Page Menu
Home
c4science
Search
Configure Global Search
Log In
Files
F69108732
DynamicsDiagonalSmallStrainQuad4.h
No One
Temporary
Actions
Download File
Edit File
Delete File
View Transforms
Subscribe
Mute Notifications
Award Token
Subscribers
None
File Metadata
Details
File Info
Storage
Attached
Created
Sun, Jun 30, 07:12
Size
13 KB
Mime Type
text/x-c++
Expires
Tue, Jul 2, 07:12 (1 d, 23 h)
Engine
blob
Format
Raw Data
Handle
18585219
Attached To
rGOOSEFEM GooseFEM
DynamicsDiagonalSmallStrainQuad4.h
View Options
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_DYNAMICS_DIAGONAL_SMALLSTRAIN_QUAD4_H
#define GOOSEFEM_DYNAMICS_DIAGONAL_SMALLSTRAIN_QUAD4_H
// -------------------------------------------------------------------------------------------------
#include "Macros.h"
#include <cppmat/cppmat.h>
// -------------------------------------------------------------------------------------------------
namespace
GooseFEM
{
namespace
Element
{
namespace
Diagonal
{
namespace
SmallStrain
{
// ========================== N.B. most loops are unrolled for efficiency ==========================
template
<
class
Material
>
class
Quad4
{
public:
// class variables
// ---------------
// constitutive response per integration point, per element
std
::
unique_ptr
<
Material
>
mat
;
// matrices to store the element data
cppmat
::
matrix
<
double
>
x
,
u
,
v
,
f
,
M
,
D
,
dNx
,
dNxi
,
w
,
V
,
dNxi_n
,
w_n
,
V_n
;
// dimensions
size_t
nelem
,
nip
=
4
,
nne
=
4
,
ndim
=
2
;
// signals for solvers
bool
changed_f
=
false
,
changed_M
=
true
,
changed_D
=
true
;
// class functions
// ---------------
// constructor
Quad4
(
std
::
unique_ptr
<
Material
>
mat
,
size_t
nelem
);
// recompute relevant quantities after "x", "u", or "v" have been externally updated
void
updated_x
();
void
updated_u
();
void
updated_v
();
};
// =================================================================================================
template
<
class
Material
>
inline
Quad4
<
Material
>::
Quad4
(
std
::
unique_ptr
<
Material
>
_mat
,
size_t
_nelem
)
{
// copy from input
nelem
=
_nelem
;
mat
=
std
::
move
(
_mat
);
// allocate matrices
// -
x
.
resize
({
nelem
,
nne
,
ndim
});
u
.
resize
({
nelem
,
nne
,
ndim
});
v
.
resize
({
nelem
,
nne
,
ndim
});
f
.
resize
({
nelem
,
nne
,
ndim
});
// -
M
.
resize
({
nelem
,
nne
*
ndim
,
nne
*
ndim
});
D
.
resize
({
nelem
,
nne
*
ndim
,
nne
*
ndim
});
// -
dNx
.
resize
({
nelem
,
nip
,
nne
,
ndim
});
// -
V
.
resize
({
nelem
,
nip
});
V_n
.
resize
({
nelem
,
nne
});
// -
dNxi
.
resize
({
nip
,
nne
,
ndim
});
dNxi_n
.
resize
({
nne
,
nne
,
ndim
});
// -
w
.
resize
({
nip
});
w_n
.
resize
({
nne
});
// zero initialize matrices (only diagonal is written, no new zero-initialization necessary)
M
.
setZero
();
D
.
setZero
();
// shape function gradient at all Gauss points, in local coordinates
// - k == 0
dNxi
(
0
,
0
,
0
)
=
-
.25
*
(
1.
+
1.
/
std
::
sqrt
(
3.
));
dNxi
(
0
,
0
,
1
)
=
-
.25
*
(
1.
+
1.
/
std
::
sqrt
(
3.
));
dNxi
(
0
,
1
,
0
)
=
+
.25
*
(
1.
+
1.
/
std
::
sqrt
(
3.
