scholarly journals Formulation of the 2-Dimensional Beam Defined by the Absolute Nodal Coordinates with the Algebraic Constraints (The 1st Report, Formulation Based on the Canonical Theory)

2013 ◽  
Vol 79 (805) ◽  
pp. 3014-3024
Author(s):  
Kensuke HARA ◽  
Masahiro WATANABE
Keyword(s):  
Absolute Nodal Coordinates ◽  
Canonical Theory ◽  
Nodal Coordinates ◽  
The Absolute ◽  
Algebraic Constraints

A Numerical Approach to Solving Flexible Multibody Systems Using the Absolute Nodal Coordinate Formulation

1999 ◽  
Author(s):  
R. Y. Yakoub ◽  
A. A. Shabana
Keyword(s):  
Absolute Nodal Coordinate Formulation ◽  
Sparse Matrix ◽  
Mass Matrix ◽  
Numerical Approach ◽  
Absolute Nodal Coordinates ◽  
Absolute Nodal Coordinate ◽  
Velocity Transformation ◽  
Flexible Multibody ◽  
Nodal Coordinates ◽  
The Absolute

Abstract By utilizing the fact that the absolute nodal coordinate formulation leads to a constant mass matrix, a Cholesky decomposition of the mass matrix can be used to obtain a constant velocity transformation matrix. This velocity transformation can be used to express the absolute nodal coordinates in terms of the generalized Cholesky coordinates. In this case, the inertia matrix associated with the Cholesky coordinates is the identity matrix, and therefore, an optimum sparse matrix structure can be obtained for the augmented multibody equations of motions. The implementation of a computer procedure based on the absolute nodal coordinate formulation and Cholesky coordinates is discussed in this paper. A flexible four-bar linkage is presented in this paper in order to demonstrate the use of Cholesky coordinates in the simulation of the small and large deformations in flexible multibody applications. The results obtained from the absolute nodal coordinate formulation are compared to those obtained from the floating frame of reference formulation.

Absolute Nodal Coordinates in Digital Image Correlation

2012 ◽  
Vol 53 (5) ◽  
pp. 807-818 ◽  
Author(s):  
M. Langerholc ◽  
J. Slavič ◽  
M. Boltežar
Keyword(s):  
Digital Image Correlation ◽  
Digital Image ◽  
Image Correlation ◽  
Absolute Nodal Coordinates ◽  
Nodal Coordinates
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