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ElementQuad4Planar.cpp
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Thu, Aug 15, 07:15
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Sat, Aug 17, 07:15 (1 d, 21 h)
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19891199
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rGOOSEFEM GooseFEM
ElementQuad4Planar.cpp
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#include <catch2/catch.hpp>
#include <xtensor/xrandom.hpp>
#include <xtensor/xmath.hpp>
#include <GooseFEM/GooseFEM.h>
TEST_CASE
(
"GooseFEM::ElementQuad4Planar"
,
"ElementQuad4Planar.h"
)
{
SECTION
(
"GradN"
)
{
GooseFEM
::
Mesh
::
Quad4
::
Regular
mesh
(
3
,
3
);
GooseFEM
::
Vector
vec
(
mesh
.
conn
(),
mesh
.
dofs
());
GooseFEM
::
Element
::
Quad4
::
QuadraturePlanar
quad
(
vec
.
AsElement
(
mesh
.
coor
()));
auto
dNdx
=
quad
.
GradN
();
REQUIRE
(
xt
::
has_shape
(
dNdx
,
{
mesh
.
nelem
(),
quad
.
nip
(),
mesh
.
nne
(),
mesh
.
ndim
()}));
}
SECTION
(
"dV"
)
{
GooseFEM
::
Mesh
::
Quad4
::
Regular
mesh
(
3
,
3
);
GooseFEM
::
Vector
vec
(
mesh
.
conn
(),
mesh
.
dofs
());
GooseFEM
::
Element
::
Quad4
::
QuadraturePlanar
quad
(
vec
.
AsElement
(
mesh
.
coor
()));
auto
dV
=
quad
.
dV
();
REQUIRE
(
xt
::
has_shape
(
dV
,
quad
.
shape_qtensor
<
0
>
()));
REQUIRE
(
xt
::
has_shape
(
dV
,
quad
.
shape_qscalar
()));
REQUIRE
(
xt
::
allclose
(
dV
,
0.5
*
0.5
));
}
SECTION
(
"interp_N_vector"
)
{
GooseFEM
::
Mesh
::
Quad4
::
Regular
mesh
(
3
,
3
);
GooseFEM
::
Vector
vector
(
mesh
.
conn
(),
mesh
.
dofsPeriodic
());
GooseFEM
::
Element
::
Quad4
::
QuadraturePlanar
quad
(
vector
.
AsElement
(
mesh
.
coor
()));
auto
u
=
vector
.
allocate_nodevec
(
1.0
);
auto
ue
=
vector
.
AsElement
(
u
);
auto
uq
=
quad
.
Interp_N_vector
(
ue
);
REQUIRE
(
xt
::
allclose
(
uq
,
1.0
));
}
SECTION
(
"GradN_vector"
)
{
GooseFEM
::
Mesh
::
Quad4
::
Regular
mesh
(
3
,
3
);
GooseFEM
::
Vector
vec
(
mesh
.
conn
(),
mesh
.
dofs
());
GooseFEM
::
Element
::
Quad4
::
QuadraturePlanar
quad
(
vec
.
AsElement
(
mesh
.
coor
()));
size_t
td
=
3
;
xt
::
xtensor
<
double
,
2
>
F
=
xt
::
zeros
<
double
>
({
td
,
td
});
xt
::
xtensor
<
double
,
2
>
EPS
=
xt
::
zeros
<
double
>
({
td
,
td
});
F
(
0
,
1
)
=
0.1
;
auto
coor
=
mesh
.
coor
();
auto
disp
=
xt
::
zeros_like
(
coor
);
for
(
size_t
n
=
0
;
n
<
mesh
.
nnode
();
++
n
)
{
for
(
size_t
i
=
0
;
i
<
mesh
.
ndim
();
++
i
)
{
for
(
size_t
j
=
0
;
j
<
mesh
.
ndim
();
++
j
)
{
disp
(
n
,
i
)
+=
F
(
i
,
j
)
*
coor
(
n
,
j
);
}
}
}
auto
f
=
quad
.
GradN_vector
(
vec
.
AsElement
(
disp
));
REQUIRE
(
xt
::
has_shape
(
f
,
{
mesh
.
nelem
(),
quad
.
nip
(),
td
,
td
}));
REQUIRE
(
xt
::
has_shape
(
f
,
quad
.
shape_qtensor
<
2
>
()));
for
(
size_t
e
=
0
;
e
<
mesh
.
nelem
();
++
e
)
{
for
(
size_t
q
=
0
;
q
<
quad
.
nip
();
++
q
)
{
REQUIRE
(
xt
::
allclose
(
xt
::
view
(
f
,
e
,
q
),
xt
::
transpose
(
F
)));
}
}
}
SECTION
(
"GradN_vector_T"
)
{
GooseFEM
::
Mesh
::
Quad4
::
Regular
mesh
(
3
,
3
);
GooseFEM
::
Vector
vec
(
mesh
.
conn
(),
mesh
.
dofs
());
GooseFEM
::
Element
::
Quad4
::
QuadraturePlanar
quad
(
vec
.
