Weak solvability of antiplane frictional contact problems for elastic cylinders

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• 作者：Stanisł ; aw Migó ; rski ; Anna Ochal ; Mircea Sofonea
• 关键词：Antiplane problem ; Elastic material ; Frictional contact process ; Hemivariational inequality ; Clarke subdifferential ; Weak solution
• 刊名：Nonlinear Analysis: Real World Applications
• 出版年：2010
• 出版时间：February 2010
• 年：2010
• 卷：11
• 期：1
• 页码：172-183
• 全文大小：786 K

文摘

We study a mathematical model which describes the antiplane shear deformations of a cylinder in frictional contact with a rigid foundation. The process is static, the material behavior is described with a linearly elastic constitutive law and friction is modeled with a general slip dependent subdifferential boundary condition. We derive a variational formulation of the model which is in a form of a hemivariational inequality for the displacement field. Then we prove the existence of a weak solution to the model and, under additional assumptions, its uniqueness. The proofs are based on abstract results for operator inclusions in Banach spaces. Finally, we present concrete examples of friction laws for which our results are valid.