Information Technology Reference
In-Depth Information
FIGURE 6.21
Stresses at nodes 3, 6, and 9.
Similar to the displacement calculation, this is much smaller than the correct value of
133 kNm.
The finite element solution using four elements does not appear to be very accurate
in comparison with the values obtained by other methods. This is hardly a surprising
conclusion, considering the choice of simple trial functions and the modeling with only
four elements. One would suspect that greater accuracy would be achieved by using a
higher order polynomial. For a given element, this requires more nodes if an interpolation
polynomial is to be employed. The same problem (Fig. 6.14a) was solved using the elements
of Fig. 6.22a. Here, higher order polynomials were chosen in the trial displacements, and
nodes between the corners were added to the elements. The resulting displacement pattern
remains the same as in Fig. 6.8. The midspan u y displacement along the bottom edge is
computed to be 1
10 4 m, and the moment is found to be 140.69 kNm. Both of these
values are more accurate than corresponding values obtained using elements with lower
order polynomials.
A variety of cases with an increasing number of elements were computed. The results are:
.
4273
×
Elements with nodes
Elements with nodes
at the corners only
at and between the corners
No. of
No. of
u y Displace-
Moment
No. of
u y Displace-
Moment
10 - 4
10 - 4
Elements
Unknowns
ment
(
m
)
(kNm)
Unknowns
ment
(
m
)
(kNm)
4
14
0.875
99.99
36
1.4273
140.69
9
27
1.0794
116.68
72
1.5998
138.46
16
44
1.2082
123.48
120
1.6987
136.10
36
90
1.3758
128.95
252
1.8430
134.64
(14)
These results are plotted in Figs. 6.22b and c. As might be expected, the accuracy of the
solution increases with an increase in the number of degrees of freedom.
Search WWH ::




Custom Search