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1
Errors in FE Modelling (Section 5.10)
■
Modelling error
: arises because physical reality is replaced by
a mathematical model.
◆
Example: A beam that can resist both axial and transverse loads
being modelled as one with bending resistance only ignoring the
axial resistance.
■
Discretization error
: arises because a mathematical model is
implemented in a piecewise manner.
◆
Example: Perimeter, p, of a circle being computed with a finite
number of straight segments.
θ
=2
π
/n
;
b=2r
sin
(
θ
/2)
;
p=nb=2nr
sin
(
π
/n)
(p/r)
exact
= 2
π
.
(p/r)
n=6
=6 (4.5 %)
and
(p/r)
n=12
=6.212 (1.1 %)
(Error shown in parentheses. No modelling error here)
θ
b
r
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Roundoff error and illconditioning
■
Numerical (roundoff) error
: arises because a computer uses
a finite number of significant digits to represent a number.
■
Such error may cause problem in
illconditioned
systems.
■
Illconditioned system
: small changes in structural parameters
or loading (i.e., in matrix entries) produce large changes in the
solution and the solution may be inaccurate.
■
Example
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 Spring '08
 PETERIFJU

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