JEC COMPOSITES MAGAZINE - Issue #112 - April/May 2017 - 52

AERONAUTlCS structures
wich structures. This paper describes how
this tool interacts with commercial finite
element (FE) software (MSC Nastran), and
demonstrates its efficiency on the test-case
of a typical dual launch system (see Figure
1 for instance).

Fig.1: view of a typical spatial structure application, courtesy of CNES/ESA/Arianespace

Fig.2: Workflow of the XComp optimisation tool

large project, which took place from 2015 to
2017 and resulted in the development of a
prototype tool implemented in Python-3.
This prototype uses a new global design
strategy to size large-scale composite sand-

52

Overview of the optimisation strategy
Figure 2 shows the principle of the global
design strategy used in this work. It follows
in essence the indirect two-step approach
described in the literature [1], where the
material is first seen as a homogenised
equivalent material, characterized by its
total thickness and a set of stiffness parameters that fully define its elastic behaviour
[3]. These continuous parameters are then
used as design variables for a first optimisation step focusing on mass minimisation,
where the mechanical specifications of the
structure are enforced as the optimisation
constraints. Then, the continuous thickness
distribution and stiffness distribution are
used as the targets for a second optimization
step, where the variables are the number
and orientations of the layers defining
the composite skins. The outcome of the
second optimisation step is a fully-defined
composite structure.
The major advantage of the two-step
approach is that it deals separately with
structural analysis and laminate combinatorial optimisation, which makes it
possible to optimize complex composite
structures within a practical computational
time. Indeed, the first step combines a
computationally expensive finite element
analysis of the structures with an effective
gradient-based optimisation, while the
second step combines a computationally
expensive laminate lay-up combinatorial
optimisation with an analytic evaluation of
the homogenised shell stiffness. However,
this strategy comes with a significant
disadvantage. Since no structural analysis is
performed during the second optimisation
step, the designers need to check that the
design fulfils its specifications and then to
repair the solution as needed.
A three-step approach
To overcome this limitation and adapt the
tool to composite sandwich materials, the

jec composites magazine / No112 April - May 2017

approach described in this paper differs from
the general two-step scheme in several ways.
First, the material is a composite sandwich,
i.e. a thick shell made of two identical thin
monolithic composite skins and a thick
honeycomb core in-between. However,
for any given material for the honeycomb
core, a sandwich shell can be treated as a
homogeneous shell, whose behaviour is
fully described by the thickness of both
the skin and the core, and the stiffness
properties of the skin. These properties are
thus the variables of the first optimisation
step. Indeed, the membrane and bending
stiffness matrices of the sandwich panels
are parameterised using the stiffness of the
skins, the thickness of the core material
and the thickness of the skins. Additionally,
for thick sandwich shells, transverse shear
stiffness cannot be neglected. In the present
work, the transverse shear stiffness matrix
of the sandwich material is evaluated as a
function of the design variables, using a
dedicated response surface.
In the second optimisation step - stacking
sequence retrieval - the composite skins are
not represented as the usual lay-up of unidirectional layers, but the stacking sequence
table (SST) representation is used instead.
This representation makes it possible,
among others, to enforce manufacturing
constraints related to the blending of the
composite panels in a variable thickness
structure (for instance, the proper spacing
of ply drops). The corresponding stacking
sequence retrieval problem is solved using a
dedicated evolutionary algorithm [2].
Finally, a third optimisation step is introduced in order to restore the feasibility of
the final result with respect to the mechanical constraints. Indeed, when optimising
the composite lay-ups, the thickness of the
structure at any given location is rounded to
a discrete number of layers. It is then very
likely that at least one of the mechanical
constraints will be violated in the process.
This last step enables the design to evolve
slightly (adding or subtracting at most one
layer) in order to ensure that the final solution remains within the feasible domain. As
a final note, the first and third optimisation
steps are run with the MSC Nastran SOL
200 finite element optimization software,
Table of Contents for the Digital Edition of JEC COMPOSITES MAGAZINE - Issue #112 - April/May 2017
