Item Details

Comparison of Finite-Difference Schemes for Analysis of Shells of Revolution

by Ahmed K. Noor and Wendell B. Stephens
Format
Book; Government Document; Online; EBook
Published
Washington, D.C. : National Aeronautics and Space Administration ; [Springfield, Va. : For sale by the National Technical Information Service], 1973.
Language
English
Series
NASA Technical Note
Summary
Several finite difference schemes are applied to the stress and free vibration analysis of homogeneous isotropic and layered orthotropic shells of revolution. The study is based on a form of the Sanders-Budiansky first-approximation linear shell theory modified such that the effects of shear deformation and rotary inertia are included. A Fourier approach is used in which all the shell stress resultants and displacements are expanded in a Fourier series in the circumferential direction, and the governing equations reduce to ordinary differential equations in the meridional direction. While primary attention is given to finite difference schemes used in conjunction with first order differential equation formulation, comparison is made with finite difference schemes used with other formulations. These finite difference discretization models are compared with respect to simplicity of application, convergence characteristics, and computational efficiency. Numerical studies are presented for the effects of variations in shell geometry and lamination parameters on the accuracy and convergence of the solutions obtained by the different finite difference schemes. On the basis of the present study it is shown that the mixed finite difference scheme based on the first order differential equation formulation and two interlacing grids for the different fundamental unknowns combines a number of advantages over other finite difference schemes previously reported in the literature.
Description
43 p. : ill. ; 27 cm.
Mode of access: Internet.
Notes
  • Prepared at Langley Research Center.
  • Cover title.
  • Bibliography: p. 24-25.
Series Statement
NASA technical note ; NASA TN D-7337
Logo for Copyright Not EvaluatedCopyright Not Evaluated
Technical Details

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    a| Comparison of finite-difference schemes for analysis of shells of revolution c| by Ahmed K. Noor and Wendell B. Stephens.
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    a| Washington, D.C. : b| National Aeronautics and Space Administration ; a| [Springfield, Va. : b| For sale by the National Technical Information Service], c| 1973.
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    a| 43 p. : b| ill. ; c| 27 cm.
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    a| NASA technical note ; v| NASA TN D-7337
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    a| Prepared at Langley Research Center.
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    a| Cover title.
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    a| Bibliography: p. 24-25.
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    a| Several finite difference schemes are applied to the stress and free vibration analysis of homogeneous isotropic and layered orthotropic shells of revolution. The study is based on a form of the Sanders-Budiansky first-approximation linear shell theory modified such that the effects of shear deformation and rotary inertia are included. A Fourier approach is used in which all the shell stress resultants and displacements are expanded in a Fourier series in the circumferential direction, and the governing equations reduce to ordinary differential equations in the meridional direction. While primary attention is given to finite difference schemes used in conjunction with first order differential equation formulation, comparison is made with finite difference schemes used with other formulations. These finite difference discretization models are compared with respect to simplicity of application, convergence characteristics, and computational efficiency. Numerical studies are presented for the effects of variations in shell geometry and lamination parameters on the accuracy and convergence of the solutions obtained by the different finite difference schemes. On the basis of the present study it is shown that the mixed finite difference scheme based on the first order differential equation formulation and two interlacing grids for the different fundamental unknowns combines a number of advantages over other finite difference schemes previously reported in the literature.
    538
      
      
    a| Mode of access: Internet.
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    a| Finite differences.
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    a| Elastic plates and shells.
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    0
    a| Body of revolution x| Mathematical models.
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    a| Stephens, Wendell B.
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    a| United States. b| National Aeronautics and Space Administration.
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    a| Langley Research Center.
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