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Finite-Element Method for Framed Structures

  • William WeaverJr.
  • James M. Gere

Abstract

Matrix analysis of framed structures may be considered as a subset of the more general method of finite elements [1–4]. Any continuum can be partitioned into subregions called finite elements. These subregions are of finite size and usually have simpler geometries than the boundaries of the original continuum. Such a partitioning serves to convert a problem involving an infinite number of degrees of freedom to one with a finite number in order to simplify the solution process. Applications in solid mechanics consist of framed structures, two-and three-dimensional solids, plates, shells, and so on. One-, two-, and three-dimensional finite elements may be required for such analyses. However, the members of framed structures are relatively long compared to their cross-sectional dimensions, so only one-dimensional finite elements are needed to model them.

Keywords

Stiffness Matrix Frame Structure Virtual Work Nodal Displacement Linear Differential Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Weaver, W., Jr., and Johnston, P. R., Finite Elements for Structural Analysis, Prentice-Hall, Englewood Cliffs, New Jersey, 1984.Google Scholar
  2. 2.
    Weaver, W., Jr., and Johnston, P. R., Structural Dynamics by Finite Elements, Prentice-Hall, Englewood Cliffs, New Jersey, 1987.Google Scholar
  3. 3.
    Zienkiewicz, O. C., and Taylor, R., The Finite Element Method, 4th ed., McGraw-Hill, New York, 1989.Google Scholar
  4. 4.
    Cook, R. D., Concepts and Applications of Finite Element Analysis, 2nd ed., Wiley, New York, 1981.Google Scholar
  5. 5.
    Timoshenko, S. P., and Goodier, J. N., Theory of Elasticity, 3rd ed., McGraw-Hill, New York, 1970.Google Scholar

Copyright information

© Van Nostrand Reinhold 1990

Authors and Affiliations

  • William WeaverJr.
    • 1
  • James M. Gere
    • 1
  1. 1.Stanford UniversityUSA

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