Static Buckling and Free Vibration Behaviour of Skew Magneto-Electroelastic Plates

Abstract

This dissertation comprises the investigation on structural characteristics of skew magneto-electro-elastic (SMEE) plates through static, buckling, and free vibration analysis. Magneto-electro-elastic plates with multilayered and functionally graded types are considered for the analysis. The numerical analysis is performed by developing a finite element model based on the coupled constitutive equations and shear deformation theories. A transformation matrix is developed to account for the skew edges introduced as a geometrical change, and utilized to specify boundary conditions on the skew edges. Influence of boundary conditions and material stacking sequences on the displacement, stresses, buckling load, and natural frequency of the SMEE plates has been investigated. Particular emphasis has been placed to study the effect of skew angles and aspect ratios on the stresses, electric displacement, magnetic induction, and natural frequencies. The present study reveals that the skew angle and the aspect ratio significantly influence the structural behaviour of the SMEE plates. The buckling behaviour of multilayered SMEE plate under uniaxial and biaxial in-plane loading is investigated. The in-plane stress distribution within the SMEE plate due to the enacted force is considered to be equivalent to the applied inplane compressive loads in the pre-buckling range and the same stress distribution is used to derive the potential energy functional of the SMEE plate. The nondimensional critical buckling load is attained from the solution of the allied linear eigenvalue problem. Influence of skew angle, stacking sequence, span to thickness ratio, aspect ratio and boundary conditions on the critical buckling load and their corresponding mode shapes has been investigated comprehensively. Further, the finite element formulation is extended to assess the static response and free vibration characteristics of a functionally graded skew magneto-electroelastic (FGSMEE) plate. The material grading of FGSMEE plate is considered across the thickness using power law distribution. The influence of skew angle on the primary quantities such as displacements, electric potential, and magnetic potential, and secondary quantities such as stresses, electric displacement, and magneticiv induction is studied in detail. In addition, the effect of power-law gradient, thickness ratio, boundary conditions, and aspect ratio on the static response and free vibration characteristics of FGSMEE plate has been investigated. The major defect encountered in the preparation of functionally graded structures is porosity. Hence, the influence of porosity on the static responses and free vibration of functionally graded rectangular and skew magneto-electro-elastic plate is also considered for the investigation. The porosity in the FG material is accounted as local density using modified power law. The displacements, potentials, and stresses for the porous skew plate are established through static analysis. The influence of different porosity distributions on the FGSMEE plate has also been studied. The effect of porosity volume, skew angle, and the geometrical parameters such as aspect ratio, thickness ratio, and boundary conditions on the behaviour of porous FGSMEE plate is investigated.