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Validity of Almansi theorems for anisotropic boundary elements
Abstract In the generalized formulation and application of the boundary element method it is crucial to investigate the well-posedness characteristics when both arbitrary traction as well as displacement distributions on a boundary subset are simultaneously prescribed. For an isotropic linearly elastic solid Almansi demonstrated that the existence of a solution could not always be guaranteed. However, a proper boundary element model can be constructed to solve for a self-consistent dataset since Almansi proved that only a unique solution could exist therein. The validity of those theorems for generally anisotropic linearly elastic solids is established in this paper. These results also furnish the basis of applicability of all other spatially discretized procedures, such as finite difference, finite element, etc. besides the boundary element method, where an analogous transfer matrix technique is implemented for elliptic problems.
Validity of Almansi theorems for anisotropic boundary elements
Abstract In the generalized formulation and application of the boundary element method it is crucial to investigate the well-posedness characteristics when both arbitrary traction as well as displacement distributions on a boundary subset are simultaneously prescribed. For an isotropic linearly elastic solid Almansi demonstrated that the existence of a solution could not always be guaranteed. However, a proper boundary element model can be constructed to solve for a self-consistent dataset since Almansi proved that only a unique solution could exist therein. The validity of those theorems for generally anisotropic linearly elastic solids is established in this paper. These results also furnish the basis of applicability of all other spatially discretized procedures, such as finite difference, finite element, etc. besides the boundary element method, where an analogous transfer matrix technique is implemented for elliptic problems.
Validity of Almansi theorems for anisotropic boundary elements
Dasgupta, Gautam (author)
Engineering Analysis ; 5 ; 89-94
1988-01-01
6 pages
Article (Journal)
Electronic Resource
English
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