Parallel Genetic Algorithms in the Optimization of Composite Structures

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.

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.

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.

Summary form only given. This article gives a brief overview of theoretical advances, computing trends, applications and future perspectives in parallel genetic algorithms. It explains basic terms and behavior of (parallel) genetic algorithms. Genetic algorithms are easily parallelized algorithms, therefore two kinds of possible parallelism, data parallelism and control parallelism, are mentioned and described towards them. Parallelism of genetic algorithms brings many advantages and gains. Classifications of these algorithms are often based on the type of computing model, a walk strategy and the used computing machinery. Afterwards significant milestones in the theory with latest advances are briefly mentioned. Then current trends in parallel computing with stress computer architectures of parallel systems, interconnection topologies, operating systems, parallel (genetic) libraries and programming paradigms are reviewed shortly. The sufficient space is devoted to the latest applications of parallel genetic algorithms. After the discussion section, perspectives of the algorithms are predicted till the year 2005. The information in the article is segregated into two periods before and after the year 2000 in all chapters. The second period is more interesting and of higher importance, because it highlights recent research efforts and gives some hints about possible future trends. That is why we devote much space to the second period. As there is no such an overview of the recent period of parallel genetic algorithms, our investigation could be appealing and useful in many aspects.

In order to explore the optimization of composite wing structure, this paper reviews the past research works of optimization of composite wing structures worldwide and in China. It concludes that most optimization methods and calculations are useful but only applied with specified theoretic model. Then relevant composite optimization theories and strength constraints with composite lamination failure criteria, stability, aeroelasticity are sorts out. Optimizing algorithm and applied solution rounding strategy are also listed. Concentrating on weight-reduction analysis on the thickness, sequence, and angle of the composite stacking under multiple constraints, a practical model of a composite wing structure example with a large aspect ratio is completed, and the calculation is based on the finite element analysis tool Nastran and the genetic algorithm Matlab program. Two optimal solutions are given with detailed differences and the comparison of the composite structure parameters before and after calculation is also recorded. The application example indicates the feasibility of the optimization method and quadratic rounding process, the detail structure performance improvements with skin lamination change under the calculation are illustrated at the same time.

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

This paper provides an overview of the cabapilities, features and applications of the general-purpose program OPTICOM for calculation and optimization of composite structures. The problems related to long-fiber laminates, composites with randomly oriented short fibers, hybrids and sandwich structures can efficiently be treated. The program allows calculating mechanical and residual stresses and strains, stiffness and compliance matrices, strength coefficients, resonance frequencies and critical buckling loads. The optimization process utilizes three alternative algorithms and can be performed under multiple loads and combined static and dynamic constraints. The program can provide minimum weight, minimum thickness, optimal orientation, minimum number of plies, maximum rigidity, as well as optimal configurations for simultaneous failure of all layers. The structure and performance of the program allow studying the influence of design parameters (materials, stacking sequence, ply orientation, geometric configurations, applied loads, environmental conditions, design constraints, residual stresses,... etc) on the design objectives.

This study presents a comprehensive thermal analysis, design, and optimization framework for electrothermal heating systems integrated into composite wing structures. Thermal behavior is first investigated using finite volume simulations conducted with a commercial solver. An in-house thermal solver is then developed based on the governing heat transfer equations and a second-order finite difference discretization scheme. The in-house solver is validated against the commercial solver, showing a maximum deviation of less than 1%. The validated solver is subsequently coupled with a genetic algorithm to perform multi-objective optimization of the electrothermal heating system. A novel correlation for the convection heat transfer coefficient over airfoil surfaces is developed based on extensive turbulent flow simulations and a genetic algorithm. The developed correlation equation has significantly lower percent relative error (from 34% to 6%) compared to flat plate correlations. The developed convection coefficient is incorporated into the optimization process. Key design variables, including heat generation intensity, heater strip dimensions, and the thermal conductivity of composite and surface protection materials, are included in the optimization process. An original objective function is formulated to simultaneously minimize electrical power consumption, prevent ice formation on the external surface, and limit internal temperatures to safe operating ranges for composite materials. The optimized design is evaluated under both spatially varying and constant convection heat transfer coefficients to assess the impact of convection modeling assumptions. The proposed methodology provides a unified and extensible framework for the optimal design of electrothermal ice protection systems and can be readily extended to three-dimensional composite wing configurations.