AsElement
(
mesh
.
coor
()));
size_t
td
=
3
;
xt
::
xtensor
<
double
,
2
>
F
=
xt
::
zeros
<
double
>
({
td
,
td
});
xt
::
xtensor
<
double
,
2
>
EPS
=
xt
::
zeros
<
double
>
({
td
,
td
});
F
(
0
,
1
)
=
0.1
;
auto
coor
=
mesh
.
coor
();
auto
disp
=
xt
::
zeros_like
(
coor
);
for
(
size_t
n
=
0
;
n
<
mesh
.
nnode
();
++
n
)
{
for
(
size_t
i
=
0
;
i
<
mesh
.
ndim
();
++
i
)
{
for
(
size_t
j
=
0
;
j
<
mesh
.
ndim
();
++
j
)
{
disp
(
n
,
i
)
+=
F
(
i
,
j
)
*
coor
(
n
,
j
);
}
}
}
auto
f
=
quad
.
GradN_vector_T
(
vec
.
AsElement
(
disp
));
REQUIRE
(
xt
::
has_shape
(
f
,
{
mesh
.
nelem
(),
quad
.
nip
(),
td
,
td
}));
REQUIRE
(
xt
::
has_shape
(
f
,
quad
.
shape_qtensor
<
2
>
()));
for
(
size_t
e
=
0
;
e
<
mesh
.
nelem
();
++
e
)
{
for
(
size_t
q
=
0
;
q
<
quad
.
nip
();
++
q
)
{
REQUIRE
(
xt
::
allclose
(
xt
::
view
(
f
,
e
,
q
),
F
));
}
}
}
SECTION
(
"SymGradN_vector"
)
{
GooseFEM
::
Mesh
::
Quad4
::
Regular
mesh
(
3
,
3
);
GooseFEM
::
Vector
vec
(
mesh
.
conn
(),
mesh
.
dofs
());
GooseFEM
::
Element
::
Quad4
::
QuadraturePlanar
quad
(
vec
.
AsElement
(
mesh
.
coor
()));
size_t
td
=
3
;
xt
::
xtensor
<
double
,
2
>
F
=
xt
::
zeros
<
double
>
({
td
,
td
});
xt
::
xtensor
<
double
,
2
>
EPS
=
xt
::
zeros
<
double
>
({
td
,
td
});
F
(
0
,
1
)
=
0.1
;
EPS
(
0
,
1
)
=
0.05
;
EPS
(
1
,
0
)
=
0.05
;
auto
coor
=
mesh
.
coor
();
auto
disp
=
xt
::
zeros_like
(
coor
);
for
(
size_t
n
=
0
;
n
<
mesh
.
nnode
();
++
n
)
{
for
(
size_t
i
=
0
;
i
<
mesh
.
ndim
();
++
i
)
{
for
(
size_t
j
=
0
;
j
<
mesh
.
ndim
();
++
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
(
xt
::
has_shape
(
eps
,
{
mesh
.
nelem
(),
quad
.
nip
(),
td
,
td
}));
REQUIRE
(
xt
::
has_shape
(
eps
,
quad
.
shape_qtensor
<
2
>
()));
REQUIRE
(
xt
::
has_shape
(
dV
,
{
mesh
.
nelem
(),
quad
.
nip
(),
td
,
td
}));
REQUIRE
(
xt
::
has_shape
(
dV
,
quad
.
shape_qtensor
<
2
>
()));
REQUIRE
(
xt
::
has_shape
(
epsbar
,
{
td
,
td
}));
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
(
"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
::
QuadraturePlanar
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
.
Todiagonal
();
REQUIRE
(
M
.
size
()
==
vec
.
ndof
());
REQUIRE
(
xt
::
allclose
(
M
,
1.0
));
}
SECTION
(
"Int_gradN_dot_tensor2_dV"
)
{
GooseFEM
::
Mesh
::
Quad4
::
Regular
mesh
(
3
,
3
);
GooseFEM
::
Vector
vec
(
mesh
.
conn
(),
mesh
.
dofsPeriodic
());
GooseFEM
::
Element
::
Quad4
::
QuadraturePlanar
quad
(
vec
.
AsElement
(
mesh
.
coor
()));
size_t
td
=
3
;
xt
::
xtensor
<
double
,
2
>
F
=
xt
::
zeros
<
double
>
({
td
,
td
});
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
<
mesh
.
ndim
();
++
i
)
{
for
(
size_t
j
=
0
;
j
<
mesh
.
ndim
();
++
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
,
0.0
));
}
}
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