Slope discontinuities in the finite element absolute nodal coordinate formulation: gradient deficient elements |
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Authors: | Ahmed A Shabana Luis G Maqueda |
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Affiliation: | (1) Department of Mechanical Engineering, University of Illinois at Chicago, 842 West Taylor Street, Chicago, IL 60607, USA |
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Abstract: | In this paper, the treatment of the slope discontinuities in the finite element absolute nodal coordinate formulation (ANCF)
is discussed. The paper explains the fundamental problems associated with developing a constant transformation that accounts
for the slope discontinuities in the case of gradient deficient ANCF finite elements. A procedure that allows for the treatment
of slope discontinuities in the case of gradient deficient finite elements which do not employ full parameterization is proposed
for the special case of commutative rotations. The use of the proposed procedure leads to a constant orthogonal element transformation that describes the element initial
configuration. As a consequence, one obtains in the case of large deformation and commutative rotations, a constant mass matrix
for the structures. In order to achieve this goal, the concept of the intermediate finite element coordinate system is invoked. The intermediate finite element coordinate system used in this investigation serves to define the element reference
configuration, follows the rotation of the structure, and maintains a fixed orientation relative to the structure coordinate
system. Since planar rotations are always commutative, the procedure proposed in this investigation is applicable to all planar
gradient deficient ANCF finite elements. |
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Keywords: | Slope discontinuities Absolute nodal coordinate formulation Thin finite elements Coordinate transformation |
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