Static and Dynamic Finite Element Analysis of Laminated Composite Plates

Abstract

Fibre Reinforced Laminated composites are widely used in Aerospace and Civil Engineering Structures due to its higher strength to weight and stiffness to weight ratio. The present study is concerned with the analysis of plates made of continuous fibre reinforced laminated composite materials, using finite element method. Specifically the study concerns the behaviour of laminated plates including transverse shear deformations, and transverse normal stresses and strains. Two Displacement models with six and eleven degrees of freedom per node based on Higher Order Shear Deformation Theory (HOSDT) are considered to derive finite element formulation. First displacement model considers transverse displacement, rotations and their higher order terms. While second displacement model is based on inplane and transverse displacements, rotations and their higher order terms. Stiffness matrix, load vector and mass matrix of eight - node Quadrilateral isoparametric finite element are derived considering two displacement models. The objective is to study the performance of above derived finite elements in static and dynamic analysis of laminated composite plate. Finite element analysis is carried out to evaluate displacements and stresses under static load with varying width-to-thickness ratio, material anisotropy, and number of layers of the fibers with different angle of orientation and support conditions. Further free vibration analysis is carried out using finite element method to obtain natural frequencies and corresponding mode shapes. Results for plate deformations, internal stresses and natural frequencies for several examples are compared with the results available in literatures for evaluating accuracy of displacement models. Computer programs are developed for automatic meshing of laminated composite plate, for static analysis to obtain deflection and interlaminar stresses under uniform and sinusoidal loading, for dynamic analysis to obtain natural frequencies and mode shapes. The programs are capable to handle any number of elements, geometry, support conditions and loading. Further to explore the concept of intelligent structure and to enhance its application in the field of structural engineering, study on a composite laminate embedded with smart patches of piezoelectric material is presented. A displacement model with two mechanical degrees of freedom and one electrical degree of freedom (i.e. voltage) is considered. Finite element formulation is derived using 8-node isoparametric element based on considered displacement fields. Electromechanical coupling behaviour is studied from direct piezoelectric effect (Sensing action) and converse piezoelectric effect (actuation action). Analysis of piezoelectric laminated composite is illustrated through an example of bimorph beam constructed by two PVDF beam using developed computer program.