Civil Engineering Reference
In-Depth Information
Figure 1.7
A mesh of finite elements over a rectangular region having a
central hole.
an improvement in geometric accuracy in the vicinity of the discontinuity but
also solution accuracy, as is discussed in subsequent chapters.
The geometry depicted in Figure 1.7 could represent the finite element
model of several physical problems. For plane stress analysis, the geometry
would represent a thin plate with a central hole subjected to edge loading in the
plane depicted. In this case, the finite element solution would be used to exam-
ine stress concentration effects in the vicinity of the hole. The element mesh
shown could also represent the case of fluid flow around a circular cylinder. In
yet another application, the model shown could depict a heat transfer fin at-
tached to a pipe (the hole) from which heat is transferred to the fin for dissipa-
tion to the surroundings. In each case, the formulation of the equations govern-
ing physical behavior of the elements in response to external influences is quite
different.
Figure 1.8a shows a truss module that was at one time considered a
building-block element for space station construction [21]. Designed to fold in
accordion fashion into a small volume for transport into orbit, the module, when
deployed, extends to overall dimensions 1.4 m
×
1.4 m
×
2.8 m. By attaching
such modules end-to-end, a truss of essentially any length could be obtained.
The structure was analyzed via the finite element method to determine the
vibration characteristics as the number of modules, thus overall length, was
varied. As the connections between the various structural members are pin or
ball-and-socket joints, a simple axial tension-compression element (Chapter 2)
was used in the model. The finite element model of one module was composed
of 33 elements. A sample vibration shape of a five-module truss is shown in
Figure 1.8b.
The truss example just described involves a rather large structure modeled
by a small number of relatively large finite elements. In contrast, Figure 1.9
shows the finite element model of a very thin tube designed for use in heat
