Edge-cracked stiffened panels analyzed by caustics

Externally bonded composite patches have been proven to be an effective method for repairing damaged aircraft structural components. They are ease in application and provide excellent in-service performance. The major function of a repair is to reduce the stress intensity factor at the crack tip. Calculation of stress intensity factor of a repaired crack has been performed by analytical and numerical methods. However, these methods are based on simplifying assumptions regarding material behavior and repair conditions. In the present paper an experimental determination of mode-I stress intensity factor (SIF), K_I, at the tip of an edge-crack or a V-notch reinforced with double bonded strips or with compression pre-stresses applied along the crack surfaces is undertaken by using the optical method of caustics. This method is simple in its application and has successfully been used for the solution of a host of crack problems of engineering importance.     

Dynamic near three-to-one internal resonance in composite stiffened panels

Nonlinear dynamic of composite stiffened panels to parametric and three-to-one internal resonances is investigated. The ordinary differential equation of two mode shapes is established by using Galerkin method and the condition of three-to-one internal resonance between the first mode (1,3) and the second mode (3,1) is examined near the principal resonance 2:1 of the first mode. Then, the nonlinear behavior of the two buckling mode shapes is analyzed using a perturbation analysis. We show the existence of jump phenomena for the two modes indicating a complex dynamic of the structure near the three-to-one internal resonance for the HM Graphite/epoxy materials.     

Fracture mechanics analysis of curved stiffened panels using BEM

A dual boundary element method is developed for a analysis of reinforced cracked shallow shells. Boundary integral equations are derived from the Betti’s reciprocal theorem for a cracked shallow shell with transverse frames and longitudinal stiffeners. The effect of frames and stiffeners are treated as a distribution of line body forces. The radial basis function is used to transform domain integrals to boundary integrals. Stress intensity factors are evaluated from crack opening displacements. The effect of curvature on the stress intensity factors is illustrated by numerical examples. Three examples are presented to demonstrate the accuracy of this method compared with solutions obtained using the finite element method.     

Piezo-electric control of stiffened panels subject to interactive buckling

The paper examines the feasibility of piezo-electric control of stiffened plates carrying axial compression and subject to interaction of local and overall buckling. A simple control strategy involving piezo-electric patches along the tips of the stiffeners carrying equal and opposite electric fields to resist bending of the stiffeners was found to effectively counteract the adverse effects of mode interaction and imperfection-sensitivity. For the dynamic problem, this strategy needed to be supplemented with patches attached to the surfaces of the plate in the middle of the panel to damp out local buckling oscillations. Two panels were considered, these being scaled replicas of each other. This enabled an examination of the scaling laws of response with practical applications in view. The results demonstrate that the structural performance of optimally designed stiffened structures can be enhanced with minimal energy consumption by appropriately designed piezo-electric patch configuration.     

Influence of post-buckling behaviour on optimum design of stiffened panels

For an eccentrically stiffened wide panel under compression the optimality of a design with simultaneous occurrence of buckling as a wide Euler column and local buckling of the plate between the stiffeners is investigated. The total amount of material per unit width of the panel is prescribed. As a function of the distribution of this material in the plate and the stiffeners the maximum carrying capacities are calculated approximately by application of Galerkin's method. The design with the highest carrying capacity and the design with the best ability to retain axial stiffness, corresponding to given imperfections, are determined. It is shown that imperfections move the optimum away from the coincident buckling mode design.     

