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.

The Elastic Plane With a Circular Insert, Loaded by a Tangentially Directed Force

1962 ◽  
Vol 29 (2) ◽  
pp. 362-368 ◽  
Author(s):  
M. Hete´nyi ◽  
J. Dundurs
Keyword(s):  
Closed Form ◽  
Elastic Properties ◽  
Classical Theory ◽  
Theory Of Elasticity ◽  
Elastic Plane ◽  
Elementary Functions ◽  
Explicit Formulas ◽  
Concentrated Force

The problem treated is that of a plate of unlimited extent containing a circular insert and subjected to a concentrated force in the plane of the plate and in a direction tangential to the circle. The elastic properties of the insert are different from those of the plate, and a perfect bond is assumed between the two materials. The solution is exact within the classical theory of elasticity, and is in a closed form in terms of elementary functions. Explicit formulas are given for the components of stress in Cartesian co-ordinates, and also in polar co-ordinates at the circumference of the insert.

Nonlinear Vibration of Thin Elastic Plates, Part 2: Internal Resonance by Amplitude-Incremental Finite Element

1984 ◽  
Vol 51 (4) ◽  
pp. 845-851 ◽  
Author(s):  
S. L. Lau ◽  
Y. K. Cheung ◽  
S. Y. Wu
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Internal Resonance ◽  
Harmonic Excitation ◽  
Plate Element ◽  
Elastic Plates ◽  
Simply Supported ◽  
Speed Up ◽  
Numerical Process ◽  
Thin Elastic Plates

The simple amplitude-incremental triangular plate element derived in Part 1 of this paper is applied to treat the large-amplitude periodic vibrations of thin elastic plates with existence of internal resonance. A simply supported rectangular plate with immovable edges (b/a = 1.5) and having linear frequencies ω13 = 3.45 ω11 is selected as a typical example. The frequency response of free vibration as well as forced vibration under harmonic excitation are computed. To the best knowledge of the authors, these very interesting results for such plate problems have not appeared in literature previously. Some special considerations to simplify and to speed up the numerical process are also discussed.

Transverse bending of infinite and semi-infinite thin elastic plates. I

1957 ◽  
Vol 53 (1) ◽  
pp. 248-255 ◽  
Author(s):  
W. A. Bassali
Keyword(s):  
Boundary Condition ◽  
Complex Variable ◽  
Practical Importance ◽  
Complex Potentials ◽  
Two Dimensional ◽  
Elastic Plates ◽  
Simply Supported ◽  
Physical Conditions ◽  
Transverse Bending ◽  
Thin Elastic Plates

In recent years several authors have treated the fundamental problems of two-dimensional statical elasticity for isotropic and aeolotropic materials by the use of functions of a complex variable; references are given at the end of (7). In this paper Stevenson's notation (8,9) is adopted. Dawoud (2) has expressed the continuity conditions across a curve between two differently loaded regions in terms of the complex potentials and particular integrals for the two regions. A form of the boundary condition defining certain types of boundary constraint, including the rigidly clamped and hinged boundaries, has been introduced by the author and Dawoud (1). The introduction of this boundary condition is of practical importance, since neither rigidly clamped nor simply supported conditions can be realized fully under actual physical conditions and thus any case met in practice must lie somewhere between these two limiting cases.

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.

Simply supported annular plates transversely loaded by a concentrated force applied at an arbitrary point

1995 ◽  
Vol 30 (3) ◽  
pp. 211-215
Author(s):  
A Strozzi ◽  
E Dragoni ◽  
V Ciavatti
Keyword(s):  
Series Solution ◽  
Annular Plate ◽  
Arbitrary Point ◽  
Experimental Tests ◽  
Concentrated Force ◽  
Simply Supported ◽  
Annular Plates ◽  
Aspect Ratios ◽  
Wide Range ◽  
Plate Geometry

An analysis is performed for a thin, annular plate, simply supported at its inner boundary, free at its periphery, and loaded by a concentrated force applied at any plate position. A purely flexural model is adopted, for which a series solution is obtained with the aid of an algebraic manipulator. Experimental tests are carried out for a specific plate geometry and the results obtained are compared to the analytical forecasts. A diagram is presented which summarizes the plate theoretical deflection by the loaded point for a wide range of aspect ratios of the annular plate and of normalized loaded positions.

scholarly journals Self-dual singularity through lasing and antilasing in thin elastic plates

2021 ◽  
Vol 103 (13) ◽  
Author(s):  
M. Farhat ◽  
P.-Y. Chen ◽  
S. Guenneau ◽  
Y. Wu
Keyword(s):  
Elastic Plates ◽  
Thin Elastic Plates

scholarly journals Spacetime modulation in floating thin elastic plates

2021 ◽  
Vol 104 (1) ◽  
Author(s):  
Mohamed Farhat ◽  
Sebastien Guenneau ◽  
Pai-Yen Chen ◽  
Ying Wu
Keyword(s):  
Elastic Plates ◽  
Thin Elastic Plates
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