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Piezoelectric smart laminated structure, the paper, considering the damp heat effect, geometric nonlinearity and piezoelectric effects and other factors, a systematic study of the hot and humid conditions with delaminated piezoelectric laminated beam after buckling and delamination Bifurcation and Chaos expansion, with damage piezoelectric laminated cylindrical shells with delaminated piezoelectric laminated beam under axial load and lateral cyclic loading elastoplastic buckling and delamination propagation problem, exposing the depth shown its the essential characteristics of the mechanical behavior. The research in this paper not only has the important academic value, but also has a strong engineering and applied significance. The research work of this paper is as follows. After buckling and delamination expansion, under the hot and humid conditions with Delamination piezoelectric laminated beam. Based movable boundary variational principle with delaminated piezoelectric laminated beam nonlinear equilibrium equations and the corresponding boundary conditions. Application the Griffith guidelines, set up the the delamination front edge of the energy release rate expressions. In numerical analysis, the equation of unknown function space applications discrete finite difference method, the nonlinear terms linearization, the whole problem with iterative method for solving. In the numerical example, discussed in detail the changes in voltage, temperature and humidity, delamination length and depth of the impact of the post-buckling behavior of piezoelectric laminated beam with Delamination and delamination of the leading edge of the energy release rate. Consider the effects of damage within the composite ply laminated cylindrical shell Bifurcations and Chaos with damage piezoelectric layer in finite deformation conditions,. The Galerkin truncation technology, and the introduction of a new state variable, the comprehensive application of nonlinear dynamics of modern analytical methods, qualitative analysis of complex nonlinear dynamic systems composed of piezoelectric laminated cylindrical shells with damage effects bifurcation diagram, Poincare mapping, the time course of the curve and phase plane trajectory reveals its rich nonlinear mechanical behavior, and the effects of hot and humid effect, damage parameters and external electrical load with damage piezoelectric laminated circular cylindrical shells Bifurcation and Chaos characteristics. Elastoplastic mechanical stress ball tensor orthotropic material mixed hardening yield criterion, the guidelines dimensionless Mises criterion for isotropic material isomorphism, thereby establishing the mixed hardening cross-anisotropic material incremental elastoplastic constitutive equations. Based on the classical nonlinear plate theory, considering the hot and humid conditions, transverse shear deformation, geometric nonlinearity and piezoelectric effect, established with Delamination piezoelectric laminated beam under axial loads Incremental nonlinear balance equation. On this basis, the application of J integral theory to study the elastic-plastic laminated structures delamination leading edge of the expansion problem. The numerical example, the piezoelectric effect, hot and humid conditions, delamination length and depth of the elastic-plastic layer with delamination piezoelectric aggregate beam delamination of the leading edge of the energy release rate. With delaminated piezoelectric laminated beam under horizontal cyclic loading incremental nonlinear mixed hardening orthotropic materials incremental elastoplastic constitutive relations, consider the effect of the contact between the delamination equations of motion. In addition, based on the theory of elastic-plastic fracture, application of J integral principle, obtained by the the delamination front edge of the energy release rate, according to the Paris fatigue crack growth criterion, delamination expansion rate in the leading edge of the delamination under cyclic loading, and then apply cycle jumping method to calculate the length of the extension of the leading edge of the delamination. In numerical analysis, the equation of unknown function space applications discrete finite difference method, discrete time using the Newmark method, and linearizing all nonlinear terms, the whole problem using iterative method, using loop jump at the same time to simplify the fatigue of a huge number of incremental cumulative analysis. Example, specific discussion of the piezoelectric effect, hot and humid conditions, delamination length and depth with delaminated piezoelectric elasto-plastic laminated beam delamination leading edge of the energy release rate and extended length.
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