Slope discontinuities and T-sections can be modeled in a straight forward manner using fully parameterized absolute nodal coordinate formulation (ANCF) finite elements that have a complete set of gradient vectors. Linear transformations that define the element connectivity can always be obtained and used to preserve ANCF desirable features that include constant mass matrix and zero Coriolis and centrifugal forces in the case of spinning structures. The objective of this paper is to develop a general method that allows for modeling slope discontinuities and T-sections using gradient deficient ANCF finite elements that do not have a complete set of coordinate lines and gradient vectors. Linear connectivity conditions that preserve all the ANCF desirable features including the constant mass matrix are developed at the nodes of slope discontinuities. At these nodes of discontinuity, one can always define a complete set of independent coordinate lines that lie on the structure. These coordinate lines can be used to define a complete set of independent gradient vectors at these nodes. Since the proposed method is based on linear coordinate transformations, the method can be implemented in a preprocessor computer program. The application of the proposed general method is demonstrated using ANCF gradient deficient beam element example.

1.
Bonet
,
J.
, and
Wood
,
R. D.
, 1997,
Nonlinear Continuum Mechanics for Finite Element Analysis
,
Cambridge University Press
,
Cambridge, UK
.
2.
Ogden
,
R. W.
, 1984,
Non-Linear Elastic Deformations
,
Dover
,
New York
.
3.
Spencer
,
A. J. M.
, 1980,
Continuum Mechanics
,
Longman
,
London
.
4.
Dmitrochenko
,
O.
, and
Mikkola
,
A.
, 2009, “
Shear Correction for Thin Plate Finite Elements Based on the Absolute Nodal Coordinate Formulation
,”
Proceedings of ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference—DETC2009
, Aug. 30–Sep. 2, Paper No. DETC2009-86750.
5.
Gerstmayr
,
J.
, 2009, “
A Corotational Approach for 3D Absolute Nodal Coordinate Elements
,”
Proceedings of ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference—DETC2009
, Aug. 30–Sep. 2, Paper No. DETC2009-87476.
6.
Gerstmayr
,
J.
, and
Shabana
,
A. A.
, 2006, “
Analysis of Thin Beams and Cables Using the Absolute Nodal Coordinate Formulation
,”
Nonlinear Dyn.
0924-090X,
45
, pp.
109
130
.
7.
García-Vallejo
,
D.
,
Mayo
,
J.
,
Escalona
,
J. L.
, and
Dominguez
,
J.
, 2004, “
Efficient Evaluation of the Elastic Forces and the Jacobian in the Absolute Nodal Coordinate Formulation
,”
Nonlinear Dyn.
0924-090X,
35
(
4
), pp.
313
329
.
8.
Mikkola
,
A. M.
, and
Matikainen
,
M. K.
, 2006, “
Development of Elastic Forces for the Large Deformation Plate Element Based on the Absolute Nodal Coordinate Formulation
,”
ASME J. Comput. Nonlinear Dyn.
1555-1423,
1
(
2
), pp.
103
108
.
9.
Schwab
,
A. L.
, and
Meijaard
,
J. P.
, 2005, “
Comparison of Three-Dimensional Beam Elements for Dynamic Analysis: Finite Element Method and Absolute Nodal Coordinate Formulation
,”
Proceedings of the ASME 2005 International Design Engineering Technical Conferences & Computer and Information in Engineering Conference (DETC2005-85104)
, Long Beach, CA, Sep. 24–28.
10.
Sopanen
,
J. T.
, and
Mikkola
,
A. M.
, 2003, “
Description of Elastic Forces in Absolute Nodal Coordinate Formulation
,”
Nonlinear Dyn.
0924-090X,
34
(
1–2
), pp.
53
74
.
11.
Sugiyama
,
H.
,
Koyama
,
H.
, and
Yamashita
,
H.
, 2009, “
Performance of Curved Beam Elements Using the Absolute Nodal Coordinate Formulation
,”
Proceedings of ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference—DETC2009
, Aug. 30–Sep. 2, 2009, Paper No. DETC2009–86312.
12.
Sugawara
,
Y.
,
Shinohara
,
K.
, and
Kobayashi
,
N.
, 2009, “
Quantitative Validation of Dynamic Stiffening Represented by Absolute Nodal Coordinate Formulation
,”
Proceedings of ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference—DETC2009
, Aug. 30–Sep. 2, Paper No. DETC2009-86955.
13.
Yoo
,
W. S.
,
Lee
,
J. H.
,
Park
,
S. J.
,
Sohn
,
J. H.
,
Pogorelov
,
D.
, and
Dimitrochenko
,
O.
, 2004, “
Large Deflection Analysis of a Thin Plate: Computer Simulation and Experiment
,”
Multibody Syst. Dyn.
1384-5640,
11
(
2
), pp.
185
208
.
14.
Shabana
,
A. A.
, and
Mikkola
,
A. M.
, 2003, “
Use of the Finite Element Absolute Nodal Coordinate Formulation in Modeling Slope Discontinuity
,”
ASME J. Mech. Des.
0161-8458,
125
, pp.
342
350
.
15.
Shabana
,
A. A.
, 2008,
Computational Continuum Mechanics
,
Cambridge University Press
,
New York
.
16.
Shabana
,
A. A.
, and
Maqueda
,
L. G.
, 2008, “
Slope Discontinuities in the Finite Element Absolute Nodal Coordinate Formulation: Gradient Deficient Elements
,”
Multibody Syst. Dyn.
1384-5640,
20
, pp.
239
249
.
17.
Maqueda
,
L. G.
, and
Shabana
,
A. A.
, 2009, “
Numerical Investigation of the Slope Discontinuities in Large Deformation Finite Element Formulations
,”
Nonlinear Dyn.
0924-090X,
58
, pp.
23
37
.
18.
Goetz
,
A.
, 1970,
Introduction to Differential Geometry
,
Addison-Wesley
,
Reading, MA
.
19.
Kreyszig
,
E.
, 1991,
Differential Geometry
,
Dover
,
New York
.
20.
Lan
,
P.
, and
Shabana
,
A. A.
, 1991, “
Integration of B-Spline Geometry and ANCF Finite Element Analysis
,”
Nonlinear Dyn.
0924-090X,
61
, pp.
193
206
.
21.
Sanborn
,
G. G.
, and
Shabana
,
A. A.
, 2009, “
On the Integration of Computer Aided Design and Analysis Using the Finite Element Absolute Nodal Coordinate Formulation
,”
Multibody Syst. Dyn.
1384-5640,
22
, pp.
181
197
.
This content is only available via PDF.
You do not currently have access to this content.