1
2
3
4
5
6
7
8
9
10
r, x
s, y
t, z
Pressure p acts on the
bottom (z) face
Problem 7.36
Given:
Let uniform pressure p act normal to
one face of a quadratic tetrahedron that has
straight edges and midedge nodes.
What
are the consistent loads at the nodes on this
face.
Solution:
Let us make the element aligned with the
xyz axes so this can be as easy as
possible.
We will use area coordinates to obtain an
exact solution.
From Eq. 7.34, for a planar 2D element
N
1
ξ
1
2
ξ
1
⋅
1
−
(
)
⋅
=
N
2
ξ
2
2
ξ
2
⋅
1
−
(
)
⋅
=
N
3
ξ
3
2
ξ
3
⋅
1
−
(
)
⋅
=
N
4
4
ξ
1
⋅
ξ
2
⋅
=
N
5
4
ξ
2
⋅
ξ
3
⋅
=
N
6
4
ξ
3
⋅
ξ
1
⋅
=
Adapt these for the bottom face of the 3D element using
N
5
4
ξ
1
⋅
ξ
2
⋅
=
N
8
4
ξ
2
⋅
ξ
3
⋅
=
N
6
4
ξ
3
⋅
ξ
1
⋅
=
N d
⋅
N
1
0
0
0
N
1
0
0
0
N
1
N
2
0
0
0
N
2
0
0
0
N
2
....
....
....
N
10
0
0
0
N
10
0
0
0
N
10
⎛
⎜
⎜
⎜
⎝
⎞
⎟
⎟
⎟
⎠
u
1
v
1
w
1
u
2
v
2
w
2
....
u
10
v
10
w
10
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎝
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎠
⋅
=
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 Fall '10
 Folkman
 National secondary road, Roads in Ireland, A⋅

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