A contribution to contact problems for a class of solids and structures. (English) Zbl 0597.73114
The paper is divided into two parts. In the first part the authors derive an implicit variational inequality, being the weak (variational) formulation of the boundary value problem for a linear elastic body in a frictional contact with a rigid support on a part of the boundary. Applying a general duality theory to Signorini’s problem with friction, they obtain the quasi-variational inequality defined on the surface of a possible contact only and expressed in terms of stresses.
The second part of the paper concerns the dual formulation of the obstacle problem for a von Kármán plate. In an earlier paper the authors have formulated the dual obstacle problem in terms of static and kinematic fields [see ibid. 37, 135-141 (1985; Zbl 0578.73051)]. In the paper under review they propose a novel approach to the same dual obstacle problem in which a kinematic field is not explicitly present.
The second part of the paper concerns the dual formulation of the obstacle problem for a von Kármán plate. In an earlier paper the authors have formulated the dual obstacle problem in terms of static and kinematic fields [see ibid. 37, 135-141 (1985; Zbl 0578.73051)]. In the paper under review they propose a novel approach to the same dual obstacle problem in which a kinematic field is not explicitly present.
Reviewer: K.S.Parihar
MSC:
74A55 | Theories of friction (tribology) |
74M15 | Contact in solid mechanics |
49J40 | Variational inequalities |
74K20 | Plates |
74S30 | Other numerical methods in solid mechanics (MSC2010) |
35A15 | Variational methods applied to PDEs |