Global shared-layer blending method for stacking sequence optimization design and blending of composite structures

A global shared-layer blending (GSLB) method is proposed for obtaining manufacturable stacking sequence of composite structures with blending and design rules. The method combines the traditional SLB technique with an evaluation algorithm of spatial variation of panels, where the manufacturability of laminates is enhanced by identifying and minimizing the ply-drops, and controlling the laminate transition drop boundaries. In addition, a blended design scheme is also proposed, which is achieved by using the stacking sequence table technique. A composite wing structure is selected to validate the efficiency and accuracy of the proposed method. Results show that the GSLB method can be used for generating more manufacturable designs of large-scale composite structure with multiple engineering constraints.     

A genetic algorithm with memory for optimal design of laminated sandwich composite panels

This paper is concerned with augmenting genetic algorithms (GAs) to include memory for continuous variables, and applying this to stacking sequence design of laminated sandwich composite panels that involves both discrete variables and a continuous design variable. The term “memory” implies preserving data from previously analyzed designs. A balanced binary tree with nodes corresponding to discrete designs renders efficient access to the memory. For those discrete designs that occur frequently, an evolving database of continuous variable values is used to construct a spline approximation to the fitness as a function of the single continuous variable. The approximation is then used to decide when to retrieve the fitness function value from the spline and when to do an exact analysis to add a new data point for the spline. With the spline approximation in place, it is also possible to use the best solution of the approximation as a local improvement during the optimization process. The demonstration problem chosen is the stacking sequence optimization of a sandwich plate with composite face sheets for weight minimization subject to strength and buckling constraints. Comparisons are made between the cases with and without the binary tree and spline interpolation added to a standard GA. Reduced computational cost and increased performance index of a GA with these changes are demonstrated.     

An integrated optimisation for the weight,the structural performance and the cost of composite structures

An integrated optimisation methodology is proposed to optimise the manufacturing cost as well as the structural performance and the weight of composite laminated plates manufactured by the resin transfer moulding (RTM) process. In the present approach, the fibre type, the number of fabrics, the layer stacking sequence and the fibre volume fraction are optimised to minimise the structural weight and the material cost of composite structure under the stiffness constraint and the mould filling time constraint which is a part of process cycle time. With the results obtained, it is investigated how the weight and the material cost are traded-off. The optimisation methodology suggests a guide to cost-effective material selection in the preliminary conceptual design stage.     

Robust design – A concept for imperfection insensitive composite structures

Robust design is a philosophy that aims to ensure that a structure will be tolerant to unknown variations and imperfections. This is an important consideration as highly optimised critical structures are required to survive unexpected loading and operating conditions. In some ways, robust design appears to be similar to damage tolerant design but its application to aerospace structural design is neither well established nor understood. In order to demonstrate the differences between the two concepts, a stiffened composite panel has been analysed for damage tolerance and robustness properties. Damage tolerance has been studied experimentally with the panel subjected to impact damage. The effect of laminate stacking sequence on the robustness of the panel has been assessed using finite element analysis and a Robust Index applied to quantify the robustness. The differences between designs are discussed together with the possible future directions for robust design applied to aerospace composite structures.     

Multilayered composite structure design optimisation using distributed/parallel multi-objective evolutionary algorithms

This paper presents a research work on stacking sequence design optimisation for multilayered composite plate using a parallel/distributed evolutionary algorithm. The stacking sequence of fibres has a dramatic influence on the strength of multilayered composite plates. Multiple layers of fibre-reinforced material systems offer versatility in engineering material design due to the fact that the stacking sequence of each orthotropic layer can offer full advantage of superior mechanical properties. Numerical results show that the optimal composite structures have lower weight, higher stiffness and also affordable cost when compared to the extreme and intermediate composite structures. In addition, the benefits of using a parallel optimisation system are also presented.     

Optimal design of composite wing structures with blended laminates

In this paper we formulate the problem of wing box design optimization using composite laminates with blending constraints. The use of composite laminates necessitates the inclusion of fiber orientation angle of the layers as well as total thickness of the laminate as design variables in the design optimization problem. The wing box design problem is decomposed into several independent local panel design problems. In general such an approach results in a nonblended solution with no continuity of laminate lay ups across the panels, which may not only increase the lay up cost but may also be structurally unsafe due to discontinuities. The need for a blended solution increases the complexity of the problem many fold. In this paper we impose the blending constraints globally by using a guide based design methodology within the genetic algorithm optimization scheme and compare the results with the published ones. Two different blending schemes – outer and inner blending are presented. The result shows that the optimum design obtained using the current methodology has better continuity of laminate lay ups and also the reported weight of the composite wing box is on the lower side. Finally, a parametric study of the effect of global deflection constraint on the total weight of the optimum design is presented.     

