Mechanical Analysis of a Thin Solid Circular Plate Deflected by Transverse Periphery Forces and by a Central Load

1995 ◽  
Vol 209 (2) ◽  
pp. 77-86 ◽  
Author(s):  
E Dragoni ◽  
A Strozzi
Keyword(s):  
Circular Plate ◽  
Series Solution ◽  
Analytical Form ◽  
Mechanical Analysis ◽  
Basic Model ◽  
Sinusoidal Load ◽  
Load Effects ◽  
Title Problem ◽  
Plate Loading ◽  
Central Load

A thin, solid, circular plate deflected by a number of transverse, concentrated, periphery forces, not necessarily angularly equispaced or equally oriented, and sustaining a central, transverse, equilibrating load, is mechanically analysed via a purely flexural model. This problem is interpreted as a angularly dephased combination of a relatively simple model. This fundamental scheme consists of a plate loaded by a single periphery force, by a central load of equal intensity and opposite direction, and by a sinusoidal periphery line loading whose wavelength equals the plate border and whose intensity renders the plate loading self-equilibrated. When a sequence of basic schemes, possibly referring to loads of different intensity, is combined, respecting the condition that the resultant of the periphery loads is equilibrated by a central force alone, the sinusoidal load effects vanish and the title problem is recovered. A series solution in terms of plate deflections is obtained for the basic model, whose coefficients are analytically evaluated via a computer algebra package. The series sum is expressed in finite terms involving the dilogarithmic function, valid over the whole plate region. In particular, the series is summed in analytical form for the whole plate periphery, along which the boundary deflections are expressed in closed form.

Exact deflection expressions for a thin solid circular plate loaded by periphery couples

2001 ◽  
Vol 215 (3) ◽  
pp. 341-351 ◽  
Author(s):  
A Nobili ◽  
A Strozzi ◽  
P Vaccari
Keyword(s):  
Closed Form ◽  
Circular Plate ◽  
Series Solution ◽  
Analytical Form ◽  
Mechanical Analysis ◽  
Boundary Line ◽  
Plate Edge ◽  
Line Load ◽  
Title Problem ◽  
Radial Axis

A mechanical analysis is carried out for a thin, solid, circular plate, deflected by a series of periphery-concentrated couples with a radial or circumferential axis. Although such couples need not be of equal intensity or angularly equispaced, they must constitute a self-equilibrated system of couples. This problem is decomposed into a combination of two basic models, the first of which considers a single periphery couple with a radial axis, and the second addresses an edge couple with a circumferential axis. In both models the concentrated border couple is equilibrated by a sinusoidal boundary line load of proper intensity, whose wavelength equals the plate edge. When such basic configurations are combined, respecting the condition that the system of concentrated couples be self-equilibrated, the effects of the sinusoidal loads cancel out, and the title problem is recovered. A classical series solution in terms of purely flexural plate deflections is achieved for the two basic models, where the series coefficients are computed with the aid of an algebraic manipulator. For both models, the series is summed in analytical form over the whole plate region. Closed-form deflection formulae can thus be easily derived from the two basic models for any combination of self-equilibrated edge couples, where some selected relevant situations are developed in detail.

On the Existence of a Solution for a Solid Circular Plate Bilaterally Supported Along Two Antipodal Boundary Arcs and Loaded by a Central Transverse Concentrated Force

2000 ◽  
Vol 68 (5) ◽  
pp. 809-812 ◽  
Author(s):  
G. Monegato ◽  
A. Strozzi
Keyword(s):  
Circular Plate ◽  
Plate Theory ◽  
Reaction Force ◽  
Mechanical Analysis ◽  
Square Root ◽  
Existence Of A Solution ◽  
Concentrated Force ◽  
Boundary Constraints ◽  
Title Problem ◽  
The One

A purely flexural mechanical analysis is presented for a thin, solid, circular plate, deflected by a central transverse concentrated force, and bilaterally supported along two antipodal periphery arcs, the remaining part of the boundary being free. This problem is modeled in terms of a singular integral equation of the Prandtl type, which possesses a unique solution expressed in terms of a reaction force containing a factor exhibiting square root endpoint singularities. This solution is then shown not to respect the requested boundary constraints. It is therefore concluded that, within the framework of the purely flexural plate theory, the title problem cannot admit the weighted L2 solution here examined. It cannot, however, be excluded that a solution to the title problem exists, which possesses stronger endpoint singularities than those examined in this paper, or is of a more general form than the one considered here.

