叠层复合材料方板多孔形状优化

采用一种无梯度仿生技术——基于等限制Tsai-Hill值准则的固定网格渐进优化方法(FGESO),研究了叠层复合材料方板在拉剪荷载时不同孔数、不同叠层构造条件下的最优孔形问题。在孔的周围不断把限制Tsai-Hill值小于删除标准的材料删除,直到稳定状态达到,然后提高删除标准继续迭代,直到达到指定的开孔面积。与传统渐进优化方法(ESO)的不同之处在于利用节点而不是单元的限制Tsai-Hill值来确定需要删除的材料,因此得到了比ESO更光滑的结果。例子证明了方法的普适性和有效性。还研究了两孔方板最优孔形的优化历程,结果反映了相邻开孔相互影响的一些规律。     

Optimal lay-up design of variable stiffness laminated composite plates by a layer-wise optimization technique

The optimal lay-up design for the maximum fundamental frequency of variable stiffness laminated composite plates is investigated using a layer-wise optimization technique. The design variables are two fibre orientation angles per ply. Thin plate theory is used in conjunction with a p-element to calculate the fundamental frequencies of symmetrically and antisymmetrically laminated composite plates. Comparisons with existing optimal solutions for constant stiffness symmetrically laminated composite plates show excellent agreement. It is observed that the maximum fundamental frequency can be increased considerably using variable stiffness design as compared to constant stiffness design. In addition, optimal lay-ups for the maximum fundamental frequency of variable stiffness symmetrically and antisymmetrically laminated composite plates with different aspect ratios and various combinations of free, simply supported and clamped edge conditions are presented. These should prove a useful benchmark for optimal lay-ups of variable stiffness laminated composite plates.     

Particle swarm-based structural optimization of laminated composite hydrokinetic turbine blades

Composite blade manufacturing for hydrokinetic turbine application is quite complex and requires extensive optimization studies in terms of material selection, number of layers, stacking sequence, ply thickness and orientation. To avoid a repetitive trial-and-error method process, hydrokinetic turbine blade structural optimization using particle swarm optimization was proposed to perform detailed composite lay-up optimization. Layer numbers, ply thickness and ply orientations were optimized using standard particle swarm optimization to minimize the weight of the composite blade while satisfying failure evaluation. To address the discrete combinatorial optimization problem of blade stacking sequence, a novel permutation discrete particle swarm optimization model was also developed to maximize the out-of-plane load-carrying capability of the composite blade. A composite blade design with significant material saving and satisfactory performance was presented. The proposed methodology offers an alternative and efficient design solution to composite structural optimization which involves complex loading and multiple discrete and combinatorial design parameters.     

铺设角度与铺层顺序对层合板稳定性的影响

以层合板结构的临界屈曲载荷系数最大化为优化目标,基于改进型模拟退火算法对层合板结构铺设角度和铺层顺序进行优化。由于层合板结构的铺层角度是离散变量,模拟退火算法适合求解离散变量的优化问题。利用模拟退火算法优化层合板铺层,在算法内采用并行计算、引入记忆功能同时设置双阈值终止准则,有效地提高了优化过程的收敛速度,同时避免优化过程中出现局部最优解。以临界屈曲载荷系数作为目标函数,选取复合材料层合板的铺设角度顺序为设计变量,采用改进的模拟退火算法得出复合材料层合板的最优铺设角度以及铺层顺序。     

Particle swarm optimization approach for multi-objective composite box-beam design

This paper presents a multi-agent search technique to design an optimal composite box-beam helicopter rotor blade. The search technique is called particle swarm optimization (‘inspired by the choreography of a bird flock’). The continuous geometry parameters (cross-sectional dimensions) and discrete ply angles of the box-beams are considered as design variables. The objective of the design problem is to achieve (a) specified stiffness value and (b) maximum elastic coupling. The presence of maximum elastic coupling in the composite box-beam increases the aero-elastic stability of the helicopter rotor blade. The multi-objective design problem is formulated as a combinatorial optimization problem and solved collectively using particle swarm optimization technique. The optimal geometry and ply angles are obtained for a composite box-beam design with ply angle discretizations of 10°, 15° and 45°. The performance and computational efficiency of the proposed particle swarm optimization approach is compared with various genetic algorithm based design approaches. The simulation results clearly show that the particle swarm optimization algorithm provides better solutions in terms of performance and computational time than the genetic algorithm based approaches.     

