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On the contact reaction in a solid circular plate simply supported along an edge arc and deflected by a central transverse concentrated force
Author(s) -
Monegato G.,
Strozzi A.
Publication year - 2005
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200310198
Subject(s) - arc (geometry) , transverse plane , enhanced data rates for gsm evolution , geometry , materials science , geology , mechanics , physics , engineering , structural engineering , mathematics , telecommunications
Abstract A static, purely flexural mechanical analysis is presented for a Kirchhoff solid circular plate, deflected by a transverse central force, and bilaterally supported along a single periphery arc, the remaining part of the boundary being free. The contact reaction is assumed to be formed by a distributed reaction force accompanied by a distributed moment with radial axis. This plate problem is formulated in terms of an integral equation of the Prandtl type, supplemented by a vertical and a rotational equilibrium condition. It is shown that the Prandtl equation coupled to the equilibrium condition possesses a unique solution in a proper scale of weighted Sobolev‐type spaces, with certain smoothness properties, and that no solution exists if the distributed moment is absent. Finally, the behaviour of the solution at the endpoints of the support is clarified.