Abstract:
Composite materials are widely used in aerospace, automobile, sports equipment,
structural equipments and many other applications due to their superiorities like high
strength weight ratio over monolithic materials. In many composite structural
elements, holes of different shapes are made with a view to satisfying the design
requirements. The presence of holes in the composite elements will crcatc strcss
concentrations, which will rcduce the mechanical strength of thcm. Thercforc, it is of
grcat importance to investigate the state of stress around the holes for thc safety and
proper design of such elements. To meet the various practical design rcquirements,
further investigation is essential in this field, which is done by the help of numerical
techniques.
In this thesis finite difference method, one of the popular numerical techniques, is
used for the solution of two-dimensional elastic problems of unidircctional
composite lamina incorporating a hole located at the center of the lamina. To
consider the arbitrary boundary shapes and different boundary conditions an cfficient
boundary management technique is followed. An effective programming code has
been developed in FORTRAN language (Lahey FORTRAN 90) to solve the
problems by finite difference method based on displacement potential function
formulation. Using finite difference method, results are obtained for various
configurations of composite lamina including holes of differcnt shapes, i.e. circular
and square hole and they are compared.
In order to compare the results by the present finite difference method, another
numerical technique i.e. finite element method is used. One of the existing standard
commercial software (FEMLAB 3.0) is used for the finite element solution. Somc
results by finite difference method are compared with the available analytical results
also. It is observed that the results agree well within the acceptable limit, which also
confirms to the reliability of the present finite difference solution.
