Topology design for composite components of minimum weight

This work presents a new philosophy for optimisation of composite structures in relation to lightweight design. It is based on Michell optimum lay-out theory, which uses orthogonal mesh structures disposed in the direction of principal stress trajectories, associated with an absolutely uniform distribution of stress in the fibres. The fibres in the composite component micro structure are disposed orthogonally like the minimum weight Michell structures, with voids filled with resin. This is the same mechanical principle which governs the optimisation of natural composites such as bones, horn, trees etc. Based on this natural rule, a procedure to find the optimum topology for the design of optimum composite mechanical components has been developed. A CAD-CAE software system based on finite element analysis using ABAQUS produces interactively on a screen the structure of optimum topology where the optimum fibre arrangement will be made.     

Optimum design of laminated fibre composite plates

A method is presented for the minimum weight optimum design of laminated fibre composite plates, subject to multiple inplane loading conditions, which includes stiffness, strength and elastic stability constraints. The buckling analysis is based on an equivalent orthotropic plate approach leading to two uncoupled eigenproblems per load condition. Overall computational efficiency is achieved by using constraint deletion techniques in conjunction with Taylor series approximations for the constraints retained. The optimization algorithm used, namely the method of inscribed hyperspheres, is a sequence of linear programs technique which exhibits rapid convergence in this application. Several example problems are given to demonstrate that the method presented offers an efficient and practical optimum design procedure for the fundamental and recurring problem treated.     

Compensation of chromatic dispersion-induced power fading using optimised chirped fibre Bragg grating for millimetre-wave radio-over-fibre system

Compensation of fibre dispersion-induced power fading in an externally modulated sub- carrier multiplexed radio-over-fibre transmission link using the chirped fibre Bragg grating (CFBG) has been investigated. The results show that periodic power fading caused by fibre chromatic dispersion is significantly reduced and the optimum transmission distance can be increased by proper design of grating parameters and optimum selection of apodisation profile. The investigation also reveals that carrier-to-noise ratio and bit-error rate of 156 Mbps DPSK signal are also significantly improved using the CFBG with asymmetric apodisation profile as the dispersion compensator.     

Studies on fly ash/coir/sugarcane reinforced epoxy polymer matrix composite

In the past years studies were conducted on natural fibre reinforced polymer composites to observe their mechanical properties in order to decide their industrial applications. These composites have already been used in many applications from aerospace to sporting equipment. These green composites can be used as a replacement for synthetic composites. This is because the natural fibres are eco-friendly, biodegradable, renewable, etc. In this work, an attempt is made to reinforce fly ash, coir fibre and sugarcane fibre with epoxy polymer matrix. Central composite design under response surface methodology (RSM), one of the approaches of design of experiments (DOE) is used to determine optimum sample preparation conditions of fly ash, coir fibre and sugarcane fibre. Both tensile and flexural (three-point bending) tests are conducted on these fabricated composites to determine their materialistic characteristics. Analysis of variance (ANOVA) is carried out using Minitab software to find the influence of fly ash, coir fibre, sugarcane fibre on composites. Regression equations obtained from analysis of variance is used to calculate values. Experimental and calculated values are compared and their error % are calculated and tabulated. Response surface optimization study is carried to find the optimized parameters of composites. It is observed that, increase in wt.% of coir fibre and decrease in wt.% of fly ash and sugarcane fibre, increases yield stress and these parameters have mixed impact on ultimate tensile stress. The addition of fly ash, coir fibre and sugarcane fibre in low percentages increases Young's modulus. Increase in wt.% of fly ash and coir fibre and decrease in wt.% of sugarcane, increases flexural modulus and flexural stress.     

Optimum stacking sequence design of laminated composite circular plates with curvilinear fibres by a layer-wise optimization method

The optimum stacking sequence design for the maximum fundamental frequency of symmetrically laminated composite circular plates with curvilinear fibres is investigated for the first time using a layer-wise optimization method. The design variables are two fibre orientation angles per layer. The fibre paths are constructed using the method of shifted paths. The first-order shear deformation plate theory and a curved square p-element are used to calculate the objective function. The blending function method is used to model accurately the geometry of the circular plate. The equations of motion are derived using Lagrange’s method. The numerical results are validated by means of a convergence test and comparison with published values for symmetrically laminated composite circular plates with rectilinear fibres. The material parameters, boundary conditions, number of layers and thickness are shown to influence the optimum solutions to different extents. The results should serve as a benchmark for optimum stacking sequences of symmetrically laminated composite circular plates with curvilinear fibres.     

