Date:

2025-04-30

Title of Paper:

On the formulation of the planar ANCF triangular finite elements

Journal:

Nonlinear Dynamics

Summary:

In this paper, new planar isoparametric triangular finite elements (FE) based on the absolute
nodal coordinate formulation (ANCF) are developed.
The proposed ANCF elements have six coordinates per
node: two position coordinates that define the absolute
position vector of the node and four gradient coordinates that define vectors tangent to coordinate lines
(parameters) at the same node. To shed light on the
importance of the element geometry and to facilitate
the development of some of the new elements presented
in this paper, two different parametric definitions of
the gradient vectors are used. The first parametrization, called area parameterization, is based on coordinate lines along the sides of the element in the reference configuration, while the second parameterization,
called Cartesian parameterization, employs coordinate
lines defined along the axes of the structure (body) coordinate system. The fundamental differences between the ANCF parameterizations used in this investigation and the parametrizations used for conventional
finite elements are highlighted. The Cartesian parameterization serves as a unique standard for the triangular FE assembly. To this end, a transformation
matrix that defines the relationship between the area
and the Cartesian parameterizations is introduced for
each element in order to allow for the use of standard FE assembly procedure and define the structure
(body) inertia and elastic forces. Using Bezier geometry and a linear mapping, cubic displacement fields
of the new ANCF triangular elements are systematically developed. Specifically, two new ANCF triangular finite elements are developed in this investigation, namely four-node mixed-coordinate and threenode ANCF triangles. The performance of the proposed new ANCF elements is evaluated by comparison
with the conventional linear and quadratic triangular
elements as well as previously developed ANCF rectangular and triangular elements. The results obtained
in this investigation show that in the case of small and
large deformations as well as finite rotations, all the
elements considered can produce correct results, which
are in a good agreement if appropriate mesh sizes are
used.

Co-author:

Pappalardo C M, Wang T, Shabana A A

Volume:

89(2)

Page Number:

1019-1045

Translation or Not:

No

Date of Publication:

2017-04-08