Analysis of a Laminated Composite Panel with Discrete Variable Stiffeners

Abstract

This research addresses a new analysis of the elastic field of laminated composite structures under the influence of discrete stiffeners at the bounding surfaces. In this work, theory of elasticity, a new potential function, constitutive relations for composite materials, special lamination theory and finite-difference computational algorithm are integrated to develop a new computational scheme for stress analysis of laminated composite structures. Specific contribution are follows: A new mathematical formulation is developed for the analysis of structural components of laminated composites with mixed and changeable boundary conditions. In this formulation, the displacement components of plane elasticity are expressed in terms of a single potential function, which satisfies one of the equilibrium equations automatically. The remaining equilibrium equation is transformed into a fourth order partial differential equation of the unknown potential function. Thus the mixed boundary value plane elasticity problem is reduced to the solution of a single fourth order partial differential equation. The finite difference technique is used to develop an efficient computational algorithm based on the potential function formulation. A general computer program is developed based on the finite difference computational algorithm, which is capable of dealing with almost all the special cases of composite material, namely orthotropic and anisotropic lamina, angle-ply and cross-ply symmetric laminates, symmetric balanced laminates, etc., with mixed and changeable physical conditions at the surfaces of the structural composites. The application of the computational scheme is investigated to stress analysis of disxxi NOMENCLATURE xxii cretely stiffened panels of laminated composites. A number of practical problems of interest are solved and results are presented in the form of graphs. The problem includes symmetric and antisymmetric discretely stiffened laminated cantilever under shear loading, a laminated panel with periodic axial stiffeners subjected to eccentric loading and a laminated cantilever panel with discrete variable stiffeners. Finally, in an attempt to validate the new computational method, the potential function solutions are compared with both analytical and numerical solutions obtained by standard computational method. For this purpose, finite element solutions are obtained using the commercial FEM software, SAP2000. For all the problems, both the numerical solutions are found to be in excellent agreement with each other, which in turn, establishes the suitability and appropriateness of the present potential function computational scheme.