Yield Point Load of an Annular Plate

1959 ◽  
Vol 26 (3) ◽  
pp. 454-455
Author(s):  
Philip G. Hodge
Keyword(s):  
Yield Point ◽  
Annular Plate ◽  
Point Load ◽  
Uniform Load ◽  
Simply Supported

Abstract The yield point load is computed for an annular plate, simply supported at its inner and outer edges and subjected to a uniform load. A previously published solution is shown to be incorrect.

scholarly journals Green's function of the clamped punctured disk

1977 ◽  
Vol 20 (2) ◽  
pp. 175-181 ◽  
Author(s):  
Mitsuru Nakai ◽  
Leo Sario
Keyword(s):  
Green’S Function ◽  
Circular Plate ◽  
Green's Function ◽  
American Mathematical Society ◽  
Point Load ◽  
Thin Elastic Plate ◽  
Constant Sign ◽  
Boundary Circle ◽  
Simply Supported ◽  
Image Position

If a thin elastic circular plate B: ∣z∣ < 1 is clamped (simply supported, respectively) along its edge ∣z∣ = 1, its deflection at z ∈ B under a point load at ζ ∈ B, measured positively in the direction of the gravitational pull, is the biharmonic Green's function β(z, ζ) of the clamped plate (γ(z, ζ) of the simply supported plate, respectively). We ask: how do β(z, ζ) and γ(z, ζ) compare with the corresponding deflections β0(z, ζ) and γ0(z, ζ) of the punctured circular plate B0: 0 < ∣ z ∣ < 1 that is “clamped” or “simply supported”, respectively, also at the origin? We shall show that γ(z, ζ) is not affected by the puncturing, that is, γ(·, ζ) = γ0(·, ζ), whereas β(·, ζ) is:on B0 × B0. Moreover, while β((·, ζ) is of constant sign, β0(·, ζ) is not. This gives a simple counterexmple to the conjecture of Hadamard [6] that the deflection of a clampled thin elastic plate be always of constant sign:The biharmonic Gree's function of a clampled concentric circular annulus is not of constant sign if the radius of the inner boundary circle is sufficiently small.Earlier counterexamples to Hadamard's conjecture were given by Duffin [2], Garabedian [4], Loewner [7], and Szegö [9]. Interest in the problem was recently revived by the invited address of Duffin [3] before the Annual Meeting of the American Mathematical Society in 1974. The drawback of the counterexample we will present is that, whereas the classical examples are all simply connected, ours is not. In the simplicity of the proof, however, there is no comparison.

The Axisymmetrical Steady-State Response of Internally Damped Annular Double-Plate Systems

1982 ◽  
Vol 49 (2) ◽  
pp. 417-424
Author(s):  
T. Irie ◽  
G. Yamada ◽  
Y. Muramoto
Keyword(s):  
Steady State ◽  
Transfer Matrix ◽  
Annular Plate ◽  
Steady State Response ◽  
Transfer Matrices ◽  
Simply Supported ◽  
State Response ◽  
Double Plate System ◽  
Force Transmissibility ◽  
Concentric Circles

The axisymmetrical steady-state response of an internally damped, annular double-plate system interconnected by several springs uniformly distributed along concentric circles to a sinusoidally varying force is determined by the transfer matrix technique. Once the transfer matrix of an annular plate has been determined analytically, the response of the system is obtained by the product of the transfer matrices of each plate and the point matrices at each connecting circle. By the application of the method, the driving-point impedance, transfer impedance, and force transmissibility are calculated numerically for a free-clamped system and a simply supported system.

scholarly journals Peridynamic Higher-Order Beam Formulation

2020 ◽  
Author(s):  
Zhenghao Yang ◽  
Erkan Oterkus ◽  
Selda Oterkus
Keyword(s):  
Finite Element Method ◽  
Cantilever Beam ◽  
Higher Order ◽  
Point Load ◽  
Transverse Displacement ◽  
Lagrange Equations ◽  
Concentrated Load ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Good Agreement

Abstract In this study, a novel higher-order peridynamic beam formulation is presented. The formulation is obtained by using Euler-Lagrange equations and Taylor’s expansion. To demonstrate the capability of the presented approach, several different beam configurations are considered including simply supported beam subjected to distributed loading, simply supported beam with concentrated load, clamped-clamped beam subjected to distributed loading, cantilever beam subjected to a point load at its free end and cantilever beam subjected to a moment at its free end. Transverse displacement results along the beam obtained from peridynamics and finite element method are compared with each other and very good agreement is obtained between the two approaches.

Experiments on the Buckling of Simply-Supported Rectangular Plates

1969 ◽  
Vol 73 (703) ◽  
pp. 607-608 ◽  
Author(s):  
A. C. Mills
Keyword(s):  
Experimental Investigation ◽  
Theoretical Analysis ◽  
Boundary Conditions ◽  
Buckling Load ◽  
Theoretical Solution ◽  
Rectangular Plates ◽  
Uniform Load ◽  
Simply Supported

In ref. (1) Pope presents a theoretical analysis of the buckling of rectangular plates tapered in thickness under uniform load in the direction of taper. An experimental investigation into the end load buckling problem for a plate having simply-supported edges with the sides prevented from moving normally in the plane of the plate is described in ref. (2). For these boundary conditions the theoretical solution is exact. However, the compatability equation is not satisfied exactly when the sides are free to move in the plane of the plate. This experimental investigation demonstrates that the buckling load is nevertheless adequately predicted by the analysis in these circumstances.

Limit Analysis and Yield-Line Theory

1968 ◽  
Vol 35 (2) ◽  
pp. 357-362 ◽  
Author(s):  
Antoni Sawczuk ◽  
P. G. Hodge
Keyword(s):  
Limit Analysis ◽  
Single Point ◽  
Point Load ◽  
Simply Supported ◽  
Yield Line ◽  
Yield Line Theory ◽  
Line Theory ◽  
The Relationship ◽  
Line Analysis ◽  
General Method

The relationship between limit analysis and yield-line analysis is investigated. Attention is restricted to simply supported, isotropic slabs subjected to single-point loadings. It is found that conventional yield-line analyses quite often give substantial overestimates of the carrying capacity. A general method is formulated for finding the yield-point load, and various examples are considered.

The yield point load of a conical shell

1969 ◽  
Vol 11 (1) ◽  
pp. 129-143 ◽  
Author(s):  
Richard H. Lance ◽  
Chen-hsiung Lee
Keyword(s):  
Yield Point ◽  
Conical Shell ◽  
Point Load

Bending of Simply-Supported Elliptic Plates: B.P.M. Solutions With Second-Order Derivative Boundary Conditions

1989 ◽  
Vol 56 (2) ◽  
pp. 356-363 ◽  
Author(s):  
R. Parnes
Keyword(s):  
Boundary Conditions ◽  
Perturbation Method ◽  
Higher Order ◽  
Point Load ◽  
Second Order ◽  
Boundary Perturbation ◽  
Simply Supported ◽  
Elliptic Plate ◽  
Elliptic Domain ◽  
Boundary Perturbation Method

A higher-order boundary perturbation method (B.P.M.) is formulated to treat a class of problems defined in an elliptic domain with associated boundary conditions expressed in terms of second-order derivatives. The method is applied to study a simply-supported elliptic plate subjected to a central lateral point load. The accuracy is investigated and the B.P.M. solution is found to yield highly accurate results for moderately elliptic domains.

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