Mechanical Engineering Commons^™

Implementation And Performance Comparisons For The Crisfield And Stiff Arc Length Methods In Fea, Thomas W. Silvers

Electronic Theses and Dissertations

In Nonlinear Finite Element Analysis (FEA) applied to structures, displacements at which the tangent stiffness matrix KT becomes singular are called critical points, and correspond to instabilities such as buckling or elastoplastic softening (e.g., necking). Prior to the introduction of Arc Length Methods (ALMs), critical points posed severe computational challenges, which was unfortunate since behavior at instabilities is of great interest as a precursor to structural failure. The original ALM was shown to be capable in some circumstances of continued computation at critical points, but limited success and unattractive features of the formulation were noted and addressed in extensive subsequent …