Summary
In many problems in nonlinear solid mechanics, the finite element method is executed incrementally, with the positive definite stiffness matrix updated after one or more load (or time) increments. In solving the resulting large linear perturbed systems, it is often attractive to use Cholesky triangularization, followed by forward and backward substitution. The present investigation introduces and demonstrates an iterative procedure for updating the triangular factors of the updated stiffness matrix. An approximate convergence criterion is formulated. Simple examples are presented indicating rapid convergence. In the scalar case this method exactly tracks the Taylor series.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Nicholson, D. Iterative triangularization of updated finite element stiffness matrices. Acta Mechanica 174, 241–249 (2005). https://doi.org/10.1007/s00707-004-0137-7
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-004-0137-7