Loss of Contact in the Vicinity of a Right-Angle Corner for a Simply Supported, Laterally Loaded Plate

1981 ◽  
Vol 48 (3) ◽  
pp. 597-600 ◽  
Author(s):  
L. M. Keer ◽  
A. F. Mak
Keyword(s):  
Integral Transform ◽  
Space Region ◽  
Rectangular Plates ◽  
Elastic Plates ◽  
Concentrated Force ◽  
Simply Supported ◽  
Quarter Space ◽  
Loss Of Contact ◽  
Restraining Force ◽  
Laterally Loaded

The solutions to problems of laterally loaded, simply supported rectangular plates are classical ones that can be found in standard textbooks. It is found that forces directed downward must be present to prevent the corners of the plate from rising up during bending. The objective of the present analysis is to determine the extent to which such a plate will rise if the corner force is not present and the plate is unilaterally constrained. Rather than determine the solution for a rectangular plate, we consider a laterally loaded, simply supported plate which occupies a quarter space region. The plate is unilaterally constrained and may rise at the corner due to an absence of restraining force there. Using integral transform techniques appropriate to the quarter space for elastic plates, the region of lost contact is determined for a general loading. The special loading due to a concentrated force is given as an example.

Rectangular Plates on Unilateral Edge Supports: Part 1—Theory and Numerical Analysis

1986 ◽  
Vol 53 (1) ◽  
pp. 146-150 ◽  
Author(s):  
J. P. Dempsey ◽  
Hui Li
Keyword(s):  
Singular Integral Equations ◽  
Integral Transforms ◽  
Rectangular Plates ◽  
Centrally Symmetric ◽  
Solution Methods ◽  
Dual Series Equations ◽  
Finite Integral ◽  
Loss Of Contact ◽  
Laterally Loaded ◽  
Numerical Approaches

The corners of a simply supported, laterally loaded rectangular plate must be anchored to prevent them from lifting off the supports. If no such anchors are provided, and the supports are unilateral or capable of exerting forces in one direction only, parts of the plate will bend away from the supports upon loading. The loss of contact when uplift of laterally loaded rectangular plates is not prevented is examined in this paper. Arbitrary centrally symmetric loading is considered. Finite integral transforms convert the coupled dual-series equations that result from the Levy-Nadai approach to two coupled singular integral equations. Different solution methods are applicable for sagged and unsagged supports; these two numerical approaches are discussed in detail.

Flexure by a Concentrated Force of the Infinite Plate on a Circular Support

1963 ◽  
Vol 30 (2) ◽  
pp. 225-231 ◽  
Author(s):  
J. Dundurs ◽  
Tung-Ming Lee
Keyword(s):  
Elastic Properties ◽  
Classical Theory ◽  
Infinite Plate ◽  
Arbitrary Point ◽  
Convergent Series ◽  
Elastic Plates ◽  
Concentrated Force ◽  
Simply Supported ◽  
Uniformly Convergent ◽  
Thin Elastic Plates

Treated is the flexure of an infinite plate which is simply supported on a circle and subjected to a concentrated force at an arbitrary point. The portion of the plate inside the circular support is allowed to have elastic properties that are different from those of the outside part. The solution is exact within the framework of the classical theory of thin elastic plates and is in the form of a uniformly convergent series. Several previously known solutions appear as limiting cases of the results given here.

Rectangular Plates on Unilateral Edge Supports: Part 2—Implementation; Concentrated and Uniform Loading

1986 ◽  
Vol 53 (1) ◽  
pp. 151-156 ◽  
Author(s):  
J. P. Dempsey ◽  
Hui Li
Keyword(s):  
Unilateral Contact ◽  
Rectangular Plates ◽  
Uniform Pressure ◽  
Computer Implementation ◽  
Concentrated Loads ◽  
Uniform Loading ◽  
Loss Of Contact ◽  
Implementation Aspects ◽  
Laterally Loaded ◽  
Support Reactions

Rectangular plates in unilateral contact with sagged and unsagged supports laterally loaded by centrally concentrated loads and uniform pressure are examined. The loss of contact and the redistribution of deflections, moments, and support reactions are presented. Computer implementation aspects are discussed.

