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.
