The Bending and Stretching of Plates

International Series of Monographs on Aeronautics and Astronautics: Solid and Structural Mechanics, Vol. 6

1st Edition - January 1, 1964
Author: E. H. Mansfield
Editors: R. L. Bisplinghoff, W. S. Hemp
Language: English
eBook ISBN:
9 7 8 - 1 - 4 8 3 2 - 2 2 6 6 - 0

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… Read more

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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.

PrefacePrincipal NotationPart I Small-Deflexion Theory Chapter I. Derivation of the Basic Equations 1.1 Stress-Strain Relations 1.2 Rotation of Axes of Reference 1.3 Equilibrium 1.4 Differential Equation for the Deflexion 1.5 Effect of Forces in the Plane of the Plate 1.6 General Boundary Conditions Chapter II. Rectangular Plates 2.1 Plates with All Edges Simply Supported 2.2 Plates with Two Opposite Edges Simply Supported 2.3 Plates with All Edges Clamped Chapter III. Plates of Various Shapes 3.1 Circular Plates 3.2 Uniformly Loaded Sector Plate 3.3 Sector and Wedge-Shaped Plates with General Boundary Conditions 3.4 Elliptical Plate 3.5 Equilateral Triangular Plate 3.6 Isosceles Right-Angled Triangular Plate Chapter IV. Plates Whose Boundaries are Amenable to Conformal Transformation 4.1 Governing Differential Equation in Complex Coordinates 4.2 General Solution for a Clamped Plate 4.3 General Solution for a Simply Supported Plate 4.4 Square Plate with Rounded Corners Chapter V. Plates with Variable Rigidity 5.1 Flexure and Torsion of a Strip of Variable Rigidity 5.2 Rectangular Plate with Exponential Variation of Rigidity 5.3 Rectangular Plate with Linear Variation of Rigidity 5.4 Circular Plates 5.5 Circular Plates with Rotational Symmetry Chapter VI. Approximate Methods 6.1 The Strain Energy of a Deformed Plate 6.2 Principle of Minimum Total Potential Energy—Ritz Method 6.3 The Galerkin Method 6.4 A Variational Method 6.5 Method of Boundary Error MinimizationPart II Large-Deflexion Theory Chapter VII. General Equations and Some Exact Solutions 7.1 Governing Differential Equations 7.2 Cylindrical Deflexion of Long Strip 7.3 Uniformly Loaded Circular Plate 7.4 Flexure and Torsion of a Thin Strip with Lateral Thickness Variation Chapter VIII. Approximate Methods in Large-Deflexion Analysis 8.1 Perturbation Method for Normally Loaded Plates 8.2 Perturbation Method in Post-Buckling Problems 8.3 An Energy Method Chapter IX. Asymptotic Large-Deflexion Theories for Very Thin Plates 9.1 Membrane Theory 9.2 Inextensional TheoryAuthor IndexSubject Index