Mathematical Modeling for Mechanical Analysis of Composite Structures

Abstract

The usage of composite materials in the structural analysis have increased extensively in recant decades across various engineering applications. The functionally graded materials (FGM) are advanced composite materials which are significantly used for fabrication and have improved the performance of structural components due to their unique combination of properties. The advancements in material technologies in last few years have played a crucial role in the development of modeling and analysis techniques of composite structures. Therefore, it is essential to mathematically model these structures. The mathematical modeling consists of converting any physical phenomenon into mathematical problem. Composite plates are the most significant structural elements that have been studied by many researchers in the past. The analysis of composite plates have been carried out in terms of three mechanical responses: static, buckling and free vibration. Different solution methodologies have been adopted to derive the governing mathematical system and predict the accurate mechanical response of composites plates. In this light, the current work focuses on different modeling and solution techniques to study the structural behavior of composite structures. The thesis aims to propose a new higher order hyperbolic shear deformation theory for mechanical analysis of cross-ply and angle-ply multi-layered plates. Analytical solutions to the static and buckling responses of symmetric and anti-symmetric laminates are presented. The theory incorporate secant hyperbolic function in terms of thickness variable in the displacement field. Also the developed theory assumes non-linear distribution of displacements and ensures that the top and lower surfaces of the plates have zero transverse shear stresses. The equilibrium equations are derived by implementing the principle of virtual work (PVW). The consideration of stiffness characteristics is essential in the analysis of cross-ply and angle-ply laminates when solving the governing