Civil Engineering Reference
In-Depth Information
Exact solution
Nonlinear relationship
5
6
7
0
2
3
4
8
1
Aspect ratio
Figure 5.16 Effect of aspect ratio of finite elements on the accuracy of results.
analyses performed on the member. Therefore, most general-purpose finite
element computer programs specify a maximum value for the aspect
ratio that should not be exceeded; otherwise, the results will be inaccurate.
Figure 5.16
presents a schematic diagram showing the effect of aspect ratio
on the accuracy of results. The best aspect ratio is one and the maximum
value, as an example the value recommended by ABAQUS [1.29], is five.
It should be noted that the smaller the aspect ratio, the larger the number
of elements and the longer the computational time. Hence, it is recom-
mended to start with an aspect ratio of one and mesh the structural steel
member and compare the numerical results against test results or exact
closed-form solutions. Then, we can repeat the procedure using aspect ratios
of two and three and plot the three numerical results against test results or
exact solutions. After that, we can go back and choose different short dimen-
sions smaller or larger than that initially chosen for the shell finite element
and repeat the aforementioned procedures and again plot the results against
test results or exact closed-form solutions. Plotting the results will determine
the best finite element mesh that provides accurate results with less compu-
tational time. The studies we conduct to choose the best finite element mesh
are commonly called as
convergence studies
. It should be noted that in regions
of the structural member where the stress gradient is small, aspect ratios
higher than five can be used and still can produce satisfactory results.
Similar to structural steel members, concrete slab decks can be
meshed using the same approach. If we use solid elements to model the
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