyses of viscoelasticity structure with damage under the varied temperature field are investigated. The main researching contents include: nonlinear dynamic responses for viscoelastic rectangular...