The Bending of the Clamped Sectorial Plate

1944 ◽  
Vol 11 (3) ◽  
pp. A134-A139
Author(s):  
G. F. Carrier
Keyword(s):  
Boundary Condition ◽  
Integral Equation Method ◽  
Rectangular Plates ◽  
Uniform Pressure ◽  
Bending Moments ◽  
Concentrated Load ◽  
Design Problems ◽  
Simply Supported ◽  
Computational Work ◽  
The Relationship

Abstract The problem of evaluating the bending moments, existing in a uniformly loaded clamped plate having the form of a sector of a ring, is one which arises in connection with the stress analysis of reinforced piston heads and in other design problems. In this paper, expressions are derived for the bending moments along the edges of such a plate. Similar problems, i.e., those of the clamped rectangular plate under uniform pressure, under a central concentrated load, and that of the simply supported sector of a disk under uniform pressure, have been discussed by previous authors. The general approach used in the foregoing problems is adopted in the present case; a considerable reduction in the computational work is achieved, however, by the use of an integral-equation method of solving the boundary-condition equations. Numerical results are obtained for plates of various dimensions, and the edge moment distributions are plotted for these cases. Curves are also plotted which indicate the relationship existing between the maximum bending moments derived for sectorial plates and those previously obtained for clamped rectangular plates of similar size.

Nonlinear Vibrations of Rectangular Plates With Different Boundary Conditions: Theory and Experiments

2005 ◽  
Author(s):  
M. Amabili ◽  
C. Augenti
Keyword(s):  
Boundary Condition ◽  
Good Accuracy ◽  
Continuation Method ◽  
Laser System ◽  
Normal Displacement ◽  
Vibration Modes ◽  
Rectangular Plates ◽  
Geometric Imperfections ◽  
Simply Supported ◽  
Actual Geometry

Large-amplitude vibrations of rectangular plates subjected to harmonic excitation are investigated. The von Ka´rma´n nonlinear strain-displacement relationships are used to describe the geometric nonlinearity. A specific boundary condition, with restrained normal displacement at the plate edges and fully free in-plane displacements, not previously considered, has been introduced as a consequence that it is very close to the experimental boundary condition. Results for this boundary condition are compared to nonlinear results previously obtained for: (i) simply supported plates with immovable edges; (ii) simply supported plates with movable edges, and (iii) fully clamped plates. The nonlinear equations of motion are studied by using a code based on arclength continuation method. A thin rectangular stainless-steel plate has been inserted in a metal frame; this constraint is approximated with good accuracy by the newly introduced boundary condition. The plate inserted into the frame has been measured with a 3D laser system in order to reconstruct the actual geometry and identify geometric imperfections (out-of-planarity). The plate has been experimentally tested in laboratory for both the first and second vibration modes for several excitation magnitudes in order to characterize the nonlinearity of the plate with imperfections. Numerical results are able to follow experimental results with good accuracy for both vibration modes and for different excitation levels once the geometric imperfection is introduced in the model. Effects of geometric imperfections on the trend of nonlinearity and on natural frequencies are shown; convergence of the solution with the number of generalized coordinates is numerically verified.

Solving the Deflection Equations of Thick Plate under Concentrated Load

2012 ◽  
Vol 594-597 ◽  
pp. 2659-2663
Author(s):  
Dan Zhang
Keyword(s):  
Rectangular Plate ◽  
Thick Plate ◽  
Numerical Results ◽  
Reciprocal Theorem ◽  
Rectangular Plates ◽  
Concentrated Load ◽  
Simply Supported ◽  
Thick Rectangular Plate ◽  
Reciprocal Theorem Method

According to reciprocal-theorem method (RTM), the deflection equations of thick rectangular plate with two edges simply supported and two edges free under concentrated load are obtained in this paper. Simultaneously through the programming computation, the numerical results with actual value are obtained, which further showed the accuracy and superiority of RTM to solve the bending of thick rectangular plates.

Bending of Thick Rectangular Plates with Different Boundaries under Concentrated Load

2010 ◽  
Vol 163-167 ◽  
pp. 1440-1444
Author(s):  
Ying Jie Chen ◽  
Gang Li ◽  
Zhen Xian Zhang ◽  
Bao Lian Fu
Keyword(s):  
Analytical Solutions ◽  
Thick Plate ◽  
Engineering Application ◽  
Reciprocal Theorem ◽  
Rectangular Plates ◽  
Concentrated Load ◽  
Simply Supported ◽  
The Third ◽  
Thick Rectangular Plate ◽  
Reissner’S Theory

Reciprocal theorem method (RTM) is generalized to solve the problem of bending of thick rectangular plate under concentrated load with four edges fixed and with two opposite edges fixed, the third edge simply supported, and the fourth edge free based on Reissner’s theory. The analytical solutions of the thick plate are given, and the relevant date and diagram are given to guidance engineering application.

