ISSN:
0029-5981
Keywords:
three-dimensional
;
least-squares finite element
;
deformation
;
rate formulation
;
Engineering
;
Numerical Methods and Modeling
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
The development of a three-dimensional least-squares finite 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 field equations exactly. Both velocity and Cauchy stress rate fields were discretized by the same linear interpolation function. The discretization always yields a sparse, symmetric, and positive-definite coefficient matrix. A conjugate gradient iterative solver with incomplete-Choleski preconditioner was used to solve the resulting linear system of equations. Issues such as finite element formulation, mesh design, code efficiency, 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 finite 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 finite element technique for deformation analysis. © 1997 John Wiley & Sons, Ltd.
Additional Material:
14 Ill.
Type of Medium:
Electronic Resource
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