The continuity of the position-vector gradients at the nodal points of a finite element mesh does not always ensure the continuity of the gradients at the element interfaces. Discontinuity of the gradients at the interface not only adversely affects the quality of the simulation results, but can also lead to computer models that do not properly represent realistic physical system behaviors, particularly in the case of soft and fluid material applications. In this study, the absolute nodal coordinate formulation (ANCF) finite elements
are used to define general curvature-continuity conditions that allow for eliminating or minimizing the discontinuity of the position gradients at the element interface. For the ANCF solid element, with four-node surfaces,
it is shownthat continuity of the gradients tangent to an arbitrary point on a surface is ensured as the result of the continuity of the gradients at the nodal points. The general ANCF continuity conditions are applicable to both reference-configuration straight and curved geometries. These conditions are formulated without the need for using the computer-aided-design knot vector
and knot multiplicity, which do not account properly for the concept of system degrees of freedom. The ANCF curvature-continuity conditions are written in terms of constant geometric coefficients obtained using the matrix of position-vector gradients that defines the reference-configuration geometry. The formulation of these conditions is demonstrated using the ANCF fully
parameterized three-dimensional solid and tetrahedral elements, which employ a complete set of position gradients as nodal coordinates. Numerical results are presented in order to examine the effect of applying the curvature-continuity conditions on achieving a higher degree of smoothness at the element interfaces in the case of soft and fluid materials.
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Performance Evaluation of ANCF Tetrahedral Elements in the Analysis of Liquid Sloshing
Abstract The performance of the absolute nodal coordinate formulation (ANCF) tetrahedral element in the analysis of liquid sloshing is evaluated in this paper using a total Lagrangian nonincremental solution procedure. In this verification study, the results obtained using the ANCF tetrahedral element are compared with the results of the ANCF solid element which has been previously subjected to numerical verification and experimental validation. The tetrahedral-element model, which allows for arbitrarily large displacements including rotations, can be systematically integrated with computational multibody system (MBS) algorithms that allow for developing complex sloshing/vehicle models. The new fluid formulation allows for systematically increasing the degree of continuity in order to obtain higher degree of smoothness at the element interface, eliminate dependent variables, and reduce the model dimensionality. The effect of the fluid/container interaction is examined using a penalty contact approach. Simple benchmark problems and complex railroad vehicle sloshing scenarios are used to examine the performance of the ANCF tetrahedral element in solving liquid sloshing problems. The simulation results show that, unlike the ANCF solid element, the ANCF tetrahedral element model exhibits nonsmoothness of the free surface. This difference is attributed to the gradient discontinuity at the tetrahedral-element interface, use of different meshing rules for the solid- and tetrahedral-elements, and the interaction between elements. It is shown that applying curvature-continuity conditions leads, in general, to higher degree of smoothness. Nonetheless, a higher degree of continuity does not improve the solution accuracy when using the ANCF tetrahedral elements.
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- Award ID(s):
- 1632302
- NSF-PAR ID:
- 10290993
- Date Published:
- Journal Name:
- Journal of Verification, Validation and Uncertainty Quantification
- Volume:
- 5
- Issue:
- 3
- ISSN:
- 2377-2158
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1115/1.4048464