));
dNxi
(
0
,
1
,
1
)
=
-
.25
*
(
1.
-
1.
/
std
::
sqrt
(
3.
));
dNxi
(
0
,
2
,
0
)
=
+
.25
*
(
1.
-
1.
/
std
::
sqrt
(
3.
));
dNxi
(
0
,
2
,
1
)
=
+
.25
*
(
1.
-
1.
/
std
::
sqrt
(
3.
));
dNxi
(
0
,
3
,
0
)
=
-
.25
*
(
1.
-
1.
/
std
::
sqrt
(
3.
));
dNxi
(
0
,
3
,
1
)
=
+
.25
*
(
1.
+
1.
/
std
::
sqrt
(
3.
));
// - k == 1
dNxi
(
1
,
0
,
0
)
=
-
.25
*
(
1.
+
1.
/
std
::
sqrt
(
3.
));
dNxi
(
1
,
0
,
1
)
=
-
.25
*
(
1.
-
1.
/
std
::
sqrt
(
3.
));
dNxi
(
1
,
1
,
0
)
=
+
.25
*
(
1.
+
1.
/
std
::
sqrt
(
3.
));
dNxi
(
1
,
1
,
1
)
=
-
.25
*
(
1.
+
1.
/
std
::
sqrt
(
3.
));
dNxi
(
1
,
2
,
0
)
=
+
.25
*
(
1.
-
1.
/
std
::
sqrt
(
3.
));
dNxi
(
1
,
2
,
1
)
=
+
.25
*
(
1.
+
1.
/
std
::
sqrt
(
3.
));
dNxi
(
1
,
3
,
0
)
=
-
.25
*
(
1.
-
1.
/
std
::
sqrt
(
3.
));
dNxi
(
1
,
3
,
1
)
=
+
.25
*
(
1.
-
1.
/
std
::
sqrt
(
3.
));
// - k == 2
dNxi
(
2
,
0
,
0
)
=
-
.25
*
(
1.
-
1.
/
std
::
sqrt
(
3.
));
dNxi
(
2
,
0
,
1
)
=
-
.25
*
(
1.
-
1.
/
std
::
sqrt
(
3.
));
dNxi
(
2
,
1
,
0
)
=
+
.25
*
(
1.
-
1.
/
std
::
sqrt
(
3.
));
dNxi
(
2
,
1
,
1
)
=
-
.25
*
(
1.
+
1.
/
std
::
sqrt
(
3.
));
dNxi
(
2
,
2
,
0
)
=
+
.25
*
(
1.
+
1.
/
std
::
sqrt
(
3.
));
dNxi
(
2
,
2
,
1
)
=
+
.25
*
(
1.
+
1.
/
std
::
sqrt
(
3.
));
dNxi
(
2
,
3
,
0
)
=
-
.25
*
(
1.
+
1.
/
std
::
sqrt
(
3.
));
dNxi
(
2
,
3
,
1
)
=
+
.25
*
(
1.
-
1.
/
std
::
sqrt
(
3.
));
// - k == 3
dNxi
(
3
,
0
,
0
)
=
-
.25
*
(
1.
-
1.
/
std
::
sqrt
(
3.
));
dNxi
(
3
,
0
,
1
)
=
-
.25
*
(
1.
+
1.
/
std
::
sqrt
(
3.
));
dNxi
(
3
,
1
,
0
)
=
+
.25
*
(
1.
-
1.
/
std
::
sqrt
(
3.
));
dNxi
(
3
,
1
,
1
)
=
-
.25
*
(
1.
-
1.
/
std
::
sqrt
(
3.
));
dNxi
(
3
,
2
,
0
)
=
+
.25
*
(
1.
+
1.
/
std
::
sqrt
(
3.
));
dNxi
(
3
,
2
,
1
)
=
+
.25
*
(
1.
-
1.
/
std
::
sqrt
(
3.
));
dNxi
(
3
,
3
,
0
)
=
-
.25
*
(
1.
+
1.
/
std
::
sqrt
(
3.
));
dNxi
(
3
,
3
,
1
)
=
+
.25
*
(
1.
