## Thin Plates and Shells: Theory: Analysis, and ApplicationsPresenting recent principles of thin plate and shell theories, this book emphasizes novel analytical and numerical methods for solving linear and nonlinear plate and shell dilemmas, new theories for the design and analysis of thin plate-shell structures, and real-world numerical solutions, mechanics, and plate and shell models for engineering applications. It includes computer processes for finite difference, finite element, boundary element, and boundary collocation methods as well as other variational and numerical methods. It also contains end-of-chapter examples and problem/solution sets, a catalog of solutions for cylindrical and spherical shells, and tables of the most commonly used plates and shells. |

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This book is a good book to start the "Theory of Shell Structures". I will give it a 5 star for its lucid explanations.

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the explanations are very clear

### Contents

1 | |

4 | |

7 | |

8 | |

14 | |

17 | |

23 Stresses Stress Resultants and Stress Couples | 20 |

24 The Governing Equation for Deflections of Plates in Cartesian Coordinates | 24 |

123 Statics of Shells | 333 |

124 Strain Energy of Shells | 340 |

125 Boundary Conditions | 341 |

126 Discussion of the Governing Equations of the General Linear Shell Theory | 344 |

127 Types of State of Stress for Thin Shells | 346 |

Problems | 347 |

The Membrane Theory of Shells | 349 |

132 The Fundamental Equations of the Membrane Theory of This Shells | 350 |

25 Boundary Conditions | 27 |

26 Variational Formulation of Plate Bending Problems | 36 |

Problems | 41 |

References | 42 |

Rectangular Plates | 43 |

33 Naviers Method Double Series Solution | 47 |

34 Rectangular Plates Subjected to a COncentrated Lateral Force P | 54 |

35 Levys Solution Single Series Solution | 60 |

36 Continuous Plates | 71 |

37 Plates on an Elastic Foundation | 76 |

38 Plates with Variable Stiffness | 81 |

39 Rectangular Plates Under Combined Lateral and Direct Loads | 84 |

310 Bending of Plates with Small Initial Curvature | 88 |

Problems | 90 |

References | 92 |

Circular Plates | 95 |

43 Axisymmetric Bending of Circular Plates | 98 |

44 The Use of Superposition for the Axisymmetric Analysis of Circular Plates | 109 |

45 Circular Plates on Elastic Foundation | 113 |

46 Asymmetric Bending of Circular Plates | 116 |

47 Circular Plates Loaded by an Eccentric Lateral Concentrated Force | 119 |

48 Circular Plates of Variable Thickness | 122 |

Problems | 128 |

References | 132 |

Bending of Plates of Various Shapes | 133 |

53 SectorShaped Plates | 135 |

54 Triangular Plates | 137 |

55 Skew Plates | 139 |

Problems | 140 |

References | 141 |

Plate Bending by Approximate and Numerical Methods | 143 |

62 The Finite Difference Method FDM | 144 |

63 The Boundary Collocation Method BCM | 152 |

64 The Boundary Element Method BEM | 156 |

65 The Galerkin Method | 166 |

66 The Ritz Method | 171 |

67 The Finite Element Method FEM | 175 |

Problems | 186 |

References | 188 |

Advanced Topics | 191 |

72 Orthotropic and Stiffened Plates | 197 |

73 The Effect of Transverse Shear Deformation on the Bending of Elastic Plates | 207 |

74 LargeDeflection Theory of Thin Plates | 215 |

75 Multilayered Plates | 231 |

76 Sandwich Plates | 233 |

Problems | 237 |

References | 239 |

Buckling of Plates | 241 |

83 The Equilibrium Method | 245 |

84 The Energy Method | 255 |

85 Buckling Analysis of Orthotropic and Stiffened Plates | 259 |

86 Postbuckling Behavior of Plates | 265 |

87 Buckling of Sandwich Plates | 270 |

Problems | 272 |

References | 273 |

The Vibration of Plates | 275 |

92 Free Flexural Vibrations of Rectangular Plates | 276 |

93 Approximate Methods in Vibration Analysis | 278 |

94 Free Flexural Vibrations of Circular Plates | 284 |

95 Forced Flexural Vibrations of Plates | 286 |

Problems | 288 |

References | 289 |

Introduction to the General Shell Theory | 291 |

102 General Definitions and Fundamentals of Shells | 293 |

103 Brief Outline of the Linear Shell Theories | 294 |

104 LoadingCarrying Mechanism of Shells | 299 |

References | 300 |

Geometry of the Middle Surface | 303 |

112 Principal Directions and Lines of Curvature | 304 |

113 The First and Second Quadratic Forms of Surfaces | 307 |

114 Principal Curvatures | 310 |

115 Unit Vectors | 311 |

116 Equations of Codazzi and Gauss Gaussian Curvature | 312 |

117 Classification of Shell Surfaces | 313 |

118 Specialization of Shell Geometry | 316 |

Problems | 324 |

The General Linear Theory of Shells | 325 |

122 Kinematics of Shells | 326 |

133 Applicability of The Membrane Theory | 351 |

134 The Membrane Theory of Shells of Revolution | 352 |

135 Symmetrically Loaded Shells of Revolution | 356 |

136 Membrane Analysis of Cylindrical and Conical Shells | 361 |

137 The Membrane Theory of Shells of an Arbitrary Shape in Cartesian Coordinates | 368 |

Problems | 371 |

