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Finite Plane Strain of Incompressible Elastic Solids by the Finite Element Method

Published online by Cambridge University Press:  07 June 2016

J. Tinsley Oden
J. Tinsley Oden*
Affiliation:
University of Alabama in Huntsville
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Summary

The finite element method is extended to the problem of finite plane strain of elastic solids. A highly elastic body subjected to two-dimensional deformations is represented by an assembly of triangular elements of finite dimension. The displacement fields within each element are approximated by linear functions of the local coordinates. Non-linear stiffness relations involving generalised node forces and displacements are derived from energy considerations. For demonstration purposes, the non-linear stiffness equations are applied to the problems of finite simple shear and generalised shear. For finite simple shear, it is shown that these relations are in exact agreement with finite elasticity theory. Convergence rates of finite element representations of these problems are briefly examined.

Type
Research Article
Information
Aeronautical Quarterly , Volume 19 , Issue 3 , August 1968 , pp. 254 - 264
Copyright
Copyright © Royal Aeronautical Society. 1968

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References

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