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.     

Frequency optimization of laminated composite angle-ply plates with circular hole

The fundamental frequencies of simply supported symmetrically laminated composite angle-ply plates with central circular holes with a given material system are maximized with respect to fibre orientations. The first-order shear deformation (FSDT) theory is used for finite element analysis. Modified feasible direction (MFD) method is used for the optimization routine. Also, the optimum fibre orientations are obtained using golden section (GS) method to compare with MFD method. Finally, the significant effects of different number of layers, boundary conditions, plate aspect ratios, hole diameter-to-width ratio, material anisotropy and antisymmetric lay-up on the results are demonstrated.     

Normal stress distribution adjacent to optimum holes in composite plates

An approximate solution in the form of a polynomial is presented for the normal stress distribution adjacent to a class of optimum holes in symmetrically laminated infinite composite plates under uniaxial loading. Comparison of the present approximate solution with that of the finite element method shows good agreement. The approximate solution is useful in assessing the strength of the laminated composite plates with holes. The present simple solution will be of immense use to design engineers who are interested in obtaining quick and reliable solutions for circular and optimized holes in symmetrically laminated composite plates.     

Determination of optimum effective parameters on thermal buckling of hybrid composite plates with quasi-square cut-out using a genetic algorithm

ABSTRACT

The thermal buckling load on perforated composite plates is affected by several parameters, including design variables such as cut-out orientation, fibre angle, bluntness of cut-out corners, cut-out size to plate size ratio and stacking sequence. This study investigates the effect of these parameters on the thermal buckling load of a composite plate with a quasi-square cut-out. Optimal values of the parameters are determined using a genetic algorithm to achieve the maximum buckling load. The composite used herein is a four-layer laminated composite plate. The stacking sequences of the plate are also studied. Stability equations are obtained using first order shear deformation theory. The results showed that a plate with a quasi-square cut-out is more resistant to thermal buckling than one with a circular cut-out; thermal buckling of a composite plate is dependent on various parameters, and the maximum thermal buckling load can be achieved by appropriate selection of these parameters.     

Vibration analysis of laminated composite plates: TV-holography and finite element method

An experimental and numerical investigation into the structural behaviour of symmetrically laminated carbon fibre-epoxy composite rectangular plates subjected to vibration. The laminated composite plates are composed on layers of Grafil XAS carbon fibres preimpregnated in 914C Fibredux epoxy resin and each plate was vibrated by a piezoelectric transducer (PZT) attached onto its surface. The specimens tested were of two different length to width ratios and of symmetric stacking sequence. In this study the short edges of the plate were of various combinations of clamp and free support conditions, and the long edges of the plate were of various combinations of free and simple support conditions. Experimental and finite element studies were carried out in parallel. The experimental vibrational response of the test plates were obtained using a TV-holography technique. The comparison between experimental results and finite element results are reasonably good in all the cases studied.     

复合材料对称层合板特征值问题的灵敏度分析

由于复合材料层合板的横向剪切模量较低,因此基于克希霍夫理论而计算的层合板特征值及其灵敏度与实际情况相差较大。本文采用层合板的一阶剪切变形理论,将纤维铺设角、材料参数和从层合板的中面到第K层板上表面的距离Z_K视为设计变量,研究了对称层合板特征值的灵敏度计算问题。     

Maximum stiffness design of laminated composite plates via a constrained global optimization approach

The optimal lamination arrangements of laminated composite plates with maximum stiffness subject to side constraints are investigated via a constrained multi-start global optimization approach. In the optimal design process, the deformation analysis of laminated composite plates is accomplished by utilizing a shear deformable laminated composite finite element and the optimal design problem, which has been converted into an unconstrained minimization problem via the general augmented Lagrangian method, is solved by utilizing the proposed unconstrained multi-start global optimization technique to determine the optimal fiber angles and layer group thicknesses of the laminated composite plates for attaining maximum stiffness and simultaneously satisfying the imposed side constraints. The feasibility of the proposed constrained multi-start global optimization algorithm is validated by means of a simple but representative example and its applications are demonstrated by means of a number of examples on the maximum stiffness design of symmetrically laminated composite plates. The effects of length-to-thickness ratio, aspect ratio, and number of layer groups upon the optimum fiber angles and layer group thicknesses of the plates are investigated.     

