 ElastostaticsPrem K. Kythe
Chapter 6 in Fundamental Solutions for Differential Operators and Applications, 1996, pp 138-161 from Springer Abstract: Abstract We shall discuss some basic concepts and results from the theory of linear elasticity, derive the fundamental solutions for the elastostatic operator in R 2 and R3, and present some applications. The theory of linear elastic continua is developed under the assumption that they undergo small strains. The linear theory of elasticity is based on the following two basic assumptions: (i) The material is subject to an infinitesimal strain and the stress is expressed as a linear function of strain, and (ii) any variation in the orientation of this material due to displacements is negligible. These assumptions lead to small strain and equilibrium equations under an undeformed geometry. The linearity assumption is an attempt to simplify the mathematical aspect of the behavior of solids. Although we assume that the material properties are linear, the deformations in a body may not be completely linear. For example, under certain loads, various materials exhibit plastic deformation while others creep with time, or they may crack in which case the stresses are redistributed. Date: 1996 There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-4106-5_7 Ordering information: This item can be ordered from DOI: 10.1007/978-1-4612-4106-5_7 Access Statistics for this chapter More chapters in Springer Books from Springer |
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