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.     

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.     

含冲击损伤缝合层板剩余压缩强度

通过对含冲击损伤缝合复合材料层板进行压缩实验,揭示了含损伤缝合层板在压缩载荷下的破坏模式和破坏机制.将冲击损伤等效为圆孔,利用杂交单元计算冲击后缝合层板的应力分布,采用基于特征曲线概念的点应力判据预测了含损伤缝合层板的剩余压缩强度.研究结果表明:冲击损伤近似为圆形;缝合和未缝合层板冲击后压缩的损伤模式不同;采用开口等效法可以有效分析缝合层板的剩余压缩强度;特征距离、损伤面积是影响计算结果的主要因素.     

含冲击损伤缝合层板剩余压缩强度

通过对含冲击损伤缝合复合材料层板进行压缩实验, 揭示了含损伤缝合层板在压缩载荷下的破坏模式和破坏机制。将冲击损伤等效为圆孔, 利用杂交单元计算冲击后缝合层板的应力分布, 采用基于特征曲线概念的点应力判据预测了含损伤缝合层板的剩余压缩强度。研究结果表明: 冲击损伤近似为圆形; 缝合和未缝合层板冲击后压缩的损伤模式不同; 采用开口等效法可以有效分析缝合层板的剩余压缩强度; 特征距离、 损伤面积是影响计算结果的主要因素。     

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.     

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.     

Structural optimization of composite panels under strength and stability restrictions

The paper addresses a problem of optimization of structure of a composite material for smooth panels under strength and stability restrictions. Types of optimal structures have been substantiated. A series of numerical experiments have been carried out to verify the conclusions stated.     

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.     

Structural optimization of composite material for aircraft panels with strength,stability, and deflection restrictions

A theoretical approach is put forward for the structural design (in terms of the number of layers, layer thickness, and reinforcement orientation angle) for laminated composite material of minimalweight aircraft panels with restrictions on their strength, stability, and deflection. We deduce dependences for calculation of potential number of uniform-strength layers in a stack, for which the strength criterion in the form of equality is satisfied. A problem of structural optimization for a composite made up of uniform-strength layers is formulated and solved. The structures with reinforcement orientation angles [0], [90], [0, 90], [±], [±₁, ±₂], [0, ±], [90, ±], and [0, 90, ±] are demonstrated to be the optimal ones, depending on the load type and magnitude. We derived the necessary and sufficient sets of equations for the determination of design parameters. Several examples and particular loading cases are discussed.Translated from Problemy Prochnosti, No. 6, pp. 33–47, November–December, 2004     

多损伤复合材料加筋壁板高周疲劳特性及剩余压缩强度

为研究常用于飞机垂尾的复合材料加筋壁板的冲击疲劳特性,设计了该型加筋壁板多点冲击试验、高周疲劳试验及剩余压缩强度试验。讨论了不同冲击能量对筋条边缘冲击损伤的影响,及施加低应力水平的疲劳载荷后各冲击损伤区域的扩展情况,对比分析了疲劳对冲击后剩余压缩强度的影响。结果表明:40J能量冲击后的损伤面积和凹坑深度较大,C扫描损伤形貌很不规则。100万次低应力疲劳后主损伤区附近衍生出新损伤,导致压缩破坏时产生向上、下夹具扩展的裂痕。该型加筋壁板疲劳后破坏载荷保持率为95.6%,有较好的抗冲击疲劳能力,为加筋壁板耐久性及后屈曲设计提供了思路。     

Designing cutouts for optimum residual strength in plane structural elements

The paper presents a new approach for shape optimisation of structures with residual strength as the design objective. It must be emphasized that flaws are inevitably present in most structures, and hence the influence of cracks on optimised shapes needs to be investigated. Numerical simulation of cracks using the finite element method requires a very fine mesh to model the singularity at crack tip. This makes fracture calculations computationally intensive. Furthermore, for a damage tolerance based optimisation numerous cracks are to be considered along the structural boundary, and fracture analysis needs to be repeated for each crack at every iteration, thus making the whole process extremely computationally expensive for practical purpose. Moreover, the lack of information concerning crack size, orientation, and location makes the formulation of the optimisation problem difficult. As a result, little attention has been paid to date to consider fracture parameters in the optimisation objective. To address this, the paper presents a methodology for the shape optimisation of structures with strength and durability as the design objectives. In particular, the damage tolerance optimisation is illustrated via the problem of optimal design of a ‘cutout in a rectangular block under biaxial loading’. A parametric shape representation has been used to describe the problem geometry. Damage tolerance based optimisation was performed using nonlinear programming algorithms, and NE-NASTRAN was used for finite element analysis. The first order mathematical programming algorithms, viz: the Broydon–Fletcher–Goldfarb–Shanno (BFGS) and the Fletcher–Reeves (Conjugate Direction) Methods were evaluated as the potential algorithms for optimising the residual strength in the presence of flaws. Another recently developed Sequential Unconstrained Minimisation Technique (SUMT), based on an exterior penalty function method and especially suited for large problems, was also investigated for fracture based optimisation. The effects of the orientation and the number of boundary cracks on the optimal solutions were also studied. It has been shown that the residual strength optimised shapes can be different from the corresponding and commonly adopted stress optimised solution. This emphasises the need to explicitly consider residual strength as the design objective. In all cases a significant reduction in the maximum stress intensity factor was achieved with the generation of a ‘near’ uniform fracture critical surface. The design space near the optimal region was found to be relatively flat. This is beneficial as a significant structural performance enhancement is important rather than precise identification of the local/global optimum solution. The optimal solutions obtained using the nonlinear programming algorithms were compared against those obtained in the literature using a heuristic optimisation method (Biological algorithm). The results obtained using the two methods, employing inherently different (gradient-based and gradient-less) algorithms, were found to agree very well.     

