A three-dimensional least-squares finite element technique for deformation analysis

✍ Scribed by Allen H. P. Siu; Y. K. Lee

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 558 KB
• Volume: 40
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/(sici)1097-0207(19971130)40:22<4159::aid-nme239>3.0.co;2-a

✦ Synopsis

The development of a three-dimensional least-squares ÿnite element technique suitable for deformation analysis was presented. By adopting a spatial viewpoint, a consistent rate formulation that treats deformation as a process was established. The technique utilized the least-squares variational principle that minimizes the squares of errors encountered in any attempt to meet the ÿeld equations exactly. Both velocity and Cauchy stress rate ÿelds were discretized by the same linear interpolation function. The discretization always yields a sparse, symmetric, and positive-deÿnite coe cient matrix. A conjugate gradient iterative solver with incomplete-Choleski preconditioner was used to solve the resulting linear system of equations. Issues such as ÿnite element formulation, mesh design, code e ciency, and time integration were addressed. A set of linear elastic problems was used for patch-test; both homogeneous and non-homogeneous deformations were considered. Additionally, two ÿnite elastic deformation problems were analysed to gauge the overall performance of the technique. The results demonstrated the computational feasibility of a three-dimensional least-squares ÿnite element technique for deformation analysis.