Design and Manufacture of Conical Shell Structures Using Prepreg Laminates

The design and manufacture of unstiffened composite conical structures is very challenging, as the variation of the fiber orientations, lay-up and the geometry of the ply pieces have a significant influence on the thickness imperfections and ply angle deviations imprinted to the final part. This paper deals with the manufacture of laminated composite cones through the prepeg/autoclave process. The cones are designed to undergo repetitive buckling tests without accumulating permanent damage. The aim is to define a process that allows the control of fiber angle deviations and the removal of thickness imperfections generated from gaps and overlaps between ply pieces. Ultrasonic scan measurements are used to proof the effectiveness of the proposed method.     

Ply level uncertainty effects on failure curves and optimal design of laminated composites using directional bat algorithm

The present study investigates the effect of both ply level material uncertainty and ply angle uncertainty on the failure envelope, strength characteristics and design of laminated composite. Multiple failure envelopes and distributions of the strength parameters are obtained for Tsai-Wu and maximum stress criteria using Monte Carlo simulation. A newly developed directional bat algorithm (dBA) is then used to perform the constrained design optimization of laminated composite for the first time while considering uncertainty effects. The effect of ply level uncertainty on failure envelopes and the corresponding optimal design of laminated composite structures is thus quantified.     

Optimal design of a composite structure

This paper presents a design methodology for a laminated composite stiffened panel, subjected to multiple in-plane loads and bending moments. Design variables include the skin and stiffener ply orientation angles and stiffener geometry variables. Optimum designs are sought which minimize structural weight and satisfy mechanical performance requirements. Two types of mechanical performance requirements are placed on the panel, maximum strain and minimum strength. Minimum weight designs are presented which document that the choice of mechanical performance requirements cause changes in the optimum design. The effects of lay-up constraints which limit the ply angles to user specified values, such as symmetric or quasi-isotropic laminates, are also investigated.     

遗传演化结构优化算法

ESO算法是近年来提出的一种结构优化算法,它可以应用于多个领域。在土木工程方面,利用ESO算法可以寻找结构最优的拓扑形状,指导结构的设计。但这种算法存在先天的局限性,即无法保证它所得到的解是最优解。为此,将遗传算法与ESO算法揉合在一起,形成了一种新的遗传ESO算法,简称为GESO算法。GESO算法把群体的概念借鉴到ESO中,巧妙地解决了遗传算法费时和ESO易陷入局部最优解的两个问题。实例证明它得到的结果大多优于ESO算法。     

A fibre direction compressive failure criterion for long fibre laminates at ply scale,including stacking sequence and laminate thickness effects

Long fibre laminate compressive failure is due to a microbuckling instability which leads to a kink band and a brittle failure of the fibres. This failure mechanism is well known, but more or less pertinently explained in the literature. Some references also showed that local microbuckling instability depends on parameters that belong to the scale of the elementary ply, like thickness and corresponding lay-up. The compressive strength of the unidirectional ply is therefore no more an intrinsic material property, but results from a structural effect of the design. In this paper, the so-called “structure effect” is included in a simple way as an analytical formula in the phenomenological compressive failure criterion which was initially presented by Budiansky and Fleck works. The criterion presented is expressed analytically for unidirectional composite and stands for the local compressive failure strength at ply scale in fibres direction.     

Optimization of laminated composite structure considering uncertainty effects

In this paper, the most conservative Tsai–Wu failure envelopes are obtained for laminated composite considering material as well as ply angle uncertainty. The uncertainty analysis is performed using Monte Carlo simulation (MCS). The obtained failure envelopes are then used as the constraint functions to perform the minimum weight design optimization problem using particle swarm optimization (PSO). Results show increase in weight of the laminate from the deterministic results and it varies from 4% to 50% depending upon the stacking sequence and loading condition. Substantial effects of uncertainty on the failure envelope and optimal design are quantified.     

