Oñate Carbonell 2013b - Revision history

Cinmemj at 08:15, 7 June 2019

2019-06-07T08:15:24Z

2019-06-07T08:11:54Z

2018-05-10T12:16:43Z

2018-02-26T14:54:11Z

‎6 SPLIT OF THE INTERNAL VIRTUAL POWER INTO DEVIATORIC AND VOLUMETRIC COMPONENTS

2018-02-26T14:52:50Z

2018-02-26T14:51:55Z

2018-02-26T10:00:47Z

2018-02-26T09:59:53Z

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 We present a mixed velocity-pressure finite element formulation for solving the updated Lagrangian equations for quasi and fully incompressible fluids. Details of the governing equations for the conservation of momentum and mass are given in both differential and variational form. The finite element interpolation  uses an equal  order approximation for the velocity and pressure unknowns. The procedure for obtaining stabilized FEM solutions is outlined. The  solution in time of the discretized governing conservation equations using an incremental iterative segregated scheme is described. The linearization of these equations and the derivation of the corresponding tangent stiffness matrices is detailed. Other iterative  schemes for the direct computation of  the nodal velocities and pressures at the updated configuration are presented. The advantages and disadvantages of choosing the current or the updated configuration as the reference configuration in the Lagrangian formulation are discussed.
-'''keywords''' Updated Lagrangian formulation, incompressible fluids, finite element method, incremental solution, tangent matrix, mixed formulation, stabilized method
+'''Keywords''': Updated Lagrangian formulation, incompressible fluids, finite element method, incremental solution, tangent matrix, mixed formulation, stabilized method
 ==1 INTRODUCTION==

← Older revision		Revision as of 08:11, 7 June 2019
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−	~~Accepted for publication in ''Computational Mechanics''~~
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	==Abstract==		==Abstract==

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 This work was partially supported by the Advanced Grant project SAFECON of the European Research Council (ERC).
-===BIBLIOGRAPHY===
+==References==
 <div id="cite-1"></div>

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 | style="text-align: center;" | <math>\begin{array}{r}  \displaystyle \int _{{}^{n}V} \delta{v}^T {~}^n \rho {~}^{n+1} {a}  d {~}^{n}V   +\int _{{}^{n}V} \left(\left\{\delta \dot {E}\right\}^T  \left\{{S}'\right\}+ J\delta \dot E_v p \right)d{~}^{n}V -\\ - \displaystyle \int _{{}^{n+1}V} \delta{v}^T  {~}^{n+1}{b}~ d{~}^{n+1} V - \int _{{}^{n+1}\Gamma _t} \delta{v}^T {~}^{n+1} {t}~d {~}^{n+1} \Gamma = 0\end{array} </math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (39)

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-| style="text-align: center;" | <math>\fbox{$\displaystyle \begin{array}{r}  \displaystyle \int _{{}^{n}V} \delta{v}^T {~}^n \rho {~}^{n+1} {a}  d {~}^{n}V   +\int _{{}^{n}V} \left(\left\{\delta \dot {E}\right\}^T  \left\{{S}'\right\}+ J\delta \dot E_v p \right)d{~}^{n}V -\\ - \displaystyle \int _{{}^{n+1}V} \delta{v}^T  {~}^{n+1}{b}~ d{~}^{n+1} V - \int _{{}^{n+1}\Gamma _t} \delta{v}^T {~}^{n+1} {t}~d {~}^{n+1} \Gamma = 0\end{array}$} </math>
+| style="text-align: center;" | <math>\begin{array}{r}  \displaystyle \int _{{}^{n}V} \delta{v}^T {~}^n \rho {~}^{n+1} {a}  d {~}^{n}V   +\int _{{}^{n}V} \left(\left\{\delta \dot {E}\right\}^T  \left\{{S}'\right\}+ J\delta \dot E_v p \right)d{~}^{n}V -\\ - \displaystyle \int _{{}^{n+1}V} \delta{v}^T  {~}^{n+1}{b}~ d{~}^{n+1} V - \int _{{}^{n+1}\Gamma _t} \delta{v}^T {~}^{n+1} {t}~d {~}^{n+1} \Gamma = 0\end{array} </math>
 |-
 | style="text-align: center;" | <math> - \displaystyle \int _{{}^{n+1}V} \delta{v}^T  {~}^{n+1}{b}~ d{~}^{n+1} V - \int _{{}^{n+1}\Gamma _t} \delta{v}^T {~}^{n+1} {t}~d {~}^{n+1} \Gamma = 0  </math>

← Older revision	Revision as of 10:00, 26 February 2018
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-<!-- metadata commented in wiki content
+Accepted for publication in ''Computational Mechanics''
-==UPDATED LAGRANGIAN MIXED FINITE ELEMENT  FORMULATION FOR QUASI AND FULLY  INCOMPRESSIBLE  FLUIDS==
 ==Abstract==

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 |}
-The tangent constitutive tensor <math display="inline">\boldsymbol{\cal C}_T</math> is deduced from Eqs.([[#eq-1|A.1]]), ([[#eq-2|A.2]])-([[#eq-4|A.4]]) as
+The tangent constitutive tensor <math display="inline">\boldsymbol{\cal C}_T</math> is deduced from Eqs.([[#eq-1|A.1]])-([[#eq-4|A.4]]) as
 <span id="eq-9"></span>