Analysis of a stress singularity in a non-linear Flamant problem for certain models of a material

✍ Scribed by V.M. Mal’kov; Yu.V. Mal’kova

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 274 KB
• Volume: 72
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/j.jappmathmech.2008.08.006

✦ Synopsis

A generalized plane problem in the non-linear theory of elasticity is considered for a half-plane loaded on the boundary with a concentrated external force (the non-linear Flamant problem). The properties of the material of the half-plane are described by different (known) models, and each model of the nonlinearly elastic material generates its own specific boundary-value problem. Analytical solutions of the problems are obtained for two models of an incompressible material: the neo-Hookean model and the Bartenev-Khazanovich model, and a model of a compressible semi-linear (harmonic) material. The dependence of the stress state as a whole on the adopted model of the material and the effect of the model of the material on the form of the stress singularity in the neighbourhood of a pole are investigated.