+
1.
/
std
::
sqrt
(
3.
));
// integration point weight at all Gauss points
w
(
0
)
=
1.
;
w
(
1
)
=
1.
;
w
(
2
)
=
1.
;
w
(
3
)
=
1.
;
// shape function gradient at all nodes, in local coordinates
// - k == 0
dNxi_n
(
0
,
0
,
0
)
=
-
0.5
;
dNxi_n
(
0
,
0
,
1
)
=
-
0.5
;
dNxi_n
(
0
,
1
,
0
)
=
+
0.5
;
dNxi_n
(
0
,
1
,
1
)
=
0.0
;
dNxi_n
(
0
,
2
,
0
)
=
0.0
;
dNxi_n
(
0
,
2
,
1
)
=
0.0
;
dNxi_n
(
0
,
3
,
0
)
=
0.0
;
dNxi_n
(
0
,
3
,
1
)
=
+
0.5
;
// - k == 1
dNxi_n
(
1
,
0
,
0
)
=
-
0.5
;
dNxi_n
(
1
,
0
,
1
)
=
0.0
;
dNxi_n
(
1
,
1
,
0
)
=
+
0.5
;
dNxi_n
(
1
,
1
,
1
)
=
-
0.5
;
dNxi_n
(
1
,
2
,
0
)
=
0.0
;
dNxi_n
(
1
,
2
,
1
)
=
+
0.5
;
dNxi_n
(
1
,
3
,
0
)
=
0.0
;
dNxi_n
(
1
,
3
,
1
)
=
0.0
;
// - k == 2
dNxi_n
(
2
,
0
,
0
)
=
0.0
;
dNxi_n
(
2
,
0
,
1
)
=
0.0
;
dNxi_n
(
2
,
1
,
0
)
=
0.0
;
dNxi_n
(
2
,
1
,
1
)
=
-
0.5
;
dNxi_n
(
2
,
2
,
0
)
=
+
0.5
;
dNxi_n
(
2
,
2
,
1
)
=
+
0.5
;
dNxi_n
(
2
,
3
,
0
)
=
-
0.5
;
dNxi_n
(
2
,
3
,
1
)
=
0.0
;
// - k == 3
dNxi_n
(
3
,
0
,
0
)
=
0.0
;
dNxi_n
(
3
,
0
,
1
)
=
-
0.5
;
dNxi_n
(
3
,
1
,
0
)
=
0.0
;
dNxi_n
(
3
,
1
,
1
)
=
0.0
;
dNxi_n
(
3
,
2
,
0
)
=
+
0.5
;
dNxi_n
(
3
,
2
,
1
)
=
0.0
;
dNxi_n
(
3
,
3
,
0
)
=
-
0.5
;
dNxi_n
(
3
,
3
,
1
)
=
+
0.5
;
// integration point weight at all nodes
w_n
(
0
)
=
1.
;
w_n
(
1
)
=
1.
;
w_n
(
2
)
=
1.
;
w_n
(
3
)
=
1.