复合材料加筋板极限压缩承载能力可靠性分析

基于Abaqus软件用户子程序,利用渐进失效分析方法对复合材料加筋板极限压缩承载能力进行预测。算例分析表明,对于加筋板1和2,本文方法给出的极限压缩强度与实验结果的误差分别为2.53%和1.68%。在结构可靠性分析过程中,为提高计算效率,利用屈曲载荷与极限压缩强度之间的关系建立功能函数,只需对极限压缩承载能力进行一次分析。对于加筋板1和2,本文方法相对经典可靠性方法的计算误差分别为-1.04%和-1.01%,计算时间仅为经典可靠性方法的1.18%和1.66%。     

含预置损伤复合材料加筋板的单轴压缩屈曲分析

通过试验和有限元方法分析了单轴压缩下加筋板的失效模式.研究了三种预置损伤位置及四种损伤尺寸的复合材料T型加筋板的线性及非线性屈曲行为,比较了损伤对临界屈曲载荷和最大失效载荷的影响.研究结果表明:损伤位置在桁条间蒙皮时,损伤的尺寸对其临界屈曲载荷和最大失效载荷影响较小;损伤位置在桁条区蒙皮时,加筋板的临界屈曲载荷随损伤尺寸的增加而明显降低,最大降低50%;损伤位置在桁条边凸缘处蒙皮时,加筋板最大失效载荷所受影响随损伤尺寸的增加而明显降低,最大降低25%.从而得到了复合材料加筋板临界屈曲载荷比和最大失效载荷比与损伤位置及尺寸的关系图.     

Theoretical analysis of the sound absorption characteristics of periodically stiffened micro-perforated plates

The vibro-acoustic responses and sound absorption characteristics of two kinds of periodically stiffened micro-perforated plates are analyzed theoretically. The connected periodical structures of the stiffened plates can be ribs or block-like structures. Based on fundamental acoustic formulas of the micro-perforated plate of Maa and Takahashi, semi-analytical models of the vibrating stiffened plates are developed in this paper. Approaches like the space harmonic method, Fourier transforms and finite element method （FEM） are adopted to investigate both kinds of the stiffened plates. In the present work, the vibro-acoustic responses of micro-perforated stiffened plates in the wavenumber space are expressed as functions of plate displacement amplitudes. After approximate numerical solutions of the amplitudes, the vibration equations and sound absorption coefficients of the two kinds of stiffened plates in the physical space are then derived by employing the Fourier inverse transform. In numerical examples, the effects of some physical parameters, such as the perforation ratio, incident angles and periodical distances etc., on the sound absorption performance are examined. The proposed approaches are also validated by comparing the present results with solutions of Takahashi and previous studies of stiffened plates. Numerical results indicate that the flexural vibration of the plate has a signif- icant effect on the sound absorption coefficient in the water but has little influence in the air.     

Buckling analysis of discretely stiffened composite curved panels under compression and shear

An analytical method for the buckling discretely thin-wall stiffened composite curved panels under compression and shear is presented by use of finite strip-element method.In the report a simplified scheme for complex displacement functions is developed. It enables that computation to be performed in real number algebra easily. And a simple and easy way to satisify the boundary conditions is introduced.Numerical results are given and are in good agreement with available data.     

Buckling of eccentrically stiffened elastic-plastic panels on two simple supports or multiply supported

Buckling due to axial compression is investigated for elastic-plastic, stiffened wide panels either continuous in the longitudinal direction over several transverse supports or finite and supported along the two edges. An analytical treatment is given of the bifurcation behaviour and of the initial post-bifurcation behaviour of perfect panels compressed into the plastic range. The behaviour of initially imperfect panels is computed numerically using an incremental method. In each increment a linear problem is solved by a combined Rayleigh Ritz-finite element method. Computed examples show a considerable imperfection-sensitivity, both for panels that bifurcate in the plastic range, and for panels with a yield stress a little above the elastic bifurcation stress.     

A direct complex stress function approach for modelling stiffened panels containing multiple site damage

The analysis of stiffened panel structures containing multiple site damage (MSD) is addressed through the complex variable method, in association with the requirement for displacement compatibility. The method is extended by replacing the usual single crack stress and displacement functions by those for a series of arbitrary straight collinear cracks which are used to model exactly the main and secondary crack damage in the sheet. It is shown that the problem can be reduced to a system of linear equations for the unknown forces at the attachment points between the sheet and the stiffener from which the stress intensity factor of the collinear cracks can be determined. The stress intensity factor and the attachment force distribution are determined for several configurations and compared with those from numerically based approaches.     

