Further numerical techniques for planar elastostatic analysis by the boundary integral equation method
Doctoral Thesis
1984
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University of Cape Town
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Abstract
Prior experience of the Finite Element Method stimulated interest and led to research into the Boundary Integral Equation Method, specifically for the solution of planar elastostatic problems. A complete expose of the mathematical theory of the Boundary Integral Equation Method is given. The basis of the method is traced and the similarities and differences as opposed to the Finite Element Method, are highlighted. The numerical implementation of the method, using constant, linear and quadratic interpolation functions over the boundary segments is developed and then inclusion in computer programs is discussed. Attention is given to the problem of numerical integration over a singularity, for which detailed expressions are given. The verification and applicability of the technique is thoroughly investigated in five fully documented examples. Solutions to the problem of traction discontinuities at a corner are proposed and an analysis of the inclusion of body forces, together with documented examples, are described. Also investigated is the nonsymmetric form of the resulting matrices. It is proven that no direct and practical way can be found to render these matrices symmetric. By investigating the error in the numerical integration process, the suitability of segments is also discussed. Emphasis is placed on the solution of non-homogeneous domains and domains which extend to infinity. The development of the necessary numerical techniques required in both cases is discussed and fully documented. Finally, a method of automatically improving the accuracy of the solution of the Boundary Integral Equation Method by using p and h convergence adaptive processes is also presented.
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Includes bibliography.
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Howell, G. 1984. Further numerical techniques for planar elastostatic analysis by the boundary integral equation method. University of Cape Town.