Bending analysis of simply supported and clamped thin elastic plates by using a modified version of the LMFS

2021 ◽  
Author(s):  
Wenzhen Qu ◽  
Linlin Sun ◽  
Po-Wei Li
Keyword(s):  
Elastic Plates ◽  
Bending Analysis ◽  
Simply Supported ◽  
Thin Elastic Plates

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.

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.

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

Stability of Thin Elastic Plates Covering an Arbitrary Simply Connected Region and Subject to any Admissible Boundary Conditions

1953 ◽  
Vol 20 (1) ◽  
pp. 23-29
Author(s):  
G. A. Zizicas
Keyword(s):  
Boundary Conditions ◽  
Direct Method ◽  
Elastic Plates ◽  
Simple Manner ◽  
Particular Solutions ◽  
Isotropic Plates ◽  
Simply Connected Region ◽  
Simply Connected ◽  
A Direct Method ◽  
Thin Elastic Plates

Abstract The Bergman method of solving boundary-value problems by means of particular solutions of the differential equation, which are constructed without reference to the boundary conditions, is applied to the problem of stability of thin elastic plates of an arbitrary simply connected shape and subject to any admissible boundary conditions. A direct method is presented for the construction of particular solutions that is applicable to both anisotropic and isotropic plates. Previous results of M. Z. Krzywoblocki for isotropic plates are obtained in a simple manner.

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