Cutout reinforcements for shear loaded laminate and sandwich composite panels

This paper presents the numerical and experimental studies of shear loaded laminated and sandwich carbon/epoxy composite panels with cutouts and reinforcements aiming at reducing the cutout stress concentration and increasing the buckling stability of the panels. The effect of different cutout sizes and the design and materials of cutout reinforcements on the stress and buckling behaviour of the panels are evaluated. For the sandwich panels with a range of cutout size and a constant weight, an optimal ratio of the core to the face thickness has been studied for the maximum buckling stability. The finite element method and an analytical method are employed to perform parametric studies. In both constant stress and constant displacement shear loading conditions, the results are in very good agreement with those obtained from experiment for selected cutout reinforcement cases. Conclusions are drawn on the cutout reinforcement design and improvement of stress concentration and buckling behaviour of shear loaded laminated and sandwich composite panels with cutouts.     

Free vibration of composite rectangular plates with rectangular cutouts

A simple numerical method based on the Rayleigh principle is presented for predicting the natural frequencies of composite rectangular plates which exhibit special and general orthotropy. The method is illustrated for simply-supported rectangular plates having central rectangular cutouts and double square cutouts. The results are compared with the reported finite element and analytical results.     

Global/local analysis of composite plates with cutouts

 The study focuses on the development of a simple and accurate global/local method for calculating the static response of stepped, simply-supported, isotropic and composite plates with circular and elliptical cutouts. The approach primarily involves two steps. In the first step a global approach, the Ritz method, is used to calculate the response of the structure. Displacement based Ritz functions for the plate without the cutout are augmented with a perturbation function, which is accurate for uniform thickness plates only, to account for the cutout. The Ritz solution does not accurately satisfy the natural boundary conditions at the cut-out boundary, nor does it accurately model the discontinuities caused by abrupt thickness changes. Therefore, a second step, local in nature is taken in which a small area in the vicinity of the hole and encompassing other points of singularities is discretized using a fine finite element mesh. The displacement boundary conditions for the local region are obtained from the global Ritz analysis. The chosen perturbation function is reliable for circular cutout in uniform plates, therefore elliptical cutouts were suitably transformed to circular shapes using conformal mapping. The methodology is then applied to the analysis of composite plates, and its usefulness successfully proved in such cases. The proposed approach resulted in accurate prediction of stresses, with considerable savings in CPU time and data storage for composite flat panels.     

Effects of Cut-Out Orientation and Fiber Angle on Stress Concentration in an Infinite Orthotropic Plate

Abstract

The presence of cutout in structures may result in strength degradation due to alteration of load lines around the cutout. The effects of these cutouts on stress field should be studied carefully while designing of any material. This article presents the optimum design of an infinite orthotropic plate weakened by complex cutout using a genetic algorithm where cutout orientations and fiber angles are considered as design variables. The stress concentration factor is used as fitness function derived using the Muskhelishvili’s complex variable approach for various in-plane loadings. The effects of cutout orientation and fiber angles on stress concentration are discussed.     

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.     

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.     

Effective widths of compression-loaded of perforated cross-ply laminated composites

In this study the influence of eccentric circular cutouts on the prebuckling and postbuckling stiffness, and effective widths of compression loaded laminated composite plates are presented. The effective-widths concept is derived based on nonlinear finite element analysis for the plates with and without cutout. Several behavioral trends are described that initially appear to be nonintuitive. The results demonstrate a complex interaction between cutout size and the degree of plate orthotropy that affects the axial stiffness and effective width of plate subjected to compression loads. Also these investigations show that the cutout dimension have a more considerable effect on prebuckling stiffness compare to postbuckling one. It will show that the stiffness ratio of the postbuckling over prebuckling is increased by cutout size. Considering the effective-width ratios concept provide a simple means for incorporating the postbuckling strength and stiffness of plate subcomponents into the design of stiffened structures.     

Finite element dynamic stability analysis of laminated composite skew plates containing cutouts based on HSDT

The finite element dynamic stability analysis of laminated composite skew structures subjected to in-plane pulsating forces is carried out based on the higher-order shear deformation theory (HSDT). The two boundaries of the instability regions are determined using the method proposed by Bolotin. The numerical results obtained for square and skew plates with or without central cutout are in good agreement with those reported by other investigators. The new results for laminated skew plate structures containing cutout in this study mainly show the effect of the interactions between the skew angle and other various parameters, for example, cutout size, the fiber angle of layer and thickness-to-length ratio. The effect of the magnitude of the periodic in-plane load on the dynamic instability index is also investigated.     

