This article is cited in 1 paper

Refined geometrically nonlinear formulation of a thin-shell triangular finite element

V. V. Kuznetsov, S. V. Levyakov

Novosibirsk State Technical University, Novosibirsk, 630092

Abstract: A refined geometrically nonlinear formulation of a thin-shell finite element based on the Kirchhoff–Love hypotheses is considered. Strain relations, which adequately describe the deformation of the element with finite bending of its middle surface, are obtained by integrating the differential equation of a planar curve. For a triangular element with 15 degrees of freedom, a cost-effective algorithm is developed for calculating the coefficients of the first and second variations of the strain energy, which are used to formulate the conditions of equilibrium and stability of the discrete model of the shell. Accuracy and convergence of the finite-element solutions are studied using test problems of nonlinear deformation of elastic plates and shells.

Keywords: thin shell, nonlinear deformation, finite-element method, invariants, kinematic group, planar curve.

UDC: 539.3

Received: 25.04.2006
Accepted: 31.08.2006

 English version: Journal of Applied Mechanics and Technical Physics, 2007, 48:5, 755–765

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