;
// Note, the above is a specialization of the following:
//
// - Shape function gradients
//
// dNxi(0,0) = -.25*(1.-xi(k,1)); dNxi(0,1) = -.25*(1.-xi(k,0));
// dNxi(1,0) = +.25*(1.-xi(k,1)); dNxi(1,1) = -.25*(1.+xi(k,0));
// dNxi(2,0) = +.25*(1.+xi(k,1)); dNxi(2,1) = +.25*(1.+xi(k,0));
// dNxi(3,0) = -.25*(1.+xi(k,1)); dNxi(3,1) = +.25*(1.-xi(k,0));
//
// - Gauss point coordinates and weights
//
// xi(0,0) = -1./std::sqrt(3.); xi(0,1) = -1./std::sqrt(3.); w(0) = 1.;
// xi(1,0) = +1./std::sqrt(3.); xi(1,1) = -1./std::sqrt(3.); w(1) = 1.;
// xi(2,0) = +1./std::sqrt(3.); xi(2,1) = +1./std::sqrt(3.); w(2) = 1.;
// xi(3,0) = -1./std::sqrt(3.); xi(3,1) = +1./std::sqrt(3.); w(3) = 1.;
//
// - Nodal coordinates and weights
//
// xi(0,0) = -1.; xi(0,1) = -1.; w(0) = 1.;
// xi(1,0) = +1.; xi(1,1) = -1.; w(1) = 1.;
// xi(2,0) = +1.; xi(2,1) = +1.; w(2) = 1.;
// xi(3,0) = -1.; xi(3,1) = +1.; w(3) = 1.;
}
// =================================================================================================
template
<
class
Material
>
inline
void
Quad4
<
Material
>::
updated_x
()
{
#pragma omp parallel
{
// intermediate quantities
cppmat
::
cartesian2d
::
tensor2
<
double
>
J_
,
Jinv_
;
double
Jdet_
;
// local views of the global arrays (speeds up indexing, and increases readability)
cppmat
::
tiny
::
matrix2
<
double
,
8
,
8
>
M_
,
D_
;
cppmat
::
tiny
::
matrix2
<
double
,
4
,
2
>
dNxi_
,
dNx_
,
x_
;
cppmat
::
tiny
::
vector
<
double
,
4
>
w_
,
V_
;
// loop over all elements (in parallel)
#pragma omp for
for
(
size_t
e
=
0
;
e
<
nelem
;
++
e
)
{
// pointer to element positions
x_
.
map
(
&
x
(
e
));
// nodal quadrature
// ----------------
// pointer to element mass/damping matrix, nodal volume, and integration weight
M_
.
map
(
&
M
(
e
));
D_
.
map
(
&
D
(
e
));
V_
.
map
(
&
V_n
(
e
));
w_
.
map
(
&
w_n
(
0
));
// loop over nodes, i.e. the integration points
for
(
size_t
k
=
0
;
k
<
nne
;
++
k
)
{
// - pointer to the shape function gradients (local coordinates)
dNxi_
.
map
(
&
dNxi_n
(
k
));
// - Jacobian
// J(i,j) += dNxi(m,i) * xe(m,j)
J_
(
0
,
0
)
=
dNxi_
(
0
,
0
)
*
x_
(
0
,
0
)
+
dNxi_
(
1
,
0
)
*
x_
(
1
,
0
)
+
dNxi_
(
2
,
0
)
*
x_
(
2
,
0
)
+
dNxi_
(
3
,
0
)
*
x_
(
3
,
0
);
J_
(
0
,
1
)
=
dNxi_
(
0
,
0
)
*
x_
(
0
,
1
)
+
dNxi_
(
1
,
0
)
*
x_
(
1
,
1
)
+
dNxi_
(
2
,
0
)
*
x_
(
2
,
1
)
+
dNxi_
(
3
,
0
)
*
x_
(
3
,
1
);
J_
(
1
,
0
)
=
dNxi_
(
0
,
1
)
*
x_
(
0
,
0
)
+
dNxi_
(
1
,
1
)
*
x_
(
1
,
0
)
+
dNxi_
(
2
,
1
)
*
x_
(
2
,
0
)
+
dNxi_
(
3
,
1
)
*
x_
(
3
,
0
);
J_
(
1
,
1
)
=
dNxi_
(
0
,
1
)
*
x_
(
0
,
1
)
+
dNxi_
(
1
,
1
)
*
x_
(
1
,
1
)
+
dNxi_
(
2
,
1
)
*
x_
(
2
,
1
)
+
dNxi_
(
3
,
1
)
*
x_
(
3
,
1
);
// - determinant of the Jacobian
Jdet_
=
J_
.
