Abstract:
Due to increasing demands of composite materials in various applications, they have
received wide attention of the researchers for their analyses with a view to using
them safely, effectively, and efficiently. These materials are anisotropic and
non-homogeneous from the macroscopic point of view which makes the analysis
more difficult than that of isotropic homogeneous materials. Although experimental
or numerical procedures can be used for the purpose of analysis, theatrics methods arc
not always suitable. Experimental procedures arc usually costly and not practical for
regular general purpose use. Therefore, a simple analytical method is always sought
as an alternative. Besides, irrespective .of the accuracy of any numerical solution,
analytical solution is always desirable.
In this study, an analytical method is developed for the analysis of elastic field in
structures of orthotropic composite materials under mixed mode of boundary
conditions. Replacing the two displacement components by a single displacement
potential function, the two dimensional elasticity problems are reduced to the
solution of a single fourth order partial differential equation of a single unknown
function. Also, all the boundary conditions are expressed in terms of the
displacement potential function. The solution of the differential equation is obtained
in the form of an infinite series, the coefficients of which are determined satisfying
, the boundary conditions. The method is demonstrated by solving some practical
problems of composite panels, columns, and beams under mixed boundary
conditions. Further, a finite difference scheme based on the displacement potential
function is formulated to cover wider category of boundary value problems which
cannot be conveniently dealt with by the analytical method. In addition to the
problems solved by the analytical method, some additional problems are also solved
by the finite difference scheme.
To verify the validity of the analytical method, a commercial code, ANSYS. is used
to solve the same problems using rectangular plane e1cmcnts. The analytical results
are compared with those obtained by the finite difference method and finite element
method. It is noted that the results agree well within the acceptable limit. This
establishes the soundness and reliability of the analytical method.
