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df81a151
Commit
df81a151
authored
4 years ago
by
Christophe Geuzaine
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typo
parent
3af503ce
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Pipeline
#7930
passed
4 years ago
Stage: test
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Elasticity/wrench2D.pro
+21
-21
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Elasticity/wrench2D.pro
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21 deletions
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View file @
df81a151
...
...
@@ -14,24 +14,24 @@
Run (button at the bottom of the left panel)
------------------------------------------------------------------- */
/*
/*
Particularities of linear elasticity in GetDP:
Instead of a vector field "u = Vector[ ux, uy, uz ]", the displacement field
is regarded as two (2D case) or three (3D case) scalar fields.
Unlike conventional formulations, GetDP formulation is then written in terms
of the gradient "grad u" of the displacement field, which is a non-symmetric
tensor, and the needed symmetrization (to define the strain tensor and relate
it to the stress tensor) is done via the constitutive relationship (Hooke law).
This unusual formulation allows to take advantage of the powerful geometrical
Instead of a vector field "u = Vector[ ux, uy, uz ]", the displacement field
is regarded as two (2D case) or three (3D case) scalar fields.
Unlike conventional formulations, GetDP formulation is then written in terms
of the gradient "grad u" of the displacement field, which is a non-symmetric
tensor, and the needed symmetrization (to define the strain tensor and relate
it to the stress tensor) is done via the constitutive relationship (Hooke law).
This unusual formulation allows to take advantage of the powerful geometrical
and homological GetDP kernel, which relies on the operators grad, curl and div.
The "grad u" formulation entails a small increase of assembly work but makes
in counterpart lots of geometrical features implemented in GetDP (change of
coordinates, function spaces, etc...) applicable to elastic problems
out-of-the-box, since the scalar fields { ux, uy, uz } have exactly the same
geometrical properties as, e.g. an electric scalar potential or a temperature
field.
field.
*/
Include
"wrench2D_common.pro"
;
...
...
@@ -65,18 +65,18 @@ Group {
}
Function
{
/*
/*
Material coefficients
No need of regionwise definition ( E[{Wrench}] = ... ; )
as this model comprises only one region.
If there is more than one region and coefficients are not particularised,
the same value holds for all of them.
as this model comprises only one region.
If there is more than one region and coefficients are not particularised,
the same value holds for all of them.
*/
E
[]
=
Young
;
nu
[]
=
Poisson
;
/*
/*
Volume force components applied to the region "Vol_Force_Mec"
Gravity could be defined here as well ( force_y[] = 7000*9.81; ) ;
Gravity could be defined here as well ( force_y[] = 7000*9.81; ) ;
*/
force_x
[]
=
0
;
force_y
[]
=
0
;
...
...
@@ -103,7 +103,7 @@ Function {
EPD: a[] = lambda + 2 mu b[] = mu c[] = lambda
3D: a[] = lambda + 2 mu b[] = mu c[] = lambda
respectively for the 2D plane strain (EPD), 2D plane stress (EP
S
) and 3D cases.
respectively for the 2D plane strain (EPD), 2D plane stress (EP
C
) and 3D cases.
*/
Function
{
...
...
@@ -155,14 +155,14 @@ Constraint {
are less naturally accounted for within the "grad u" formulation; but they
could be easily implemented with e.g. a Lagrange multiplier.
The finite element shape (e.g. triangles or quadrangles in 2D) has no influence
The finite element shape (e.g. triangles or quadrangles in 2D) has no influence
in the definition of the FunctionSpaces. The appropriate shape functions
are determined by GetDP at a much lower level on basis of the information
contained in the *.msh file.
Second order elements are hierarchically implemented by adding to the first
order node-based shape functions a set of second order edge-based functions
to complete a basis for 2D order polynomials on the reference element.
Second order elements are hierarchically implemented by adding to the first
order node-based shape functions a set of second order edge-based functions
to complete a basis for 2D order polynomials on the reference element.
*/
// Domain of definition of the "ux" and "uy" FunctionSpaces
...
...
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