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

The development of a three-dimensional least-squares nite element technique suitable for deformation anal- ysis 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 eld equations exactly. Both velocity and Cauchy stress rate elds were discretized by the same linear interpolation function. The discretization always yields a sparse, symmetric, and positive-de nite 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 nite 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 con- sidered. Additionally, two nite 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 nite element technique for deformation analysis.