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Plates : theories and applications

Author: K Bhaskar
Publisher: New Delhi, India ; Chichester, England : Wiley : Ane Books Pvt. Ltd., 2014. ©2014
Series: Ane/Athena Books
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:

Plates: Theories and Applications provides a comprehensive introduction to plate structures, covering classical theory and applications.

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Genre/Form: Electronic books
Additional Physical Format: Print version:
Bhaskar, K.
Plates : theories and applications.
New Delhi, India ; Chichester, England : Wiley, ©2014
335 pages
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: K Bhaskar
ISBN: 9781118894804 1118894804 1118893875 9781118893876
OCLC Number: 889265676
Notes: Includes index.
Description: 1 online resource (357 pages).
Contents: PART A CLASSICAL THEORY AND STRAIGHTFORWARD APPLICATIONS 1 Definition of a Thin Plate 1 1.1 The Elasticity Approach 1 1.2 A Test Problem 4 1.3 The Case of a Thin Plate 7 2 Classical Plate Theory 11 2.1 Assumptions of Classical Plate Theory 12 2.2 Moment-Curvature Relations 16 2.3 Equilibrium Equations 18 2.4 Governing Biharmonic Equation 21 2.5 Boundary Conditions 21 2.6 Solution of a Problem 26 2.7 Inclusion of an Elastic Foundation / Thermal Effects 28 2.7.1 Elastic Foundation 28 2.7.2 Thermal Effects 29 2.8 Strain Energy of the Plate 30 3 A Critical Assessment of Classical Plate Theory 33 3.1 CPT Solution for the Test Problem of Section 1.2 33 3.2 Comparison with the Elasticity Solution 35 3.3 Why the Plane-Stress Constitutive Law? 37 4 Analysis of Rectangular Plates 40 4.1 Recapitulation of Fourier Series 40 4.2 Navier's Method 43 4.3 Levy's Method 50 4.4 Closed-form Solution for a Plate with Corner Supports 59 5 Analysis of Circular Plates 69 5.1 Equations of the Theory of Elasticity 69 5.2 Equations of CPT 71 5.3 Solution of Axisymmetric Problems 75 6 Free and Forced Vibrations 89 6.1 Equations of Motion 89 6.2 Free Vibration Analysis 91 6.3 Forced Vibration Analysis 99 7 Effect of In-plane Forces on Static Flexure, Dynamics and Stability 103 7.1 Governing Equations for Combined Bending and Stretching 103 7.2 Analysis for Stability 108 7.3 Static Flexure 115 7.4 Free Vibrations 117 8 Approximate Solutions 121 8.1 Analytical and Numerical Methods 121 8.2 Rayleigh-Ritz Method 122 8.2.1 Static Flexure 122 8.2.2 Buckling 130 8.2.3 Free Vibration Analysis 140 8.3 Galerkin s Method 147 Appendix Solutions for Problems 162 PART B COMPLICATING EFFECTS AND CORRESPONDING THEORIES 9 Anisotropic, Laminated and Functionally-Graded Plates 191 9.1 CPT for Homogeneous Anisotropic Plates 191 9.1.1 The Anisotropic Constitutive Law 191 9.1.2 Plate Equations 199 9.2 Classical Laminated Plate Theory 203 9.3 CPT for Functionally-Graded Plates 215 10 Elasticity Solutions for Plates 220 10.1 Cylindrical Bending of a Cantilevered Plate Strip Under Tip Shear 220 10.1.1 Homogeneous Strip 221 10.1.2 A Laminated Strip 228 10.2 Flexure of Simply Supported Rectangular Plates/Laminates Due to Transverse Loading 233 10.3 Vibrations and Stability of Simply Supported Rectangular Plates and Laminates 238 10.4 Solutions for Rectangular Plates with Other Edge Conditions 240 10.5 Corner Reactions in Simply Supported Plates Insight Obtained from Elasticity Solutions 242 10.6 Plates under Thermal Loads 246 11 Shear Deformation Theories 248 11.1 First-order Shear Deformation Theory 249 11.2 Higher-order Theories 260 12 Variable Thickness Plates 267 12.1 Stepped versus Smooth Thickness Variation 267 12.2 Rectangular Plates 268 12.3 Circular Plates 272 13 Plate Buckling due to Non-Uniform Compression 276 13.1 The In-plane Problem 276 13.2 Determination of the Critical Load 284 13.3 Some Other Approaches 287 14 Non-Linear Flexure and Vibrations 290 14.1 Cylindrical Bending of a Simply Supported Plate Strip 290 14.1.1 Case (a): Immovable Edges 290 14.1.2 Case (b): Freely Movable Edges 299 14.1.3 Observations from the Above Solutions 305 14.2 Moderately Large Deformation Theory 306 14.3 Flexure of a Simply Supported Rectangular Plate 312 14.4 Nonlinear Vibrations of a Rectangular Plate 318 15 Post-Buckling Behaviour 324 15.1 Post-Buckling of a Column 324 15.2 Post-Buckling of a Rectangular Plate 326 15.3 Effective Width 333 Index
Series Title: Ane/Athena Books
Responsibility: K. Bhaskar, T.K. Varadan.

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