A non-linear beam space-time finite element formulation using quaternion algebra: interpolation of the Lagrange multipliers and the appearance of spurious modes
✍ Scribed by C. Bottasso
- Publisher
- Springer
- Year
- 1992
- Tongue
- English
- Weight
- 645 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0178-7675
No coin nor oath required. For personal study only.
✦ Synopsis
In this work a three-field space-time beam finite element formulation is expressed in quaternion algebra. The unitary quaternion condition is enforced by means of an extension of the augmented Lagrangian method.
The continuity requirements implied by the constrained energy principle obtained in this way lead to interpolations of the Lagrange multipliers which prove to be inappropriate when the beam is subject to certain boundary conditions. In particular, the tangent matrix becomes singular and the eigenvector of the multiplier degrees of freedom associated with the zero eigenvalue presents a checkerboard pattern. It is shown that this pathological behavior can be avoided if continuous-multiplier elements are employed.