Influence of microstructure on axial strength of unidirectional continuous fibre reinforced aluminium matrix composites

Abstract

Systematic empirical investigations on the relationship between microstructural features and mechanical performance of unidirectionally reinforced continuous fibre Al matrix composites (CFAMCs) carried out by the present authors in recent years are summarised. The employment of a high strength matrix alloy and the development of a strong fibre/matrix interface are beneficial to maximise the strengthening effect of the fibre reinforcement. Processing defects, such as second brittle phases in the matrix, non-infiltration defects, matrix solidification shrinkage voids, excessive interfacial reactions, the presence of reaction products on the interface, weak interfacial binding, and excessively high fibre volume fraction reduce composite strength to different extents via a number of different mechanisms. Criteria for the microstructure design of CFAMCs for optimum fibre strengthening efficiency are proposed.     

A genetic algorithm approach to single and multiobjective structural optimization with discrete–continuous variables

A search procedure with a philosophical basis in molecular biology is adapted for solving single and multiobjective structural optimization problems. This procedure, known as a genetic algorithm (GA). utilizes a blending of the principles of natural genetics and natural selection. A lack of dependence on the gradient information makes GAs less susceptible to pitfalls of convergence to a local optimum. To model the multiple objective functions in the problem formulation, a co-operative game theoretic approach is proposed. Examples dealing with single and multiobjective geometrical design of structures with discrete–continuous design variables, and using artificial genetic search are presented. Simulation results indicate that GAs converge to optimum solutions by searching only a small fraction of the solution space. The optimum solutions obtained using GAs compare favourably with optimum solutions obtained using gradient-based search techniques. The results indicate that the efficiency and power of GAs can be effectively utilized to solve a broad spectrum of design optimization problems with discrete and continuous variables with similar efficiency.     

The engineering optimisation of hybrid composite/ metallic wing boxes for buckling and strength constraints

The minimum weight design of multidirectional carbon fibre reinforced plastic (CFRP) plates under uniaxial compression is first considered. The results of this study are applied to the optimisation of multi-spar wing bend boxes under bending and vertical shear loading, using geometric programming. The basic structural form is a metallic multi-spar substructure supporting CFRP composite covers in which the layers are either blocked or uniformly distributed. A corrugated web design with variable wing depth is also treated, and the method is applied to the optimisation of flat and corrugated composite shear webs as a separate case. The nature of the work involves a simple modelling approach using engineer's bending theory, and a variety of orthotropic panel buckling equations adapted for geometric programming are used as constraints. In all the cases considered, the optimum scantling dimensions and layer directions are given as design equations which could be used for initial sizing.     

Design and performance analysis of code families for multi-dimensional optical CDMA

A code design algorithm for application in multi-dimensional optical code division multiple access (MD-OCDMA) for asynchronous optical fibre communication is proposed. Two-dimensional (2D) wavelength-time or space-time OCDMA and three-dimensional (3D) space-wavelength-time OCDMA are subsets of MD-OCDMA. Some applications and the performance analysis of the algorithm in 2D multipulse per row codes and 3D multipulse per plane codes are shown. In the applications discussed, this design ensures a maximum cross-correlation of '1' between any two codes. The performance metrics studied are the probability of error due to multiple-access interference for different numbers of active users and optimum temporal length for different values of cardinality. The performance analysis shows that the proposed 2D design offers very low probability of error due to multiple-access interference at lower cardinality when compared with other 2D designs using equivalent code dimension. A comparison of the proposed 3D design with an existing 3D design shows better performance at lower cardinality. The 3D designs show better performance when compared with the 2D designs.     

