JEC COMPOSITES MAGAZINE - Issue #88 - April 2014 - Special JEC Americas Spring Edition - 48

optimisation

and the triaxial layup, the concentrated
load requires thicker layups than all the
distributed loadings, while the linearly
varying distributed load with the maximum load at the fixed end requires the
lightest thickness profile. The thickness
profile results well explain the fact that
the beam thickness is proportional to the
maximum resultant bending moments.
What is not obvious from the results is
the power exponent (n), which determines the shape of the thickness profile
curve. The n values of the four curves in
Fig. 3 from the top (heaviest) to bottom
(lightest) profiles are 0.7, 1.25, 1.5 and
2.25. Under the concentrated P load,
the optimal exponent n=0.7 makes the
thickness profile close to a cosine curve
of a quarter of the wavelength. Under
the linearly varying distributed load
with w=wo (lx-x)/lx, n=2.25 makes the

thickness profile close to a cosine curve
of half the wavelength.
In addition to the C-Ply [0/±45/0]
triaxial layup, we considered other layups
such as another triaxial layup with a
different off-axis angle of [0/±25/0],
a biaxial layup of [±12.5], and a quasiisotropic layup of [0/±45/90]. Fig. 4
(a) shows the thickness profiles subject to the concentrated load with the
various C-Ply layups. Aluminium was
also considered for comparison with
the C-Ply composite layups. Fig. 4 (b)
shows the relative weight of composite
beams with the various layups compared
with the weight of the aluminium beam.
The QI beam is nearly 36% lighter than
the Al beam, while both triaxial layups
are 44-49% lighter and the biaxial layup
is 51% lighter. The weight saving could

be significant if one takes an aggressive
design approach such as triaxial or biaxial
C-Ply laminates without increasing the
manufacturing cost too much by taking
advantage of the pre-plied multi-layups
of C-Ply laminates.
Other metals such as magnesium (Mg),
beryllium (Be), titanium (Ti), copper
(Cu) and steel were considered. Fig.
5 shows a weight comparison of the
various metal beams with the QI C-Ply
laminate. The specific densities (ρ)
and Young's moduli (E) of the beam
materials are listed in the table below
the comparison chart. Except for the Be
beam case, whose stiffness is nearly 3.5
times higher than the QI laminate, the
metal beams are significantly heavier
than the QI C-Ply beam mostly because
of these metals' higher density.

1.6 2.7 1.74 1.85 4.5 8.5 7.85

E[GPa] 81.2 70

Fig. 3: Optimal thickness profile along beam length subject to concentrated and distributed loading
conditions

Fig. 4: (a) Optimal thickness profiles along beam length subject to concentrated loading with various
C-Ply layups and aluminium; (b) Relative weight compared with aluminium

48 jec composites magazine / No88 April 2014

287 109 105 206

Fig. 5: Relative weight of various metal beams
compared with QI C-Ply composite laminates

As demonstrated with the examples
above, Profile Rank is an easy-to-use
method to obtain an optimum profile for
composite beam structures by introducing reasonable profile shape functions. Profile Rank is a robust method
that avoids most local optimum and
convergence issues. The Profile Rank
calculation for the optimal beam weight
demonstrates that significant weight
reductions can easily be achieved using
C-Ply composites compared with other
choices of metals such as aluminium
(Al), titanium (Ti), etc. n
More information: www.udayton.edu

http://www.udayton.edu

JEC COMPOSITES MAGAZINE - Issue #88 - April 2014 - Special JEC Americas Spring Edition

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