The use of a genetic algorithm to improve the postbuckling strength of stiffened composite panels susceptible to secondary instabilities

The use of genetic algorithms (GAs) for structural optimisation is well established but little work has been reported on the inclusion of damage variables within an optimisation framework. This approach is particularly useful in the optimisation of composite structures which are prone to delamination damage. In this paper a challenging design problem is presented where the objective was to delay the catastrophic failure of a postbuckling secondary-bonded stiffened composite panel susceptible to secondary instabilities. It has been conjectured for some time that the sudden energy release associated with secondary instabilities may initiate structural failure, but this has proved difficult to observe experimentally. The optimisation methodology confirmed this indirectly by evolving a panel displaying a delayed secondary instability whilst meeting all other design requirements. This has important implication in the design of thin-skinned lightweight aerostructures which may exhibit this phenomenon.     

Weight optimisation of a salient pole synchronous generator by a new genetic algorithm validated by finite element analysis

In this study, a new approach for genetic algorithm (GA) is proposed and compared with conventional GA (CGA) in the weight optimisation of a 2-MVA salient pole synchronous machine. The main differences between the two algorithms are that, in the newly proposed method, individuals are paired and crossed over based on the Mendelian rules of genetics, and the mutation operator is omitted. The rules concern the segregation of Alleles and the independent assortment of Alleles. This approach is comprehensive and conceptually accurate since its framework uses Mendelian population genetics. The operation CPU time is longer in the new approach when compared to the conventional one but can be ignored in electric machine design since it is not a real-time process. The results of the analytic solution and the new and CGA implementation methods are compared in terms of weight, efficiency and temperature. The results obtained are similar to those of the conventional ones and even better in some cases. A finite element analysis (FEA) is done to realise the machine designs optimised by the new GA (NGA) and CGA for the case of a fixed 24-pole design. Hence the improvement over CGA achieved by NGA has been validated through FEA.     

Concurrent optimization of stacking sequence and stiffener layout of a composite stiffened panel

This article is to optimally design laminated composite stiffened panels by optimizing both stacking sequences of the panel skin and stiffeners as well as the layout of stiffeners. Starting from initial designs of stiffener layout and stacking sequences for each stiffener and the panel skin, the problem is formulated with discrete and continuous variables, where discrete 0/1 variables represent the absence/presence of each layer in initial stacking sequences, and continuous variables represent layer thicknesses. A first-level approximate problem is established to make the problem explicit. Genetic algorithm is used to determine the existence of each layer in the laminates. When the number of retained layers in stiffener becomes zero, that stiffener can be seen as unnecessary and removed. For individual fitness calculation, a second-level approximate problem is constructed to optimize continuous ply thicknesses of retained layers. Correspondingly, laminated stacking sequences and stiffener layout are concurrently optimized.     

Optimization of composite stiffened panels under mechanical and hygrothermal loads using neural networks and genetic algorithms

The present work develops an optimization procedure for a geometric design of a composite material stiffened panel with conventional stacking sequence using static analysis and hygrothermal effects. The procedure is based on a global approach strategy, composed by two steps: first, the response of the panel is obtained by a neural network system using the results of finite element analyses and, in a second step, a multi-objective optimization problem is solved using a genetic algorithm. The neural network implemented in the first step uses a sub-problem approach which allows to consider different temperature ranges. The compression load and relative humidity of the air are assumed to be constants throughout the considered temperature range.     

Structural optimisation of random discontinuous fibre composites: Part 2 – Case study

This is the second paper in a two part series presenting the development of a stiffness optimisation algorithm to intelligently optimise the fibre architecture of discontinuous fibre composites. A Multi-Criteria Decision Making (MCDM) strategy is used to select parameters associated with the fibre architecture, to produce components that satisfy stiffness, cost and mass criteria.The model has been successfully demonstrated using an automotive spare wheel well geometry, which shows that a highly optimised discontinuous fibre composite solution can compete against a continuous fabric counterpart in terms of specific stiffness, whilst presenting an opportunity for significant cost reduction. This could potentially lead to the application of composite materials into new areas where cost has previously been prohibitive.     