Wave localization in randomly disordered periodic layered piezoelectric structures

Considering the mechnoelectrical coupling, the localization of SH-waves in disordered periodic layered piezoelectric structures is studied. The waves propagating in directions normal and tangential to the layers are considered. The transfer matrices between two consecutive unit cells are obtained according to the continuity conditions. The expressions of localization factor and localization length in the disordered periodic structures are presented. For the disordered periodic piezoelectric structures, the numerical results of localization factor and localization length are presented and discussed. It can be seen from the results that the frequency passbands and stopbands appear for the ordered periodic structures and the wave localization phenomenon occurs in the disordered periodic ones, and the larger the coefficient of variation is, the greater the degree of wave localization is. The widths of stopbands in the ordered periodic structures are very narrow when the properties of the consecutive piezoelectric materials are similar and the intervals of stopbands become broader when a certain material parameter has large changes. For the wave propagating in the direction normal to the layers the localization length has less dependence on the frequency, but for the wave propagating in the direction tangential to the layers the localization length is strongly dependent on the frequency.The project supported by National Natural Science Foundation of China (10632020, 10672017 and 20451057).     

含冲击损伤复合材料层板及加筋壁板剩余强度研究

应用含刚度折减的椭圆形弹性核模拟了层板的损伤问题,研究了复合材料层板及加筋壁板冲击后的剩余强度问题。利用含椭圆核各向异性杂交应力有限单元对损伤层板进行了应力分析,采用基于特征曲线概念的点应力判据预测了含损伤层板、加筋壁板的剩余强度;基于Abaqus用户子程序uel实现了该方法在工程中的应用,并讨论各种参数对剩余强度的影响。研究结果表明此方法是有效的。     

无穷大周期加筋微穿孔板结构振动响应及吸声特性

研究在平面声波斜入射情况下,无穷大双周期加筋的微穿孔薄板结构的振动响应及吸声性能.首先在马大猷和Takahashi微穿孔板声学理论基础上,建立了微穿孔加筋薄板结构振动的半解析模型;然后应用傅里叶变换及空间波数分析方法,将周期加筋微穿孔薄板的振动位移及辐射声压表示为频域内波数的分量迭加形式;最后通过对波数分量进行求解,并利用傅里叶逆变换得到双周期加筋的微穿孔薄板的振动响应及吸声系数表达式.计算结果表明,薄板的弯曲振动在水中对吸声的影响较大,空气中仅对轻质穿孔板的低频吸声效果有一定影响;同时微穿孔率对周期加筋薄板吸声系数的影响明显,通过改变穿孔率和加筋周期等可有效地提高水中微穿孔薄板结构的吸声性能.     

Vibration of stiffened annular sector plates using the spline element method

Summary Vibrations of a stiffened annular sector plate with arbitrary boundary conditions are analysed using the spline element method. The plate is idealized as a system of an annular sector plate and curved beams rigidly connected to each other. To demonstrate the accuracy of the present method several examples are solved, and the results are compared with those obtained analytically and by other numerical methods. Good accuracy is obtained. The effect of stiffening beams on the frequencies of stiffened annular sector plates is also investigated.

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Bestimmung der Schwingungen versteifter Kreisringsegment-Platten mit Hilfe der Spline-Element-Methode

Übersicht Die Schwingungen versteifter Sektorplatten werden mittels der Spline-Element-Methode untersucht. Die Platte wird als ein System von Sektorplatte und gebogenen Trägern idealisiert. An Zahlenbeispielen wird gezeigt, daß bezüglich der üblichen analytischen Methode und numerischen Methoden die genaue Lösung erhalten wird. Der Effekt versteifender, gebogener Träger auf die Frequenzen wird untersucht.