Transverse vibration of symmetrically laminated rectangular composite plates

A general numerical method for estimation of the vibrational response of symmetrically laminated rectangular composite plates is presented. This is based on the Rayleigh-Ritz method using the admissible 2-D orthogonal polynomials to derive the governing eigenvalue equation. The natural frequencies and mode shapes for the laminated plates are obtained by solving this governing eigenvalue equation. Several test problems are solved to demonstrate the accuracy and flexibility of the proposed method. The present results, where possible, are verified with those available values from the literature. The effects of the material, number of layers and fibre orientation upon the frequencies and mode shapes are discussed. This study may provide valuable information for researchers and engineers in design applications.     

The Artificial Bee Colony algorithm in layer optimization for the maximum fundamental frequency of symmetrical laminated composite plates

In this study the layer optimization was carried out for maximizing the lowest (first) fundamental frequency of symmetrical laminated composite plates subjected to any combination of the three classical boundary conditions, and the applicability of the Artificial Bee Colony (ABC) algorithm to the layer optimization was investigated. The finite element method was used for calculating the first natural frequencies of the laminated composite plates with various stacking sequences. The ABC algorithm maximizes the first natural frequency of the laminated composite plate defined as an objective function. The optimal stacking sequences were determined for two layer numbers, twenty boundary conditions and two plate length/width ratios. The outer layers of the composite plate had a stiffness increasing effect, and as the number of clamped plate edges was increased both he stiffness and natural frequency of the plate increased. The optimal stacking sequences were in good agreement with those determined by the Ritz-based layerwise optimization method (Narita 2003: J. Sound Vibration 263 (5), 1005–1016) as well as by the genetic algorithm method combined with the finite element method.     

基于低能量冲击损伤阻抗的复合材料薄壁结构铺层顺序设计

建立了有效的复合材料层合板结构冲击损伤分析方法,层合板面内损伤采用改进的Chang/Chang 失效准则做判据,得到面内各类损伤形式。层间损伤采用与Mixed-Mode粘接元等效的TIEBREAK接触模拟。利用此分析方法,从复合材料薄壁结构设计需要出发,研究了在低能量冲击下,铺层的层间角度、铺层方向、铺层重叠对层合板结构冲击损伤阻抗的影响规律,并对它们的综合影响进行了总体分析,得到了能提高层合板结构损伤阻抗的铺层顺序设计指导。最后用该设计指导对某种铺层结构进行了重新设计和有限元模拟,验证了该设计指导的可行性和有效性。     

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.     

复合材料层合板的铺层几何对结构声传输的影响

采用基于复合材料一阶剪切理论－Mindilin理论的板单元和基于Rayleigh表面分方程的边界元,对嵌在无限障板上的复合材料层合板在低频简谐平面声波斜入射情况下,建立了考虑流体结构耦合的传声计算模型,并利用该模型计算研究了对称角铺设、反对称角铺设和正交铺设等不同铺设方式对层合板传声损失的影响以及在板侧流体介质分别为空气和水时层合板的传声特性,指出层合板的铺层几何对其传声损失有较大影响,应在设计中引起注意。     

对称层合板复合材料的屈曲变形解析

提出了如何利用2 元多项式位移函数来分析层合板复合材料的屈曲问题。在解析中同时 考虑到层合板的面外剪切变形。解析表明屈曲载荷在多项式项数大于20 以上时趋于稳定, 可得到 高精度的解。本文并对对称角铺设层合板进行了系统地数值解析, 明确了在各种边界拘束条件下 材料的工程弹性系数, 层合板长宽比, 铺层数, 层合角对屈曲载荷的影响, 从而以达到优化设计。同 时, 验证了本解析法对任意边界条件下的层合板的屈曲解析是非常有效的。      

Optimal curved fibre orientations of a composite panel with cutout for improved buckling load using the Efficient Global Optimization algorithm

Composite structures with cutouts (like panels with holes) are a challenge to design because discontinuities of this kind provoke stress concentrations and become critical regions. With curved fibres, the effect of these discontinuities can be decreased by choosing the fibre paths properly. In this article, fibre-path optimization to improve the buckling load of laminated composite panels with cutouts is studied. Two fibre path parameterizations are tested: the usual curvilinear Cartesian and the radial one, proposed in this article, in which the fibre orientations vary linearly with the Euclidean distance from the centre of the panel. To reduce the simulation costs associated with the optimization, the Efficient Global Optimization (EGO) algorithm is used. EGO is a technique based on a stochastic process approach (Kriging) that approximates expensive-to-evaluate functions and sequentially maximizes the expected improvement to update the surrogate at each iteration. A stiffened panel with a cutout subjected to compression and in-plane shearing loads is analysed. The results show that the buckling load when curved fibres are used is substantially higher than the buckling load for straight-fibre laminates. In addition, the optimization framework indicates a low final computational burden.     

