In this investigation, comparison of finite element solutions obtained using the B-spline approach and the absolute nodal coordinate formulation (ANCF) is performed. Furthermore, equivalence of the two formulations with different orders of polynomials and degrees of continuity is demonstrated by several numerical examples. The degree of continuity can be easily controlled in B-spline elements by changing knot multiplicities, while continuity conditions associated with higher order derivatives need to be imposed to achieve C2 and higher continuities in ANCF elements. In order to compare element performances of the third and quartic B-spline and ANCF elements, the three-node quartic ANCF beam element is developed. It is demonstrated in several numerical examples that use of B-spline and ANCF elements with same orders and continuities leads to identical results. Furthermore, effects of polynomial orders and continuities on the accuracy and numerical convergence are demonstrated.
- Design Engineering Division and Computers and Information in Engineering Division
Comparison of Finite Element Solutions of Non-Rational B-Spline and ANCF Elements in the Analysis of Flexible Multibody Systems
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Yamashita, H, & Sugiyama, H. "Comparison of Finite Element Solutions of Non-Rational B-Spline and ANCF Elements in the Analysis of Flexible Multibody Systems." Proceedings of the ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 4: 8th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A and B. Washington, DC, USA. August 28–31, 2011. pp. 889-897. ASME. https://doi.org/10.1115/DETC2011-47349
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