Application research in multi-objective constrained optimization of composite wing structure

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.

Fibre Reinforced Plastics (FRPs) have been used in many practical structural applications due to their excellent strength and weight characteristics as well as the ability for their properties to be tailored to the requirements of a given application. Thus, designing with FRPs can be extremely challenging, particularly when the number of design variables contained in the design space is large. For example, to determine the ply orientations and the material properties optimally is typically difficult without a considered approach. Optimization of composite structures with respect to the ply angles is necessary to realize the full potential of fibre-reinforced materials. Evaluating the fitness of each candidate in the design space, and selecting the most efficient can be very time consuming and costly. Structures composed of composite materials often contain components which may be modelled as rectangular plates or cylindrical shells, for example. Modelling of components such as plates can be useful as it is a means of simplifying elements of structures, and this can save time and thus cost. Variations in manufacturing processes and user environment may affect the quality and performance of a product. It is usually beneficial to account for such variances or tolerances in the design process, and in fact, sometimes it may be crucial, particularly when the effect is of consequence. The work conducted within this project focused on methodologies for optimally designing fibre-reinforced laminated composite structures with the effects of manufacturing tolerances included. For this study it is assumed that the probability of any tolerance value occurring within the tolerance band, compared with any other, is equal, and thus the techniques are aimed at designing for the worst-case scenario. This thesis thus discusses four new procedures for the optimization of composite structures with the effects of manufacturing uncertainties included.

Genetic Algorithms (GAs) are a powerful technique for search and optimization problems, and are particularly useful in the optimization of composite structures. The search space for an optimal composite structure is generally discontinuous and strongly multimodal, with the possibility for many local sub-optimal solutions or even singular extrema. These facts severely limit gradient-type approaches to optimization, bringing this broad class of problems under scrutiny for application of GAs. Examples described here of the successful use of parallel GAs to design composite structures by the authors include energy-absorbing laminated beams [1], airfoils with tailored bending-twisting coupling [2], and flywheel structures [3]. Optimal design of laminated composite beams was performed using a GA with a specialized finite element model to design material stacking sequences to maximize the mechanical energy absorbed before fracture. An initial GA approach to the optimal design of a specialized, idealized composite airfoil is now being refined for a practical application. The optimum stacking sequence to produce a desired twisting response while minimizing weight, maximizing in-plane stiffness and maintaining acceptable stress levels is determined. The GA has also been used to maximize the Specific Energy Density (SED) of composite flywheels. SED is defined as the amount of rotational energy stored per unit mass. Optimization of SED was achieved by allowing the GA to search for various flywheel shapes and allowing the GA to pick material sequences along the radius of the flywheel.KeywordsAutomated DesignGenetic AlgorithmsComposite MaterialLaminated StructureOptimization

Concurrent multi-material and multi-scale design optimization of fiber-reinforced composite material and structures for minimum structural compliance

Cost optimization of composite aircraft structures including variable laminate qualities

Grillage topologies are commonly used in many composite structural applications to produce low mass designs that have a high stiffness. While composite failure criteria are being compared in many different simple structures, for example plates and tubes, literature must also compare more complicated applications, including grillages, as there are distinct differences in behaviour. This paper therefore performs analysis of grillage structures with more up to date failure criteria, taken from the world wide failure exercise, than previously investigated. The grillage theory selected is that of Navier theory with elastic equivalent properties due to its low computational expense for use with a genetic algorithm to optimise a composite structure. The results take an example from leisure boatbuilding showing the grillages produced from the different limit states, comparing the cost and mass. The final results show that the method allows a rapid analysis of grillages and that the selection of the limit state has an important effect on the optimised grillage topology.

Currently, the most important structural design aims are weight reduction, corrosion resistance, high stiffness and vibration damping in several industrial applications, which can be provided by the application of advanced fiber-reinforced plastic (FRP) composites. The main research aim was to develop novel and innovative multicellular plate structures that utilize the benefits of lightweight advanced FRP and aluminum materials, as well as to combine the advantageous characteristics of cellular plates and sandwich structures. Two new multicellular plate structures were developed for the structural element of a transport vehicle. The first structure consists of carbon-fiber-reinforced plastic (CFRP) face sheets and pultruded glass-fiber-reinforced plastic (GFRP) stiffeners. The second structure consists of carbon-fiber-reinforced plastic face sheets and aluminum (Al) stiffeners. The second main goal of this research was the development of an optimization method of minimal weight for the newly developed all-FRP structure and the CFRP-Al structure, considering seven design constraints. The third main purpose was to confirm in a real case study that lightweight multicellular composite constructions, optimized by the flexible tolerance optimization method, provide significant weight saving (86%) compared to the all-steel structure. The added value of the research is that optimization methods were developed for the constructed new composite structures, which can be applied in applications where weight saving is the primary aim.