det
();
// - integration point volume
V_
(
k
)
=
w_
(
k
)
*
Jdet_
;
// - assemble element mass matrix
// M(m+i,n+i) += N(m) * rho * V * N(n);
M_
(
k
*
2
,
k
*
2
)
=
mat
->
rho
(
e
,
k
)
*
V_
(
k
);
M_
(
k
*
2
+
1
,
k
*
2
+
1
)
=
mat
->
rho
(
e
,
k
)
*
V_
(
k
);
// - assemble element non-Galilean damping matrix
// D(m+i,n+i) += N(m) * alpha * V * N(n);
D_
(
k
*
2
,
k
*
2
)
=
mat
->
alpha
(
e
,
k
)
*
V_
(
k
);
D_
(
k
*
2
+
1
,
k
*
2
+
1
)
=
mat
->
alpha
(
e
,
k
)
*
V_
(
k
);
}
// Gaussian quadrature
// -------------------
// pointer to element integration volume and weight
V_
.
map
(
&
V
(
e
));
w_
.
map
(
&
w
(
0
));
// loop over Gauss points
for
(
size_t
k
=
0
;
k
<
nip
;
++
k
)
{
// - pointer to the shape function gradients (local/global coordinates)
dNxi_
.
map
(
&
dNxi
(
k
));
dNx_
.
map
(
&
dNx
(
e
,
k
));
// - Jacobian
// J(i,j) += dNxi(m,i) * xe(m,j)
J_
(
0
,
0
)
=
dNxi_
(
0
,
0
)
*
x_
(
0
,
0
)
+
dNxi_
(
1
,
0
)
*
x_
(
1
,
0
)
+
dNxi_
(
2
,
0
)
*
x_
(
2
,
0
)
+
dNxi_
(
3
,
0
)
*
x_
(
3
,
0
);
J_
(
0
,
1
)
=
dNxi_
(
0
,
0
)
*
x_
(
0
,
1
)
+
dNxi_
(
1
,
0
)
*
x_
(
1
,
1
)
+
dNxi_
(
2
,
0
)
*
x_
(
2
,
1
)
+
dNxi_
(
3
,
0
)
*
x_
(
3
,
1
);
J_
(
1
,
0
)
=
dNxi_
(
0
,
1
)
*
x_
(
0
,
0
)
+
dNxi_
(
1
,
1
)
*
x_
(
1
,
0
)
+
dNxi_
(
2
,
1
)
*
x_
(
2
,
0
)
+
dNxi_
(
3
,
1
)
*
x_
(
3
,
0
);
J_
(
1
,
1
)
=
dNxi_
(
0
,
1
)
*
x_
(
0
,
1
)
+
dNxi_
(
1
,
1
)
*
x_
(
1
,
1
)
+
dNxi_
(
2
,
1
)
*
x_
(
2
,
1
)
+
dNxi_
(
3
,
1
)
*
x_
(
3
,
1
);
// - determinant and inverse of the Jacobian
Jdet_
=
J_
.
det
();
Jinv_
=
J_
.
inv
();
// - integration point volume
V_
(
k
)
=
w_
(
k
)
*
Jdet_
;
// - shape function gradients (global coordinates)
// dNx(m,i) += Jinv(i,j) * dNxi(m,j)
for
(
size_t
m
=
0
;
m
<
nne
;
++
m
)
{
dNx_
(
m
,
0
)
=
Jinv_
(
0
,
0
)
*
dNxi_
(
m
,
0
)
+
Jinv_
(
0
,
1
)
*
dNxi_
(
m
,
1
);
dNx_
(
m
,
1
)
=
Jinv_
(
1
,
0
)
*
dNxi_
(
m
,
0
)
+
Jinv_
(
1
,
1
)
*
dNxi_
(
m
,
1
);
}
}
}
// set signals
changed_f
=
false
;
changed_M
=
true
;
changed_D
=
true
;
}
// #pragma omp parallel
}
// =================================================================================================
template
<
class
Material
>
inline
void
Quad4
<
Material
>::
updated_u
()
{
#pragma omp parallel
{
// intermediate quantities
cppmat
::
cartesian2d
::
tensor2
<
double
>
gradu_
;
cppmat
::
cartesian2d
::
tensor2s
<
double
>
eps_
,
sig_
;
// local views of the global arrays (speeds up indexing, and increases readability)
cppmat
::
tiny
::
matrix2
<
double
,
4
,
2
>
dNx_
,
u_
,
f_
;
cppmat
::
tiny
::
vector
<
double
,
4
>
V_
;
// loop over all elements (in parallel)
#pragma omp for
for
(
size_t
e
=
0
;
e
<
nelem
;
++
e
)
{
// pointer to element forces, displacements, and integration volume
f_
.