A framework for designing robust supply chains considering product development issues

The primary objective of the design for supply chain (DFSC) is the selection of an appropriate product family. Moreover, it deals with the selection of the optimal combination among the different conflicting criteria while making a trade-off between the supply chain cost, sales profit and the product design complexities. In this research, to address the DFSC issues a product platform approach has been proposed which amalgamates the component modularity as well as the function modularity in the product design. The optimisation model proposed in this paper for the product development and the supply chain design is based on a generic bill of materials (GBOM) representation. The complete framework includes vital decision-making needed for designing a robust supply chain such as locating plants to alleviate the likely dominance of production cost and market mediation cost on product variety and imparting process flexibility of the located plants. The optimisation model proposed in this paper, models the supply chain cost, sales profit and product design complexity as three criteria that altogether determine the robustness of the supply chain and the underlying product development approach. Certain parameters like process flexibility, flow types and drivers of the product variety dominance have been controlled in the design framework. To resolve the complexity of the proposed model a genetic algorithm (GA) technique has been proposed. The proposed GA adopts an arithmetic crossover, a dynamic mutation and a variable penalty strategy to produce optimal results in a very short computational time. To validate the proposed model, a simulated case study of the wiring harness supplier of an AGV manufacturer has been studied.     

A scatter search algorithm for stacking sequence optimisation of laminate composites

This paper explores the metaheuristic approach called scatter search for lay-up sequence optimisation of laminate composite panels. Scatter search is an evolutionary method that has recently been found to be promising for solving combinatorial optimisation problems. The scatter search framework is flexible and allows the development of alternative implementations with varying degree of sophistication. The main objective of this paper is to demonstrate the effectiveness of the proposed scatter search algorithm for the combinatorial problem like stacking sequence optimisation of laminate composite panels. Preliminary investigations have been carried out to compare the optimal stacking sequences obtained using scatter search algorithm for buckling load maximisation with the best known published results. Studies indicate that the optimal buckling load factors obtained using the proposed scatter search algorithm found to be either superior or comparable to the best known published results.

Later, two case studies have been considered in this paper. Thermal buckling optimisation of laminated composite plates subjected to temperature rise is considered as the first case study. The results obtained are compared with an exact enumerative study conducted on the problem to demonstrate the effectiveness and performance of the proposed scatter search algorithm. The second case study is optimisation of hybrid laminate composite panels for weight and cost with frequency and buckling constraints. The two objectives are considered individually and also collectively to solve as multi-objective optimisation problem. Finally the computational efficiency of the proposed scatter search algorithm has been investigated by comparing the results with various implementations of genetic algorithm customised for laminate composites. It was shown in this paper through numerical experiments that the scatter search is capable of finding practical solutions for optimal lay-up sequence optimisation of composite laminates and results are comparable and sometimes even superior to genetic algorithms.     

Efficient modelling and optimisation of hybrid multilayered plates subject to ballistic impact

Among the key challenges present in the modelling and optimisation of composite structures against impact is the computational expense involved in setting up accurate simulations of the impact event and then performing the iterations required to optimise the designs. It is of more interest to find good designs given the limitations of the resources and time available rather than the best possible design. In this paper, low cost but sufficiently accurate finite element (FE) models were generated in LS Dyna for several experimentally characterised materials by semi-automating the modelling process and using existing material models. These models were then used by an optimisation algorithm to generate new hybrid offspring, leading to minimum weight and/or cost designs from a selection of isotropic metals, polymers and orthotropic fibre-reinforced laminates that countered a specified impact threat. Experimental validation of the optimal designs thus identified was then successfully carried out using a single stage gas gun. With sufficient computational hardware, the techniques developed in this pilot study can further utilise fine meshes, equations of state and sophisticated material models, so that optimal hybrid systems can be identified from a wide range of materials, designs and threats.     

Circumferential stiffness tailoring of general cross section cylinders for maximum buckling load with strength constraints

Stiffness tailoring of laminated composite structures using steered fibre tows is a design method that maximally uses the directional properties of composite materials. Cylindrical structures usually have circular cross sections while some application, geometric or aerodynamic requirements can necessitate other cross sections, e.g. elliptical. Circumferential tailoring can increase the buckling load of thin cylinders by compensating for non-uniform sectional loading such as bending and/or varying radius of curvature in general cylinders. Here, strength constraints are considered in maximum buckling load design, to ensure that the failure load is greater than the buckling load. A two-step optimisation framework is used to separate the theoretical and manufacturing issues in design. A computationally cheap semi-analytical finite difference method is used to solve the linear static and buckling problems. Conservative failure envelopes based on Tsai-Wu failure criterion are used for strength evaluation. To avoid repetitive analyses, successive convex approximation method is used. For demonstration, circumferential tailoring framework is applied to a circular cylinder under bending and an elliptical cylinder under axial compression. The improvements in buckling capacity of variable over constant stiffness designs are shown and verified using nonlinear buckling analysis in the commercial FEM software Abaqus^TM, and the mechanisms of improvements are investigated.     

