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New Variational Formulations of Hybrid Stress ElementsIn the variational formulations of finite elements by the Hu-Washizu and Hellinger-Reissner principles the stress equilibrium condition is maintained by the inclusion of internal displacements which function as the Lagrange multipliers for the constraints. These versions permit the use of natural coordinates and the relaxation of the equilibrium conditions and render considerable improvements in the assumed stress hybrid elements. These include the derivation of invariant hybrid elements which possess the ideal qualities such as minimum sensitivity to geometric distortions, minimum number of independent stress parameters, rank sufficient, and ability to represent constant strain states and bending moments. Another application is the formulation of semiLoof thin shell elements which can yield excellent results for many severe test cases because the rigid body nodes, the momentless membrane strains, and the inextensional bending modes are all represented.
Document ID
Document Type
Conference Paper
Pian, T. H. H. (Massachusetts Inst. of Tech. Cambridge, MA, United States)
Sumihara, K. (Massachusetts Inst. of Tech. Cambridge, MA, United States)
Kang, D. (Massachusetts Inst. of Tech. Cambridge, MA, United States)
Date Acquired
August 12, 2013
Publication Date
June 1, 1984
Publication Information
Publication: NASA. Lewis Research Center Nonlinear Struct. Anal.
Subject Category
Funding Number(s)
Distribution Limits
Work of the US Gov. Public Use Permitted.

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