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Computational Tensor Analysis of Shell Structures: Lecture Notes in Engineering, cartea 58

Autor Steve Naomis, Paul C. M. Lau
en Limba Engleză Paperback – 7 aug 1990
This book presents a method which is capable of evaluating the deformation characteristics of thin shell structures A free vibration analysis is chosen as a convenient means of studying the displacement behaviour of the shell, enabling it to deform naturally without imposing any particular loading conditions. The strain-displacement equations for thin shells of arbitrary geometry are developed. These relationships are expressed in general curvilinear coordinates and are formulated entirely in the framework of tensor calculus. The resulting theory is not restricted to shell structures characterized by any particular geometric form, loading or boundary conditions. The complete displacement and strain equations developed by Flugge are approximated by the curvilinear finite difference method and are applied to computing the natural frequencies and mode shapes of general thin shells. This approach enables both the displacement components and geometric properties of the shell to be approximated numerically and accurately. The selection of an appropriate displacement field to approximate the deformation of the shell within each finite difference mesh is discussed in detail. In addition, comparisons are made between the use of second and third-order finite difference interpolation meshes.
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Specificații

ISBN-13: 9783540528524
ISBN-10: 3540528520
Pagini: 324
Ilustrații: XII, 309 p.
Dimensiuni: 170 x 242 x 17 mm
Greutate: 0.52 kg
Ediția:Softcover reprint of the original 1st ed. 1990
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Lecture Notes in Engineering

Locul publicării:Berlin, Heidelberg, Germany

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Cuprins

1. Introduction.- 2. General Theory.- 2.1 A Summary of the Tensorial Quantities Required in the Formulation of a Shell Theory.- 2.2 Surface Geometry.- 2.3 The Strain Tensor.- 2.4 The Stress Tensor.- 2.5 The Constitutive Equations.- 2.6 The Theory of Shells.- 3. Numerical Fundamentals.- 3.1 The Curvilinear Finite Difference Method.- 3.2 The Numerical Computation of the Surface Geometric Quantities.- 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.- 3.6 Boundary Conditions.- 3.7 The Numerical Solution of the Eigenvalue Problem.- 4. Numerical Implementation.- 4.1 A Second Order Implementation.- 4.2 A Third Order Implementation.- 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.