Journal
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
Volume 38, Issue 32-33, Pages 5703-5726Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/S0020-7683(00)00361-9
Keywords
curved beam; uniform bending; multi-connected cross-section; compatibility equations; degenerate boundary conditions; exact 3D elastic solution
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The paper presents a coherent theory of the uniform bending problem in a circular curved beam, with multi-connected cross-section, having a large radius of curvature with respect to its width. The three-dimensional elastic problem is solved, in the case of linear homogeneous isotropic body, assuming the stress tenser as the unknown and by exactly satisfying the field compatibility equations. The mathematical structure of the governing boundary value problem (BVP), enlightened here for the first time, is unexpectedly complicated: a fourth-order elliptic (variable coefficients) partial differential equation with two degenerate unstable boundary conditions (i.e. involving second and third order partial derivatives in a direction that becomes tangent at several points of the boundary). Such a kind of BVP seems to be typical of the curved beam bending problem since it also appears in the displacement approach (Mentrasti, 2001. part II, Int. J. Solids Struct. 38, 5727-5745). As a final point, it is reduced to a simpler problem by an ad hoc integral representation, assuming the p-convexity of the cross-section domain. (C) 2001 Elsevier Science Ltd. All rights reserved.
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