Nonlinear Mechanical Analysis For Elasto-Plastic Laminated Structures Including Damage Effect

In this dissertation, considering elasto-plastic laminated plates with matrix crack damage and interfacial damage, the buckling, postbuckling, nonlinear dynamic response behaviors as well as the piezoelectric active control of elasto-plastic laminated plates with damage are systematically studied, and the essential character of the mechanical property can be illustrated precisely. The research results not only contribute to the enrichment and development of elasto-plastic damage theory, but also have an important meaning in the practical engineering. The main results contain as follows.The nonlinear mechanical behaviors of elasto-plastic laminated plates with matrix crack damage are investigated. Based on the assumption that the plastic deformation is related to the spherical stress tensor, a new generalized mixed hardening yield criterion for anisotropic damage materials is presented. Then using the continuum damage mechanics theory, and in the basis of the irreversible thermodynamic theory and the generalized mixed hardening yield criterion, the new incremental elasto-plastic damage constitutive equations and damage evolution equations are deduced. By adopting the above constitutive relations, and using the nonlinear plate theory, the incremental nonlinear dynamic governing equations for elasto-plastic laminated plates with matrix crack damage are established. Through applying the Galerkin method, finite difference method, Newmark-βmethod and iterative procedure, the governing equations are solved. The buckling, postbuckling and nonlinear dynamic responses for elasto-plastic laminated plates with matrix crack damage are analyzed. The influences of damage effect, load parameters, geometric and material parameters on the nonlinear static/dynamic behaviors are discussed in detail, and the differences of the mechanical behaviors between the elastic laminated plates and elasto-plastic laminated plates with matrix crack damage are revealed. Meanwhile, a simple negative velocity feed back control algorithm coupling the direct and converse piezoelectric effects is used to actively control the dynamic response of the elasto-plastic plates with matrix crack damage through closed loop control. The influences of feedback control gain and piezoelectric patches's position on the control effect are discussed, and the comparisons of the control effect between the elastic laminated plates and elasto-plastic laminated plates are given.The nonlinear mechanical behaviors of elasto-plastic laminated plates with interfacial damage are investigated. Two characteristic analysis models are developed. Without considering the interfacial damage evolution, and using the interfacial weakly bonded constitutive relations, a displacement field that reflects the interfacial damage is proposed by introducing the Heaviside step function and shape functions. Then applying the Von Karman nonlinear plate theory, the first interfacial damage analysis model based on the interfacial weakly bonded model is established. On the basis of this model, the incremental buckling equilibrium equation for elasto-plastic laminated plates with interfacial damage is derived. Through applying the Galerkin method and iterative process, the equation is solved. The effects of interfacial damage, induced load ratio and material anisotropy on the critical buckling load of elasto-plastic laminated plates are discussed. The second model is based on the Shear-Lag theory. Considering the interfacial damage evolution, and by using the Cohesive Zone theory, the incremental interfacial damage constitutive equations and damage evolution equations are established. Then by associating with the Shear-Lag theory, a new and simple model for elasto-plastic laminated structures with interfacial damage is established. The model simplifies the interfacial damage problems greatly, and suits for the nonlinear mechanical analysis of both elastic and elasto-plastic laminated structures. On the basis of the model, the incremental nonlinear dynamic governing equations are obtained, and the difference method, Newmark-βmethod and iterative procedure are adopted to solve the equations. The effects of interfacial damage on stress and displacement distributions, nonlinear dynamic response of elasto-plastic laminated plates are discussed in detail.