Parametric study of the post-buckling strength of structural core sandwich panels

Post-buckling strength of simply supported orthotropic corrugated board panels subjected to edge compressive loading has been investigated using geometrically non-linear finite element analysis (FEA). Adjustments of the transverse shear stiffnesses in the FEA were necessary and performed by comparing the critical buckling load calculated by FEA with a closed form solution. The collapse load of the sandwich plate was calculated based on material failure of the facings predicted from Tsai-Wu failure theory. Parametric studies were performed to investigate the sensitivity of the collapse load to changes in the transverse shear stiffnesses of the core, initial out-of-plane imperfections, asymmetry in board construction, slenderness ratio and eccentric loading of the plate. It was found that a reduction of the transverse shear stiffnesses of the core below a certain limit produces a significant reduction in the collapse load. Panels are said to be insensitive to imperfections and this holds true when the imperfections are the same as or lesser than the thickness of the panel, but a 40% reduction of the collapse load is observed for imperfections that are ten times the panel thickness. From a design point of view it is shown that a symmetrical board is preferred because an asymmetric board as well as eccentric loading of the panel significantly reduce the collapse load. It is also shown that the critical buckling load is directly related to the slenderness ratio of the panel whereas the collapse load is not.     

Compressive and shear buckling analysis of metal matrix composite sandwich panels under different thermal environments

Combined inplane compressive and shear buckling analysis was conducted on flat rectangular sandwich panels using the Rayleigh-Ritz minium energy method with a consideration of transverse shear effect of the sandwich core. The sandwich panels were fabricated with titanium honeycomb core and laminated metal matrix composite face sheets. The results show that slightly slender (along the unidirectional compressive loading axis) rectangular sandwich panels have the most desirable stiffness-to-weight ratios for aerospace structural applications; the degradation of buckling strength sandwich panels with rising temperature is faster in shear than in compression; and the fiber orientation of the face sheets for optimum combined-load buckling strength of sandwich panels is a strong function of both loading condition and panel aspect ratio. Under the same specific weight and panel aspect ratio, a sandwich panel with metal matrix composite face sheets has a much higher buckling strength than one having monolithic face sheets.     

Battle damage repair of a helicopter composite frame-to-skin junction – A sole external repair approach

Research was conducted to examine the effectiveness of a rapid repair to a helicopter composite frame-to-skin junction subjected to battlefield damage. The repair design consists of a laminate patch and aluminium angle bracket adhesively bonded and riveted, respectively, to the helicopter external surface. The assessment involved a relative comparison of three models, representing pristine, damaged and repaired configurations. Computational analyses were conducted to examine the stiffness and buckling onset load of the overall structure and the strengths of individual components (laminates, adhesive bondlines and rivets) under three typical load conditions, namely in-plane shear, axial compression and transverse compression. The results showed that the damage would cause significant stiffness and strength reduction. The repair could sufficiently restore the stiffness and static strength for the load cases considered. However, for the specimen without support from its adjacent helicopter structure, it is predicted that the failure mode under the transverse compression loading would be via buckling under a relatively low load. A compression test was conducted to further validate the repair design. The result agreed well with the prediction. It showed that compared with an un-repaired damaged specimen, the external repair increased the strength by 83%. The equivalent far field failure strain exceeded 3300 με which is considered satisfactory for a rapid field battle damage repair (BDR).     

Mechanical buckling of functionally graded material cylindrical shells surrounded by Pasternak elastic foundation

In this study, the mechanical buckling of functionally graded material cylindrical shell that is embedded in an outer elastic medium and subjected to combined axial and radial compressive loads is investigated. The material properties are assumed to vary smoothly through the shell thickness according to a power law distribution of the volume fraction of constituent materials. Theoretical formulations are presented based on a higher-order shear deformation shell theory (HSDT) considering the transverse shear strains. Using the nonlinear strain–displacement relations of FGMs cylindrical shells, the governing equations are derived. The elastic foundation is modelled by two parameters Pasternak model, which is obtained by adding a shear layer to the Winkler model. The boundary condition is considered to be simply-supported. The novelty of the present work is to achieve the closed-form solutions for the critical mechanical buckling loads of the FGM cylindrical shells surrounded by elastic medium. The effects of shell geometry, the volume fraction exponent, and the foundation parameters on the critical buckling load are investigated. The numerical results reveal that the elastic foundation has significant effect on the critical buckling load.     

