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These shape functions can be used to evaluate the stiffness matrices for quadrilateral
elements.
EXAMPLE 6.13 Undesirable Interior Angles
It was pointed out that the coordinate transformation functions
ξ
=
ξ(
x, y
)
and
η
=
η(
must be continuous, differentiable, and invertible. In some instances, these require-
ments are not satisfied. This can occur if the slave elements are too distorted. This example
illustrates a transformation that violates these requirements and should be avoided.
First, investigate the effect of large interior angles on the Jacobian matrix. Consider the
element shown in Fig. 6.44a. Note that this element has an interior angle greater than
x, y
)
π
.
We wish to map a square master element
m
of Fig. 6.39b into the slave element
e
in the
global system.
FIGURE 6.44
Inappropriate shape for the elements of Example 6.13.
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