Efficient Evaluation of the Elastic Forces and the Jacobian in the Absolute Nodal Coordinate Formulation |
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Authors: | García-Vallejo D Mayo J Escalona J L Domínguez J |
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Institution: | (1) Department of Mechanical and Materials Engineering, University of Seville, Camino de los Descubrimientos s/n, 41092 Seville, Spain |
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Abstract: | This paper develops a new procedure for evaluating the elastic forces, the elastic energy and the jacobian of the elastic
forces in the absolute nodal coordinate formulation. For this procedure, it is fundamental to use some invariant sparse matrices
that are integrated in advance and have the property of transforming the evaluation of the elastic forces in a matrix multiplication
process. The use of the invariant matrices avoids the integration over the volume of the element for every evaluation of the
elastic forces. Great advantages can be achieved from these invariant matrices when evaluating the elastic energy and calculating
the jacobian of the elastic forces as well. The exact expression of the jacobian of the differential system of equations of
motion is obtained, and some advantages of using the absolute nodal coordinate formulation are pointed out. Numerical results
show that there is important time saving as a result of the use of the invariant matrices. |
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Keywords: | absolute nodal coordinates invariant matrices multibody systems nonlinear elastic forces |
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