Computational Tensor Analysis of Shell Structures (Lecture Notes in Engineering): 58 - Brossura

Naomis, Steve

Brossura

ISBN 10: 3540528520 ISBN 13: 9783540528524

Casa editrice: Springer-Verlag, 1990

Riassunto

The authors describe a method for static and free vibration analyses of thin shell structures. The contents include: development of a thin shell theory, use of curvilinear mesh and finite differences to approximate the geometry and deformation characteristics of thin shells, development of formulae for transformation of components and equations in global and local coordinate systems, assessment of the accuracy of various approximations for displacement components and area integrations, computing issues of eigen solutions and presentation of numerical values of normalized mode shapes of example shell structures. This book is useful for both engineers and researchers who work on the static and dynamic analyses of shell structures. It assumes familiarity with tensor calculus and finite difference method.

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Contenuti

1. Introduction.- 2. General Theory.- 2.1 A Summary of the Tensorial Quantities Required in the Formulation of a Shell Theory.- 2.1.1 Base Vectors.- 2.1.2 Metric Tensors.- 2.1.3 Coordinate Transformations.- 2.1.4 Christoffel Symbols.- 2.1.5 Covariant Derivatives.- 2.2 Surface Geometry.- 2.2.1 Curvilinear Coordinates on a Surface.- 2.2.2 Geometry of a Curved Surface.- 2.3 The Strain Tensor.- 2.4 The Stress Tensor.- 2.5 The Constitutive Equations.- 2.6 The Theory of Shells.- 2.6.1 Shell Geometry.- 2.6.2 Deformation Characteristics.- 2.6.3 The Change in Curvature Tensor.- 2.6.4 The Strain-Displacement Equations.- 2.6.5 Interpretation and Discussion of the Strain-Displacement Equations.- 3. Numerical Fundamentals.- 3.1 The Curvilinear Finite Difference Method.- 3.2 The Numerical Computation of the Surface Geometric Quantities.- 3.2.1 Base Vectors and Metric Tensors.- 3.2.2 The Christoffel Symbol.- 3.2.3 The Curvature Tensor.- 3.2.4 Covariant Derivative of the Curvature Tensor.- 3.3 The Principle of Virtual Displacements.- 3.4 Discretization and Displacement Fields.- 3.5 The Numerical Implementation of the General Surface Stress, Strain and Displacement Components.- 3.5.1 The General Surface Displacement Components.- 3.5.2 The General Strain Tensor.- 3.5.3 The General Stress Tensor.- 3.6 Boundary Conditions.- 3.7 The Numerical Solution of the Eigenvalue Problem.- 4. Numerical Implementation.- 4.1 A Second Order Implementation.- 4.1.1 Second Order CFD Approximation.- 4.1.2 Numerical Integration Scheme.- 4.1.3 Numerical Examples.- 4.2 A Third Order Implementation.- 4.2.1 Third Order CFD Approximation.- 4.2.2 Boundary Conditions.- 5. Numerical Applications.- 5.1 Simply Supported Plate.- 5.2 Cantilever Plate.- 5.3 Spherical Cap on a Square Base.- 5.4 Cylindrical Panel.- 5.5 Curved Fan Blade.- 5.6 Conical Shell Panel.- 5.7 Cylindrical Tank.- 6. Summary.- References.- Appendix A: Displacement Transformations.- Appendix B: Finite Difference Expressions.- Appendix C: Numerical Integration of the Stiffness Matrix.- Appendix D: Application of the CFD method to the Analysis of Beam Bending Problems with Fixed Edges.- Appendix E: Transformation of the Generalized Eigenvalue Problem to Standard Form.- Appendix F: Numerical Results.- Simply supported plate.- Cantilever plate.- Curved fan blade.- Spherical shell.- Cylindrical panel.- Cylindrical tank.- Conoidal shell.

Dettagli dell'edizione

• Editore: Springer-Verlag
• Data di pubblicazione: 1990
• Lingua: Inglese
• ISBN 10: 3540528520
• ISBN 13: 9783540528524
• Rilegatura: Copertina flessibile
• Numero di pagine: 324
• Contatto del produttore: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3,69115 Heidelberg, Germany; Heidelberg; Germania