Nonlinear Statics/dynamics Analysis Of Piezoelastic Laminated Structures With Damage Under Hygrothermal Conditions

In this dissertation, considering piezoelectric laminated structures under hygrothermal conditions as the subjects investigated, the postbuckling and delamination growth of delaminated piezoelectric elastic and elasto-plastic laminated beams, postbuckling and fatigue delamination growth of piezoelectric elasto-plastic laminated beams under cyclic load, as well as bifurcation and chaos behaviors of piezoelectric laminated cylindrical shell including damage effects, are systematically studied, and the essential character of the mechanical property can be illustrated precisely. The research results are significant not only in the academic but also in the practical engineering. The main results contain as follows.The postbuckling and delamination growth of piezoelectric laminated beam with delamination is investigated. Based on the variational principle of moving boundary, the nonlinear governing equations of the piezoelectric laminated beams with delamination are derived, and the corresponding boundary and matching conditions are given. In calculating, the finite difference method and iterative method are adopted. According to the Griffith criterion, the formulas of energy release rate along the delamination front are obtained. In the numerical examples, the effects of hygrothermal, voltages, delamination length and depth on the postbuckling and energy release rate are discussed in detail.Under the case of finite deformation, considering the damage effect in the composite laminated layers, the bifurcation and chaos of the damaged piezoelectric laminated cylindrical shells are systematically studied. By applying the Galerkin method, introducing new variables, and employing the modern methods in nonlinear dynamics, the complex nonlinear dynamic system of the piezoelectric laminated cylindrical shells with damage are investigated qualitatively. The time history, phase plane portrait, Poincare map, bifurcation diagram and so on, for the nonlinear system are determined and the plenty and complex nonlinear dynamical behaviors are revealed. The influence of the hygrothermal effect, damage and external applied voltage on the bifurcation and chaos of the piezoelectric laminated cylindrical shell with damage are considered in detail.Based on the elasto-plastic mechanics, a yield criterion that is related to the spherical tensor of stress is proposed to describe the mixed hardening of damaged orthotropic materials, and the dimensionless form of which is isomorphic with the Mises criterion for isotropic materials. Based on the classical nonlinear plate theory, the incremental nonlinear equilibrium equations of the piezoelectric elasto-plastic laminated beams with delamination are obtained, and the equations are solved by the finite difference method and iteration method. Furthermore, adopting the elasto-plastic fracture mechanics and J theory, the energy release rates along the delamination front are studied. In numerical examples, the effects of the hygrothermal conditions, yield stress, voltage, slenderness ratio, delamination size, and delamination length on postbuckling behavior and energy release rate are discussed.Based on the incremental elasto-plastic constitutive equations, by considering hygrothermal environments, transverse shear deformation, geometrical nonlinearity and piezoelectric effect, the incremental nonlinear governing equations of the piezoelectric elasto-plastic laminated beams with delamination are acquired. Besides, according to elasto-plastic fracture dynamics and J-integral theory, the energy release rate along the delamination is obtained. Then, applying the Paris law, the delamination growth rate is arrived and using cyclic skip method, the delamination growth lengths along the delamination fronts under cycle load are finally determined. Through applying the finite difference method, Newmark method and iterative procedure, the governing equations are solved. The effects of voltages, variation of temperature and humidity, delamination length and depth on the energy release rate and delamination growth length for the laminated elasto-plastic beams are discussed.