Analysis of elastic field in structural elements of laminated composites by displacement potential approach

Abstract

Composite materials drew attention of researchers from all over the world due to their outstanding advantages over conventional materials. They are being increasingly used as structural elements in almost all engineering applications. To take full advantage and ensure reliable performance of these materials in an application, it is indispensable to analyze various aspects of these materials. However, these are anisotropic and microscopically non homogeneous materials due to the presence of two phases in them. This makes the analytical investigation quite complicated due to mathematical difficulties. Therefore, only numerical and experimental approaches are extensively used in the field of composites, especially in the case of mixed boundary conditions. A reliable analytical method of analysis of these materials under mixed boundary conditions still seems to be lacking. In this study, an analytical method is developed to analyze the elastic field in structural c1cmcnts of laminated composite materials under mixed boundary conditions. The two displacement components of the two-dimensional elasticity problem are expressed in terms of a single displacement potential function, which satisfies one of the equilibrium cquations automatically. The other equilibrium equation is transformed into a fourth ordcr partial differential equation of unknown displacement potential function. Thus, the two dimcnsional mixed boundary value elasticity problem is reduced to the solution of a single fourth order partial differential equation. The solution of the fourth order partial diffcrcntial cquation is obtained in the form of Fourier series. To demonstrate the method, it is applicd to a rectangular panel consisting of (i) cross-ply laminated composite and (ii) angle-ply laminated composite. Analytical solutions of different components of stress and displacement are presented in the form of graphs. Further, the effects of laminate thickness, fiber orientation, and panel aspect ratio on the components of stress and displacement have been discussed in details. The results conform to the intuitively cxpected characteristics of the structures which verify that the method developed in the study can be applied reliably to structural elements of laminated composites under mixed boundary conditions to analyze elastic field.