doc:user:elements:volumes:elements_formulation
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doc:user:elements:volumes:elements_formulation [2013/07/12 19:13] – created joris | doc:user:elements:volumes:elements_formulation [2016/03/30 15:23] – external edit 127.0.0.1 | ||
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- | ====== | + | ====== |
- | Dans l' | + | Following the classical approach |
- | ===== Formulation standard | + | ===== Standard formulation===== |
- | La formulation | + | When using the standard |
- | ===== Sous intégration sélective | + | ===== Selective Reduced Integration |
- | La réponse classique au phénomène de locking | + | The classical solution to the locking |
- | + | < | |
- | < | + | |
</ | </ | ||
- | Lors de la **sous intégration sélective**, la pression est calculée au centre de l' | + | When using **Selective Reduced Integration**, pressure is computed at the element center but deviatoric stresses are computed using 4 integration |
- | + | ||
- | Le calcul des forces internes est effectué via la formule ci-dessous | + | |
- | + | ||
- | $$ F^{int} = \underbrace{\int_{V(t)}{ [B]^{T} {s} \ } dV}_{4 \ points \ d' | + | |
- | | + | |
- | où | + | The integration of internal forces is done with the formula: |
- | * $s$ est le déviateur des contraintes | + | $$ F^{int} = \underbrace{\int_{V(t)}{ [B]^{T} {s} \ } dV}_{4 \ integration \ points \ in \ 2D - 8 \ in \ 3D} + |
- | | + | \underbrace{\int_{V(t)}{ |
- | * $[B]^T$ | + | |
- | Le calcul de l' | + | where |
+ | * $s$ is the stress deviator | ||
+ | * p is the pressure | ||
+ | * $[B]^T$ is the " | ||
- | ===== Sous intégration sélective avec report de pression ===== | + | The evaluation of the pressure integral using only one integration point may lead to imprecision (for example, on elements situated near the axis in a axisymmetric case). A solution consists in estimating the pressure at the element center, then, reporting it on each deviatoric integration point and calculating the pressure integral with 4 points (8 in 3D) instead of only one (see [[# |
- | L' | + | ===== Selective Reduced Integration with Pressure Report ===== |
+ | Integrating the pressure using only one integration point leads to inaccuracies due to an erroneous estimation of the element volume (this can become quite significant in axisymmetric near the revolution axis or when the mesh is highly distorted). The solution consists in calculating the pressure at the element center. Then, since its value is constant over the element, it can be integrated at each integration point used to compute deviatoric stresses. Therefore, the pressure is reported at these integration point to compute the pressure integral using these four points. This method ('' | ||
- | ===== Formulation | + | ===== EAS Formulation===== |
- | Une autre méthode d' | + | Another method which can avoid locking |
- | | + | |
- | | + | - double |
doc/user/elements/volumes/elements_formulation.txt · Last modified: 2018/11/27 08:42 by boman