IMPULSIVE LOADING OF A SIMPLY SUPPORTED CIRCULAR PLATE

1967 ◽  
Author(s):  
Norman Jones
Keyword(s):  
Circular Plate ◽  
Impulsive Loading ◽  
Simply Supported

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.

Flexure of a Circular Plate With a Ring of Holes

1962 ◽  
Vol 29 (3) ◽  
pp. 489-496 ◽  
Author(s):  
H. Kraus
Keyword(s):  
Circular Plate ◽  
Shear Force ◽  
General Boundary Condition ◽  
Uniform Pressure ◽  
Simply Supported ◽  
Moment Distribution ◽  
Theory Of Plates ◽  
Circular Holes ◽  
The Moment ◽  
Kirchhoff Theory

The problem of the moment distribution resulting from a uniform pressure load acting over the surface of a circular plate containing a ring of equally spaced circular holes with, and without, a central circular hole is solved within the framework of the Poisson-Kirchhoff theory of plates. A general boundary condition is applied at the outer rim of the plate to make the solution valid for a range of conditions from the simply supported case to the clamped case. The edges of the perforations are allowed to be either free or to have a net shear force acting. Numerical results in the form of curves are given for typical cases, and the results of a photoelastic test are also presented.

Optimum Support Position for Flat Plate Subjected to Pressure

1961 ◽  
Vol 65 (612) ◽  
pp. 832-834 ◽  
Author(s):  
R. Kitching
Keyword(s):  
Flat Plate ◽  
Circular Plate ◽  
Normal Pressure ◽  
Constant Thickness ◽  
Bending Stress ◽  
Plate Material ◽  
Concentric Ring ◽  
Simply Supported ◽  
Ring Radius ◽  
Supporting Ring

When a circular plate of constant thickness is simply supported on a concentric ring and is subjected to a uniform normal pressure, there is a radius for the supporting ring giving optimum bending stress conditions in the plate. Assuming the plate deflections are small, it is concluded that the required supporting ring radius varies between 70·1 and 73·0 per cent of the outside radius of the plate, depending on the value of Poisson's Ratio for the plate material.

Impulsive Loading of a Simply Supported Circular Rigid Plastic Plate

1968 ◽  
Vol 35 (1) ◽  
pp. 59-65 ◽  
Author(s):  
Norman Jones
Keyword(s):  
Yield Condition ◽  
Impulsive Loading ◽  
Bending Moments ◽  
Circular Plates ◽  
Governing Equations ◽  
Rigid Plastic ◽  
Static Loads ◽  
Simply Supported ◽  
Experimental Values ◽  
Theoretical Procedure

It is clear from a survey of literature on the dynamic deformation of rigid-plastic plates that most work has been focused on plates in which either membrane forces or bending moments alone are considered important, while the combined effect of membrane forces and bending moments on the behavior of plates under static loads and beams under dynamic loads is fairly well established. This paper, therefore, is concerned with the behavior of circular plates loaded dynamically and with deflections in the range where both bending moments and membrane forces are important. A general theoretical procedure is developed from the equations for large deflections of plates and a simplified yield condition due to Hodge. The results obtained when solving the governing equations for the particular case of a simply supported circular plate loaded with a uniform impulsive velocity are found to compare favorably with the corresponding experimental values recorded by Florence.

Virtual Experimental Studies on Carbon Fiber Smart Materials Resistivity Tomography

2009 ◽  
Vol 79-82 ◽  
pp. 283-286
Author(s):  
Ya Wen Dai ◽  
Zhuo Qiu Li ◽  
Xiao Yu Zhang ◽  
Si Rong Zhu
Keyword(s):  
Carbon Fiber ◽  
Circular Plate ◽  
Strain Distribution ◽  
Principal Strain ◽  
Virtual Experiment ◽  
Sensitive Layer ◽  
Resistivity Tomography ◽  
Virtual Experiments ◽  
Simply Supported ◽  
Finite Element Software

With the emergence of large-size complex structures, conventional discrete sensors can’t meet the requirement of structure health monitoring because they can only sense the strain in a single direction. In this paper, based on sensing and covering properties of carbon fiber smart material (CFSM), an idea of a sensitive layer placed on the structure surface was proposed. By setting finite electrodes on the edge of the sensitive layer, the stress field of tested structure is transformed to electric field which is apt to be tested, and with resistivity tomography technology (ERT), field(global) monitoring on civil engineering structure can be realized. To avoid impact resulting from measuring errors caused by misc factors in experiment, CFSM ERT system was utilized in virtual experiments. Virtual Experiments were conducted on ANSYS finite element software aided by its excellent abilities in coupled field analysis. The virtual experiments included two cases: circular plate simply supported at its perimeter under single loading of different values in the center, and circular plate simply supported at its perimeter under multipoint loading in different positions. In the virtual experiments current incentive in adjacent electrodes and voltage measurement in other adjacent electrodes were implemented, and the measured voltage data was transmitted to the ERT system to obtain the contour plot of resistivity distribution. It indicates that for the single loaded CFSM virtual experiment with tensile strain, its resistivity is increased with the load increase. Compared with 1st and 2nd principal strain distribution in structure tested area, resistivity distribution will qualitatively reflect force field of structure. In multipoint loaded CFSM virtual experiment with compress strain, resistivity descends. Compared with 3rd and 2nd principal strain distribution in structure tested area, low resistivity area just locates at area of biggest strain. Based on virtual experiment, efficiency of CFSM ERT system is demonstrated, greatly supporting the consequent practical application.

On limiting cases in the flexure of simply supported regular polygonal plates

1969 ◽  
Vol 65 (3) ◽  
pp. 831-834 ◽  
Author(s):  
K. Rajaiah ◽  
Akella Kameswara Rao
Keyword(s):  
Circular Plate ◽  
Regular Polygons ◽  
Circular Plates ◽  
Axisymmetric Loading ◽  
Simply Supported ◽  
Significant Factors

AbstractLimiting solutions are derived for the flexure of simply supported many-sided regular polygons, as the number of sides is increased indefinitely. It is shown that these solutions are different from those for simply supported circular plates. For axisymmetric loading, circular plate solutions overestimate the deflexions and the moments by significant factors.

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