On the integral equation formulations of some 2D contact problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:234

Article

Junghanns, P.²  Monegato, G.¹  Strozzi, A.³ 

[1] Politecn Torino, Dipartimento Matemat, I-10129 Turin, Italy

[2] TU Chemnitz, Fac Math, Chemnitz, Germany

[3] Univ Modena, Dipartimento Ingn Meccan & Civile, I-41100 Modena, Italy

关键词: Integral equation;    Contact problem;    Weakly singular kernel;    Solution behavior;   

DOI  :  10.1016/j.cam.2010.01.021

来源: Elsevier

【 摘 要 】

Two integral equations, representing the mechanical response of a 20 infinite plate supported along a line and subject to a transverse concentrated force, are examined. The kernels of the integral operators are of the type (x - y) In vertical bar x - y vertical bar and (x - y)(2) In vertical bar x - y vertical bar. In spite of the fact that these are only weakly singular, the two equations are studied in a more general framework, which allows us to consider also solutions having non-integrable endpoint singularities. The existence and uniqueness of solutions of the equations are discussed and their endpoint singularities detected. Since the two equations are of interest in their own right, some properties of the associated integral operators are examined in a scale of weighted Sobolev type spaces. Then, new results on the existence and uniqueness of integrable solutions of the equations that in some sense are complementary to those previously obtained are derived. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free