Optimal design of laminated composites: with focus on aircraft structures

The demand for more efficient commercial aircraft with lower maintenance and operation
cost has promoted more extensive use of composite materials for a significant
reduction in weight and fuel consumption. Making a structure as light as possible suggests
solving an optimization problem with the goal of mass minimization. To avoid
failure modes related to composite structures, such as delamination and transverse
matrix crack propagation, some design guidelines are commonly suggested by aircraft
industries. These guidelines are: symmetry, covering ply, disorientation, percentage
rule, balance, and contiguity of the layup.
The manufacturability of the final design with available technologies must be guaranteed.
Different regions may be subject to different loads in a large-scale structure.
Laminate thickness may vary throughout the structure depending on the distributed
loads in an optimized design. Additionally, for large-scale composite structures, such
as an aircraft wing or fuselage, stiffeners are added to enhance structural performance
in carrying compressive and tensile loads. The stiffeners divide the structure into
smaller panels. To ensure manufacturability of a composite structure, it is crucial for
the plies to be continuous among adjacent panels while the laminate thickness varies.
Continuity of plies in adjacent panels, which is commonly referred to as blending, is
a particularly difficult constraint to deal with.
A feasible composite structure has to have sufficient stiffness and strength while complying
with the aforementioned design and manufacturability guidelines. The feasibility
of a composite structure is evaluated through the constraints added to the
optimization problem.
The variables in the design of a composite structure include, but are not limited to,
ply stacking sequences and thickness distribution. Depending on the application, it
may also be desirable to design the shape of a structure. Holes may be required in
the design of parts such as ribs of aircraft wings to reduce the weight. Therefore,
the shape and the topology may be additional variables in the design of a composite
structure.
Optimization of a composite structure subject to the design, manufacturing, and
strength related guidelines is a very challenging problem. Fulfilling the manufacturability
guideline in particular has been a major goal in recent studies. This confirms
the interest of the experts in the field in the applicability of their proposed methods to
real-life engineering problems. However, an investigation among the existing research, revealed that these methods require a significantly large number of computations and
their inherent complexity makes them inadmissible for application to real structures.
This motivated performing the present research with the goal of developing a design
tool that can optimize complex fiber-reinforced composite structures in practice.
The present research consists of a design tool for the optimization of variable stiffness
composite structures (where fibers are not steered), and a method which is developed
mainly for the optimization of an aircraft wing. To optimize a variable stiffness
composite structure, the proposed method separates the optimization of stacking
sequences from the optimization of the thickness distribution. A set of laminates
with optimized stacking sequences with respect to the problem at hand is generated
and stored in a reference table known as the Stacking Sequence Table (SST). The
laminates in an SST must satisfy the desired laminate design guidelines. As long as
the ply stacks in a design are selected from the SST, manufacturability of the final
design is guaranteed. Next, a novel level-set gradient based method is introduced for
the global optimization of ply drop locations. The proposed method aims at turning
the discrete optimization problem associated with the integer number of plies into a
continuous problem. This is done through the way the problem is parametrized; the
design variables are never rounded in this approach. The level-set function gives the
optimum thickness distribution over the structure for a specific SST.
The developed method is verified by its application to the well-known horseshoe panel
optimization problem. To investigate the performance of the method in dealing with
a real problem, the proposed method is then applied to the layup optimization of a
composite skin and rib structure of a wing. Local buckling and allowable strain are
considered as the constraint of the problem and a standard finite element package is
used to calculate buckling factors.
The structural optimization of an aircraft wing is a highly complex problem. This
is due to the large number of variables as well as structural and aerodynamics constraints
influencing the design of skins and stiffeners. To make it computationally
more efficient, a large problem can be decomposed into several smaller subproblems
(subsystems) while preserving the couplings among these subproblems. A special
method is subsequently introduced for the optimization of interacting skins and ribs
of an aircraft wing box.