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high performance iterative solution procedure for solving problems in structural mechanics using the finite element method
xiv, 150 leaves : illustrations ; 28 cm.
The preconditioned conjugate gradient (PCG) algorithm is
widely accepted and used as a method for solving the
algebraic equations arising from finite element
discretizations of problems in structural mechanics. The
advantages of the algorithm are its ease of implementation,
low storage requirements, and its rate of convergence. These
features are available provided a good preconditioner is
given. In this study, a multilevel, recursively defined
preconditioner, for use with the PCG algorithm is developed,
implemented and tested. The preconditioner is constructed
from a sequence of hierarchical vec tor spaces arising from
the p version of the finite element method, and has been
applied to the linearized elasticity equations in both two
and three dimensions. It may also be applied to other model
problems in structural mechanics such as equivalent single
layer plate and shell theories. Numerical studies have been
conducted using quadrilateral elements for two dimensional
problems up to p = 8, and in three dimensions, serendipity
brick elements were used up to p = 5. Various numerical
studies were performed on laminated plates, subjected to
bending and torsional loads, in order to assess the
efficiency of the iterative procedure. The effects of
element span ratios, stopping criterion, polynomial order,
orthotropic material properties, and plate span ratios, on
the number of iterations required for convergence has been
investigated. Results indicate that the preconditioner can
be used to produce an efficient iterative solver for problems
"Major Subject: Mechanical Engineering".
Issued also on microfiche from University Microfilms Inc.
Includes bibliographical references: pages 125-135.