Three Dimensional Vibration Analysis of Rectangular Plates With Undamaged and Damaged Boundaries by the Spectral Collocation Method

2011 ◽  
Author(s):  
Ma’en S. Sari ◽  
Eric A. Butcher
Keyword(s):  
Boundary Conditions ◽  
Collocation Method ◽  
Vibration Analysis ◽  
Numerical Technique ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Rectangular Plates ◽  
Elastic Plates ◽  
Simply Supported ◽  
Grid Points

This paper presents a new numerical technique for the free vibration analysis of isotropic three dimensional elastic plates with damaged boundaries. In the study, it is assumed that the plates have free lateral surfaces, and two opposite simply supported edges, while the other edges could be clamped, simply supported or free. For this purpose, the Chebyshev collocation method is applied to obtain the natural frequencies of three dimensional plates with damaged clamped boundary conditions, where the governing equations and boundary conditions are discretized by the presented method and put into matrix vector form. The damaged boundaries are represented by distributed translational springs. In the present study the boundary conditions are coupled with the governing equation to obtain the eigenvalue problem. Convergence studies are carried out to determine the sufficient number of grid points used. First, the results obtained for the undamaged plates are verified with previous results in the literature. Subsequently, the results obtained for the damaged three dimensional plates indicate the behavior of the natural vibration frequencies with respect to the severity of the damaged boundary. This analysis can lead to an efficient technique for damage detection of structures in which joint or boundary damage plays a significant role in the dynamic characteristics. The results obtained from the Chebychev collocation solutions are seen to be in excellent agreement with those presented in the literature.

Forced Axisymmetric Motions of Circular Elastic Plates

1965 ◽  
Vol 32 (4) ◽  
pp. 893-898 ◽  
Author(s):  
R. S. Weiner
Keyword(s):  
Elastic Plate ◽  
Integral Transform ◽  
Plate Theory ◽  
Uniform Pressure ◽  
Elastic Plates ◽  
Pressure Loading ◽  
Concentric Ring ◽  
Simply Supported ◽  
Arbitrary Time Dependence ◽  
Central Load

Axisymmetric motions of a circular elastic plate are considered here according to the Poisson-Kirchhoff plate theory. A concentric ring loading of arbitrary time dependence is examined and used to construct solutions for a concentrated central load and for a uniform pressure loading. The boundary of the plate is considered to be elastically built-in in a manner that prevents transverse edge motion and provides a restoring edge moment linearly related to edge rotation. Thus, limiting cases are a clamped plate and a simply supported plate. Finally, a discussion relating this work to the integral-transform approach of Sneddon is presented to enable physical interpretation and generalization of his approach.

Exact Solution for Simply Supported and Multilayered Magneto-Electro-Elastic Plates

2001 ◽  
Vol 68 (4) ◽  
pp. 608-618 ◽  
Author(s):  
E. Pan
Keyword(s):  
Composite Structures ◽  
Three Dimensional ◽  
Layered Composite ◽  
Rectangular Plates ◽  
Elastic Plates ◽  
Homogeneous Solutions ◽  
Simply Supported ◽  
Special Cases ◽  
Multilayered Plates ◽  
Simple Formalism

Exact solutions are derived for three-dimensional, anisotropic, linearly magneto-electro-elastic, simply-supported, and multilayered rectangular plates under static loadings. While the homogeneous solutions are obtained in terms of a new and simple formalism that resemble the Stroh formalism, solutions for multilayered plates are expressed in terms of the propagator matrix. The present solutions include all the previous solutions, such as piezoelectric, piezomagnetic, purely elastic solutions, as special cases, and can therefore serve as benchmarks to check various thick plate theories and numerical methods used for the modeling of layered composite structures. Typical numerical examples are presented and discussed for layered piezoelectric/piezomagnetic plates under surface and internal loads.

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