Low-velocity impact damage on dispersed stacking sequence laminates. Part I: Experiments

The stacking sequence design of composite laminates is often limited to combinations of 0°, 90°, and ±45° fibre angle plies. Furthermore, in order to comply to certain stiffness requirements, clustering of plies becomes unavoidable. Although such laminates might have the desired stiffness properties, they may show poor impact and/or compression-after-impact behaviour.A method to redesign the traditional stacking sequences such that the alternative laminates have improved damage resistance whilst keeping similar in-plane and bending stiffness properties as their original traditional stacking sequences is proposed. This method makes use of optimisation tools based on genetic algorithms. In the alternative laminates, the difference between fibre angles of two consecutive plies is maximised and allowed to vary in the 0–90° fibre angle range at intervals of 5°. Manufacturing of such laminates is practical nowadays as the industry is changing its production techniques into accurate automated fibre-placement and tape-laying technologies. A two-step approach is proposed for the design of laminates. In the first step, the optimal laminate is designed in the traditional fashion to cope with the expected quasi-static loads on the structure. The second step consists of redesigning this laminate to better withstand impact loads by dispersing its stacking sequence while keeping similar stiffness properties as in the first step.A traditional laminate and two dispersed stacking sequence alternative layups were tested under low-velocity impact and compression-after-impact loads in order to compare their impact resistance and damage tolerance characteristics. The evaluation of these laminates will also be carried out by the innovative numerical tools proposed in the follow-up of the present paper.     

Performance modelling of a solar road panel prototype using finite element analysis

Performance prediction is a critical step towards the acceptance of a new pavement structure. This is true for both conventional and innovative designs; however, it is particularly important for innovative designs that attempt to redefine pavement design practices. One such innovative design concept is the solar road panel; a road panel with a transparent surface that generates electricity through embedded solar cells. Despite the work completed by multiple organisations towards the development of this concept, questions exist about the viability of these panels as a structural pavement surface. This paper investigates these questions through a finite element modelling approach that assesses a prototype panel's performance on a variety of structural bases. Overall, this paper finds that it is possible to design a solar road panel to withstand traffic loading and that a concrete structural base allows for substantial optimisation to the analysed prototype design.     

Multiple objective optimisation of composite sandwich structures for rail vehicle floor panels

This paper describes the application of an ant colony optimisation (ACO) algorithm to the multiple objective optimisation of a rail vehicle floor sandwich panel. The ACO algorithm was used to search a design space that was defined by sandwich theory and a material database in order to identify constructions that were optimal with respect to low mass and low cost. A broad range of mass and cost optimal sandwich material designs were identified successfully. These provided mass savings of up to 60% compared to existing plywood-based flooring systems, although mass savings above 40% had an associated cost premium.     

基于遗传算法的大型风机复合材料叶片根部强度优化设计

为了提高复合材料叶片承担载荷的能力, 尤其是承受最大弯矩的叶片根部的承载能力, 研究了遗传算法的优化原理并将遗传算法应用到复合材料叶片根部铺层的优化设计中。针对复合材料层压结构遗传算法优化设计中, 层压结构参数具有离散型的特点, 提出了适合复合材料层压结构遗传算法优化设计的整数编码策略, 以整数来表征层压结构参数。在分析层压结构强度的基础上, 针对结构强度优化的目标构造了可用于遗传算法的适应度函数。同时参考了一定的铺层规则, 在铺层角度限制为工程中常用的四种角度的前提下, 应用遗传算法对叶片根部进行了铺层优化设计。结果表明, 由于遗传算法特有的处理离散型问题的优势, 在叶片根部的铺层优化设计中应用遗传算法是可行和可信的。     

Using a Genetic Algorithm to Generate D‐optimal Designs for Mixture Experiments

We propose and develop a genetic algorithm (GA) for generating D‐optimal designs where the experimental region is an irregularly shaped polyhedral region. Our approach does not require selection of points from a user‐defined candidate set of mixtures and allows movement through a continuous region that includes highly constrained mixture regions. This approach is useful in situations where extreme vertices (EV) designs or conventional exchange algorithms fail to find a near‐optimal design. For illustration, examples with three and four components are presented with comparisons of our GA designs with those obtained using EV designs and exchange‐point algorithms over an irregularly shaped polyhedral region. The results show that the designs produced by the GA perform better than, if not as well as, the designs produced by the exchange‐point algorithms; however, the designs produced by the GA perform better than the designs produced by the EV. This suggests that GA is an alternative approach for constructing the D‐optimal designs in problems of mixture experiments when EV designs or exchange‐point algorithms are insufficient. Copyright © 2012 John Wiley & Sons, Ltd.