The scaled flexibility matrix method for the efficient solution of boundary value problems in 2D and 3D layered elastic media
✍ Scribed by Anthony P. Peirce; Eduard Siebrits
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 300 KB
- Volume
- 190
- Category
- Article
- ISSN
- 0045-7825
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✦ Synopsis
We present a method that extends the ¯exibility matrix method for multilayer elasticity problems to include problems with very thin layers. This method is particularly important for solving problems in which one or a number of very thin layers are juxtaposed with very thick layers. The standard ¯exibility matrix method suers from round-o errors and poor scaling of the ¯exibility equations which occur when one of the layers in the multilayered medium becomes much smaller than the others. The method proposed in this paper makes use of power series expansions of the various components of the ¯exibility matrix in order to arrive at a system of equations that is appropriately scaled. The eectiveness of the scaled ¯exibility matrix method is demonstrated on a number of test problems.