An improved parametric formulation for the variationlly correct distortion immune three-noded bar element

Mukherjee, Somenath and Manju, S (2011) An improved parametric formulation for the variationlly correct distortion immune three-noded bar element. Structural Engineering and Mechanics, 38 (3). 000-000.

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A new method of formulation of a class of elements that are immune to mesh distortion effects is proposed here. The simple three-noded bar element with an offset of the internal node from the element center is employed here to demonstrate the method and the principles on which it is founded upon. Using the function space approach, the modified formulation is shown here to be superior to the conventional isoparametric version of the element since it satisfies the completeness requirement as the metric formulation, and yet it is in agreement with the best-fit paradigm in both the metric and the parametric domains. Furthermore, the element error is limited to only those that are permissible by the classical projection theorem of strains and stresses. Unlike its conventional counterpart, the modified element is thus not prone to any errors from mesh distortion. The element formulation is symmetric and thus satisfies the requirement of the conservative nature of problems associated with all self-adjoint differential operators. The present paper indicates that a proper mapping set for distortion immune elements constitutes geometric and displacement interpolations through parametric and metric shape functions respectively, with the metric components in the displacement/strain replaced by the equivalent geometric interpolation in parametric co-ordinates.

Item Type: Article
Uncontrolled Keywords: metric and parametric; unsymmetric and symmetric formulations; element distortion; best-fit paradigm; variational correctness; orthogonal projection; function spaces; modified shape functions.
Subjects: ENGINEERING > Structural Mechanics
Depositing User: Ms Indrani V
Date Deposited: 03 Oct 2012 05:21
Last Modified: 11 Oct 2012 05:18

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