Collapse analysis of composite cylindrical panels with small cutouts

A finite element study was conducted to determine the effects of notches on the load bearing capability and radial displacements of axially loaded composite cylindrical panels. The panel considered assumed that eight symmetrically placed graphite/epoxy plies were used. A mesh refinement in the vicinity of the cutout was conducted in order to study the non-linear collapse analysis. In addition, the effect of different size cutouts with aspect ratios (axial dimension of cutout divided by circumferential dimension) of 2·0 and 0·5 was studied. The findings indicated that as the surface area of the cutout increased, the buckling load decreased. Cutouts with aspect ratios of 2·0 appeared to be capable of carrying higher loads than notches with an aspect ratio of 0·5.     

Mechanical Buckling Analysis of Composite Panels with/without Cutouts

A simplified analytical solution suitable for simple stacking sequences was developed using the Euler buckling theory,the structure’ s equations of equilibrium and laminate panel mathematical formulation.Comparing these results with numerical results reveals the accuracy of the method and even more,allows us to validate the numerical analysis.Therefore,two important results are obtained:a simplified analytical solution for the buckling problem and validation of the numerical results.Another important and novel finding is related to the influence of the angle ply orientation and of the cutouts,on the buckling load.Under symmetrical boundary conditions and loading case,rectangular panels with elliptical cutouts,give better results for 90° oriented plies than for 0 oriented ones.With a compression load applied in the X direction,and with material properties 10 times better in X direction than in Y direction,the best results are obtained when the load is aligned with the Y direction associated to the material reference frame.Moreover,panels with cutouts seem to behave better than panels without cutouts under certainply orientation angles.     

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。     

Maximization of fundamental frequency of axially compressed laminated curved panels with cutouts

Free vibration analyses of laminated curved panels with central circular cutouts and subjected to axial compressive forces are carried out by employing the Abaqus finite element program. The fundamental frequencies of these composite laminated curved panels with a given material system are then maximized with respect to fiber orientations by using the golden section method. Through parametric studies, the significant influences of the panel aspect ratio, the panel curvature, the cutout size and the compressive force on the maximum fundamental frequencies, the optimal fiber orientations and the associated fundamental vibration modes of these panels are demonstrated and discussed.     

Local fibre reinforcement of holes in composite multilayered plates

For various technical reasons, cutouts such as holes in thin-walled structures are inevitable and are of significant technical relevance. Unfortunately holes lead to an undesired stress concentration at the hole vicinity and a reduced strength of the structure. Therefore in practice a local reinforcement in the form of a ring is usually applied around the hole. The increasing requirements for modern structures in terms of low weight and high strength lead to the question of an optimal reinforcement design. The present paper addresses the new but well-approved techniques of the use of curved fibre format to determine the aforementioned optimal design of the reinforcement. The optimization of cutouts in laminated composite plates under bi-axial tensile loading conditions has been investigated using two approaches: the finite element and the Rayleigh-Ritz method. The used methodology implemented successfully theoretical results based on the complex potential theory. For the considered problems, the proposed methods were shown to successfully produce a constant objective function around the hole boundary under biaxial loading. The optimal reinforcement of holes in laminated composite plates illustrated that the optimum depends on the degree of orthotropy. Significant reduction of stress concentrations were demonstrated. The results obtained illustrate the necessity and usefulness of the applied optimization procedure.     

剪切载荷下含椭圆形大开口层合板的试验研究

在面内纯剪切载荷作用下, 采用试验与有限元模拟方法研究了结构中心设置椭圆形大开口的正方形复合材料层合板的应力/应变集中现象及屈曲、 后屈曲行为, 通过测试结果对试验件失效模式进行了评估。研究结果表明: 层合板开口附近应力/应变集中程度很高; 大尺寸开口使结构稳定性显著降低, 且开口层合板具有较好的后屈曲承载能力; 由于弯曲产生高水平的层间应力, 导致局部分层损伤并伴有基纤剪切破坏; 随着横向挠度的增加, 各应力集中区域的纤维发生拉伸断裂, 导致整体结构瞬间发生脆性失效。有限元模拟结果与试验结果符合较好。     

The effect of cutout positioning on the dynamic characteristics of a curved composite panel

An investigation of the effects of eccentrically located square cutouts on the natural frequencies and mode shapes of circular, cylindrical composite panels was conducted. A video holographic interferometry technique was used to determine experimentally the first five natural frequencies and mode shapes of the panels. Numerically, predictions for these same data were obtained using a finite element method. A clamped-free-clamped-free boundary condition was selected for this study. Cutouts were eccentrically located in both the circumferential and axial directions. The experimental and numerical results for both the natural frequencies and mode shapes correlated well. The per cent differences between the experimental and numerical frequencies averaged around 7% and were in all cases less than 10%. It was observed that, in general, panels with eccentrically located cutouts experienced only small frequency deviations from those with centered cutouts. The amount of variation observed tended to increase with cutout size.     

