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Computational Continuum Mechanics, 3rd Edition
book

Computational Continuum Mechanics, 3rd Edition

by Ahmed A. Shabana
February 2018
Intermediate to advanced content levelIntermediate to advanced
368 pages
11h 34m
English
Wiley
Content preview from Computational Continuum Mechanics, 3rd Edition

CHAPTER 6FINITE ELEMENT FORMULATION: SMALL-DEFORMATION, LARGE-ROTATION PROBLEM

In the preceding chapter, a nonlinear finite element formulation for the large-deformation analysis was presented. This formulation, which is consistent with the motion description used in the theory of continuum mechanics and can be used to correctly describe an arbitrary rigid-body motion, leads to a constant mass matrix and nonlinear vector of elastic forces. The formulation imposes no restrictions on the amount of rotation or deformation within the element, except for the restriction imposed by the order of the interpolating polynomials used. In large-deformation problems, in general, the shape of deformation of the bodies can be complex and this, in turn, necessitates the use of a large number of finite element nodal coordinates in order to be able to correctly capture the geometry of deformation. Therefore, in the analysis of the large-deformation problem using the absolute nodal coordinate formulation (ANCF) discussed in the preceding chapter, one simply selects an adequate number of finite elements and formulates the equations of motion in terms of the element nodal coordinates. There is no need to introduce another reference frame or be concerned with the use of coordinate reduction techniques. The ANCF results published in the literature demonstrated that this formulation can be used in modeling very large deformations with relatively small number of finite elements compared to other existing ...

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Publisher Resources

ISBN: 9781119293217Purchase book