The number of independent compatibility equations in the mechanics of deformable solids

✍ Scribed by D.V. Georgiyevskii; B.Ye. Pobedrya

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 341 KB
• Volume: 68
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/j.jappmathmech.2004.11.015

✦ Synopsis

The number of independent compatibility equations in terms of stresses, involved in formulating the basic problem in the mechanics of deformable solids in terms of stresses in Nn, is the same as the number of Saint-Venant compatibility equations in R ~ and the number of independent components of the KrOner and Riemann-Christoffel tensors. The existence of the Bianchi identities does not reduce this number. Counterexamples are given to show that the number of Beltrami-Mitchell equations cannot be reduced from six to three in the classical and new formulations of the problem in terms of stresses for a three-dimensional body.