考虑弹性支撑时蜂窝芯剪切屈曲强度的插值求解方法

结合最小余能原理和薄板剪切屈曲失稳理论,给出了蜂窝芯等效剪切屈曲强度的理论表达式。将胞壁等效为受弹性支撑的梁,通过对固支和简支条件下的屈曲强度进行插值求解实际胞壁间为弹性支撑时的剪切屈曲强度。然后,利用三点短梁弯曲试验测量常用Nomex蜂窝芯的剪切屈曲强度,并与弹性支撑下的理论解进行对比,试验结果与理论解吻合较好,验证了理论方法的有效性。最后,讨论了剪切屈曲强度的各向异性及蜂窝高度对剪切屈曲强度的影响。结果表明,剪切屈曲强度的各向异性程度与蜂窝高度无关,但随着蜂窝高度的增加,蜂窝芯的纵向和横向剪切屈曲强度均逐渐减少,减小幅度逐渐减缓。     

基于三维Puck失效准则及唯象模量退化的复合材料臂杆屈曲分析

针对碳纤维增强树脂基复合材料（CFRP）臂杆结构在压缩和扭转载荷条件下屈曲与后屈曲问题,采用三维Puck失效准则和基于唯象分析的模量退化方法,同时考虑层合结构就位效应及沿纤维方向应力对横向强度的影响,建立了一种适用于考虑渐进失效CFRP结构的屈曲分析方法,并通过编写有限元软件ANSYS的USERMAT子程序进行了数值实现。与文献中实验结果的对比表明,上述方法能够分析复合材料结构的渐进失效过程和后屈曲承载特性,预测精度高。进而采用此方法,详细分析了某航天器臂杆结构在承受压缩与扭转载荷条件下的屈曲载荷及后屈曲特性。      

Experimental investigations on buckling of cylindrical shells under axial compression and transverse shear

This paper presents experimental studies on buckling of cylindrical shell models under axial and transverse shear loads. Tests are carried out using an experimental facility specially designed, fabricated and installed, with provision forin-situ measurement of the initial geometric imperfections. The shell models are made by rolling and seam welding process and hence are expected to have imperfections more or less of a kind similar to that of real shell structures. The present work thus differs from most of the earlier investigations. The measured maximum imperfections δ_max are of the order of ±3t (t = thickness). The buckling loads obtained experimentally are compared with the numerical buckling values obtained through finite element method (FEM). In the case of axial buckling, the imperfect geometry is obtained in four ways and in the case of transverse shear buckling, the FE modelling of imperfect geometry is done in two ways. The initial geometric imperfections affect the load carrying capacity. The load reduction is considerable in the case of axial compression and is marginal in the case of transverse shear buckling. Comparisons between experimental buckling loads under axial compression, reveal that the extent of imperfection, rather than its maximum value, in a specimen influences the failure load. Buckling tests under transverse shear are conducted with and without axial constraints. While differences in experimental loads are seen to exist between the two conditions, the numerical values are almost equal. The buckling modes are different, and the experimentally observed and numerically predicted values are in complete disagreement.     

Scale effects on buckling analysis of orthotropic nanoplates based on nonlocal two-variable refined plate theory

This article presents the buckling analysis of orthotropic nanoplates such as graphene using the two-variable refined plate theory and nonlocal small-scale effects. The two-variable refined plate theory takes account of transverse shear effects and parabolic distribution of the transverse shear strains through the thickness of the plate, hence it is unnecessary to use shear correction factors. Nonlocal governing equations of motion for the monolayer graphene are derived from the principle of virtual displacements. The closed-form solution for buckling load of a simply supported rectangular orthotropic nanoplate subjected to in-plane loading has been obtained by using the Navier’s method. Numerical results obtained by the present theory are compared with first-order shear deformation theory for various shear correction factors. It has been proven that the nondimensional buckling load of the orthotropic nanoplate is always smaller than that of the isotropic nanoplate. It is also shown that small-scale effects contribute significantly to the mechanical behavior of orthotropic graphene sheets and cannot be neglected. Further, buckling load decreases with the increase of the nonlocal scale parameter value. The effects of the mode number, compression ratio and aspect ratio on the buckling load of the orthotropic nanoplate are also captured and discussed in detail. The results presented in this work may provide useful guidance for design and development of orthotropic graphene based nanodevices that make use of the buckling properties of orthotropic nanoplates.     