     

Wave localization in a disordered periodic viaduct undergoing out-of-plane vibration

In this contribution, wave localization in a disordered periodic viaduct (DPV) undergoing out-of-plane vibration is investigated. The DPV is assumed to be composed of infinite spans with each span deviating from the standard span slightly. Each span is supposed to be composed of two longitudinal beams and a pier linked by three springs. By using the governing equations for the pier and beams as well as the joint conditions at the beam-beam-pier junction, the transfer matrix for each span of the viaduct undergoing out-of-plane vibration is derived. Based on the derived transfer matrix for each span, the wave transfer matrices for the spans of the DPV are obtained. According to the Wolf’s algorithm, the Lyapunov exponents for the wave motion of the DPV are calculated. With the proposed model, the influences of the pier-height and beam-length disorders on the wave localization are examined. Also, the interactive effect of the damping and disorders on the wave localization in the DPV is investigated. Moreover, by the wave transfer matrix method, the wave conversion phenomenon in the DPV is studied.     

Vibration damping characteristics of a thin cylindrical shell stiffened with viscoelastic rings

Summary The vibrations of a circular cylindrical shell reinforced with viscoelastic rings are theoretically treated. The frequency equation is derived using the transfer matrix together with the stiffness matrix. The numerical example surveys the damping effect of viscoelastic rings upon the dynamic behavior of the system.

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Übersicht Die Schwingungen einer durch viskoelastische Kreisringe versteiften dünnwandigen Kreiszylinderschale werden theoretisch behandelt. Die Frequenzgleichung wird durch eine Kombination der Übertragungsmatrix mit der Steifigkeitsmatrix abgeleitet. An numerischen Beispielen wird ein Überblick über die dämpfende Wirkung der viskoelastischen Kreisringe auf das dynamische Verhalten des Systems gewonnen.

     

Reliability assessment of post-buckling compressive strength of laminated composite plates and stiffened panels under axial compression

A method for reliability assessment of the post-buckling compressive strength of laminated composite plates and stiffened panels under axial compression is presented in the paper. The prediction of the post-buckling compressive strength is performed by a progressive failure analysis which was developed based on a progressive stiffness degradation model and a nonlinear finite element analysis with a new explicit through-thickness integration scheme. A method coupled with the finite element analysis is proposed for reliability assessment where a finite difference method combined with an improved first-order reliability algorithm that omits the non-important random variables but retains sufficient accuracy was developed for reliability estimation. Two numerical examples are described demonstrating the capabilities of the method developed.     

Study on wave localization in disordered periodic layered piezoelectric composite structures

The two-dimensional wave propagation and localization in disordered periodic layered 2-2 piezoelectric composite structures are studied by considering the mechanic-electric coupling. The transfer matrix between two consecutive sub-layers is obtained based on the continuity conditions. Regarding the variables of mechanical and electrical fields as the elements of the state vector, the expression of the localization factors in disordered periodic layered piezoelectric composite structures is derived. Numerical results are presented for two cases—disorder of the thickness of the polymers and disorder of the piezoelectric and elastic constants of the piezoelectric ceramics. The results show that due to the piezoelectric effects, the characteristics of the wave localization in disordered periodic layered piezoelectric composite structures are different from those in disordered periodic layered purely elastic ones. The wave localization is strengthened due to the piezoelectricity. And the larger the piezoelectric constant is, the larger the wave localization factors are. It is found that slight disorder in the piezoelectric or elastic constants of the piezoelectric ceramics can lead to more prominent localization phenomenon.     

Vibration analysis of laminated composite cylindrical panels via a meshfree approach

In this paper, the free vibration of laminated composite cylindrical panels is solved by the meshfree (meshless) approach. The reproducing kernel particle approximation is employed to model the two-dimensional displacement functions. The effects of the particle distribution and the size of the domain of influence, on the convergence behavior, are studied. This study examines in detail the effects of different boundary conditions on the frequency characteristics of the cylindrical panels. The effects of the curvature of the cylindrical panels as well as the lamination scheme, on the frequencies of the panels, are also investigated. The present results are verified by comparison against results available in the open literature, with very good agreement being attained.