The general equations of the theory of elasticity are reduced to an inhomogeneous fourth-order equation assuming that there is a linear dependence of the third component of the displacement vector on the third coordinate and that a mass force potential exists. The solution of this equation is presen
Application of functions of a complex variable to certain three-dimensional problems of elasticity theory
โ Scribed by G.Z Sharafutdinov
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 551 KB
- Volume
- 64
- Category
- Article
- ISSN
- 0021-8928
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โฆ Synopsis
Methods of the theory of functions of a complex variable are applied to problems of the deformation of thin plates of constant or variable thickness considered in three dimensions. To that end, a third complex potential is added to the two complex Kolosov-Muskhelishvili potentials. The components of the displacement vector and the stress tensor are represented in terms of these three complex potentials. The formulations if the problems, characteristic for cases in which complex variables are used in problems of elasticily theory, are investigated.
๐ SIMILAR VOLUMES
A version of boundary integral equations of the first kind in dynamic problems of the theory of elasticity is proposed, based on an investigation of the analytic properties of the Fourier transformant of the displacement vector, rather than on fundamental solutions. A system of three boundary integr