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Variational Arbitrary Lagrangian-Eul...

Thoutireddy, Pururav.

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Variational Arbitrary Lagrangian-Eulerian method.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Variational Arbitrary Lagrangian-Eulerian method./
作者:	Thoutireddy, Pururav.
面頁冊數:	79 p.
附註:	Source: Dissertation Abstracts International, Volume: 64-06, Section: B, page: 2744.
Contained By:	Dissertation Abstracts International64-06B.
標題:	Applied Mechanics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3093512

Variational Arbitrary Lagrangian-Eulerian method.
Thoutireddy, Pururav.

Variational Arbitrary Lagrangian-Eulerian method. - 79 p.

Source: Dissertation Abstracts International, Volume: 64-06, Section: B, page: 2744.

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

This thesis is concerned with the development of Variational Arbitrary Lagrangian-Eulerian method (VALE) method. VALE is essentially finite element method generalized to account for horizontal variations, in particular, variations in nodal coordinates. The distinguishing characteristic of the method is that the variational principle simultaneously supplies the solution, the optimal mesh and, in case problems of shape optimization, optimal shape. This is accomplished by rendering the functional associated with the variational principle stationary with respect to nodal field values as well as with respect to the nodal positions of triangulation of the domain of analysis. Stationarity with respect to the nodal positions has the effect of the equilibriating the energetic or configurational forces acting in the nodes. Further, configurational force equilibrium provides precise criterion for mesh optimality. The solution so obtained corresponds to minimum of energy functional (minimum principle) in static case and to the stationarity of action sum (discrete Hamilton's stationarity principle) in dynamic case, with respect to both nodal variables and nodal positions. Further, the resulting mesh adaption scheme is devoid of error estimates and mesh-to-mesh transfer interpolation errors. We illustrate the versatility and convergence characteristics of the method by way of selected numerical tests and applications, including the problem of semi-infinite crack, the shape optimization of elastic inclusions and free vibration of 1-d rod.Subjects--Topical Terms:

1018410
Applied Mechanics.

Variational Arbitrary Lagrangian-Eulerian method.
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520 $a This thesis is concerned with the development of Variational Arbitrary Lagrangian-Eulerian method (VALE) method. VALE is essentially finite element method generalized to account for horizontal variations, in particular, variations in nodal coordinates. The distinguishing characteristic of the method is that the variational principle simultaneously supplies the solution, the optimal mesh and, in case problems of shape optimization, optimal shape. This is accomplished by rendering the functional associated with the variational principle stationary with respect to nodal field values as well as with respect to the nodal positions of triangulation of the domain of analysis. Stationarity with respect to the nodal positions has the effect of the equilibriating the energetic or configurational forces acting in the nodes. Further, configurational force equilibrium provides precise criterion for mesh optimality. The solution so obtained corresponds to minimum of energy functional (minimum principle) in static case and to the stationarity of action sum (discrete Hamilton's stationarity principle) in dynamic case, with respect to both nodal variables and nodal positions. Further, the resulting mesh adaption scheme is devoid of error estimates and mesh-to-mesh transfer interpolation errors. We illustrate the versatility and convergence characteristics of the method by way of selected numerical tests and applications, including the problem of semi-infinite crack, the shape optimization of elastic inclusions and free vibration of 1-d rod.
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