Generation of shape functions for rectangular plate elements

2004 ◽  
Vol 20 (8) ◽  
pp. 655-663 ◽  
Author(s):  
Charles E. Augarde
Keyword(s):  
Rectangular Plate ◽  
Shape Functions ◽  
Plate Elements

scholarly journals Frequency Domain Spectral Element Model for the Vibration Analysis of a Thin Plate with Arbitrary Boundary Conditions

2016 ◽  
Vol 2016 ◽  
pp. 1-20 ◽  
Author(s):  
Ilwook Park ◽  
Taehyun Kim ◽  
Usik Lee
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Rectangular Plate ◽  
Element Model ◽  
Spectral Element ◽  
Plate Element ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions ◽  
Plate Elements ◽  
Rectangular Plate Element

We propose a new spectral element model for finite rectangular plate elements with arbitrary boundary conditions. The new spectral element model is developed by modifying the boundary splitting method used in our previous study so that the four corner nodes of a finite rectangular plate element become active. Thus, the new spectral element model can be applied to any finite rectangular plate element with arbitrary boundary conditions, while the spectral element model introduced in the our previous study is valid only for finite rectangular plate elements with four fixed corner nodes. The new spectral element model can be used as a generic finite element model because it can be assembled in any plate direction. The accuracy and computational efficiency of the new spectral element model are validated by a comparison with exact solutions, solutions obtained by the standard finite element method, and solutions from the commercial finite element analysis package ANSYS.

Static Stability Behaviour of Plate Elements with Non-Uniform, in-Plane Stress Distribution

1979 ◽  
Vol 21 (5) ◽  
pp. 363-365
Author(s):  
P. K. Datta
Keyword(s):  
Stress Distribution ◽  
Boundary Conditions ◽  
Rectangular Plate ◽  
Plane Stress ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Static Stability ◽  
Buckling Loads ◽  
Plate Elements ◽  
Edge Loading

The results of analytically and experimentally determined buckling loads of a rectangular plate, subjected to partial edge loading and mixed boundary conditions, are presented.

New rectangular plate elements based on twist-Kirchhoff theory

2011 ◽  
Vol 200 (33-36) ◽  
pp. 2547-2561 ◽  
Author(s):  
F. Brezzi ◽  
J.A. Evans ◽  
T.J.R. Hughes ◽  
L.D. Marini
Keyword(s):  
Rectangular Plate ◽  
Plate Elements ◽  
Kirchhoff Theory

Forced Vibration of a Clamped Rectangular Plate in Fluid Media

1955 ◽  
Vol 22 (4) ◽  
pp. 568-572
Author(s):  
Gordon C. K. Yeh ◽  
Johann Martinek
Keyword(s):  
Plane Wave ◽  
Rectangular Plate ◽  
Forced Vibration ◽  
High Frequency ◽  
Equations Of Motion ◽  
Shape Functions ◽  
Lagrange Equations ◽  
Fluid Media ◽  
Set Up ◽  
Plate Deflection

Abstract Forced vibration of a thin rectangular plate clamped in a rigid infinite baffle is analyzed. The plate is assumed to separate two different fluid media and the vibration is excited by a simple plane wave of high frequency (as compared with c / 2 π ab ) normally incident from one side of the plate. Using the characteristic shape functions, the Lagrange equations of motion of the plate are set up in generalized co-ordinates. The solutions of the equations render series expressions for the plate deflection and an energy-transmission coefficient. Certain numerical results are given.

scholarly journals DYNAMICS OF RECTANGULAR ORTHOTROPIC PLATES USING CHARACTERISTIC ORTHOGONAL POLYNOMIAL – GALERKIN’S METHODS

2016 ◽  
Vol 36 (1) ◽  
pp. 50-56
Author(s):  
NN Osadebe ◽  
CM Attama ◽  
OA Oguaghamba
Keyword(s):  
Orthogonal Polynomial ◽  
Rectangular Plate ◽  
Natural Frequencies ◽  
Rectangular Plates ◽  
Trial And Error ◽  
Shape Functions ◽  
Orthotropic Plates ◽  
Approximate Methods ◽  
Simply Supported ◽  
Polynomial Theory

The assumed deflection shapes used in the approximate methods such as in the Galerkin’s method were normally formulated by inspection and sometimes by trial and error, until recently, when a systematic method of constructing such a function in the form of Characteristic Orthogonal Polynomial (COPs) was developed by Bhat in 1985. In the vibrational analyses of orthotropic rectangular plates with different boundary conditions, the study used the characteristic orthogonal polynomial theory to obtain satisfactory approximate shape functions for these plates. These functions were applied to Galerkin indirect varational method to obtain new set of fundamental natural frequencies for these plates. The results were reasonable when compared with those in the previous work. All round simply supported thin rectangular plate (SSSS), rectangular clamped plated (CCCC) and rectangular plate with one edge clamped and all others edges simply supported (CSSS) gave 5.172, 9.429 and 6.202 natural frequencies in rad /sec respectively at 0.05%, 0.0% and 22.93% difference with the previous[3] results5.170rad/sec, 9.429rad/sec and 8.048rad/sec  for SSSS, CCCC and CSSS. For others like: rectangular plate with one edge simply supported and all other edges clamped (CCSC), rectangular plate simply supported at two opposite sides and clamped at the others (CSCS) and rectangular plate clamped at two adjacent sides and simply supported at the others (CCSS) with no available results, their natural frequencies obtained are 8.041rad/sec, 6.272rad/sec and 7.106rad/sec respectively. http://dx.doi.org/10.4314/njt.v36i1.8

On Assumed Displacements for the Rectangular Plate Bending Element

1967 ◽  
Vol 71 (682) ◽  
pp. 722-724 ◽  
Author(s):  
D. J. Dawe
Keyword(s):  
Rectangular Plate ◽  
Natural Frequency ◽  
Numerical Results ◽  
Plate Bending ◽  
Rapid Convergence ◽  
Polynomial Representation ◽  
Numerical Accuracy ◽  
Lateral Deflection ◽  
Plate Elements

Summary:—A family of alternative expressions is presented suitable for the representation of the lateral deflection of rectangular plate elements in bending. Such expressions are extensions of a simple polynomial representation assumed in earlier work. The new expressions are such that not all displacement continuity conditions are met completely but, nonetheless, a criterion ensuring convergence of numerical results to true stiffness levels is satisfied. Deflection and natural frequency estimates based on one expression of the proposed family demonstrate rapid convergence and high numerical accuracy.

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