Keywords

Nonlinear finite element analysis, critical points, arc length methods, necking, tangent stiffness matrix, crisfield, stiff arc length method, failure prediction, singular

Abstract

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.

Notes

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Graduation Date

2012

Semester

Spring

Advisor

Gordon, Ali

Degree

Master of Science in Mechanical Engineering (M.S.M.E.)

College

College of Engineering and Computer Science

Department

Mechanical and Aerospace Engineering

Degree Program

Mechanical Engineering; Mechanical Systems

Format

application/pdf

Identifier

CFE0004277

URL

http://purl.fcla.edu/fcla/etd/CFE0004277

Language

English

Release Date

May 2012

Length of Campus-only Access

None

Access Status

Masters Thesis (Open Access)

Subjects

Dissertations, Academic -- Engineering and Computer Science;Engineering and Computer Science -- Dissertations, Academic

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