Geology Reference
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Figure 2. The flowchart of the proposed solution algorithm
Example 1: Reinforcement
of a Planar Frame
The 3×12m domain is descretized using a
30×120 mesh of 4 node square bi-linear elements.
A consistent mass matrix formulation has been
used (see e.g. Zienkiewicz et al. 2005). The stiff-
nes
s
and density of the base material are assumed
as
E
=
2 10
5
MPa
and
ρ
=
8000 kg/m
3
re-
spectively. A penalty power of
p
= 4, a filtering
radius of
R
= 30cm = 3
h
, and move limit of
η
=
0.2 have been used. The ratio between the stiffness
of solid and void areas is selected as
E
:
=
10
9
.
The obtained topologies at different iterations
are shown in Figure 3.
As the first example we consider a frame in plane
stress. The maximum volume of used material
should be limited to half of the volume of the
whole frame (
v
=
50
). The initial design
is depicted in Figure 3 (leftmost). The outer frame
is fixed to be solid and is non-designable. Note
that if we do not consider the non-designable
outer frame, the optimization program will obvi-
ously shorten the frame.
/
v
t
%
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