Variational approach to modeling soft and stiff interfaces in the Kirchhoff-Love theory of plates. (1st October 2020)

• Record Type: Journal Article
• Authors: Furtsev, Alexey; Rudoy, Evgeny
• Is Part Of: International journal of solids and structures. Volume 202(2020)
• Page Start: 562
• Page End: 574
• Publication Date: 2020-10-01
• Subjects: Bonded structure -- Kirchhoff-Love plate -- Composite material -- Interface conditions -- Biharmonic equation -- Asymptotic analysis; Mechanics, Applied -- Periodicals; Structural analysis (Engineering) -- Periodicals; Elastic solids -- Periodicals; Mécanique appliquée -- Périodiques; Constructions, Théorie des -- Périodiques; Solides élastiques -- Périodiques; Elastic solids; Mechanics, Applied; Structural analysis (Engineering); Periodicals; 624.18
• DOI: 10.1016/j.ijsolstr.2020.06.044
• Languages: English
• ISSNs: 0020-7683

Abstract

Abstract: Within the framework of the Kirchhoff-Love theory, a thin homogeneous layer (called adhesive) of small width between two plates (called adherents) is considered. It is assumed that elastic properties of the adhesive layer depend on its width which is a small parameter of the problem. Our goal is to perform an asymptotic analysis as the parameter goes to zero. It is shown that depending on the softness or stiffness of the adhesive, there are seven distinct types of interface conditions. In all cases, we establish weak convergence of the solutions of the initial problem to the solutions of limiting ones in appropriate Sobolev spaces. The asymptotic analysis is based on variational properties of solutions of corresponding equilibrium problems.