Bending of Circular and Ring-Shaped Plates on an Elastic Foundation

1954 ◽  
Vol 21 (1) ◽  
pp. 45-51
Author(s):  
Herbert Reismann
Keyword(s):  
Circular Plate ◽  
Elastic Foundation ◽  
Series Solution ◽  
Circular Disk ◽  
Symmetric Problem ◽  
Concentrated Load ◽  
Transverse Loads ◽  
Infinite Extent ◽  
Theory Of Plates ◽  
Pure Moment

Abstract This paper develops a method for the evaluation of deflections, moments, shears, and stresses of a circular or ring-shaped plate on an elastic foundation under transverse loads. A series solution is derived for plates subjected to edge and/or concentrated loads and is given in terms of tabulated functions. It is exact within the assumptions underlying the classical theory of plates and includes, as a particular case, the known solution of the corresponding radially symmetric problem. Two examples displaying radial asymmetry are worked. A solution is given for (a) a circular plate resting on an elastic foundation, clamped at the boundary and subjected to an arbitrarily placed concentrated load, and (b) a plate of infinite extent, resting on an elastic foundation and clamped to the boundary of a rigid circular disk to which a pure moment is applied.

Mechanical Analysis of an Annular Plate Transversely Loaded at an Arbitrary Point by a Concentrated Force

1992 ◽  
Vol 114 (3) ◽  
pp. 335-342 ◽  
Author(s):  
V. Ciavatti ◽  
E. Dragoni ◽  
A. Strozzi
Keyword(s):  
Experimental Data ◽  
Series Solution ◽  
Annular Plate ◽  
Arbitrary Point ◽  
Mechanical Analysis ◽  
Outer Edge ◽  
Concentrated Force ◽  
Acceleration Technique ◽  
Series Acceleration ◽  
Plate Geometry

An annular plate clamped at the inner rim, free at the outer edge and loaded at an arbitrary point by a concentrated force is mechanically analyzed via a purely flexural model. A series solution is achieved, whose coefficients are analytically evaluated with the aid of an algebraic manipulator. A series acceleration technique is also developed. Experimental data are obtained for a particular plate geometry, and the results retrieved in terms of deflections and stresses are compared to the analytical forecasts. A technically relevant diagram detailing the theoretical deflection of the plate at the loading point for a variety of plate proportions and load locations is also presented.

Mechanical properties characterization of a viscoelastic solid using low-frequency large-amplitude oscillatory indentations with a sharp tip

2008 ◽  
Vol 23 (6) ◽  
pp. 1557-1563
Author(s):  
N. Fujisawa ◽  
M.V. Swain
Keyword(s):  
Large Amplitude ◽  
Contact Stiffness ◽  
Dynamic Stiffness ◽  
Low Frequency ◽  
Static Condition ◽  
Mechanical Analysis ◽  
Viscoelastic Solid ◽  
Static Contact ◽  
Sinusoidal Load ◽  
Continuous Stiffness Measurement

A viscoelastic solid was contacted by a pointed indenter using low-frequency large-amplitude sinusoidal load functions to determine its contact stiffness in a manner similar to that of the continuous stiffness measurement (CSM) technique but in a quasi-static condition. The contact stiffness of a viscoelastic solid determined by the CSM technique, or the dynamic stiffness, is known, from previous CSM-based studies, to overestimate the quasi-static contact stiffness. The contact stiffness of a viscoelastic solid determined in a quasi-static manner is thus hypothesized to help predict the contact depth more accurately. A new analysis procedure based on truncated Fourier series fitting was developed specifically to process the large amplitude sinusoidal indentation data. The elastic modulus of the material characterized in this work was in agreement with that determined by dynamic mechanical analysis, thereby providing evidence for the validity of the present method in characterizing other viscoelastic materials.

scholarly journals Contact Problem Of Conducting And Heated Punch On A Multifield Foundation

2015 ◽  
Vol 20 (3) ◽  
pp. 531-564
Author(s):  
B. Rogowski
Keyword(s):  
Series Solution ◽  
Thermal Loading ◽  
Contact Region ◽  
Analytical Form ◽  
Solution Technique ◽  
Space Region ◽  
Triple Integral Equations ◽  
Infinite Region ◽  
Magnetic Potentials ◽  
Punch Problem

