Abstract:
Bilayer composites, such as metal-metal, steel-polymer, concrete-steel etc., having
different mechanical properties layer by layer are widely used for modern structures
This thesis deals with the stress analysis of two dimensional bilayer composite
materials. Materials under consideration are assumed to be perfectly bonded
together. Finite difference method is used for the solution of two dimensional elastic
problems. A numerical model for rectangular geometry based on displacement
potential function has been developed to investigate the problem. In each layer of the
composite the mechanical properties are isotropic.
Finite difference scheme has been developed for the management of boundary
conditions so that all possible mixed boundary conditions can be applied in any
boundary points as well as at the interface of isotropic layers. Special numerical
formulations yield to new formula structures are employed at the interface as well as
adjacent boundary points of the interface. An effective programming code has been
developed in FORTRAN language to solve the problems of bilayer composites.In
order to compare the results by the present finite difference method, another
numerical technique namely finite element method is used. Validation of the results
is performed by using commercially available FEM package software. It is observed
that the results agree well within the acceptable limit, which also confirms to the
reliability of the finite difference method.
At the interface, there is a single value for each displacement component but two
different values for each stress component of the bilayer composite having different
mechanical properties in each layer. Like as usual critical zone of a bilayer
composite under mechanical loading, the interfacial zone is also a zone of critical
stresses. Changing in Poisson’s ratio in any layer has significant effects on the results
of all layers of the bilayer composite. Due to the mathematical expressions of
stresses and displacements for two dimensional elastic problems, the study of the
effects of Poisson’s ratio is intricate rather the study of the effects of Modulus of
elasticity is straightforward. In general, the material having higher modulus of
elasticity experiences higher stresses.
