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 equations. The Navier solution are applied to solve the governing equations of plate satisfying the simply supported boundary conditions. The results for non-dimensional deflections, and stresses of composite laminates under the effect of sinusoidal and uniform distributed load are thus obtained. The uni-axial and bi-axial loads are incorporated to evaluate critical buckling loads. The validity of present formulation is demonstrated by comparing our results with some of the available results in literature. Also some new results are generated for future references and applications in structural analysis. The functionally graded materials (FGM) are advanced composite materials which are significantly used for fabrication and have improved the performance of structural components vii due to their unique combination of properties. During the manufacturing process, porosities may exist within the material, and hence it is necessary to assess the porosity effect while modeling the FGM. Thus, the effect of porosity distribution on static and buckling response of a functionally graded (FG) porous plate with all its edges simply supported is investigated. The plate’s displacement field is approximated based on an inverse hyperbolic shear deformation theory (IHSDT) involving five variables. The material properties of porous FG plate are assumed with an additional term of porosity and power-law is adopted for smooth variation in the direction of thickness. In this study, five types of porosity distribution functions are considered. The analytical solutions for non-dimensional deflections and critical buckling loads of FG plate are thus obtained. To validate the accuracy of present findings, the results are compared with available results in the literature, and good agreement is achieved. Moreover, the novel results are presented to study the influence of various parameters such as porosity parameter, the power-law exponent, side-thickness ratio etc. on the dimensionless deflections, stresses, and critical buckling loads. The contribution of this study is seen in its utilisation across diverse industries. The Navier’s technique provides analytical solutions and is applicable for analysis of plates with simply supported edges. Most of the problems with general boundary conditions are solved via numerical technique. The numerical solutions have gained popularity in last few decades due to its applicability in complex geometries problems. This study aims to investigate the static deformation characteristics and stress analysis of laminated and functionally graded porous plates for various combination of boundary conditions in the framework of finite element method. The variation of properties in FG material is supposed to be along the thickness direction according to the power-law (P-FGM) and sigmoid-law (S-FGM). A novel secant hyperbolic higher order shear deformation theory is utilized to approximate the displacement field of FG plate containing five unknown variables. Furthermore, three different kinds of porosity distributions are assumed in terms of thickness parameter to model the porous plate. A suitable C0 continuous isoparametric eight noded FE with 7 degrees of freedom (DOF) per node combined with biquadratic serendipity shape functions is employed to examine the desired mechanical responses of FG plates. The numerical assessments of bending deflections and buckling loads for laminated and funcionally graded(P-FGM and S-FGM) porous plate are presented. Moreover, the influences of parameters like span-thickness ratio, boundary conditions, material exponent, etc. on the dimensionless deflection, and buckling load are discussed in detail. To demonstrate the accuracy of proposed theory, the comparison study is made between present and previously published results in literature and well agreement is achieved. Additionally, several numerical illustrations with new generated results are provided to serve as benchmarks for further study of porous FG plates.