Description of Elastic Forces in Absolute Nodal Coordinate Formulation

By Jussi T. Sopanen, Aki Mikkola. 2003

186 citations recorded by the source corpus.

Subfields: Automotive Engineering, Control and Systems Engineering, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/c499f0817483b8c77b0f416386ba250480081510

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Automotive Engineering

In Control and Systems Engineering

In Mechanical Engineering

Citations in the corpus

Implicit and explicit integration in the solution of the absolute nodal coordinate differential/algebraic equations (2008, background): “One approach that bears potential for the successful integration of large deformation finite element and multibody system algorithms is based on the absolute nodal coordinate formulation (ANCF) [2–4, 12, 14–16].”
State of the Art of ANCF Elements Regarding Geometric Description, Interpolation Strategies, Definition of Elastic Forces, Validation and the Locking Phenomenon in Comparison with Proposed Beam Finite Elements (2014, methodology): “[115] introducing a transformation to a local coordinate system in which the formulation of the elastic forces is linearized.”
Simulation of planar flexible multibody systems with clearance and lubricated revolute joints (2010, methodology): “ement used in this paper still suffers from the Poisson locking problem, which was firstly studied by Sopanen and Mikkola [ 55 ].”
Analysis of Stress and Strain in the Absolute Nodal Coordinate Formulation (2006, background): “As there has been much discussion of the effect of Poisson’s ratio (Sopanen and Mikkola, 2003), it has been generally set to zero in all examples.”
Sparse matrix implicit numerical integration of the Stiff differential/algebraic equations: Implementation (2011, background): “The ANCF elastic forces can be formulated using the general continuum mechanics approach, which leads to ANCF coupled deformation modes that cannot be captured using other existing structural finite elements such as beams, plates, and shells [2, 10, 11, 16 ].”
A quaternion-based formulation of Euler–Bernoulli beam without singularity (2012, background): “This formulation owns a great advantage of constant mass matrix but might have locking problems [9–11].”
A geometrically exact beam element based on the absolute nodal coordinate formulation (2008, background): “Therefore, the condition given in (24) cannot be fulfilled which leads to the phenomena of Poisson locking, see also Sopanen and Mikkola [ 21 ].”
A new locking-free formulation for planar, shear deformable, linear and quadratic beam finite elements based on the absolute nodal coordinate formulation (2011, background): “For further information on various types of locking, such as Poisson locking, see [15], or combined shear and thickness locking, see [4].”
A new locking-free shear deformable finite element based on absolute nodal coordinates (2007, methodology): “in element n. The polynomials of the shape functions are cubic in the longitudinal element parameter x, and linear in the transverse element parameter y. For this reason, it can be shown that the cross-section remains planar after a general motion of the element [4] (Fig. 1). It is noteworthy that t”
A new model for dry and lubricated cylindrical joints with clearance in spatial flexible multibody systems (2011, background): “free ANCF-based beam elements, whose formulation only differs from the original elements in the approach of the elastic forces [34, 35].”
A comparison of finite elements for nonlinear beams: the absolute nodal coordinate and geometrically exact formulations (2008, methodology): “The most important numerical issue of the ANC formulation is that it has been shown to produce results converging to the wrong solution when Poisson’s ratio is nonzero [35, 44 ].”