Abstract:
This thesis deals with an efficient analytical scheme for the analysis of stress and displacement fields of boundary-value problems of plane elasticity with mixed boundary conditions and material discontinuity. More specifically, the mechanical behavior of a stiffened panel with an edge crack is analyzed under the influence of flexural and axial loadings, using a new analytical scheme. Earlier mathematical models of elasticity were very deficient in handling the practical stress problems of solid mechanics. Analytical methods of solution have not gained that much popularity in the field of stress analysis, mainly because of the inability of dealing with mixed boundary conditions, irregular boundary shapes, and material discontinuity. In this approach, the displacement components of plane elasticity are replaced by a single potential function and the two-dimensional elasticity problem is reduced to the solution of the potential function from a single partial differential equation of equilibrium, in which all the parameters of interest, namely stress, strain and displacements are expressed in terms of the same potential function. The solution of the differential equation is obtained in the form of infinite series, the coefficients of which are determined by satisfying the boundary conditions appropriately. The application of the method is then demonstrated through the analysis of the elastic field of a stiffened panel with an edge crack subjected to axial and flexural loadings. Some of the relevant issues of practical interest are also discussed in relation to the cracked stiffened panel. The analytical scheme is then extended to the case of composite materials, in which the effect of fiber orientation on the elastic filed of the cracked stiffened panel is investigated in details. It would be worth mentioning here that the analytical solutions of the present cracked stiffened panels even with isotropic materials are beyond the scope of the standard methods of the literature.
In an attempt to verify the reliability and accuracy of the analytical scheme developed, the present potential function solutions are compared with the
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corresponding solution obtained by two standard computational methods. The three solutions are found to be in excellent agreement with each other for all the cases of stiffeners and loadings considered, which eventually establishes the soundness and appropriateness of the analytical scheme developed.