复合材料双向波纹夹层结构力学性能

为改进传统单向波纹夹层结构横向力学性能较差的缺点,设计了一种新型复合材料双向波纹夹层结构。考虑复合材料双向夹层结构制备困难,研究了整套真空辅助成型工艺(VARI)工艺制备方案,实现双向波纹夹层结构的高效制备,以满足工程应用的需要。对制备出的复合材料双向波纹夹层结构与单向波纹夹层结构分别进行面外压缩、弯曲和剪切实验,分析了双向波纹夹层结构在不同载荷下的破坏模式及其失效机制,计算了该结构在不同荷载条件下的强度和模量,并将其与单向波纹夹层结构进行对比分析。结果表明,在压缩荷载作用下,玻璃纤维/环氧树脂芯子为主要承载部分,结构的失效主要体现在芯子的屈曲、断裂和分层;在弯曲荷载的作用下,由于纤维的抗压强度远小于抗拉强度,所以压头下方的上面板最先达到破坏荷载,结构的弯曲失效形式主要为上面板的断裂和脱粘;结构的剪切失效主要以泡沫与面板的脱粘和压溃为主,芯子和面板未见明显的破坏现象;与单向波纹夹层结构相比,双向波纹夹层结构力学性能显著提升。      

Application of third order shear deformation theory in buckling analysis of 2D-functionally graded cylindrical shell reinforced by axial stiffeners

This paper presents buckling analysis of a two-dimensional functionally graded cylindrical shell reinforced by axial stiffeners (stringer) under combined compressive axial and transverse uniform distributive load. The shell material properties are graded in the direction of thickness and length according to a simple power law distribution in terms of the volume fractions of the constituents. Primarily, the third order shear deformation theory (TSDT) is used to derive the equilibrium and stability equations. Since there is no closed form solution, the numerical differential quadrature method, (DQM), is applied for solving the stability equations. Initially, the obtained results for an isotropic shell using DQM were verified against those given in the literature for simply supported boundary conditions. The effects of load, geometrical and stringer parameters along with FG power index in the various boundary conditions on the critical buckling load have been studied. The study of results confirms that, stringers have significant effects on critical buckling load.     

Optimization of shear-deformable laminated plates under buckling and strength criteria

A shear deformable laminated theory is used to study the optimal design of rectangular plates under biaxial compressive loads. Such loads lead to plate failure by buckling or material failure which corresponds to the violation of the selected strength criterion. The minimum of the two loads (buckling load or material failure load) determines the critical failure load for a given set of problem parameters. At the optimum values of the ply angles, buckling or both failure criteria may be operational depending on the laminate thickness. The present study investigates the effect of laminate thickness on the optimal design and gives numerical results for symmetrically laminated angle-ply plates.     

Strength evaluations of sinusoidal core for FRP sandwich bridge deck panels

Fiber-reinforced polymer (FRP) sandwich deck panels with sinusoidal core geometry have shown to be successful both in new construction and the rehabilitation of existing bridge decks. This paper is focused on an experimental study of the strength evaluations of a honeycomb sandwich core under out-of-plane compression and transverse shear. The sinusoidal core is made of E-glass Chopped Strand Mat (ChSM) and Polyester resin. The compressive, tensile and shear strengths were first obtained from coupon tests. The out-of-plane compression tests were performed on representative single-cell volume elements of sandwich panels, and the tests included “stabilized” samples to induce compression failure, and “bare” samples to induce local buckling of the core. Finally, four-point bending tests were conducted to study the structural strength behavior under transverse shear. Two types of beam samples were manufactured by orienting the sinusoidal wave either along the length (longitudinal) or along the width (transverse). Both typical shear failure mode of the core material and delamination at the core–facesheet bonding interface were observed for longitudinal samples. The failure for transverse samples was caused by core panel separation. For both single-cell and beam-type specimen tests, the number of bonding layers, i.e., the amount of ChSM contact layer and resin used to embed the core into the facesheet, and the core thickness are varied to study their influence. The experimental results described herein can be subsequently used to develop design guidelines.     

