Nonlinear Bending Analysis Of The Piezoelectric Laminates Under Strong Electric Field

In recent years, smart materials have been widely used in the sophisticated weapons, aerospace vehicles, high-end construction equipments and robots. With the development of the in-depth study, the applications of smart materials have been extended to the household appliances and photographic equipments. Obviously, smart materials are improving the quality of our life. And piezoelectric material occupies an important position in the research and engineering application of smart structures due to their unique piezoelectric effects.Owing to the coupling effect of displacement and electric field, the mathematical model that reflects physical problems is complex involving the nonlinear piezoelectric effect. Most problems of the static and dynamic under the general electric field are usually studied with the linear piezoelectric effect. The electrostrictive and electroluminescent elastic effect of the piezoelectric material can not be ignored under strong electric field, the non-linear effect of piezoelectric material is evident and the displacement control result are different compared with linear case. Also, with the rapid development of large scale, low stiffness and flexible structures, geometric nonlinearity has become a important problem that we have to face.The main study and innovation was shown as follows:1. The linear model for bending analysis of the piezoelectric composite laminated plates was established with the Rayleigh-Ritz method based on the classical plate theory and the principle of minimum potential energy, in which the positive and inverse piezoelectric effect were both considered.2. The nonlinear mathematical model for bending analysis of the piezoelectric composite laminated plates was derivate by the above-mentioned theory and method, in which the electrostriction and electricity elasticity effect of piezoelectric material or geometric nonlinear of the structure were regarded in the strong electric field.3. The nonlinear mathematical model was solved by Newton-Raphson iterative method. The effect regularity of piezoelectric nonlinearity on simply supported piezoelectric laminated plates were studied.4. The impacts of the positive piezoelectric effect on center deflection of the piezoelectric smart laminated plates were discussed under three cases (linear, geometric nonlinear and piezoelectric nonlinearity).5. The difference of the control effects between linear control and nonlinear control was studied. In the practical engineering application, the ideal scheme could be selected to achieve better control effects.6. The nonlinear static control model for the piezoelectric laminated plate was established with the spline finite point method, and the inverse piezoelectric effect was considered. And the spline finite point method stiffness matrix was derived.7. The effect of the piezoelectric nonlinear on the center deflection of piezoelectric laminated plate was studied under different boundary conditions with spline finite point method.In this paper, the calculation procedures were compiled by MATLAB. The reliability of the proposed model was proved through comparing with the analytical solutions, the spline meshless method solutions and the finite element solutions. And some valuable conclusions were drawn out.