Research On Nonlinear Dynamics And Fatigue Life Analysis Of Piezoelectric Laminated Structures Including Damage Effects

The damages will easily emerge in fibre-reinforecd composite structures during the manufacturing and service processes. The emergence of damages and their further growth will drastically reduce the mechanical properties and service life of the structures. For the safe reliability of structures, it is necessary to establish the constitutive relations and mechanical modeling for different kinds of damage and analyze the effect of damage on the mechanical properties and service life of the structure. In this dissertation, considering fibre-reinforced composite laminated structure and piezoelastic laminated structures as the subjects investigated, the nonlinear dynamic response and fatigue damage prediction of piezoelectric laminated structure with different kind of damage, such as matrix crack, delamination and interfacial debonding, 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 fatigue damage life of piezoelectric viscoelastic laminated beams is investigated. Based on the viscoelastic theory and the continuum damage mechanics, and according to the Boltzmann superposition principle and strain energy equivalence, a constitutive model is established for viscoelastic composites with orthotropic damage. Supposing the damage variables remain constant throughout the thickness in each layer, considering geometric nonlinearity, transverse shear deformation and piezoelectric effect, the nonlinear governing equations of motion for the piezoelectric viscoelastic laminated beams with damage are derived by using the composite mechanics and nonlinear laminated theory. The Kachanvo damage evolution law under the once time load and the Chaboche fatigue damage development due to long time cyclic loads are employed to fatigue damage growth. Through applying the finite difference method, Newmark method, Newton-Cotes method and iterative procedure, the governing equations are solved. The cyclic skip method is utilized to shorten the calculation interval. The influences of load parameters, geometric and material parameters as well as piezoelectric effect on the nonlinear dynamic responses and fatigue damage evolution for the damaged piezoelectric viscoelastic laminated beams are discussed in detail.The fatigue damage life of piezoelectric laminated plate with matrix cracks is investigated. Based on the Talreja's damage model with tensor valued internal state variables and the invariant theory, using the thermodynamic relations, a constitutive model for fibre-reinforced composite containing matrix cracks is established. Considering geometric nonlinearity and piezoelectric effect, the nonlinear governing equations of motion for the piezoelectric viscoelastic laminated plates with matrix cracks are derived by using the Von Karman's nonlinear theory. The Kachanvo damage evolution law under the once time load and the Chaboche fatigue damage development due to long time cyclic loads are employed to fatigue damage growth.Through applying the finite difference method, Newmark method, Newton-Cotes method and iterative procedure, the governing equations are solved. The cyclic skip method is utilized to shorten the calculation interval. The influences of load parameters, geometric and material parameters as well as piezoelectric effect on the nonlinear dynamic responses and fatigue damage evolution curve for piezoelectric viscoelastic laminated plates with matrix cracks are discussed in detail. The fatigue delamination growth of piezoelectric laminated beam-plates with asymmetric delamination is investigated. Based on the nonlinear elastic plate's theory and variational principle of moving boundary, the nonlinear governing equations of the piezoelectric laminated beam-plates with delamination are derived, and the corresponding boundary and matching conditions are given. According to the Griffith criterion, the formulas of energy release rate along the delamination front are obtained. 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. In the numerical examples, the delamination growth of piezoelectric laminated beam-plates with asymmetric delamination is calculated, and the effects of voltages, asymmetry of delamination and delamination length on energy release rate and delamination growth length are discussed in detail.The fatigue delamination growth of piezoelectric laminated cylindrical shell with asymmetric delamination is investigated. Based on the variational principle of moving boundary, an analytic model of delaminated piezoelectric laminated cylindrical shell under the consideration of nonlinear contact effects is derived. Firstly, the contact force is calculated through regarding the two segments beside the delamination as two nonlinear springs connected in series. Then, the governing equation of transverse motion is modified by the nonlinear contact force and thus the penetration between two delaminated layers can be avoided. According to the Griffith criterion, the formulas of energy release rate along the delamination front are obtained. Applying the Paris law, the delamination growth lengths along the delamination fronts under cycle load are finally determined. In numerical examples, the delamination growth length of piezoelectric laminated cylindrical shell with asymmetric delamination is calculated, and the effects of voltages, stiffness factor of contact region, asymmetry of delamination and delamination length on energy release rate and delamination growth length are discussed in detail.The nonlinear dynamic response of composite laminated plate is investigated. Based on the general six-degrees-of-freedom plate theory towards the accurate stress analysis, considering the effect of interfacial damage and using the variation principle, the three-dimensional nonlinear dynamic governing equations of the laminated plates with interfacial damage are derived. Then based on the equilibrium differential equation in the elastic mechanics theory, considering the displacement and stress continuity conditions, the undetermined shape functions of governing equations are obtained. The solutions of interlaminar stress and nonlinear dynamic response for a simply supported laminated plate with interfacial damage are derived by applying the finite difference method, Newmark method, Newton-Cotes method and iterative procedure. In numerical calculation, the effects of interfacial damage on the stress in the interface and the nonlinear dynamic response of laminated plates are discussed in detail.The fatigue debonding growth of fibre-reinforecd composite with interfacial debonding is investigated. Based on the basic theory of elastic mechanics, the equilibrium differential equations of deboned and fully-bonded regions of composite are derived and the corresponding boundary conditions are given, then the calculating formulas of axial stresses in fiber and matrix are obtained. The criterion of energy release rate for interfacial debonding are obtained. Applying the Paris law, the interfacial debonding rate is arrived and using cyclic skip method, the fatigue interfacial debonding lengths under cycle load are finally determined. In numerical examples, the typical carbon/epoxy composite with interfacial debonding is calculated, and the effects of material constants, geometric constants, initial stress and external load on the distribution of stresses in fiber/matrix and interfacial debonding energy release rate and fatigue growth length are discussed in detail.