Structural optimization of rotating tapered laminated thick composite plates with ply drop-offs

In this study, structural optimization of rotating tapered thick laminated composite plates with ply drop-offs has been investigated numerically. The governing differential equations of motion of the tapered composite plate have been presented including the energy associated with the inertia force, coriolis force, displacement dependent centrifugal force and initial stress resultants due to steady state rotation. Four noded quadrilateral finite element has been formulated based on the first order shear deformation theory. Finite element analysis results are validated with experimental results for natural frequencies of the tapered plate with various configurations. Various cases of optimization problems are formulated with different objective functions in terms of maximization of natural frequencies and damping factors (individually and combined) and solved using genetic algorithm in order to obtain optimal ply sequence and ply orientation. It is shown that the optimization problem with maximization of fundamental modal damping factor without rotating condition yields the optimal layout as 90° for all the layers in the plate. It is also observed that maximization of the fundamental modal damping factor yields identical optimal orientation for uniform and all the configurations of a tapered composite plate.     

Design optimization of laminated composite structures using distributed grid resources

Parameter studies, genetic algorithms and Monte Carlo type calculations are examples of pleasantly parallel computational tasks. Pleasantly parallel computational tasks can be effectively calculated in computer clusters or grids. In this work, we consider a weight minimization problem of a laminated composite structure in the post-buckling region. The design variables are the number of layers and the layer orientations given in a discrete set of allowable angles for layer orientations. Optimization is carried out using a deterministic search process, where the lay-up configurations are generated iteratively in the design space from the selected design points of the population at the preceding cycle. Computation is performed using NorduGrid grid computing platform. In this work, we briefly go through some general grid concepts and the use of grid in optimization of laminated composite structures.     

Design Optimization of Composite Cylindrical Shells under Uncertainty

Four different approaches for the design of axially compressed cylindrical shells are presented, namely (1) the knockdown factor (KDF) concept, (2) the single perturbation load approach, (3) a probabilistic design procedure and (4) the convex anti-optimization approach. The different design approaches take the imperfection sensitivity and the scatter of input parameters into account differently. In this paper, the design of a composite cylinder is optimized considering the ply angles as design variables. The KDF concept provides a very conservative design load and in addition an imperfection sensitive design, whereas the other approaches lead to a significantly less conservative design load and to a less imperfection sensitive design configuration. The ways in which imperfection sensitivity is treated by the different approaches and how these influence the optimal design configuration is discussed.     

A two-step optimization scheme for maximum stiffness design of laminated plates based on lamination parameters

The purpose of this paper is to propose an effective solution scheme of simultaneous optimization design of layup configuration and fiber distribution for maximum stiffness design of laminated plates. Firstly, a numerical analysis of the lamination parameters feasible region for a laminated plate consisting of various given number of ply groups (each ply group may have different thickness and all the fibers in one ply group are orientated in an identical direction) is carried out, and it is found that the feasible region based on only a few ply groups is very close to the overall one determined by infinite plies. Therefore, it is suggested that the feasible region of lamination parameters of a laminated plate could be approximately determined by the layup configuration of least ply groups. Secondly, a two-step simultaneous optimization scheme of layup configuration and fiber distribution for maximum stiffness design of laminated plates is proposed. Accordingly, by using ply thickness, fiber orientation angle and fiber volume fraction in a laminated plate of least ply groups as design variables, the optimal lamination parameters for maximum stiffness is obtained. Then, taking the optimal lamination parameters as the design objective, a detailed layup design optimization is implemented by considering some limitations on manufacturing, such as preset ply thickness, and specific fiber orientation angle and a limited maximum number of consecutive plies in the same fiber orientation. Numerical examples are also presented to validate the proposed two-step optimization scheme.     

Integrated XFEM-CE analysis of delamination migration in multi-directional composite laminates

Progressive damage and failure in composites are generally complex and involve multiple interacting failure modes. Depending on factors such as lay-up sequence, loading and specimen configurations, failure may be dominated by extensive matrix crack-delamination interactions, which are very difficult to model accurately. The present study further develops an integrated extended finite element method (XFEM) and cohesive element (CE) method for three-dimensional (3D) delamination migration in multi-directional composite laminates, and validates the results with experiment performed on a double-cantilever beam (DCB). The plies are modeled by using XFEM brick elements, while the interfaces are modeled using CEs. The interaction between matrix crack and delamination is achieved by enriching the nodes of cohesive element. The mechanisms of matrix fracture and delamination migration are explained and discussed. Matrix crack initiation and propagation can be predicted and delamination migration is also observed in the results. The algorithm provides for the prediction of matrix crack angles through the ply thickness. The proposed method provides a platform for the realistic simulation of progressive failure of composite laminates.     

