Civil Engineering Reference
In-Depth Information
y
z
y
P
d
S
P
T
z
x
(a)
(b)
xy
xy
(
x
,
y
)
xz
xz
xz
d
S
y
(c)
O
z
(d)
Figure 9.13
(a) A general, noncircular section in torsion. (b) Motion of a point from
P
to
P
as a
result of cross-section rotation. (c) A differential element at the surface of a torsion
member. (d) A differential element showing the contribution of shear stress to torque.
the bending deflection is governed by a fourth-order partial differential equation.
The simplest such element is a four-node element using cubic interpolation func-
tions and having 4 degrees of freedom (displacement, two slopes, and a mixed
second derivative) at each node [4]. A similar situation exists with shell (thin
curved plate) structures. Specialized elements are required (and available) for
structural analysis of shell structures. The major point here is that a breadth of
knowledge and experience is required for a finite element analyst to become truly
proficient at selecting the correct element type(s) for a finite element model and,
subsequently interpreting the results of the analysis.
Once the element type has been selected, the task becomes that of defining
the model geometry as a mesh of finite elements. In its most rudimentary form,
this task involves defining the coordinate location of every node in the model