Cost optimization of composite aircraft structures including variable laminate qualities

A scalable parallel genetic algorithm for the Generalized Assignment Problem

During the last 20 years, structural optimization has become one of the most important topics of engineering applications. Design optimization of structure has been an interesting area of research in the field of engineering design for its ability to short the design cycle and to enhance product quality. Significant research activity has occurred in the area of structural optimization in the last decade. Especially for topology optimization of structure, many new theoretical, algorithmic, and computational contributions have resulted by researchers and engineers. Topology optimization is a powerful tool for global and multi-scale design of macrostructures, microstructures, and the cell of prescribed composite materials. The population based evolutionary algorithms have emerged as powerful mechanism for finding optimum solutions of complex optimization problems in engineering during the last two decades. Evolutionary computation is the study of computational systems which use ideas and get inspiration from natural evolution and adaptation [1]. The thinking has wide application in various engineering fields, such as computer science, artificial intelligence, operations research. Genetic algorithm is another kind of bio-inspired optimization method and it is playing an increasingly important role in studies of complex adaptive systems. Its application ranges from adaptive agents in economic theory to the use of machine learning techniques in the design of complex devices and structures, such as aircraft turbines and integrated circuits [2]. Optimization of structures can be classified into three categories: sizing, shaping, and topology optimization. In the topology optimization, it is concerned with the structure members and connectivity between members. In general, it is easily represented by discrete variables rather than by those used for continuous optimization problems. Topology optimization is the most difficult and complex among three categories and it is special useful in developing innovative conceptual designs. Structural optimization, in particular the topology optimization, has been identified as one of the most challenging tasks in structural design. Various techniques and approaches have been established during the last two decades. Topology optimization usually referred to as layout optimization or general shape optimization [3]. It lets engineers get the optimal topology of structure or new configurations during product design phase, as they are implementing the design of the size

Flexible job scheduling problem (JSP) as an optimization problem, tends to find solution for allowing different operations to be processed faster. This problem could be solved by genetic algorithm, as we have proven in another experiment. Now, we have tried to outperform state of the art, by using parallel genetic algorithm. Parallel genetic algorithm has two types and we have chosen the most popular one coarsed grained genetic algorithm, for our specific case. The results have improved time wise and are promising in some of the datasets, while a need exists for improving on other ones. In the future, we will compare both versions of parallel genetic algorithms but also compare the results to another algorithm.

Genetic algorithms offer very good performances for solving large optimization problems, especially in the domain of error-correcting codes. However, they have a major drawback related to the time complexity and memory occupation when running on a uniprocessor computer. This paper proposes a parallel decoder for linear block codes, using parallel genetic algorithms (PGA). The good performance and time complexity are confirmed by theoretical study and by simulations on BCH(63,30,14) codes over both AWGN and flat Rayleigh fading channels. The simulation results show that the coding gain between parallel and single genetic algorithm is about 0.7 dB at BER = 10﹣5 with only 4 processors.

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.

The paper proposes an optimisation strategy for the design of structures made of three-dimensional woven composites. The knowledge of the weaving architecture is essential to properly optimise the design of the structural components subjected to specific load conditions. Owing to the hierarchy and periodicity of the textile composite materials, a multi-scale parameterisation modelling strategy combining the adoption of a representative volume element and periodic boundary conditions is employed to estimate the behaviour of stiffened panels. In order to minimise the expensive computational cost, response surface method techniques are used to generate the approximated structural responses in an efficient and applicable way. The approach here proposed consists of a multi-scale parameterization analysis strategy and an optimisation framework based on the response surface technique and genetic algorithms. The optimal design results are verified by finite element analysis proving that the response surface method integrated with genetic algorithms allows to easily investigate the influence of the fabrics constitutive parameters on the structural behaviour.