Relationship Between Vibration Frequencies of Reddy and Kirchhoff Polygonal Plates With Simply Supported Edges

1997 ◽  
Vol 122 (1) ◽  
pp. 77-81 ◽  
Author(s):  
C. M. Wang ◽  
S. Kitipornchai ◽  
J. N. Reddy
Keyword(s):  
Natural Frequencies ◽  
Plate Theory ◽  
Kirchhoff Plate ◽  
Rectangular Plates ◽  
Vibration Frequencies ◽  
Third Order ◽  
Simply Supported ◽  
Kirchhoff Plate Theory ◽  
The Relationship ◽  
Exact Relationship

This paper presents an exact relationship between the natural frequencies of Reddy third-order plate theory and those of classical Kirchhoff plate theory for simply supported, polygonal isotropic plates, including rectangular plates. The relationship for the natural frequencies enables one to obtain the solutions of the third-order plate theory from the known Kirchhoff plate theory for the same problem. As examples, some vibration frequencies for rectangular and regular polygonal plates are determined using this relationship. [S0739-3717(00)01601-9]

Bending of Elastically Restrained Rectangular Plates Under Uniform Pressure

1958 ◽  
Vol 62 (575) ◽  
pp. 834-836 ◽  
Author(s):  
C. Lakshmi Kantham
Keyword(s):  
Natural Frequencies ◽  
Unit Length ◽  
Rectangular Plates ◽  
Uniform Pressure ◽  
Simply Supported ◽  
Edge Conditions ◽  
Definition Of ◽  
Elastically Restrained ◽  
Clamped Edges ◽  
Clamped Edge

In the bending and vibration of plates it is found that the values of maximum deflection and natural frequencies, respectively, vary considerably from the simply-supported to clamped edge conditions. For an estimation of these characteristics in the intermediate range a generalised boundary condition may be assumed, of which the simply-supported and clamped edges become limiting cases. While Bassali considers the ratio of edge moment to the cross-wise moment as a constant, Newmark, Lurie and Klein and other investigators, in their analyses of various structures, consider that moment and slope at an end are proportional.Here the definition of elastic restraint as given by Timoshenko, α=βM, is followed, where α is the slope at any edge, M the corresponding edge moment per unit length while β is the elastic restraint factor. β→0 and β→∞ represent the two limiting cases of simply-supported and clamped edge conditions.

Analysis of Interface Deformation of Steel-Concrete-Steel Sandwich Beam

2012 ◽  
Vol 525-526 ◽  
pp. 357-360
Author(s):  
Pei Xiu Xia ◽  
Guang Ping Zou ◽  
Zhong Liang Chang
Keyword(s):  
Sandwich Beam ◽  
Analytical Models ◽  
Sandwich Beams ◽  
Interface Deformation ◽  
Simply Supported ◽  
Interface Slip ◽  
Steel Panels ◽  
Uniformly Distributed Loads ◽  
Relationship Of ◽  
The Relationship

The effect of the interface slip is neglected in most studies on calculating deflection of sandwich beams. By taking a simply supported sandwich beams under uniformly distributed loads as an example, simplified analytical models of the interface slip are established, and corresponding clculation formulas of interface slip between steel panels and concrete and section curvatures are derived. The formula for deflection of sandwich beams are then presented. This formula reflects the relationship of influence each other between the interface slip and deflection.

Large Deflection of a Rectangular Plate Resting on a Pasternak-Type Elastic Foundation

1977 ◽  
Vol 44 (3) ◽  
pp. 509-511 ◽  
Author(s):  
P. K. Ghosh
Keyword(s):  
Rectangular Plate ◽  
Elastic Foundation ◽  
Large Deflection ◽  
Lateral Load ◽  
Bending Moments ◽  
Shear Forces ◽  
Simply Supported ◽  
Base Parameters ◽  
Square Plate

The problem of large deflection of a rectangular plate resting on a Pasternak-type foundation and subjected to a uniform lateral load has been investigated by utilizing the linearized equation of plates due to H. M. Berger. The solutions derived and based on the effect of the two base parameters have been carried to practical conclusions by presenting graphs for bending moments and shear forces for a square plate with all edges simply supported.

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