Nonlinear static, buckling and dynamic analysis of piezothermoelastic composite plates using Reissner-Mindlin theory based on a mixed hierarchic finite element formulation.

摘要

Piezoelectric materials are widely used as sensors and actuators to monitor and control the dynamic response of smart structures. This research is concerned with the development of a finite element formulation for the analysis of nonlinearly deformable piezothermoelastic composite laminates using a two-dimensional equivalent single layer plate theory. Plate displacements are based on Reissner-Mindlin first-order shear deformation theory. Geometric nonlinearity is included using Green-Lagrange strain-displacement equations in the von Karman sense. A mixed finite element formulation utilizing the modified Hellinger-Reissner variational principle has been adopted. Displacements, electric potential and transverse shear stress resultants are the independent variables.; Quadratic, cubic, and quartic Lagrangian hierarchic finite elements are employed in the spatial discretization of displacement, rotation, and electric potential variables. The transverse shear stress resultants are interpolated at the Gauss quadrature points using standard Lagrangian shape functions, which are condensed from the stiffness equations at the element level. Variation of temperature in the plate depth is assumed to be linear, where as a piecewise linear assumption is used for the electric potentials. The nonlinear solution procedure involves an explicit iteration on spheres, modification of the constant arc-length method, in conjunction with the modified Newton-Raphson incremental/iterative scheme. Hilber-Hughes-Taylor alpha-method is employed in temporally discretizing the nonlinear dynamic equations; nonlinear equations are iteratively evaluated using modified Newton-Raphson. The displacement and velocity variables are expressed using Newmark's finite difference scheme. Damping can be introduced in the system either numerically using the alpha parameter or via Rayleigh damping coefficients.; The developed finite element formulation is validated against analytical and published solutions. An eigenvalue analysis is conducted to predict critical buckling loads and the results are compared with the nonlinear buckling response of laminates with uncoupled and coupled piezoelectric effects. Postbuckling behavior of piezoelectric plates under inplane mechanical load is studied. Buckling response of composite plates under self-strained thermal loading and electric potential are investigated. Natural frequencies of composite plates laminated with PVDF (Polyvinylidene Fluoride) and PZT (Lead-Zirconate-Titanate) layers are computed for different modes of vibration. In the transient analysis of composite laminates, effects of piezoelectric coupling and geometric nonlinearity on the amplitude and time period of oscillation are investigated. Influence of alpha numerical damping and piezoelectric coupling on the amplitude decay of high frequency response of plates is also studied.; Keywords: Finite Element Analysis, Mixed Formulation, Geometric Nonlinearity, Piezoelectric Materials, Composite Laminates.