map
(
&
f
(
e
));
u_
.
map
(
&
u
(
e
));
V_
.
map
(
&
V
(
e
));
// zero initialize forces
f_
.
setZero
();
// loop over all integration points in element "e"
for
(
size_t
k
=
0
;
k
<
nip
;
++
k
)
{
// - pointer to the shape function gradients, strain and stress tensor (stored symmetric)
dNx_
.
map
(
&
dNx
(
e
,
k
));
eps_
.
map
(
&
mat
->
eps
(
e
,
k
));
sig_
.
map
(
&
mat
->
sig
(
e
,
k
));
// - displacement gradient
// gradu_(i,j) += dNx(m,i) * ue(m,j)
gradu_
(
0
,
0
)
=
dNx_
(
0
,
0
)
*
u_
(
0
,
0
)
+
dNx_
(
1
,
0
)
*
u_
(
1
,
0
)
+
dNx_
(
2
,
0
)
*
u_
(
2
,
0
)
+
dNx_
(
3
,
0
)
*
u_
(
3
,
0
);
gradu_
(
0
,
1
)
=
dNx_
(
0
,
0
)
*
u_
(
0
,
1
)
+
dNx_
(
1
,
0
)
*
u_
(
1
,
1
)
+
dNx_
(
2
,
0
)
*
u_
(
2
,
1
)
+
dNx_
(
3
,
0
)
*
u_
(
3
,
1
);
gradu_
(
1
,
0
)
=
dNx_
(
0
,
1
)
*
u_
(
0
,
0
)
+
dNx_
(
1
,
1
)
*
u_
(
1
,
0
)
+
dNx_
(
2
,
1
)
*
u_
(
2
,
0
)
+
dNx_
(
3
,
1
)
*
u_
(
3
,
0
);
gradu_
(
1
,
1
)
=
dNx_
(
0
,
1
)
*
u_
(
0
,
1
)
+
dNx_
(
1
,
1
)
*
u_
(
1
,
1
)
+
dNx_
(
2
,
1
)
*
u_
(
2
,
1
)
+
dNx_
(
3
,
1
)
*
u_
(
3
,
1
);
// - strain (stored symmetric)
// eps(i,j) = .5 * ( gradu_(i,j) + gradu_(j,i) )
eps_
(
0
,
0
)
=
gradu_
(
0
,
0
);
eps_
(
0
,
1
)
=
.5
*
(
gradu_
(
0
,
1
)
+
gradu_
(
1
,
0
)
);
eps_
(
1
,
1
)
=
gradu_
(
1
,
1
);
// - constitutive response
mat
->
updated_eps
(
e
,
k
);
// - assemble to element force
// f(m,j) += dNx(m,i) * sig(i,j) * V;
for
(
size_t
m
=
0
;
m
<
nne
;
++
m
)
{
f_
(
m
,
0
)
+=
dNx_
(
m
,
0
)
*
sig_
(
0
,
0
)
*
V_
(
k
)
+
dNx_
(
m
,
1
)
*
sig_
(
1
,
0
)
*
V_
(
k
);
f_
(
m
,
1
)
+=
dNx_
(
m
,
0
)
*
sig_
(
0
,
1
)
*
V_
(
k
)
+
dNx_
(
m
,
1
)
*
sig_
(
1
,
1
)
*
V_
(
k
);
}
}
}
// set signals
changed_f
=
true
;
changed_M
=
false
;
changed_D
=
false
;
}
}
// =================================================================================================
template
<
class
Material
>
inline
void
Quad4
<
Material
>::
updated_v
()
{
#pragma omp parallel
{
// intermediate quantities
cppmat
::
cartesian2d
::
tensor2
<
double
>
gradv_
;
cppmat
::
cartesian2d
::
tensor2s
<
double
>
epsdot_
,
sig_
;
// local views of the global arrays (speeds up indexing, and increases readability)
cppmat
::
tiny
::
matrix2
<
double
,
4
,
2
>
dNx_
,
v_
,
f_
;
cppmat
::
tiny
::
vector
<
double
,
4
>
V_
;
// loop over all elements (in parallel)
#pragma omp for
for
(
size_t
e
=
0
;
e
<
nelem
;
++
e
)
{
// pointer to element forces, displacements, and integration volume
f_
.
