Nonlinear Mechanical Analysis Of Fiber-Reinforced Composite Plates And Shells With Damage Effects

By considering geometric nonlinearity, damage effects, and viscoelasticity of the matrix synthetically, the actual state of the fiber-reinforced composite structure can be described accurately and the essential character of the mechanical property can be illustrated precisely. However, the establishment of the constitutive relations for fiber-reinforced composite with damage and corresponding damage evolution equations is very difficult. Moreover, damage effects and viscoelasticity of the matrix will cause the governing equations and boundary conditions more complicated, and new computational method is necessary to solve this problem. Due to the two reasons proposed as above, there is only little research on this field. The problem is investigated in this dissertation, and some achievements are obtained on several aspects such as the establishment of the constitutive relations with damage, the construction of the mechanical modelling and the sake of efficient computational method, etc. The research results are significant not only in theory but in the practical engineering.In this thesis, two constitutive relations with damage which is available to the bending problems for the fiber-reinforced composite structure are proposed. Based on the Talreja's damage model with tensor valued internal state variables, a set of constitutive relations with damage for the fiber-reinforced composite structure containing matrix cracks which are vertical or parallel to the fibers are derived by using invariant theory. And by generalizing the Ladeveze's damage model of the uni-ply for laminated plates, a constitutive relation with damage for fiber-reinforced composite laminated plates including shear viscoelasticity in plane is obtained.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 fiber-reinforced composite plates and shells is founded. By using finite difference method or orthogonal point collocation method, Newmark method and integration method synthetically, the nonlinear static/dynamic analyses of fiber-reinforced composite plates and shells with damage are investigated. The main researching contents are as follows: nonlinear dynamic responses and postbuckling analyses of fiber-reinforced composite plates with damage, nonlinear dynamic responses and dynamic buckling of fiber-reinforced composite shallow spherical shells with circular hole including damage effects, nonlinear...