Thermomechanical postbuckling of multilayered composite panels with cutouts

The results of a study of the detailed thermomechanical postbuckling response characteristics of flat unstiffened composite panels with central circular cutouts are presented. The panels are subjected to combined temperature changes and applied edge loading (or edge displacements). The analysis is based on a first-order shear deformation plate theory. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the plate. The postbuckling displacements, transverse shear stresses, transverse shear strain energy density, and their sensitivity coefficients are evaluated. The sensitivity coefficients measure the sensitivity of the post-buckling response to variations in the different lamination and material parameters of the panel. Numerical results are presented showing the effects of the variations in the hole diameter, laminate stacking sequence, fiber orientation, and aspect ratio of the panel on the thermomechanical postbuckling response and its sensitivity to changes in panel parameters.     

A complex potential-variational formulation for thermo-mechanical buckling analysis of flat laminates with an elliptic cutout

A semi-analytical method is developed for pre-buckling and buckling analyses of thin, symmetrically laminated composite panels with an elliptical cutout at an arbitrary location and orientation under general thermo-mechanical loading conditions. Both the pre-buckling and buckling analyses are based on the principle of stationary potential energy utilizing complex potential functions and complete polynomials. The complex potential functions capture the steep stress gradients and local deformations around the cutout, and the “complete” polynomials improve the global buckling response of the laminate. The complex potential functions in the pre-buckling state automatically satisfy the in-plane equilibrium equations, thus reducing the first variation of the total potential energy in terms of line integrals only. Because the complex potential functions for out-of-plane displacements are augmented by the “complete” polynomials, the area integral terms in the second variation of the total potential energy, referred to as the Treftz criterion, are retained in the buckling analysis. The kinematic boundary conditions are idealized by employing extensional and rotational springs (elastic restraints) with appropriate stiffness values. Based on the numerous validation problems, this analysis is proven credible for predicting the buckling load of rectangular and non-rectangular panels with a cutout.     

爆炸载荷作用下双向加筋方板的大挠度塑性动力响应

从分别列出加筋板面板以及加强筋的运动方程出发,分析了爆炸载荷作用下双向加筋固支方板的大挠度塑性动力响应。分析表明:取决于加强筋的相对刚度以及爆炸载荷峰值的大小,加筋板的运动将呈现3种不同的模式。该文限于讨论加筋板的总体变形模式,具体讨论了十字加筋以及双十字加筋固支方板在忽略弯矩影响下的薄膜解法。理论结果与已有的试验结果在多数情况下符合良好,表明该文提出的简化理论分析方法能对爆炸载荷下双向加筋方板的永久变形做出较为合理的预报。     

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.     

Postbuckling strengths of composite laminate with various shaped cutouts under in-plane shear

The aim of present investigation is to study the buckling and postbuckling response and strengths under positive and negative in-plane shear loads of simply-supported composite laminate with various shaped cutouts (i.e., circular, square, diamond, elliptical-vertical and elliptical-horizontal) of various sizes using finite-element method. The FEM formulation is based on the first order shear deformation theory which incorporates geometric nonlinearity using von Karman’s assumptions. The 3-D Tsai-Hill criterion is used to predict the failure of a lamina while the onset of delamination is predicted by the interlaminar failure criterion. The effect of cutout shape, size and direction of shear load on buckling and postbuckling responses, failure loads and failure characteristics of quasi-isotropic [i.e., (+45/−45/0/90)_2s] laminate has been discussed. In addition, the effect of composite lay-up [i.e., (+45/−45/0/90)_2s, (45/−45)_4s and (0/90)_4s] has also been reported. It is observed that the cutout shape has considerable effect on the buckling and postbucking behaviour of the quasi-isotropic laminate with large size cutout. It is also observed that the direction of shear load and composite lay-up have substantial influence on strength and failure characteristics of the laminate.