A general solution for rectangular plate bending

1979 ◽  
Vol 45 (4) ◽  
pp. 111-118 ◽  
Author(s):  
Madhujit Mukhopadhyay
Keyword(s):  
General Solution ◽  
Rectangular Plate ◽  
Plate Bending

THE SCHEME OF BIORTHOGONALIZATION OF VECTORS IN SOLVING THE PROBLEM OF RECTANGULAR PLATE BENDING

2019 ◽  
Vol 50 (6) ◽  
pp. 673-678
Author(s):  
Vladimir Ivanovich Lysukhin ◽  
Julian Fedotovich Yaremchuk
Keyword(s):  
Rectangular Plate ◽  
Plate Bending

scholarly journals Finite difference solution of plate bending using Wolfram Mathematica

2019 ◽  
Vol 13 (3) ◽  
pp. 241-247
Author(s):  
Katarina Pisačić ◽  
Marko Horvat ◽  
Zlatko Botak
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Rectangular Plate ◽  
Difference Method ◽  
Mapping Function ◽  
Equation System ◽  
Plate Bending ◽  
Wolfram Mathematica ◽  
Linear Equation System ◽  
Finite Difference Solution

This article describes the procedure of calculating deflection of rectangular plate using a finite difference method, programmed in Wolfram Mathematica. Homogenous rectangular plate under uniform pressure is simulated for this paper. In the introduction, basic assumptions are given and the problem is defined. Chapters that follow describe basic definitions for plate bending, deflection, slope and curvature. The following boundary condition is used in this article: rectangular plate is wedged on one side and simply supported on three sides. Using finite difference method, linear equation system is given and solved in Wolfram Mathematica. System of equations is built using the mapping function and solved with solve function. Solutions are given in the graphs. Such obtained solutions are compared to the finite element method solver NastranInCad.

The Effect of Transverse Shear Deformation on the Bending of Elastic Plates

1945 ◽  
Vol 12 (2) ◽  
pp. A69-A77 ◽  
Author(s):  
Eric Reissner
Keyword(s):  
General Solution ◽  
Rectangular Plate ◽  
Transverse Shear ◽  
Plate Theory ◽  
Infinite Plate ◽  
Present Theory ◽  
System Of Equations ◽  
Elastic Plates ◽  
Classical Plate Theory

Abstract A system of equations is developed for the theory of bending of thin elastic plates which takes into account the transverse shear deformability of the plate. This system of equations is of such nature that three boundary conditions can and must be prescribed along the edge of the plate. The general solution of the system of equations is obtained in terms of two plane harmonic functions and one function which is the general solution of the equation Δψ − (10/h2)ψ = 0. The general results of the paper are applied (a) to the problem of torsion of a rectangular plate, (b) to the problems of plain bending and pure twisting of an infinite plate with a circular hole. In these two problems important differences are noted between the results of the present theory and the results obtained by means of the classical plate theory. It is indicated that the present theory may be applied to other problems where the deviations from the results of classical plate theory are of interest. Among these other problems is the determination of the reactions along the edges of a simply supported rectangular plate, where the classical theory leads to concentrated reactions at the corners of the plate. These concentrated reactions will not occur in the solution of the foregoing problem by means of the theory given in the present paper.

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