Elementary Theory of Elastic Plates

1st Edition

The Commonwealth and International Library: Structures and Solid Body Mechanics Division

Authors:
Editors:
eBook ISBN: 9781483147000
Imprint: Pergamon
Published Date: 1st January 1964
Page Count: 118
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Description

Elementary Theory of Elastic Plates deals with plate theory, particularly on the elastic behavior of initially flat thin plates subjected to loads, producing deflexions. This book discusses rectangular plates and circular plates subjected to different types of load conditions. This text describes the bending moment and curvature of beams, and gives the formula of principal axes, where the location of a neutral axis that experiences zero stress and strain, can be found.
This book also notes how calculations can show small or negligible deflexions. The text discusses Possion's ratio effect and the Mohr's circle relationship. This text analyzes the various loads acting on different parts of the rectangular plate using the Navier method; the Levy's method is taken up when considerations are on other forms of boundary support on the rectangular plate. This book then addresses the circular plate that experiences bending moments and curvatures when it is placed under radially symmetric loads. This text explains the equation that is applicable in a radially symmetric case. This book also addresses understanding approximations of energy in stability problems when there is bending and twisting as shown in a strut with a certain thickness, radial length of the arms, and length of the strut.
Engineers, physicists, architects, and designers of industrial equipment subject to heavy loads will appreciate the information found in this book.

Preface

Chapter I. Basic Relationships for Rectangular Plates

1. Bending Moment and Curvature

2. Equilibrium of Plate Element: Bending and Twisting Moments in Any Direction

3. Geometry of Curvature and Twist

4. Principal Bending Moments and Principal Curvatures

5. Directions of Twisting Moments

Summary

1. The Governing Equation

2. Boundary Conditions

3. Concentrated Forces at the Corners

4. The Plate Simply Supported on All Four Sides—The Navier Method

Summary

Chapter III. The Rectangular Plate with Various Forms of Boundary Support

1. Levy's Method

2. Separation into Symmetric and Skew Symmetric Parts

Summary

Chapter IV. The Circular Plate

2. Equilibrium of Plate Element for the Radially Symmetric Case

3. The Governing Equation for the Radially Symmetric Case

4. Derivation of the Governing Equation in Polar Coordinates from the Cartesian Case

5. Examples of Solution for Cases of Radial Symmetry

6. A Note About Boundary Conditions

Summary

Chapter V. Potential Energy Methods

1. Strain Energy of Bending and Torsion

2. Total Potential Energy

3. Exact Solutions by Potential Energy

4. Approximate Solutions Using Potential Energy

5. A Note on the Lagrange Multiplier Method

6. A Note about Basic Functions

Summary

Chapter VI. Membrane Forces in the Plate: Stability

1. "Small" Deflexions

2. Membrane Forces: Effect on The Governing Equation

3. Buckling of a Rectangular Plate, Simply Supported All round, under End Thrust

4. Buckling of a Plate Simply Supported on Three Edges and Free on the Fourth

5. The Use of Energy Approximations in Problems of Stability

Summary

Appendix. Some Relevant Mathematics

1. Even and Odd Functions

2. Fourier Analysis—The Full Range Series

3. Fourier Analysis—The Half Range Series

4. a Note About "Cross Product" Terms in Certain Integrations

5. End Shortening Due to Flexure

6. Double Integration

Examples for Solution

No. of pages:
118
Language:
English
Published:
Imprint:
Pergamon
eBook ISBN:
9781483147000