Abstract

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.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.