Nonlinear finite element analysis, critical points, arc length methods, necking, tangent stiffness matrix, crisfield, stiff arc length method, failure prediction, singular
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 research. The widely used Crisfield Cylindrical and Spherical ALMs may be viewed as representing the 'state-of-the-art'. The more recent Stiff Arc Length method, which is attractive on fundamental grounds, was introduced in 2004, but without implementation, benchmarking or performance assessment. The present thesis addresses (a) implementation and (b) performance comparisons for the Crisfield and Stiff methods, using simple benchmarks formulated to incorporate elastoplastic softening. It is seen that, in contrast to the Crisfield methods, the Stiff ALM consistently continues accurate computation at, near and beyond critical points.
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Master of Science in Mechanical Engineering (M.S.M.E.)
College of Engineering and Computer Science
Mechanical and Aerospace Engineering
Mechanical Engineering; Mechanical Systems
Length of Campus-only Access
Masters Thesis (Open Access)
Dissertations, Academic -- Engineering and Computer Science;Engineering and Computer Science -- Dissertations, Academic
Silvers, Thomas W., "Implementation And Performance Comparisons For The Crisfield And Stiff Arc Length Methods In FEA" (2012). Electronic Theses and Dissertations. 4476.