Detailed design of a lattice composite fuselage structure by a mixed optimization method

In this article, a procedure for designing a lattice fuselage barrel is developed. It comprises three stages: first, topology optimization of an aircraft fuselage barrel is performed with respect to weight and structural performance to obtain the conceptual design. The interpretation of the optimal result is given to demonstrate the development of this new lattice airframe concept for the fuselage barrel. Subsequently, parametric optimization of the lattice aircraft fuselage barrel is carried out using genetic algorithms on metamodels generated with genetic programming from a 101-point optimal Latin hypercube design of experiments. The optimal design is achieved in terms of weight savings subject to stability, global stiffness and strain requirements, and then verified by the fine mesh finite element simulation of the lattice fuselage barrel. Finally, a practical design of the composite skin complying with the aircraft industry lay-up rules is presented. It is concluded that the mixed optimization method, combining topology optimization with the global metamodel-based approach, allows the problem to be solved with sufficient accuracy and provides the designers with a wealth of information on the structural behaviour of the novel anisogrid composite fuselage design.     

Analysis and design of fiber reinforced plastic composite deck-and-stringer bridges

A comprehensive study on analysis and design of fiber reinforced plastic (FRP) composite deck-and-stringer bridges is presented. The FRP decks considered consist of contiguous thin-walled box sections and are fabricated by bonding side-by-side pultruded thin-walled box beams, which are placed transversely over FRP composite stringers. In this study, we review the modeling and experimental verification of FRP structural beams, including micro/macro-mechanics predictions of ply and laminate properties, beam bending response, shear-lag effect, and local and global buckling behaviors. A simplified design analysis procedure for cellular FRP bridge decks is developed based on a first-order shear deformation macro-flexibility (SDMF) orthotropic plate solution. The present approach can allow the designers to analyze, design and optimize material architectures and shapes of FRP beams, as well as various bridge deck configurations, before their implementation in the field. Experimental studies of cellular FRP bridge decks are conducted to obtain stiffness coefficients, and an example of a cellular FRP deck on optimized winged-box FRP stringers under actual track-loading is presented to illustrate the analytical method. The experimental-analytical approach presented in this study is used to propose simplified engineering design equations for new and replacement highway FRP deck-and-stringer bridges.     

Tailoring for strength of composite steered-fibre panels with cutouts

A large number of composite parts include cutouts to accommodate windows, doors, and bolted joints. These regions are hot-spots in terms of design because they concentrate stresses, hence becoming critical in terms of the structural integrity of the part.A traditional approach to the problem of stress concentrations around cutouts is to locally increase the laminate thickness in order to improve the strength margins. Often this practice attracts more loads to the cutout besides increasing part weight. A more effective solution is to tailor the panel in-plane stiffness by means of fibre-steered laminates, and avoid the stress concentrations altogether.The present research demonstrates that it is possible to design and manufacture composite panels whose buckling and first-ply failure responses are insensitive to the existence of a central hole. Moreover, it is shown that the structural performance of these designs more than doubles that of straight-fibre configurations.     

Stability and failure of composite laminates with various shaped cutouts under combined in-plane loads

The objective of this paper is to study stability and failure of a composite laminate with a centrally placed cutout of various shapes (i.e., circular, square, diamond, elliptical-vertical and elliptical-horizontal) under combined action of uni-axial compression and in-plane shear loads. The FEM formulation based on the first order shear deformation theory and von Karman’s assumptions has been utilized. Newton–Raphson method is used to solve nonlinear algebraic equations. Failure of a lamina is predicted by the 3-D Tsai–Hill criterion whereas the onset of delamination is predicted by the interlaminar failure criterion. The effects of cutout shape, direction of shear load and composite lay-up on buckling and postbuckling responses, failure loads and failure characteristics of the laminate has been discussed. An efficient utilization of material strength is observed in the case of laminate with circular cutout as compared to the laminate with other shaped cutouts. In addition, it is also concluded that although the buckling strength of the (0/90)_4s laminate is lower than that of the (+45/?45/0/90)_2s and (45/?45)_4s laminates, but its strength is increased in the advanced stage of postbuckling deformation.