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Thesis (M.S.)--Ohio University, March, 1992. / Title from PDF t.p.

Thesis (Ph.D.)--University of Delaware, 2008. / Principal faculty advisor: John A. Pelesko, Dept. of Mathematical Sciences. Includes bibliographical references.

Thesis (M. S.)--Mechanical Engineering, Georgia Institute of Technology, 2007. / Jeffrey Streator, Committee Member ; Richard Neu, Committee Member ; Itzhak Green, Committee Chair.

Thesis (Ph.D.)--University of Delaware, 2007. / Principal faculty advisor: Robert Gilbert, Dept. of Mathematical Sciences. Includes bibliographical references.

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The boundary integral technique was implemented in a computer code for the general static analysis of three dimensional elastic solids. The was based on a formulation of the problem in which the governing boundary equation is developed from the known solution to Kelvin's problem, by the application of Betti's reciprocal relationship. Modeling the boundary of the region being analyzed with plane elements and assuming the tractions and displacements constant across these elements leads to a set of simultaneous algebraic equations approximating the boundary integral equation. Numerical techniques are used in the computer code to assemble and solve this set of equations. The operation of this code was demonstrated by the solution of several example problems. The results of these problems show the code to be successful. It's practical application however is limited due to the large solution time required. This time would be significantly reduced if a more efficient equation solver were employed. The time requirement could be a severe limitation when a relatively large number of elements is needed to model displacement gradients. The development of an element based on linear or higher order variation of displacements would greatly reduce the required mesh size in this case and thus the solution time.

The purpose of this thesis has been achieved. Vector notation has been used in developing the equations necessary for the analysis of three dimensional elastic rings. An elastic centroid for the elastic ring has been located with a tabular procedure for exacting the solution to the problem. For a comparison of the solutions between the method based on three elastic centroids with the method based on one elastic centroid, one need refer to Figures 7 and 10. Comparing the two methods, it is the author's opinion that the method herein presented is superior if for no other reason than simplicity. The development of the six equations can be readily followed and the tabular form of Figure 7 presented as an orderly means for obtaining the coefficients of the six unknowns. Figure 10 presents a method involving a similar tabular form as in Figure 7 along with the additional calculations that must be made before the correction moments and shears can be obtained. The necessity of these additional terms serves to obscure the physical significance of the final equations. / Master of Science

published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy