Civil Engineering Reference
In-Depth Information
T=50
T=50
T=50
T=25
A
C
T=0
T=50
D
B
T=0
T=50
T=25
T=0
T=0
T=0
Figure 7.34
13. Derive the conductivity matrix of a 3-noded, right-angled isosceles triangular element
suitable for discretisation of Laplace's equation. Use your element to estimate the
steady state value of the potential at the central node of the mesh with the boundary
conditions given in Figure 7.35. (Ans: 75.0)
100
100
0
100
Figure 7.35
14. A square 4-node plane element of unit side length and permeability is to be used in
the solution of Laplace's equation over a two-dimensional isotropic medium. If the
terms of the element conductivity matrix can be expressed in the form:
1
1
k
ij
=
f
ij
(x, y)
d
x
d
y,
i,j
=
1
,
2
,
3
,
4
0
0
find the function
f
14
and evaluate
k
14
explicitly.
(Ans:
f
14
=−
(
1
−
y)
2
1
+
x(
1
−
x)
,
k
14
=−
6
)
