Bending Of Rectangular Plates With Large Deflection
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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 | : T. H. Lin |
Publisher | : |
Total Pages | : 5 |
Release | : 1972 |
Genre | : Elastic plates and shells |
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 | : 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 | : Luis Guzmán-Barrón |
Publisher | : |
Total Pages | : 160 |
Release | : 1971 |
Genre | : Plates (Engineering) |
ISBN | : |
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 | : Samuel Levy |
Publisher | : |
Total Pages | : 47 |
Release | : 1942 |
Genre | : Plates (Engineering) |
ISBN | : |
The maximum stresses and center deflection at high pressures differ less than 3 percent from those derived by Boobnov for an infinitely long plate with clamped edges. This agreement suggests that clamped plates with a length-to-width ratio greater than 1.5 may be regarded as infinitely long plates for purposes of design.
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 | : Onkar P. Dixit |
Publisher | : |
Total Pages | : 38 |
Release | : 1971 |
Genre | : Concrete slabs |
ISBN | : |
Author | : E. H. Mansfield |
Publisher | : Cambridge University Press |
Total Pages | : 244 |
Release | : 2005-08-22 |
Genre | : Science |
ISBN | : 9780521018166 |
Written by one of the world's leading authorities on plate behavior, this study gives a clear physical insight into elastic plate behavior. Small-deflection theory is treated in Part 1 in chapters dealing with basic equations: including thermal effects and multi-layered anisotropic plates, rectangular plates, circular and other shaped plates, plates whose boundaries are amenable to conformal transformation, plates with variable thickness, and approximate methods. Large-deflection theory is treated in Part 2 in chapters dealing with basic equations and exact solutions; approximate methods, including post-buckling behavior; and asymptotic theories for very thin plates, including tension field theory and inextensional theory. The mathematical content is necessarily high, making the style of the book appropriate to engineers and applied mathematicians. E.H. Mansfield is a Fellow of the Royal Society, a founder member of the Fellowship of Engineering, and the author of over 100 publications.