Bending of an incomplete annular plate and related problems

Closed-form solutions and stress-concentration data are obtained for the problem of a sector of an annular plate subjected to moments and transverse forces on its radial edges. Closed-form solutions are also given for a semi-infinite plate or a circular plate subjected to a system of concentrated forces and/or moments at the edge.

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Axisymmetric Large Deflection Elastic Analysis of Hollow Annular Membranes under Transverse Uniform Loading

Symmetry ◽

10.3390/sym13101770 ◽

2021 ◽

Vol 13 (10) ◽

pp. 1770

Author(s):

Jun-Yi Sun ◽

Qi Zhang ◽

Xue Li ◽

Xiao-Ting He

Keyword(s):

Closed Form ◽

Circular Plate ◽

Large Deflection ◽

Closed Form Solution ◽

Circular Ring ◽

Form Solution ◽

Elastic Response ◽

Geometrically Nonlinear ◽

Closed Form Solutions ◽

Annular Membrane

The anticipated use of a hollow linearly elastic annular membrane for designing elastic shells has provided an impetus for this paper to investigate the large deflection geometrically nonlinear phenomena of such a hollow linearly elastic annular membrane under transverse uniform loads. The so-called hollow annular membranes differ from the traditional annular membranes available in the literature only in that the former has the inner edge attached to a movable but weightless rigid concentric circular ring while the latter has the inner edge attached to a movable but weightless rigid concentric circular plate. The hollow annular membranes remove the transverse uniform loads distributed on “circular plate” due to the use of “circular ring” and result in a reduction in elastic response. In this paper, the large deflection geometrically nonlinear problem of an initially flat, peripherally fixed, linearly elastic, transversely uniformly loaded hollow annular membrane is formulated, the problem formulated is solved by using power series method, and its closed-form solution is presented for the first time. The convergence and effectiveness of the closed-form solution presented are investigated numerically. A comparison between closed-form solutions for hollow and traditional annular membranes under the same conditions is conducted, to reveal the difference in elastic response, as well as the influence of different closed-form solutions on the anticipated use for designing elastic shells.

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Stress concentration during pellet cladding interaction: Comparison of closed-form solutions with 2D(r,θ) finite element simulations

Nuclear Engineering and Design ◽

10.1016/j.nucengdes.2013.03.019 ◽

2013 ◽

Vol 260 ◽

pp. 175-187 ◽

Cited By ~ 6

Author(s):

Jérôme Sercombe ◽

Renaud Masson ◽

Thomas Helfer

Keyword(s):

Finite Element ◽

Stress Concentration ◽

Closed Form ◽

Finite Element Simulations ◽

Closed Form Solutions

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General Solutions of Anisotropic Laminated Plates

Journal of Applied Mechanics ◽

10.1115/1.1576804 ◽

2003 ◽

Vol 70 (4) ◽

pp. 496-504 ◽

Cited By ~ 16

Author(s):

W.-L. Yin

Keyword(s):

General Solution ◽

Closed Form ◽

Analytic Functions ◽

Infinite Plate ◽

Elliptical Hole ◽

Complex Variables ◽

Laminated Plates ◽

Eigenvalues And Eigenvectors ◽

Closed Form Solutions ◽

Repeated Eigenvalues

Anisotropic laminates with bending-stretching coupling possess eigensolutions that are analytic functions of the complex variables x+μky, where the eigenvalues μk and the corresponding eigenvectors are determined in the present analysis, along with the higher-order eigenvectors associated with repeated eigenvalues of degenerate laminates. The analysis and the resulting expressions are greatly simplified by using a mixed formulation involving a new set of elasticity matrices A*, B*, and D*. There are 11 distinct types of laminates, each with a different expression of the general solution. For an infinite plate with an elliptical hole subjected to uniform in-plane forces and moments at infinity, closed-form solutions are obtained for all types of anisotropic laminates in terms of the eigenvalues and eigenvectors.

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