map
(
&
f
(
e
));
v_
.
map
(
&
v
(
e
));
V_
.
map
(
&
V
(
e
));
// zero initialize forces
f_
.
setZero
();
// loop over all integration points in element "e"
for
(
size_t
k
=
0
;
k
<
nip
;
++
k
)
{
// - pointer to the shape function gradients, strain-rate and stress tensor (stored symmetric)
dNx_
.
map
(
&
dNx
(
e
,
k
));
epsdot_
.
map
(
&
mat
->
epsdot
(
e
,
k
));
sig_
.
map
(
&
mat
->
sig
(
e
,
k
));
// - displacement gradient
// gradv_(i,j) += dNx(m,i) * ue(m,j)
gradv_
(
0
,
0
)
=
dNx_
(
0
,
0
)
*
v_
(
0
,
0
)
+
dNx_
(
1
,
0
)
*
v_
(
1
,
0
)
+
dNx_
(
2
,
0
)
*
v_
(
2
,
0
)
+
dNx_
(
3
,
0
)
*
v_
(
3
,
0
);
gradv_
(
0
,
1
)
=
dNx_
(
0
,
0
)
*
v_
(
0
,
1
)
+
dNx_
(
1
,
0
)
*
v_
(
1
,
1
)
+
dNx_
(
2
,
0
)
*
v_
(
2
,
1
)
+
dNx_
(
3
,
0
)
*
v_
(
3
,
1
);
gradv_
(
1
,
0
)
=
dNx_
(
0
,
1
)
*
v_
(
0
,
0
)
+
dNx_
(
1
,
1
)
*
v_
(
1
,
0
)
+
dNx_
(
2
,
1
)
*
v_
(
2
,
0
)
+
dNx_
(
3
,
1
)
*
v_
(
3
,
0
);
gradv_
(
1
,
1
)
=
dNx_
(
0
,
1
)
*
v_
(
0
,
1
)
+
dNx_
(
1
,
1
)
*
v_
(
1
,
1
)
+
dNx_
(
2
,
1
)
*
v_
(
2
,
1
)
+
dNx_
(
3
,
1
)
*
v_
(
3
,
1
);
// - strain (stored symmetric)
// epsdot(i,j) = .5 * ( gradv_(i,j) + gradv_(j,i) )
epsdot_
(
0
,
0
)
=
gradv_
(
0
,
0
);
epsdot_
(
0
,
1
)
=
.5
*
(
gradv_
(
0
,
1
)
+
gradv_
(
1
,
0
)
);
epsdot_
(
1
,
1
)
=
gradv_
(
1
,
1
);
// - constitutive response
mat
->
updated_epsdot
(
e
,
k
);
// - assemble to element force
// f(m,j) += dNdx(m,i) * sig(i,j) * V;
for
(
size_t
m
=
0
;
m
<
nne
;
++
m
)
{
f_
(
m
,
0
)
+=
dNx_
(
m
,
0
)
*
sig_
(
0
,
0
)
*
V_
(
k
)
+
dNx_
(
m
,
1
)
*
sig_
(
1
,
0
)
*
V_
(
k
);
f_
(
m
,
1
)
+=
dNx_
(
m
,
0
)
*
sig_
(
0
,
1
)
*
V_
(
k
)
+
dNx_
(
m
,
1
)
*
sig_
(
1
,
1
)
*
V_
(
k
);
}
}
}
// set signals
changed_f
=
true
;
changed_M
=
false
;
changed_D
=
false
;
}
}
// =================================================================================================
}}}}
// namespace ...
#endif
Event Timeline
Log In to Comment