Refined geometrically nonlinear formulation of a thin-shell triangular finite element |
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Authors: | V V Kuznetsov S V Levyakov |
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Institution: | (1) Novosibirsk State Technical University, Novosibirsk, 630092 |
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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.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 160–172, September–October, 2007. |
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Keywords: | thin shell nonlinear deformation finite-element method invariants kinematic group planar curve |
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