Development of Elastic Forces for a Large Deformation Plate Element Based on the Absolute Nodal Coordinate Formulation
- 20 May 2005
- journal article
- Published by ASME International in Journal of Computational and Nonlinear Dynamics
- Vol. 1 (2), 103-108
- https://doi.org/10.1115/1.1961870
Abstract
Dynamic analysis of large rotation and deformation can be carried out using the absolute nodal coordinate formulation. This formulation, which utilizes global displacements and slope coordinates as nodal variables, make it possible to avoid the difficulties that arise when a rotation is interpolated in three-dimensional applications. In the absolute nodal coordinate formulation, a continuum mechanics approach has become the dominating procedure when elastic forces are defined. It has recently been perceived, however, that the continuum mechanics based absolute nodal coordinate elements suffer from serious shortcomings, including Poisson’s locking and poor convergence rate. These problems can be circumvented by modifying the displacement field of a finite element in the definition of elastic forces. This allows the use of the mixed type interpolation technique, leading to accurate and efficient finite element formulations. This approach has been previously applied to two- and three-dimensional absolute nodal coordinate based finite elements. In this study, the improved approach for elastic forces is extended to the absolute nodal coordinate plate element. The introduced plate element is compared in static examples to the continuum mechanics based absolute nodal coordinate plate element, as well as to commercial finite element software. A simple dynamic analysis is performed using the introduced element in order to demonstrate the capability of the element to conserve energy.Keywords
This publication has 14 references indexed in Scilit:
- Efficient Evaluation of the Elastic Forces and the Jacobian in the Absolute Nodal Coordinate FormulationNonlinear Dynamics, 2004
- A Non-Incremental Nonlinear Finite Element Solution for Cable ProblemsJournal of Mechanical Design, 2003
- Application of Plasticity Theory and Absolute Nodal Coordinate Formulation to Flexible Multibody System DynamicsJournal of Mechanical Design, 2003
- A Non-Incremental Finite Element Procedure for the Analysis of Large Deformation of Plates and Shells in Mechanical System ApplicationsMultibody System Dynamics, 2003
- Formulation of Three-Dimensional Joint Constraints Using the Absolute Nodal CoordinatesNonlinear Dynamics, 2003
- `Solid-shell' elements with linear and quadratic shape functions at large deformations with nearly incompressible materialsComputers & Structures, 2001
- Definition of the Elastic Forces in the Finite-Element Absolute Nodal Coordinate Formulation and the Floating Frame of Reference FormulationMultibody System Dynamics, 2001
- Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: TheoryJournal of Mechanical Design, 2000
- Computer Implementation of the Absolute Nodal Coordinate Formulation for Flexible Multibody DynamicsNonlinear Dynamics, 1998
- Definition of the Slopes and the Finite Element Absolute Nodal Coordinate FormulationMultibody System Dynamics, 1997