OPTIMUM SHAPE DESIGN AND POSITIONING OF FEATURES USING THE BOUNDARY INTEGRAL EQUATION METHOD

A design optimization procedure is developed using the boundary integral equation (BIE) method for linear elastostatic two-dimensional domains. Optimal shape design problems are treated where design variables are geometric parameters such as the positions and sizing dimensions of entire features on a component or structure. A fully analytical approach is adopted for the design sensitivity analysis where the BIE is implicitly differentiated. The ability to evaluate response sensitivity derivatives with respect to design variables such as feature positions is achieved through the definition of appropriate design velocity fields for these variables. How the advantages of the BIE method are amplified when extended to sensitivity analysis for this category of shape design problems is also highlighted. A mathematical programming approach with the penalty function method is used for solving the overall optimization problem. The procedure is applied to three example problems to demonstrate the optimum positioning of holes and optimization of radial dimensions of circular arcs on structures.     

Design of copper filled fibreglass moulds for manufacturing a customized product using linear programming optimization and finite element analysis

This paper presents a design procedure and cost analysis for a mould made of glass fibre reinforced polyester filled with copper particles (GRP/copper). It also describes their potential use in rotational moulding as an alternative to steel and aluminium moulds operating at high temperatures up to 250 °C. The thermal conductivity of glass reinforced polyester (GRP) was improved by incorporating copper particles acting as fillers in the composite. An optimum composite structure consisting of 25% glass fibres, 45% polyester, and 30% copper was achieved by linear programming search optimization methods. Then a finite element analysis (FEA) of a typical GRP/copper mould made of the optimized composite structure under thermal loading was conducted. The induced thermal stresses obtained from FEA were used to check the failure condition of the mould using the Tsai–Hill failure criterion. The FEA design procedure was also used to determine the mould thickness with a safety factor of at least four. Scheduling and cost analysis showed that 76% reduction in production time and 64% reduction in manufacturing costs have been achieved with the developed method.     

Optimum laminate design for strength and stiffness

A method is presented for minimum weight optimum design of symmetric fibre-composite laminates subject to multiple in-plane loading conditions which takes into account membrane stiffness requirements and strength limitations. The problem is cast as a non-linear mathematical programming problem in which the thicknesses of material placed at preassigned orientation angles are treated as the only design variables. The non-linear programming formulation is transformed into a sequence of linear programs employing an adaptation of the method of inscribed hyperspheres in which only critical and near critical constraints are considered at each stage in the procedure. Example applications illustrate that the method presented offers an efficient and practical optimum design procedure for the fundamental and recurring problem treated.     

Simulated variance optimization for robust design

A method to aid robust design in the presence of design parameter uncertainty is described. For a given relationship between a performance measure (or output parameter) and the uncertain design parameters a probabilistic simulation is used to obtain the variance of the performance measure as a function of the nominal design parameter values. The optimum values of the latter are then obtained as those corresponding to a minimum of the computed variance, determined by means of a particular non-linear optimization algorithm in the presence of constraints. The latter are in the form of limits on the nominal values of the design parameters and a specified value for the performance measure at the nominal design point, i.e. the deterministic design target. Some problems inherent in this type of procedure are discussed and methods of solution are described. A specific example is studied and the results from the present method are compared with those previously obtained by use of another procedure. © 1998 John Wiley & Sons, Ltd.     

Round-robin analysis of the RILEM TC 162-TDF beam-bending test: Part 1—Test method evaluation

A round robin test programme was carried out on the beam-bending test recommended by the RILEM TC 162-TDF [1]. Plain concrete and steel fibre reinforced concrete (SFRC) beams were included in the test programme. The material variables for the SFRC beams consisted of two concrete strengths, three fibre dosages and three types of fibres. A comprehensive statistical analysis was carried out to determine the applicability and robustness of the test method. It was found that although inter-lab variations do occur, this was relatively small compared to the inherent material variation. It is also possible that the high variations observed could be due to the relatively small cross sections used for the test beams. Additionally, an investigation was carried out to evaluate the objectiveness of the calculation procedure proposed by RILEM TC 162-TDF to obtain the necessary design parameters. It was found that the prescribed calculation procedure was satisfactory, as the variation between the design parameters calculated at different laboratories was generally within the range of ±5%. An alternative method of obtaining the design parameters, by considering residual strengths, is suggested as it simplifies the calculation procedure and the test method. In general, the beam test was found to be a good robust test and relatively easy to carry out.     