Quantum behaved Particle Swarm Optimization (QPSO) for multi-objective design optimization of composite structures

The optimization of the large structure with the layout of stiffener is considered by a new calculation method in this study. Many number of stiffener are attached to large structures. Optimization of the large structures with design variables of plate thickness and shape of stiffener is performed. However, in order to obtain a better optimal solution, the optimization of the structure with design variable of number of stiffener and allocation of stiffener is required. But, the optimization of structure with design variable of the number of stiffener and allocation of stiffener is not performed. There are two problems. The first problem is the FEM model. FEM models need some nodes at allocation of stiffener as a characteristic of FEM. When number of stiffener and allocation of stiffener are changed by the process of the optimization of the structure, number of nodes and allocation of nodes of FEM model is also changed. Therefore, in order to ensure consistency of mesh, it is necessary to remake FEM model. In order to optimize structural, it is necessary to examine many propositions for design. However it is difficult to create and analyze the proposition for design of many numbers in restricted time. The second problem is the optimization method. When the number and allocate of stiffeners are changed, the stricture is modified and the number of design variables is changed. The optimization problem with changed number of design variables cannot be optimized by standard optimization methods. The methods of solving these problems are examined.

The static aeroelastic torsion divergence problem is the main obstacle to bring forward swept wing into massive applications. The aeroelastic tailoring technique-based radial basis function neural networks (RBFNNs) and genetic algorithm (GA) optimization in MATLAB considering the material orientation, thickness, and lay-up are elucidated in the present work. RBFNNs are used to build a surrogate model between the composite parameters and structure displacement, which is proved robust and accurate. Then an optimal structure is obtained by GA global search based on RBFNNs model with the weight constrain. The displacements of the forward swept wing caused by an approximate aerodynamic load are decreased 32.5% through finite element method (FEM) static structural analysis. The modal analysis illustrates that the first mode frequency increases by 33.0% and the second mode increases by 37.9%. A computational aeroelasticity approach is developed by in-house Hybrid Unstructured Reynolds-Averaged Navier-Stokes solver associating an open source FEM code – Calculix. The results of coupling calculations show effectiveness of aeroelastic tailoring optimization of composite forward swept wing without weight penalty. The results obtained demonstrate that for the forward swept wing, the most violent situation appears around Mach Number 1.0 where the aeroelastic tailoring optimization could decrease the torsion angle by nearly 70.0%. The torsion of forward swept wing will increase at subsonic and decrease at supersonic with the increase of velocity.

A technical and design evaluation was carried out to meet DOE hydrogen fuel targets for 2010. These targets consisted of a system gravimetric capacity of 2.0 kWh/kg, a system volumetric capacity of 1.5 kWh/L and a system cost of $4/kWh. In compressed hydrogen storage systems, the vast majority of the weight and volume is associated with the hydrogen storage tank. In order to meet gravimetric targets for compressed hydrogen tanks, 10,000 psi carbon resin composites were used to provide the high strength required as well as low weight. For the 10,000 psi tanks, carbon fiber is the largest portion of their cost. Quantum Technologies is a tier one hydrogen system supplier for automotive companies around the world. Over the course of the program Quantum focused on development of technology to allow the compressed hydrogen storage tank to meet DOE goals. At the start of the program in 2004 Quantum was supplying systems with a specific energy of 1.1-1.6 kWh/kg, a volumetric capacity of 1.3 kWh/L and a cost of $73/kWh. Based on the inequities between DOE targets and Quantum’s then current capabilities, focus was placed first on cost reduction and second on weight reduction. Both of these were to be accomplished without reduction of the fuel system’s performance or reliability. Three distinct areas were investigated; optimization of composite structures, development of “smart tanks” that could monitor health of tank thus allowing for lower design safety factor, and the development of “Cool Fuel” technology to allow higher density gas to be stored, thus allowing smaller/lower pressure tanks that would hold the required fuel supply. The second phase of the project deals with three additional distinct tasks focusing on composite structure optimization, liner optimization, and metal.

Impact analysis of fiber reinforced polymer honeycomb composite sandwich beams

The determination of lamination parameters feasible region is extremely important for design and optimization of composite structures. While the feasible region for unconstrained laminates is well-established, applying mandatory design rules alters both its size and shape. This is especially relevant in aeronautical composite structures, where design rules are quite often mandatory. However, existing studies do not specify the exact boundaries of the feasible region, which is significant since the optimum for critical loading conditions, such as buckling, often lies on or near the boundary. This work proposes an innovative approach for finding the exact feasible region with several design rules. The initial step is to generate laminate databases containing all feasible stacking sequences with the prescribed design rules, up to 36 layers. These data provide a rigorous insight into the distribution patterns. Based on this information, a simple and computationally efficient procedure, based on the exact determination of a few key boundary points, allows for the exact determination of the feasible region for any number of layers.

An optimization strategy is presented for large composite structure based on manufacturing constraints and genetic algorithm. First, on the basis of region division and key region defined, both angle and length design variables for each ply are introduced to make laminate thickness and stacking sequence be optimized simultaneously, also considering laminate ply continuity. Finally, a composite wing is optimized using the current methodology. The result shows that the optimization method can obtain optimum design satisfying manufacturing constraints and weight reduction for large composite structure.

Composite beams, plates and shells are widely used in the aerospace industry because of their advantages over the commonly used isotropic structures especially when it comes to weight savings. Buckling analyses of composite structural components must be performed in order to ensure, for instance, that a composite panel designed to be part of a control surface does not buckle thereby compromising its aerodynamic shape. Optimization of composite structures has been performed in this paper using Genetic algorithm. Genetic algorithm (GA) approaches are successfully implemented for the TSP. The buckling load of composite plate, which is obtained by the Artificial Neural Networks, was used as the fitness function in the GA to find its optimized value by arranging the ply stacking sequence.