Asymptotic analysis of thin elastic junction between two elastic bodies

Abstract

In this paper, an equilibrium problem for two elastic bodies connected by a thin junction (bridge) is analyzed. An existence of solutions is proved. Passages to limits are justified with respect to the rigidity parameter of the junction. In particular, the rigidity parameter tends to infinity and to zero. Limit models are investigated.

Keywords:

• Thin junction
• elastic body
• crack
• non-penetration boundary condition
• variational inequality

AMS subject classifications:

• 35B30
• 35J88

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation.