Strees analysis of composite laminae having holes of various shapes using finite difference techniques

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.