FUZZY OPTIMUM DESIGN OF STRUCTURES

It is pointed out that there exists a vast amount of fuzzy information in both objective and constraint functions of optimum design of structures (ODS) Thus, relatively reasonable optimum designs can only be obtained by fuzzy programming methods. While all fuzzy constraints enclose a fuzzy feasible region in decision-making space, the fuzzy optimum solution will be a sequence of points in a small fuzzy optimum subregion. In the presented procedure, optimum structural design with fuzzy constraints is transformed into a set of ordinary optimum problems by a level cuts approach which results in a sequence of optimum design schemes with different design levels. The concept of optimum design level corresponding to the most suitable scheme among the obtained sequence is also advanced in this paper.     

Optimization of basic dye removal by oil palm fibre-based activated carbon using response surface methodology

Oil palm fibre was used to prepare activated carbon using physiochemical activation method which consisted of potassium hydroxide (KOH) treatment and carbon dioxide (CO(2)) gasification. The effects of three preparation variables: the activation temperature, activation time and chemical impregnation (KOH:char) ratio on methylene blue (MB) uptake from aqueous solutions and activated carbon yield were investigated. Based on the central composite design (CCD), a quadratic model and a two factor interaction (2FI) model were respectively developed to correlate the preparation variables to the MB uptake and carbon yield. From the analysis of variance (ANOVA), the significant factors on each experimental design response were identified. The optimum activated carbon prepared from oil palm fibre was obtained by using activation temperature of 862 degrees C, activation time of 1h and chemical impregnation ratio of 3.1. The optimum activated carbon showed MB uptake of 203.83mg/g and activated carbon yield of 16.50%. The equilibrium data for adsorption of MB on the optimum activated carbon were well represented by the Langmuir isotherm, giving maximum monolayer adsorption capacity as high as 400mg/g at 30 degrees C.     

An advanced structural analysis/synthesis capability—ACCESS 2

An advanced automated design procedure for minimum weight design of structures (ACCESS 2) is reported. Design variable linking, constraint deletion, and explicit constraint approximation are used to effectively combine approach to structral synthesis is extended to problems involving fibre composite structure, thermal effects and natural frequency constraints in addition to the usual static stress and displacement limitations. Sample results illustrating these new features are given.     

Effect of coupling agent on natural fibre in natural fibre/polypropylene composites on mechanical and thermal behaviour

To enhance the adhesion between the natural fibre and the thermoplastic matrix, a coupling agent of maleic anhydride grafted polypropylene MAPP is applied. In literature, there are different guidelines of the optimum percentage required of MAPP. Therefore, a systematic work is carried out to optimise the MAPP percent with respect to the type of the natural fibre. Different parameters are investigated namely; Coupling agent ratio to the fibre (0%, 6.67%, 10%, 13.3%, 16.67%), coupling agent source, fibre type (flax, hemp, sisal), and fibre content (30%, 50%). Composite is produced using a kneader and the resulting material is assessed mechanically, thermally, microscopically and for water absorption. For different MAPP source and the natural fibre type, optimum MAPP to fibre ratio is found in average to range between 10% and 13.3% according to the investigated property (stiffness, strength and impact). Increase of MAPP is found to decrease the melting temperature. The thermal behaviour is also linked to the copolymer molecular weight.     

Reanalysis procedure for large structural systems

An efficient procedure is presented for repetitive analysis of structures, with large numbers of degrees of freedom and design variables, as they are progressively modified during the automated optimum design process. The three key elements of the procedure are: (a) lumping of the large number of design variables into a single tracing parameter; (b) operator splitting or additive decomposition of the different arrays in the governing finite element equations of the modified structure into the corresponding arrays of the original structure plus correction terms; and (c) application of a reduction method through the successive use of the finite element method and the classical Bubnov-Galerkin technique. The reanalysis procedure is applied to the linear static and free vibration problems of framed structures. Changes in both the sizing and shape (configuration) design variables are considered. For static problems the similarities between the proposed procedure and the preconditioned conjugate gradient technique are identified and are exploited to provide a physical meaning for the preconditioned residual vectors. The effectiveness of the proposed procedure is demonstrated by means of numerical examples.