Bending Of Rectangular Plates With Large Deflections
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Author | : Samuel Levy |
Publisher | : |
Total Pages | : 36 |
Release | : 1942 |
Genre | : Aeronautics |
ISBN | : |
The solution of von Karman's fundamental equations for large deflections of plates is presented for the case of asimply supported rectangular plate under combined edge compression and lateral loading. Numerical solutions are given for square plates and for rectangular plates with a width-span ratio of 3:1. The effective widths according to von Karman, Bengston, Marguerre, and Cox and with experimental results by Ramberg, McPherson, and Levy. The deflections for a square plate under lateral pressure are compared with experimental and theoretical results by Kaiser. It is found that the effective widths agree closely with Marguerre's formula and with the experimentally observed values and that the deflections agree with the experimental results and with Kaiser's work.
Author | : Chi-Teh Wang |
Publisher | : |
Total Pages | : 34 |
Release | : 1948 |
Genre | : Plates (Engineering) |
ISBN | : |
This document presents the solution of Von Karman equations for thin plates with large deflections for special cases of rectangular plates of 1.5 and 2.0 length-width ratios under uniform normal pressure. The boundary conditions approximate panels with riveted edges under normal pressure greater than that of the surrounding panels. Center deflections (to twice the plate thickness), membrane stresses, and extreme-fiber bending stresses are given as functions of the pressure. For small deflections, the results are consistent with those given by Timoshenko.
Author | : |
Publisher | : |
Total Pages | : 37 |
Release | : 1948 |
Genre | : |
ISBN | : |
Von Karman's equations for thin plates with large deflections are solved for the special cases of rectangular plates having ratios of length to width of 1.5 and 2 and loaded by uniform normal pressure. The boundary conditions are such as to approximate panels with riveted edges under normal pressure greater than that of the surrounding panels. Center deflections, membrane stresses, and extreme-fiber bending stresses are given as functions of the pressure for center deflections up to twice the thickness of the plate. For small deflections the results are consistent with those given by Timoshenko.
Author | : Stewart Way |
Publisher | : |
Total Pages | : 372 |
Release | : 1933 |
Genre | : |
ISBN | : |
Author | : A. S. Cakmak |
Publisher | : |
Total Pages | : 68 |
Release | : 1958 |
Genre | : |
ISBN | : |
Author | : Chi-Teh Wang |
Publisher | : |
Total Pages | : 113 |
Release | : 1948 |
Genre | : Boundary value problems |
ISBN | : |
Relaxation and successive approximation methods are used to solve Von Karman's equations as applied to initially flat, rectangular plates with large deflections under either normal pressure or combined normal pressure and side thrust, and several specific cases are analyzed. The general method developed may be applied to bending and combined bending and buckling problems with practically any boundary conditions to any required degree of accuracy or applied to solve the membrane theory of the plate which applies when the deflection is very large in comparison with the thickness of the plate.
Author | : Luis Guzmán-Barrón |
Publisher | : |
Total Pages | : 160 |
Release | : 1971 |
Genre | : Plates (Engineering) |
ISBN | : |
Author | : Kenneth William Suits |
Publisher | : |
Total Pages | : 35 |
Release | : 1970 |
Genre | : |
ISBN | : |
The report considers the large deflection of n-layered rectangular plates with clamped edges and a uniformly distributed load. The displacement and stress-strain relations for this plate with the above boundary conditions were obtained, using known Hookeian relations. From these, using the strain energy and variational methods, the required equilibrium equations were obtained. (Author).
Author | : E. H. Mansfield |
Publisher | : Elsevier |
Total Pages | : 161 |
Release | : 2014-05-12 |
Genre | : Technology & Engineering |
ISBN | : 1483222667 |
The Bending and Stretching of Plates deals with elastic plate theory, particularly on small- and large-deflexion theory. Small-deflexion theory concerns derivation of basic equations, rectangular plates, plates of various shapes, plates whose boundaries are amenable to conformal transformation, plates with variable rigidity, and approximate methods. Large-deflexion theory includes general equations and some exact solutions, approximate methods in large-deflexion theory, asymptotic large-deflexion theories for very thin plates. Asymptotic theories covers membrane theory, tension field theory, and inextensional theory. The book explains stress-strain relations, effect of forces in the plane of the plate, and rectangular plates that have all edges simply supported, or where plates that have all edges clamped. The text also considers plates of constant thickness whose boundaries are circular, sector-shaped, elliptical, or triangular. Muskhelishvili (1933) addresses boundary value problems of plane stress using analytical methods of the biharmonic equation. The book also investigates some approximate methods of analysis of large-deflexion behavior of plates of constant thickness where there is either a uniformly distributed load, or a compressive load in the plane of the plate in excess of that necessary to cause initial buckling. The book explains that the engineer can use the principle of minimum potential energy to investigate large deflexion of plates. The text is suitable for structural engineers in civil, mechanical or marine engineering, as well as to structural research workers and students.
Author | : L. J. Nolte |
Publisher | : |
Total Pages | : 57 |
Release | : 1957 |
Genre | : |
ISBN | : |
An approximate solution is given for large deflections of a clamped-edge rectangular plate under the combined action of edge thrust (or thermal strain) and lateral load. To determine center deflection and stresses, a one-term approximation to the lateral deflection mode is used in a modified energy method. The effects of nonrigid supports are examined for the case of zero lateral pressure, and it is found that while elongation of the supports is accountable by simple modification of edge thrust terms, support bending requires more substantial revision of the analysis. The concept of thermal load is introduced and calculation methods are provided for uniform and non-uniform temperature distribution in the plane of the plate. To establish the region of applicability of the analysis, critical loads are computed for more complex panel buckling modes. (Author).