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ElementQuad4.cpp
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Sun, Sep 29, 09:04
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5 KB
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Tue, Oct 1, 09:04 (2 d)
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rGOOSEFEM GooseFEM
ElementQuad4.cpp
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#include <catch2/catch.hpp>
#include <xtensor/xrandom.hpp>
#include <xtensor/xmath.hpp>
#include <GooseFEM/GooseFEM.h>
#define ISCLOSE(a,b) REQUIRE_THAT((a), Catch::WithinAbs((b), 1.e-12));
TEST_CASE
(
"GooseFEM::ElementQuad4"
,
"ElementQuad4.h"
)
{
SECTION
(
"dV - Gauss"
)
{
GooseFEM
::
Mesh
::
Quad4
::
Regular
mesh
(
2
,
2
);
auto
coor
=
mesh
.
coor
();
auto
top
=
mesh
.
nodesTopEdge
();
auto
right
=
mesh
.
nodesRightEdge
();
xt
::
view
(
coor
,
xt
::
keep
(
top
),
xt
::
keep
(
1
))
+=
1.0
;
xt
::
view
(
coor
,
xt
::
keep
(
right
),
xt
::
keep
(
0
))
+=
1.0
;
GooseFEM
::
Vector
vec
(
mesh
.
conn
(),
mesh
.
dofs
());
GooseFEM
::
Element
::
Quad4
::
Quadrature
quad
(
vec
.
AsElement
(
coor
));
auto
dV
=
quad
.
dV
();
auto
dV_tensor
=
quad
.
AsTensor
<
2
>
(
dV
);
REQUIRE
(
xt
::
allclose
(
xt
::
view
(
dV
,
xt
::
keep
(
0
)),
1.
/
4.
));
REQUIRE
(
xt
::
allclose
(
xt
::
view
(
dV
,
xt
::
keep
(
1
)),
2.
/
4.
));
REQUIRE
(
xt
::
allclose
(
xt
::
view
(
dV
,
xt
::
keep
(
2
)),
2.
/
4.
));
REQUIRE
(
xt
::
allclose
(
xt
::
view
(
dV
,
xt
::
keep
(
3
)),
4.
/
4.
));
for
(
size_t
e
=
0
;
e
<
mesh
.
nelem
();
++
e
)
{
for
(
size_t
q
=
0
;
q
<
quad
.
nip
();
++
q
)
{
REQUIRE
(
xt
::
allclose
(
xt
::
view
(
dV_tensor
,
xt
::
keep
(
e
),
xt
::
keep
(
q
)),
dV
(
e
,
q
)));
}
}
}
SECTION
(
"dV - Nodal"
)
{
GooseFEM
::
Mesh
::
Quad4
::
Regular
mesh
(
2
,
2
);
auto
coor
=
mesh
.
coor
();
auto
top
=
mesh
.
nodesTopEdge
();
auto
right
=
mesh
.
nodesRightEdge
();
xt
::
view
(
coor
,
xt
::
keep
(
top
),
xt
::
keep
(
1
))
+=
1.0
;
xt
::
view
(
coor
,
xt
::
keep
(
right
),
xt
::
keep
(
0
))
+=
1.0
;
GooseFEM
::
Vector
vec
(
mesh
.
conn
(),
mesh
.
dofs
());
GooseFEM
::
Element
::
Quad4
::
Quadrature
quad
(
vec
.
AsElement
(
coor
),
GooseFEM
::
Element
::
Quad4
::
Nodal
::
xi
(),
GooseFEM
::
Element
::
Quad4
::
Nodal
::
w
());
auto
dV
=
quad
.
dV
();
auto
dV_tensor
=
quad
.
AsTensor
<
2
>
(
dV
);
REQUIRE
(
xt
::
allclose
(
xt
::
view
(
dV
,
xt
::
keep
(
0
)),
1.
/
4.
));
REQUIRE
(
xt
::
allclose
(
xt
::
view
(
dV
,
xt
::
keep
(
1
)),
2.
/
4.
));
REQUIRE
(
xt
::
allclose
(
xt
::
view
(
dV
,
xt
::
keep
(
2
)),
2.
/
4.
));
REQUIRE
(
xt
::
allclose
(
xt
::
view
(
dV
,
xt
::
keep
(
3
)),
4.
/
4.
));
for
(
size_t
e
=
0
;
e
<
mesh
.
nelem
();
++
e
)
{
for
(
size_t
q
=
0
;
q
<
quad
.
nip
();
++
q
)
{
REQUIRE
(
xt
::
allclose
(
xt
::
view
(
dV_tensor
,
xt
::
keep
(
e
),
xt
::
keep
(
q
)),
dV
(
e
,
q
)));
}
}
}
SECTION
(
"int_N_scalar_NT_dV"
)
{
GooseFEM
::
Mesh
::
Quad4
::
Regular
mesh
(
3
,
3
);
GooseFEM
::
Vector
vec
(
mesh
.
conn
(),
mesh
.
dofsPeriodic
());
GooseFEM
::
MatrixDiagonal
mat
(
mesh
.
conn
(),
mesh
.
dofsPeriodic
());
GooseFEM
::
Element
::
Quad4
::
Quadrature
quad
(
vec
.