Abstract The solution for a multifield material subjected to temperature loading in a circular region is presented in an explicit analytical form. The study concerns the steady – state thermal loading infinite region (heated embedded inclusion), half – space region and two – constituent magneto – electro – thermo – elastic material region. The new mono – harmonic potential functions, obtained by the author, are used in the analysis of punch problem. The more interested case in which the contact region is annular is analyzed. By using the methods of triple integral equations and series solution technique the solution for an indentured multifield substrate over an annular contact region is given. The sensitivity analysis of obtained indentation parameters shows some interesting points. In particular, it shows that the increasing of the applied electric and magnetic potentials reduces the indentation depth in multifield materials.

Mechanical analysis of an annular plate subject to a transverse concentrated load

1989 ◽  
Vol 24 (3) ◽  
pp. 139-149 ◽  
Author(s):  
A Strozzi
Keyword(s):  
Series Solution ◽  
Simple Technique ◽  
Annular Plate ◽  
Outer Boundary ◽  
Theoretical Models ◽  
Mechanical Analysis ◽  
Approximate Methods ◽  
Concentrated Force ◽  
Concentrated Load ◽  
Series Convergence

The periphery deflection in an annular plate clamped along its inner edge and loaded at its outer boundary by a transverse concentrated force are studied via a series solution. The corrected expressions for the series coefficients are presented. The series convergence is accelerated via a simple technique. Approximate methods are proposed to account for the compliant clamp and shear strain effects on the plate deflections, and they are validated against simplified theoretical models.

Light-cured dental composites characterization by Electron Microscopy

1990 ◽  
Vol 48 (4) ◽  
pp. 428-429
Author(s):  
B. M. Culbertson ◽  
M. L. Devinev ◽  
E. C. Kao
Keyword(s):  
Electron Microscopy ◽  
Mechanical Analysis ◽  
Service Performance ◽  
Dental Composite ◽  
Dental Composites ◽  
Neat Resin ◽  
Scanning Calorimetry ◽  
Research Meeting ◽  
Formulation Variables

The service performance of current dental composite materials, such as anterior and posterior restoratives and/or veneer cements, needs to be improved. As part of a comprehensive effort to find ways to improve such materials, we have launched a broad spectrum study of the physicochemical and mechanical properties of photopolymerizable or visible light cured (VLC) dental composites. The commercially available VLC materials being studied are shown in Table 1. A generic or neat resin VLC system is also being characterized by SEM and TEM, to more fully understand formulation variables and their effects on properties.At a recent dental research meeting, we reported on the differential scanning calorimetry (DSC) and dynamic mechanical analysis (DMA) characterization of the materials in Table 1. It was shown by DSC and DMA that the materials are substantially undercured by commonly used VLC techniques. Post curing in an oral cavity or a dry environment at 37 to 50°C for 7 or more hours substantially enhances the cure of the materials.

On the influence of specimen thickness in TEM images of super-conducting vortices

1996 ◽  
Vol 54 ◽  
pp. 724-725
Author(s):  
J. Bonevich ◽  
D. Capacci ◽  
G. Pozzi ◽  
K. Harada ◽  
H. Kasai ◽  
...  
Keyword(s):  
Flux Line ◽  
Analytical Form ◽  
Realistic Model ◽  
Electron Holography ◽  
Specimen Thickness ◽  
Flux Tubes ◽  
Analytical Expression ◽  
Flux Lines ◽  
Normal Core ◽  
Two Parameters

The successful observation of superconducting flux lines (fluxons) in thin specimens both in conventional and high Tc superconductors by means of Lorentz and electron holography methods has presented several problems concerning the interpretation of the experimental results. The first approach has been to model the fluxon as a bundle of flux tubes perpendicular to the specimen surface (for which the electron optical phase shift has been found in analytical form) with a magnetic flux distribution given by the London model, which corresponds to a flux line having an infinitely small normal core. In addition to being described by an analytical expression, this model has the advantage that a single parameter, the London penetration depth, completely characterizes the superconducting fluxon. The obtained results have shown that the most relevant features of the experimental data are well interpreted by this model. However, Clem has proposed another more realistic model for the fluxon core that removes the unphysical limitation of the infinitely small normal core and has the advantage of being described by an analytical expression depending on two parameters (the coherence length and the London depth).

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