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