AsElement
(
mesh
.
coor
()),
GooseFEM
::
Element
::
Quad4
::
Nodal
::
xi
(),
GooseFEM
::
Element
::
Quad4
::
Nodal
::
w
());
xt
::
xtensor
<
double
,
2
>
rho
=
xt
::
ones
<
double
>
({
mesh
.
nelem
(),
quad
.
nip
()});
mat
.
assemble
(
quad
.
Int_N_scalar_NT_dV
(
rho
));
auto
M
=
mat
.
AsDiagonal
();
REQUIRE
(
M
.
size
()
==
vec
.
ndof
());
REQUIRE
(
xt
::
allclose
(
M
,
1.
));
}
SECTION
(
"symGradN_vector"
)
{
GooseFEM
::
Mesh
::
Quad4
::
FineLayer
mesh
(
27
,
27
);
GooseFEM
::
Vector
vec
(
mesh
.
conn
(),
mesh
.
dofs
());
GooseFEM
::
Element
::
Quad4
::
Quadrature
quad
(
vec
.
AsElement
(
mesh
.
coor
()));
xt
::
xtensor
<
double
,
2
>
F
=
xt
::
zeros
<
double
>
({
2
,
2
});
xt
::
xtensor
<
double
,
2
>
EPS
=
xt
::
zeros
<
double
>
({
2
,
2
});
F
(
0
,
1
)
=
0.1
;
EPS
(
0
,
1
)
=
0.05
;
EPS
(
1
,
0
)
=
0.05
;
xt
::
xtensor
<
double
,
2
>
coor
=
mesh
.
coor
();
xt
::
xtensor
<
double
,
2
>
disp
=
xt
::
zeros
<
double
>
(
coor
.
shape
());
for
(
size_t
n
=
0
;
n
<
mesh
.
nnode
();
++
n
)
{
for
(
size_t
i
=
0
;
i
<
F
.
shape
()[
0
];
++
i
)
{
for
(
size_t
j
=
0
;
j
<
F
.
shape
()[
1
];
++
j
)
{
disp
(
n
,
i
)
+=
F
(
i
,
j
)
*
coor
(
n
,
j
);
}
}
}
auto
eps
=
quad
.
SymGradN_vector
(
vec
.
AsElement
(
disp
));
auto
dV
=
quad
.
AsTensor
<
2
>
(
quad
.
dV
());
auto
epsbar
=
xt
::
average
(
eps
,
dV
,
{
0
,
1
});
REQUIRE
(
eps
.
shape
()[
0
]
==
mesh
.
nelem
());
REQUIRE
(
eps
.
shape
()[
1
]
==
quad
.
nip
());
REQUIRE
(
eps
.
shape
()[
2
]
==
mesh
.
ndim
());
REQUIRE
(
eps
.
shape
()[
3
]
==
mesh
.
ndim
());
for
(
size_t
e
=
0
;
e
<
mesh
.
nelem
();
++
e
)
{
for
(
size_t
q
=
0
;
q
<
quad
.
nip
();
++
q
)
{
REQUIRE
(
xt
::
allclose
(
xt
::
view
(
eps
,
e
,
q
),
EPS
));
}
}
REQUIRE
(
xt
::
allclose
(
epsbar
,
EPS
));
}
SECTION
(
"symGradN_vector, int_gradN_dot_tensor2s_dV"
)
{
GooseFEM
::
Mesh
::
Quad4
::
FineLayer
mesh
(
27
,
27
);
GooseFEM
::
Vector
vec
(
mesh
.
conn
(),
mesh
.
dofsPeriodic
());
GooseFEM
::
Element
::
Quad4
::
Quadrature
quad
(
vec
.
AsElement
(
mesh
.
coor
()));
xt
::
xtensor
<
double
,
2
>
F
=
xt
::
zeros
<
double
>
({
2
,
2
});
F
(
0
,
1
)
=
0.1
;
auto
coor
=
mesh
.
coor
();
xt
::
xtensor
<
double
,
2
>
disp
=
xt
::
zeros
<
double
>
(
coor
.
shape
());
for
(
size_t
n
=
0
;
n
<
mesh
.
nnode
();
++
n
)
{
for
(
size_t
i
=
0
;
i
<
F
.
shape
()[
0
];
++
i
)
{
for
(
size_t
j
=
0
;
j
<
F
.
shape
()[
1
];
++
j
)
{
disp
(
n
,
i
)
+=
F
(
i
,
j
)
*
coor
(
n
,
j
);
}
}
}
auto
eps
=
quad
.
SymGradN_vector
(
vec
.
AsElement
(
disp
));
auto
Fi
=
vec
.
AssembleDofs
(
quad
.
Int_gradN_dot_tensor2_dV
(
eps
));
REQUIRE
(
Fi
.
size
()
==
vec
.
ndof
());
REQUIRE
(
xt
::
allclose
(
Fi
,
0.
));
}
}
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