A high performance iterative solution procedure for solving problems in structural mechanics using the finite element method /
The preconditioned conjugate gradient (PCG) algorithm is
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| Format: | Thesis Book |
| Language: | English |
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[Place of publication not identified] :
[publisher not identified] ;
1997.
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| Subjects: | |
| Online Access: | http://proxy.library.tamu.edu/login?url=http://proquest.umi.com/pqdweb?did=736580561&sid=1&Fmt=2&clientId=2945&RQT=309&VName=PQD |
| Summary: | 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 in structural mechanics. |
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| Item Description: | Vita. "Major Subject: Mechanical Engineering". |
| Physical Description: | xiv, 150 leaves : illustrations ; 28 cm. Issued also on microfiche from University Microfilms Inc. |
| Bibliography: | Includes bibliographical references: pages 125-135. |