Composite Materials Research Progress

96
Michaël Bruyneel
a solution with SAM is reached in 6 iterations, while Conlin is still no longer able to
converge.
8.6. Topology Optimization of Laminated Composite Structures
The topology optimization problem of Figure 4.3 is here considered. In topology optimization
of isotropic material (Bendsoe 1995), the design variable is a pseudo-density μi that varies
between 0 and 1 in each finite element i (Figure 4.2). The so-called SIMP material law
(Simply isotropic Material with Penalization) takes the following form:
Ei
= μ
p 0
i E
0
ρi = μi
ρ
(8.5)
where E 0 and ρ 0 are the Young modulus and the density of the base material (e.g. steel), E
and ρ are the effective material properties, and p is the exponent of the SIMP law, chosen by
the user (1