Load–displacement behavior of glass fiber/epoxy composite plates with circular cut-outs subjected to compressive load

An experimental study of the behavior of woven glass fiber/epoxy composite laminated panels under compression is presented. Compression tests were performed on to 16 fiber-glass laminated plates with and without circular cut-outs using the compressed machine. The maximum load of failure for each of the glass-fiber/epoxy laminated plates under compression has been determined experimentally. A parametric study was performed as well to investigate the effects of varying the centrally located circular cut-out sizes and fiber angle-ply orientations on to the ultimate load. The experimental work revealed that as the cut-out size increases, the maximum load of the composite plate decreases. Also, it has been observed that cross-ply laminates possess the greatest ultimate load as compared to other types of ply stacking sequences and orientations.     

An analytical method for 3-D analysis of circular laminated composite plates

Summary In this paper, an analytical method is presented for 3-D (three-dimensional) researches of laminated composite plates. Using this method, the linear and nonlinear analytical 3-D solutions of high accuracy are obtained for circular laminated composite plates with rigidly clamped edges and under uniform transverse loading. Galerkin's method and the perturbation technique are used to obtained the solutions which satisfy the basic differential equations of linear and nonlinear 3-D problems. The geometric nonlinearity from a moderately large deflection is considered. Many numerical results of displacements and stresses are shown in figures. In the analytical method, there are not any restrictions regrading the stacking sequence of laminated composite plates, so the method may be used to analyze the 3-D problems of unsymmetrical laminated plates.     

Thermomechanical postbuckling analysis of symmetric and antisymmetric composite plates with imperfections

In the present paper the postbuckling response of symmetrically and antisymmetrically laminated composite plates subjected to a combination of uniform temperature distribution through the thickness and in-plane compressive edge loading is presented. The structural model is based on a higher-order shear deformation theory incorporating von Karman nonlinear strain displacement relations. Adopting the Galerkin procedure, the governing nonlinear partial differential equations are converted into a set of nonlinear algebraic equations, which are solved using the Newton–Raphson iterative procedure. The critical buckling temperature is obtained from the solution of the linear eigenvalue problem. Postbuckled equilibrium paths are obtained for symmetrically laminated cross-ply, quasi-isotropic and antisymmetric angle-ply composite plates with and without initial geometric imperfections. Modal participation of each mode in the postbuckling deflection is reported using a multi-term Galerkin procedure.     

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。     

Vibration of symmetrically laminated rectangular composite plates reinforced by intermediate stiffeners

An investigation of the free vibrations of symmetrically laminated rectangular plates with stiffeners based on the Rayleigh-Ritz method is presented. The assumed shape functions used in the formulation are the characteristic beam functions. It is assumed that the stiffeners and the plate are in contact at all times. The effects of the locations and orientations of the stiffeners and their relative bending and torsional stiffness to the plate on the natural frequencies and modes are examined. The effects of material properties and stacking sequence of the laminated plate are also studied.     

复合材料层合板力学性质分析及角铺设层优化设计

基于Kirchhoff经典理论,用样条有限元法以三次B样条函数构成的样条基对反对称多层角铺设层合板的三个独立位移进行插值,推导了复合材料层合板刚度阵,质量阵列式,阻尼阵列式,并由Lagrange方程导出了层合板的动力学方程,通过瑞利一李兹法建立了特征方程。分析了层合板的固有频率及不同层数和不同约束条件下的基频变化等力学特性,在Kirchhoff假设的基础上,对层合板的非线性弯曲的力学特性进行了探讨。基于样条有限元法和遗传算法进行复合材料层合板的角铺设层的优化设计,数值算列验证了算法的有效性。