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.     

复合材料加筋板低速冲击损伤及剩余压缩强度试验研究

采用落锤法对复合材料加筋板进行了低速冲击损伤（LVI）试验,根据复合材料加筋板构型,设计了冲击支持支架,研究了支持支架的间距对冲击结果的影响;用相同的冲击能量对复合材料加筋板结构中3处典型位置进行冲击,得到不同位置的损伤形貌;分别对完好件和损伤试验件进行压缩试验,将试验结果进行对比,分析不同位置的冲击损伤对结构压缩性能的影响。试验结果表明：在相同的冲击能量下,支持支架间距越小,所造成的冲击损伤越严重;在50 J冲击能量下,筋条区蒙皮处的冲击所造成的损伤不易观察,筋条间蒙皮处的冲击所造成的损伤最为明显,而筋条边缘蒙皮处的冲击可以导致筋条边缘的脱粘;冲击损伤会使加筋板屈曲载荷轻微下降,筋条间蒙皮和筋条区蒙皮冲击损伤对压缩结果影响相对较小,筋条边缘处的冲击会引起损伤处蒙皮的子层屈曲,并影响结构破坏形式,使结构压缩承载能力有较为明显的下降。     

Postbuckling analysis of composite panels with imperfection damage

In order to promote the efficient use of composite materials in civil engineering infrastructure, effort is being directed at the development of design criteria for composite structures. Insofar as design with regard to buckling of composite shells is concerned, it is well known that a key step is to investigate the influence of initial geometric imperfection. At present, imperfection sensitivity study of composite shells has not been explored in detail. Thus, the objective of this paper is to present the formulation used in developing a composite shell element and to validate the element from the composite curved panel. The non-linear formulation of the shell element is based on the updated Lagrangian method. The shell element is capable of small strain and large displacement analysis with finite rotations. In order to remove the rigid body rotation, a co-rotational method is used. Subsequently the postbuckling analyses from the modeling of the curved panel with initial imperfection damage are performed to investigate the effect of initial geometric imperfection shape and amplitude. The results are used to estimate imperfection sensitivity for such panels.     

Characteristics of joining inserts for composite sandwich panels

Composite sandwich constructions are widely employed in various light weight structures, because composite sandwich panels have high specific stiffness and high specific bending strength compared to solid panels. Since sandwich panels are basically unsuited to carry localized loads, the sandwich structure should provide joining inserts to transfer the localized loads to other structures.In this work, the load transfer characteristics of the partial type insert for composite sandwich panels were investigated experimentally with respect to the insert shape. The static and dynamic pull out tests of the composite sandwich panels composed of an aluminum honeycomb core, two laminates of carbon fiber/epoxy composite and aluminum insert, were performed. From the experiments, the effect of the insert shape on the mechanical characteristics of composite sandwich panels was evaluated.     

Smart composite panels with embedded peak strain sensors

Composite laminates are finding increasing use in load bearing structures of a safety critical nature. This trend means that it becomes increasingly important to be able to measure the accumulated damage within safety critical composite panels. The current research approaches include the use of piezoelectric patches, fibre optics, and even the intrinsic piezoresistive properties of carbon fibres themselves. The aforementioned methods do, however, suffer various difficulties in terms of manufacturing considerations, as well as the complexities associated with some of the monitoring equipment needed to interpret damage levels. A more robust concept has however recently seen development, which relies on embedding metastable ferrous elements or wires within the laminate. Not only can this smart material easily withstand the processing temperatures; but if correctly used, the elements may impart significant load-bearing capacity to the laminate. The damage assessment equipment is simple and can in fact be operated by a person with no specialised training.     

Residual strength of aircraft panels with multiple site damage

Multiple site damage (MSD) is a type of cracking that may be found in aging airplanes which can adversely affect the damage tolerance of an airframe structure. In this paper the behavior of MSD is studied by examining the interaction of cracks in stiffened and riveted panels. The hybrid finite element method, in conjunction with the complex variable theory of elasticity, is used to provide accurate and efficient solutions to these problems. Typical results include stress intensity factors at the crack tips, stress concentration factors in the stiffeners, and rivet loads for a stiffened structure with multiple cracks. Particular emphasis is placed on the derivation and interpretation of residual strength diagrams. This study produces a better understanding of the interaction between multiple cracks and provides insight for avoiding MSD in future designs.This work was supported by the Technical Center, Federal Aviation Administration, U.S. Department of Transportation     

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.     

含离散源损伤复合材料加筋板的拉伸特性

通过对含有离散源损伤的复合材料加筋板的拉伸试验和有限元模拟,研究了离散源损伤的损伤扩展与破坏特性。结果表明:复合材料加筋板的离散源损伤用穿透蒙皮切断桁条的切口来模拟是合适的,蒙皮上的穿透切口前端有很高的应力集中,桁条被切断导致加筋板传力路线改变;基于Hashin失效准则的渐进损伤有限元数值模拟方法,可以有效地模拟含切口加筋板的宏观损伤扩展和破坏过程,计算结果与试验值吻合较好。