References | 372 |

Application of the Membrane Theory to the Analysis of Shell Structures | 373 |

142 Membrane Analysis of Liquid Storage Facilities | 390 |

143 Axisymmetric Pressure Vessels | 402 |

Problems | 405 |

References | 409 |

Moment Theory of Circular Cylindrical Shells | 411 |

152 Circular Cylindrical Shells Under General Loads | 412 |

153 Axisymmetrically Loaded Circular Cylindrical Shells | 421 |

154 Circular Cylindrical Shell of Variable Thickness Under Axisymmetric Loading | 443 |

Problems | 446 |

References | 448 |

The Moment Theory of Shells of Revolution | 449 |

162 Governing Equations | 450 |

163 Shells of Revolution Under Axisymmetrical Loads | 454 |

164 Approximate Method for Solution of the Governiing Equations 1630 | 460 |

165 Axisymmetric Spherical Shells Analysis of the State of Stress at the SphericaltoCylindrical Junction | 464 |

166 Axisymmetrically Loaded Conical Shells | 475 |

167 Axisymmetric Deformation of Toroidal Shells | 478 |

Problems | 479 |

References | 481 |

Approximate Theories of Shell Analysis and Their Applications | 483 |

173 The DonnelMushtariVlasov Theory of Thin SHells | 494 |

174 Theory of Shallow Shells | 497 |

175 The Theory of Edge Effect | 507 |

Problems | 511 |

References | 514 |

Advanced Topics | 515 |

182 The Geometrically Nonlinear Shell Theory | 522 |

183 Orthotropic and Stiffened Shells | 531 |

184 Multilayered Shells | 538 |

185 Sandwich Shells | 541 |

186 The Finite Element Representation of Shells | 543 |

187 Approximate and Numerical Methods for Solution of Nonlinear Equations | 553 |

Problems | 561 |

References | 562 |

Buckling of Shells | 565 |

193 Linear Buckling Analysis of Circular Cylindrical Shells | 573 |

194 Postbuckling Analysis of Circular Cylindrical Shells | 585 |

195 Buckling of Orthotropic And Stiffened Cylindrical Shells | 590 |

196 Stability of Cylindrical Sandwich Shells | 595 |

197 Stability of Shallow Shells Under External Normal Pressure | 597 |

198 Buckling of Conical Shells | 599 |

199 Buckling of Spherical Shells | 600 |

1910 Design Stability Analysis | 602 |

Problems | 606 |

607 | |

Vibrations of Shells | 609 |

202 Free Vibrations of Cylindrical Shells | 610 |

203 Free Vibrations of Conical Shells | 618 |

204 Free Vibrations of Shallow Shells | 619 |

205 Free Vibrations of Stiffened Shells | 622 |

206 Forced Vibrations of Shells | 624 |

627 | |

Some Reference Data | 629 |

A1 Typical Properties of Selected Engineering Materials at Room Temperatures US Customary Units | 630 |

A2 Typical Properties of Selected Engineering Materials at Room Temperatures International System SI Units | 631 |

A3 Units and Conversion Factors | 632 |

Fourier Series Expansion | 635 |

B3 Coefficients of the Fourier Series | 636 |

B5 The Order of the Fourier Series Coefficients | 637 |

B6 Double Fourier Series | 639 |

640 | |

Verification of Relations of the Theory of Surfaces | 641 |

C2 Geometry of a Surface | 643 |

C3 Derivatives of Unit Coordinate Vectors | 645 |

C4 Verification of Codazzi and Gauss Equations | 649 |

Derivation of the StrainDisplacement Relations | 651 |

D2 Strain Components of the Shell | 653 |

Verification of Equilibrium Equations | 655 |

659 | |

### Other editions - View all

Thin Plates and Shells: Theory: Analysis, and Applications Eduard Ventsel,Theodor Krauthammer No preview available - 2001 |

### Common terms and phrases

approximate Assume assumptions axis bending moments boundary conditions buckling analysis circular cylindrical shell circular plate circumferential coefficients compressive conical shell consider const constitutive equations corresponding curvature curve curvilinear coordinates deflection surface deformations derivatives determined direction displacements edge effect elastic equilibrium external finite element flexural following form Fourier series function Galerkin method Gaussian curvature geometric given by Eq governing differential equation governing equations in-plane internal forces linear lines of curvature membrane forces membrane theory method middle surface natural frequency nodal nonlinear normal numerical obtain the following orthotropic parameters plane Poisson's ratio pressure principal curvatures radius rectangular plate relations Ritz method shallow shell shear forces shear stresses shell edge shell theory shells of revolution shown in Fig simply supported solution of Eq stiffeners stiffness strain components strain energy stress components stress resultants Substituting surface load theory of thin thickness thin shells tions vector zero

### Popular passages

Page 5 - Turkey, which centuries ago had been an exporter of cereals, turned at the end of the 19th and the beginning of the 20th centuries into a net importer of wheat.

Page 8 - The stress components normal to the middle surface are small compared with the other stress components and may be neglected in the stressstrain relations. 3° The normals of the undeformed middle surface are deformed into the normals of the deformed middle surface.