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Variational time integrators in comp...

Lew, Adrian Jose.

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Variational time integrators in computational solid mechanics.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Variational time integrators in computational solid mechanics./
Author:	Lew, Adrian Jose.
Description:	118 p.
Notes:	Source: Dissertation Abstracts International, Volume: 64-06, Section: B, page: 2742.
Contained By:	Dissertation Abstracts International64-06B.
Subject:	Applied Mechanics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3093493

Variational time integrators in computational solid mechanics.
Lew, Adrian Jose.

Variational time integrators in computational solid mechanics. - 118 p.

Source: Dissertation Abstracts International, Volume: 64-06, Section: B, page: 2742.

Thesis (Ph.D.)--California Institute of Technology, 2003.

This thesis develops the theory and implementation of variational integrators for computational solid mechanics problems, and to some extent, for fluid mechanics problems as well. Variational integrators for finite dimensional mechanical systems are succinctly reviewed, and used as the foundations for the extension to continuum systems. The latter is accomplished by way of a space-tune formulation for Lagrangian continuum mechanics that unifies the derivation of tyre balance of linear momentum, energy and configurational forces, all of there as Euler-Lagrange equations of an extended Hamilton's principle. In this formulation, energy conservation and the path independence of the <italic>J</italic>- and <italic>L</italic>-integrals are conserved quantities emanating from Noether's theorem. Variational integrators for continuum mechanics are constructed by mimicking this variational structure, and a discrete Noether's theorem for rather general space-tune discretizations is presented. Additionally, the algorithms are automatically (multi)symplectic, and the (multi)symplectic form is uniquely defined by the theory. For instance, in nonlinear elastodynamics the algorithms exactly preserve linear and angular momenta, whenever the continuous system does.Subjects--Topical Terms:

1018410
Applied Mechanics.

Variational time integrators in computational solid mechanics.
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100 1 $a Lew, Adrian Jose. $3 1945756
245 1 0 $a Variational time integrators in computational solid mechanics.
300 $a 118 p.
500 $a Source: Dissertation Abstracts International, Volume: 64-06, Section: B, page: 2742.
500 $a Adviser: Michael Ortiz.
502 $a Thesis (Ph.D.)--California Institute of Technology, 2003.
520 $a This thesis develops the theory and implementation of variational integrators for computational solid mechanics problems, and to some extent, for fluid mechanics problems as well. Variational integrators for finite dimensional mechanical systems are succinctly reviewed, and used as the foundations for the extension to continuum systems. The latter is accomplished by way of a space-tune formulation for Lagrangian continuum mechanics that unifies the derivation of tyre balance of linear momentum, energy and configurational forces, all of there as Euler-Lagrange equations of an extended Hamilton's principle. In this formulation, energy conservation and the path independence of the <italic>J</italic>- and <italic>L</italic>-integrals are conserved quantities emanating from Noether's theorem. Variational integrators for continuum mechanics are constructed by mimicking this variational structure, and a discrete Noether's theorem for rather general space-tune discretizations is presented. Additionally, the algorithms are automatically (multi)symplectic, and the (multi)symplectic form is uniquely defined by the theory. For instance, in nonlinear elastodynamics the algorithms exactly preserve linear and angular momenta, whenever the continuous system does.
520 $a A class of variational algorithms is constructed, termed <italic>asynchronous variational integrators</italic> (AVI), which permit: the selection of independent time steps in each element of a finite element mesh, and the local time steps need riot bear an integral relation to each other. The conservation properties of both synchronous and asynchronous variational integrators are discussed in detail. In particular, AVI are found to nearly conserve energy both locally and globally, a distinguishing feature of variational integrators. The possibility of adapting the elemental time step to exactly satisfy the local energy balance equation, obtained from the extended variational principle, is analyzed. The AVI are also extended to include dissipative systems. The excellent accuracy, conservation and convergence characteristics of AVI are demonstrated via selected numerical examples, both for conservative and dissipative systems. In these tests AVI are found to result in substantial speedups, at equal accuracy, relative to explicit Newmark.
520 $a In elastostatics, the variational structure leads to the formulation of discrete path-independent integrals and a characterization of the configurational forces acting in discrete systems. A notable example is a discrete, path-independent <italic> J</italic>-integral at the tip of a crack in a finite element mesh.
590 $a School code: 0037.
650 4 $a Applied Mechanics. $3 1018410
650 4 $a Engineering, Mechanical. $3 783786
650 4 $a Engineering, Aerospace. $3 1018395
690 $a 0346
690 $a 0548
690 $a 0538
710 2 0 $a California Institute of Technology. $3 726902
773 0 $t Dissertation Abstracts International $g 64-06B.
790 1 0 $a Ortiz, Michael, $e advisor
790 $a 0037
791 $a Ph.D.
792 $a 2003
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3093493