Article
Overview about Solution Representations for Elasticity Problems and Some Selected Particular Solutions
Mathematics and Mechanics of Solids
(2001)
Abstract
Solution representations for elasticity problems are presented in this overview article. The types of problems covered are (i) plane strain/stress for isotropic and anisotropic materials, (ii) plate bending for isotropic and anisotropic thin plates, (iii) three-dimensional plate analysis, and (iv) three-dimensional elasticity problems. The solution contributions are decomposed into homogeneous and particular solutions. All homogeneous solution representations involve arbitrary complex valued functions. Choosing different types of complex functions, it becomes possible to construct easily infinite sets of functions satisfying the governing differential equations. The solution representations are very useful for (i) solving problems analytically, (ii) analyzing a local solution behavior (as, for example, near comers, cracks, or holes), and (iii) for application in numerical methods.
Keywords
- Elasticity Problems,
- Elasticity Solutions,
- Complex Fimction Representations
Disciplines
Publication Date
April 1, 2001
DOI
10.1177/108128650100600205
Citation Information
Reinhard E. Piltner. "Overview about Solution Representations for Elasticity Problems and Some Selected Particular Solutions" Mathematics and Mechanics of Solids Vol. 6 Iss. 2 (2001) p. 193 - 220 ISSN: 1741-3028 Available at: http://works.bepress.com/reinhard_piltner/42/