Finite element evaluation of the boundary conditions for biaxial testing of high strength concrete

This paper represents a numerical investigation, using a non linear finite element approach, to evaluate the different load application platens used in the biaxial testing of concrete. Three methods are evaluated numerically: the dry ordinary solid steel testing platens, the brush platens, and the friction reducing Teflon sheets. The effect of confinement on the displacement field in addition to the stress distribution in the loading direction are presented and discussed. The shear stresses induced in the specimen are evaluated for both uniaxial and biaxial loading conditions. Finally, the buckling capacity of the brush platens is examined. The finite element results indicate that the brush platens provide the most homogeneous displacement fields. The displacement fields are close to those obtained without lateral confinement. In addition, the shear stresses induced in the specimen are the lowest for the brush platens. The current study was used to design brush bearing platens for biaxial testing of high strength concrete. A brush platen with rod dimensions of 5×5 mm cross-section and 75 mm height can be safely used in testing high strength concrete with compressive strength up to 100 MPa with a reasonable factor of safety against buckling of the brush rods.     

5A03铝合金管轴向压缩失稳形式及影响因素分析

目的研究管材在承受轴向压缩时的力学行为、失稳形式及其影响因素。方法在航空航天用5A03铝合金管准静态轴向拉伸和压缩实验的基础上,进行了管压缩过程的有限元分析。结果5A03圆管拉伸与压缩力学性能有较大差异,具有拉、压双模量倾向,拉伸屈服强度略低于压缩屈服强度,抗拉强度略低于抗压强度,且拉伸与压缩均呈现锯齿波屈服特性;高径比影响管压缩失稳形式,小于1时管试样形成单鼓,大于1时将出现双鼓,且鼓凸在管材端面摩擦较大一端优先出现。结论管材失稳鼓凸后表现为一种具有一定规律性的非轴对称屈曲压溃。     

Study of interaction curves for composite laminate subjected to in-plane uniaxial and shear loadings

In this study an attempt has been made to incorporate the effect of transverse shear on the stability of moderately thick/very thick composite laminated plates under in-plane compressive and shear loading using a Simple Higher Order Shear Deformation Theory based on four unknown displacement functions (u₀,v₀,w_b,w_s) instead of five which is commonly used in most of the higher order theories. The finite element method is employed to study the initial buckling load of laminated plates. The change in initial buckling response of thick rectangular antisymmetric laminates with respect to the fibre orientation angle has been studied. The interaction curves (between N_x and N_xy for different parameters of the laminates) are studied in detail.     

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。     

聚乙烯醇纤维改性高延性混凝土双面剪切试验及剪切韧性评价方法

为研究高延性混凝土（HDC）的剪切性能并评价其剪切韧性,设计了5组HDC试件、1组HDC基体试件（不含纤维）和1组普通混凝土对比试件,通过双面剪切试验,以纤维体积分数和HDC抗压强度为参数,分析其破坏形态、抗剪强度及峰值变形,根据试验结果提出了HDC的剪切韧性评价方法。结果表明:HDC纤维桥联作用及纤维拔出过程中吸收了大量能量,试件发生具有延性特征的剪切破坏;与基体试件和普通混凝土试件相比,HDC试件的抗剪强度和峰值变形均显著提高,其提高幅度随纤维体积分数的增加而增大;随HDC抗压强度的增大,试件抗剪强度增大,峰值变形降低;采用初始能量密度和残余剪切韧度比评价HDC的剪切韧性,其剪切韧性显著高于基体和普通混凝土。      

