Development of ANCF tetrahedral finite elements for the nonlinear dynamics of flexible structures
发布时间：2025-04-30
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- 发布时间：
- 2025-04-30
- 论文名称：
- Development of ANCF tetrahedral finite elements for the nonlinear dynamics of flexible structures
- 发表刊物：
- Nonlinear Dynamics
- 摘要：
- In this paper, methods for developing isoparametric tetrahedral finite elements (FE) based on
the absolute nodal coordinate formulation (ANCF) are
presented. The proposed ANCF tetrahedral elements
have twelve coordinates per node that include three
position and nine gradient coordinates. The fundamental differences between the coordinate parametrizations used for conventional finite elements and the
coordinate parametrizations employed for the proposed
ANCF tetrahedral elements are discussed. Two different parametric definitions are introduced: a volume
parametrization based on coordinate lines along the
sides of the tetrahedral element in the straight (undeformed) configuration and a Cartesian parametrization based on coordinate lines directed along the global
axes. The volume parametrization facilitates the development of a concise set of shape functions in a closed form, and the Cartesian parametrization serves as a
unique standard for the element assembly. A linear mapping based on the Bezier geometry is used
to systematically define the cubic position fields of
ANCF tetrahedral elements: the complete polynomialbased eight-node mixed-coordinate and the incomplete
polynomial-based four-node ANCF tetrahedral elements. An element transformation matrix that defines
the relationship between the volume and Cartesian
parametrizations is developed and used to convert the
parametric gradients to structure gradients, thereby
allowing for the use of a standard FE assembly procedure. A general computational approach is employed
to formulate the generalized inertia, external, and elastic forces. The performance of the proposed ANCF
tetrahedral elements is evaluated by comparison with
the conventional linear and quadratic tetrahedral elements and also with the ANCF brick element. In
the case of small deformations, the numerical results
obtained show that all the tetrahedral elements considered can correctly produce rigid body motion. In
the case of large deformations, on the other hand, the
solutions of all the elements considered are in good
agreement, provided that appropriate mesh sizes are
used.
- 合写作者：
- Pappalardo C M, Wang T, Shabana A A
- 卷号：
- 89(4)
- 页面范围：
- 2905-2932
- 是否译文：
- 否
- 发表时间：
- 2017-07-17