Non-linear Bending of a Circular Plate Under Normal Pressure PDF Download
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Author: Eleazer Bromberg
Publisher:
ISBN:
Category :
Languages : en
Pages : 146
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Author: Eleazer Bromberg
Publisher:
ISBN:
Category :
Languages : en
Pages : 146
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Author: Johny Hellmann
Publisher:
ISBN:
Category : Plates (Engineering)
Languages : en
Pages : 67
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Book Description
A theoretical and numerical analysis is presented for the elastic deflections and stresses of an initially flat circular plate with clamped fixed edge, under uniform normal pressure. In considering large deflection bending, i.e. deflections up to several thicknesses of the plate, we are led to two coupled partial differential equations which are given in the literature by Foppl and von Karman. We attempt an approximative solution of these equations by representing each of the unknown functions of these equations as a formal series of eigenfunctions. We choose the most natural set of eigenfunctions, the Bessel functions of index one, each of which individually satisfied all but one of the boundary conditions. We then calculate, by means of computer methods, deflection and stress results which turn out to be in strikingly good agreement with earlier theoretical and experimental results in the literature. All of this is accomplished with but a five or nine mode solution, which can be found with very little effort. (Author).
Author: Herbert Bishop Keller
Publisher:
ISBN:
Category : Bending
Languages : en
Pages : 54
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Author: Herbert B. Keller
Publisher: Forgotten Books
ISBN: 9780267754496
Category : Mathematics
Languages : en
Pages : 52
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Excerpt from Non-Linear Bending and Buckling of Circular Plates In this paper we consider a thin circular elastic plate of thickness t and radius R subjected either to a uniform lateral pressure, p, or to a uniform edge thrust, f. The first loading situation is referred to as a bending problem and the second as a buckling problem. In both cases only rotationally symmetric deformations will be considered so that all deflections and stresses are functions of a single radial coordinate, r. It is well known that the classical linear theory of plates yields solutions of these problems which are valid only for a limited range of low loads. For larger values of p and f it is necessary to apply non-linear plate theories which allow for finite deflections and account for the interaction of membrane and bending stresses. Thus we employ the von Karman equations [1] which are based on a non-linear theory of elasticity with infinitesimal strains and are valid for flat plates undergoing small but finite displacements. For rotationally symmetric deformations of circular plates these equations reduce to two coupled second order non - linear ordinary differential equations. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Author: V. G. Hart
Publisher:
ISBN:
Category : Mathematical analysis
Languages : en
Pages : 80
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The present work deals with the problem of bending of an annular or ring-shaped plate under the action of edge forces transverse to its initial plane. The resulting displacement of the middle surface of the plate is supposed finite, and we must consider the stretching of this middle surface in addition to its bending. We suppose the plate to be thin, that the width of the ring is unrestricted, and that the problem exhibits radial symmetry.
Author: Muthukrishnan Sathyamoorthy
Publisher: CRC Press
ISBN: 1351359819
Category : Mathematics
Languages : en
Pages : 548
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Book Description
Nonlinear Analysis of Structures presents a complete evaluation of the nonlinear static and dynamic behavior of beams, rods, plates, trusses, frames, mechanisms, stiffened structures, sandwich plates, and shells. These elements are important components in a wide variety of structures and vehicles such as spacecraft and missiles, underwater vessels and structures, and modern housing. Today's engineers and designers must understand these elements and their behavior when they are subjected to various types of loads. Coverage includes the various types of nonlinearities, stress-strain relations and the development of nonlinear governing equations derived from nonlinear elastic theory. This complete guide includes both mathematical treatment and real-world applications, with a wealth of problems and examples to support the text. Special topics include a useful and informative chapter on nonlinear analysis of composite structures, and another on recent developments in symbolic computation. Designed for both self-study and classroom instruction, Nonlinear Analysis of Structures is also an authoritative reference for practicing engineers and scientists. One of the world's leaders in the study of nonlinear structural analysis, Professor Sathyamoorthy has made significant research contributions to the field of nonlinear mechanics for twenty-seven years. His foremost contribution to date has been the development of a unique transverse shear deformation theory for plates undergoing large amplitude vibrations and the examination of multiple mode solutions for plates. In addition to his notable research, Professor Sathyamoorthy has also developed and taught courses in the field at universities in India, Canada, and the United States.
Author: Herbert Keller
Publisher: Andesite Press
ISBN: 9781296832452
Category :
Languages : en
Pages : 50
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This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Author: Chuen-Yuan Chia
Publisher:
ISBN:
Category : Technology & Engineering
Languages : en
Pages : 448
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Author: George Gerard
Publisher:
ISBN:
Category : Buckling (Mechanics)
Languages : en
Pages : 28
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Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 630
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