Clamped Rectangular Plates with a Central Concentrated Load

1940 ◽  
Vol 44 (352) ◽  
pp. 350-354 ◽  
Author(s):  
Dana Young
Keyword(s):  
Experimental Investigation ◽  
Rectangular Plate ◽  
Similar Data ◽  
Rectangular Plates ◽  
Maximum Deflection ◽  
Concentrated Load ◽  
Distributed Load ◽  
Method Of Solution ◽  
Clamped Edges ◽  
General Method

A general method of solution for rectangular plates with clamped edges and any kind of loading has been developed by Professor S. P. Timoshenko. The present paper gives the results of calculations using this method for the maximum deflection, moment, and edge shears for rectangular plates of various proportions with all four edges clamped and loaded by a single concentrated load at the centre. Similar data for a clamped rectangular plate with a uniformly distributed load have been given by I. A. Wojtaszak and also T. H. Evans. A report of an experimental investigation of this problem with some analytical results has been given by R. G. Sturm and R. L. Moore.

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.

The λ-method for rectangular plates

1965 ◽  
Vol 288 (1414) ◽  
pp. 371-395 ◽  
Keyword(s):  
Rectangular Plate ◽  
Complete Solution ◽  
Rectangular Plates ◽  
Concentrated Load ◽  
Master Program ◽  
Comprehensive Method ◽  
Wide Range ◽  
Fourier Sine Series ◽  
The University ◽  
Line Loads

A comprehensive method is presented for the numerical solution of the rectangular plate problem under a wide range of loadings and boundary conditions. A particular integral is obtained as a double Fourier sine series, which is the complete solution when the plate is simply supported with all edges in the same horizontal plane. This is summed to a highly convergent single series of negative exponentials in the plate variables U i . The necessary calculus for differentiation and integration is established, from which the particular slopes, moments and shears follow whether for concentrated or line loads or loads distributed uniformly over polygonal regions. By treating a concentrated moment as a force-pair, this case is deduced from that for a concentrated load. The necessary complementary functions and the ensuing simultaneous equations are formulated in a manner suited to programming for an electronic computer. A master program for rectangular plates has been developed in Mercury Autocode at the University of Sheffield. An illustrative example is included of a concentrated moment acting on a fully fixed rectangular plate.

The Bending of a Wedge-Shaped Plate

1953 ◽  
Vol 20 (1) ◽  
pp. 77-81
Author(s):  
S. Woinowsky-Krieger
Keyword(s):  
Stress Distribution ◽  
Boundary Conditions ◽  
Elastic Plate ◽  
Corner Point ◽  
Thin Elastic Plate ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions ◽  
Method Of Solution ◽  
Clamped Edges ◽  
General Method

Abstract A general method of solution is given in this paper for the problem of bending of a wedge-shaped thin elastic plate with arbitrary boundary conditions on the radial edges in the case of a single load. The solution is carried out for a plate with clamped edges and a single load on the bisector radius of the plate. Stress distribution along the edges is shown and the behavior of the solution near the corner point is discussed for several opening angles of the plate.

Under Uniformly Distributed Load are Fixed on one Side (Simple) on the Edge Simply Supported and Fixed Half Bending of Rectangular Plates

2012 ◽  
Vol 152-154 ◽  
pp. 840-845
Author(s):  
Ying Jie Chen ◽  
Bao Lian Fu ◽  
Liang Wang ◽  
Jie Wu
Keyword(s):  
Rectangular Plate ◽  
Variable Method ◽  
Engineering Practice ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Distributed Load ◽  
Uniformly Distributed Load ◽  
Surface Deflection ◽  
Mixed Variable

In this paper mixed variable method is generalized to solve the problem of bending of the rectangular plate with one side is fixed (simple) on the edge simply supported and fixed half under the action of a uniformly distributed load. Gives the surface deflection equation and a chart, the chart can be directly applied to engineering practice.

The Calculation of Maximum Deflection, Moment, and Shear for Uniformly Loaded Rectangular Plate With Clamped Edges

1937 ◽  
Vol 4 (4) ◽  
pp. A173-A176
Author(s):  
I. A. Wojtaszak
Keyword(s):  
Rectangular Plate ◽  
Maximum Deflection ◽  
Square Plate ◽  
Clamped Edges

Abstract The problem of the uniformly loaded rectangular plate with four clamped edges has been solved by H. Hencky and independently by J. Boobnoff. Hencky made refined calculations only for the case of a square plate while Boobnoff made precise calculations for several ratios of the sides of the plate. This article gives the results of calculations for maximum deflection, moment, and shear for several ratios of the sides of the plate, using Hencky’s equations. Curves are drawn with the coefficients, used in defining these maximum quantities, as ordinates and the ratios of the sides of the plate as abscissas.

The built-in rectangular plate (general method of solution)

Meccanica ◽  
1966 ◽  
Vol 1 (1-2) ◽  
pp. 76-94
Author(s):  
Osvaldo Zanaboni
Keyword(s):  
Rectangular Plate ◽  
Method Of Solution ◽  
General Method

Buckling of Rectangular Plates With Built-In Edges

1942 ◽  
Vol 9 (4) ◽  
pp. A171-A174
Author(s):  
Samuel Levy
Keyword(s):  
Exact Solution ◽  
Rectangular Plate ◽  
Infinite Series ◽  
Numerical Results ◽  
Buckling Load ◽  
Rectangular Plates

Abstract This paper presents an exact solution in terms of infinite series of the problem of buckling by compressive forces in one direction of a rectangular plate with built-in edges (zero slope, zero displacement in the direction normal to the plane of the plate). The buckling load is calculated for 14 ratios of length to width, ranging in steps of 0.25 from 0.75 to 4. On the basis of convergence, as the number of terms used in the infinite series is increased, it is estimated that the possible error in the numerical results presented is of the order of 0.1 per cent. A comparison is given with the work of other authors.

Wavelet Multi-Scale Solution for Deflection of Thin Rectangular Plates under Temperature

2012 ◽  
Vol 166-169 ◽  
pp. 2871-2875
Author(s):  
Yan Chang Wang ◽  
Ke Liang Ren ◽  
Yan Dong ◽  
Ming Guang Wu
Keyword(s):  
Differential Equations ◽  
Rectangular Plate ◽  
Thermal Environment ◽  
Operational Matrix ◽  
Rectangular Plates ◽  
Thin Rectangular Plate ◽  
Multi Scale ◽  
Scale Method ◽  
The Matrix ◽  
Operational Matrix Of Integration

To consider the deformation of thin rectangular plate under temperature. In this paper, the wavelet multi-scale method was used to solve the thin plate governing differential equations with four different initial or boundary conditions. An operational matrix of integration based on the wavelet was established and the procedure for applying the matrix to solve the differential equations was formulated, and got the deflection of thin rectangular plates under temperature. The result provides a theoretical reference for solving thin rectangular plate deflection in thermal environment using multi-scale approach.

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