Buckling analysis of embedded nanotubes using gradient continuum theory

The buckling of nanotubes embedded in an elastic matrix is modeled within the framework of Timoshenko beams. Both a stress gradient and a strain gradient approach are considered. The energy variational approach is adopted to obtain the critical buckling loads. The dependences of the buckling load on the nonlocal parameter, the stiffness of the surrounding elastic matrix, and the transverse shear stiffness of the nanotubes are obtained. The results show a significant dependence of critical buckling load on the nonlocal parameter and the stiffness of the surround matrix. The Euler beam model, which neglects the shear stiffness of the nanotubes, over-predicts the critical buckling load. It is also found that the strain gradient model provides the lower bound and the stress gradient model provides the upper bound for the critical buckling load of nanotubes. In addition to mechanical buckling, thermally induced buckling of the nanotubes embedded in an elastic matrix is also studied. All results are expressed in closed-form and therefore are easy to use by materials scientists and engineers for the design of nanotubes and their composites.     

Critical Examination of the Iosipescu Shear Test as Applied to 0degrees Unidirectional Composite Materials

Several issues regarding the application of the shear and biaxial Iosipescu tests for the shear strength characterization of unidirectional composite materials are addressed in this article. First, the nonlinear effects of specimen sliding and geometric nonlinearity on the mechanical response of 0degrees standard unidirectional graphite/polyimide Iosipescu specimens with different loading conditions and loading block geometries have been investigated. Second, an attempt has been made to improve the Iosipescu shear test to eliminate normal compressive stresses in the specimen gauge section and at the same time prevent axial splitting. Finally, several Iosipescu shear and biaxial experiments have been performed to select proper specimen geometry and loading conditions for the shear strength measurements of unidirectional composites. The nonlinear effects are examined with respect to various coefficients of friction, displacements, loading angles, and fixtures (biaxial with short and modified biaxial with long loading blocks) using nonlinear finite-element techniques. It is shown that the effect of nonlinearity is small on the stresses at the center of the standard Iosipescu specimen, but significant for the stresses near the notch root up to 2 mm applied displacements. In some cases, significant differences in the stresses calculated for different coefficients of friction have been observed. All of these results are somewhat consistent for both fixtures, but with the stress components sigma x, sigma y, and sigma xy significantly lower in the standard Iosipescu specimens tested in the fixture with the long blocks. Numerical load/displacement diagrams show that specimen sliding and geometric nonlinearity have a negligible effect on reaction forces in the biaxial fixture, and a significant effect on the reaction forces in the modified biaxial fixture. Since the various combinations of the loading conditions evaluated in this study do not eliminate transverse compressive stresses in the gauge section of the standard Iosipescu specimens, a major improvement to the Iosipescu shear test has been proposed. Using an optimized specimen geometry subjected to biaxial shear/tension loading conditions, a state of almost uniform pure shear stress can be generated in 0degrees unidirectional composite Iosipescu specimens without the possibility of axial splitting along the fibers at the roots of the notches. However, it is shown in the experimental part of this study that for the optimized Iosipescu specimen, crushing at the inner loading blocks can significantly affect the shear intralaminar failure process. Only by reducing the cross-sectional area of the optimized Iosipescu specimen can the effect of crushing on the failure process be reduced without, however, highquality shear stress fields present in the gauge section at failure.     

Plasma surface modification of advanced organic fibres

A marked improvement in the interlaminar shear strength and flexural strength of aramid/ epoxy composites is observed when the fibres are pretreated in an ammonia or ammonia/ nitrogen gaseous discharge (plasma) to introduce amine groups on to the fibre surface. Scanning electron and optical microscopic observations are used to examine the microscopic basis for these results. Scanning electron micrographs of shear fracture surfaces show clean fibre/matrix separation in composites made from untreated fibres, indicative of weak interfacial bonding. In contrast, shear fracture surfaces of composites containing plasma-treated fibres exhibit clear evidence of fibre fibrillation and matrix cracking, suggesting stronger interfacial bonding. Optical microscopic examination of flexure specimens shows that enhanced strength results mainly from reduced compressive fibre buckling and debonding, due to an increase in fibre/matrix interfacial bond strength. This increase is not accompanied by any significant change in the interlaminar fracture energy or flexural modulus of the composites, but there is an appreciable loss in transverse ballistic impact properties. These results are also examined in terms of the observed increase in fibre/matrix interfacial strength.