Influence of predetermined delaminations on buckling and postbuckling behavior of composite sandwich beams

An investigation was performed to obtain the behavior of composite sandwich beams in the presence of predetermined delaminations, due to disbonding between the faceplate and the less rigid core. An analytical model for predicting buckling and describing the postbuckling behavior of the beam was developed. Griffith's fracture energy release rate model was introduced to predict the stability of the delamination propagation under external loading.

Parametric studies over a wide range of damage sizes, and composite facings were carried out to study the effects of these parameters on the overall behavior of the beams, as well as its damage tolerance. The results demonstrate that sandwich construction is very ‘sensitive’ to the presence of predetermined delaminatoins: premature buckling failure occurs at external loads, which are significantly lower than those corresponding to a ‘perfect’ sandwich beam. The limit load is obtained before delamination propagation takes place. In ‘imperfect’ beams with composite faceplates, the layup sequence affects significantly the load carrying capacity of the beam. It was also shown that the proposed model can be used to study the influences of predetermined delaminations in composite beams.     

Integration of Mechanics and Acoustics in a Sandwich Fuselage. Part IV

Until now only the stiffened skin structural concept has been discussed. A different structural concept is the sandwich concept. Sandwiches consist out of layers. The outer layers are called facings and are generally thin and of high density. These facings are supposed to resist most of the edgewise loads and flat-wise bending moments. The inner layer is called the core and is generally rather thick and of low density. The task of the core is to separate and stabilize the two facings, transmit shear between the facings and provide most of the shear rigidity. For sandwich panels no stiffeners are needed. Therefore no mass will be lost in stiffeners resulting in a relative high value of mass per unit area of the skin which results in a better TL according to the mass law. Also the core can be made of a material with high insulation properties (acoustic and thermal). The number of discrete stiffeners can then be minimized, since they are only required at places where high concentrated forces have to be introduced (wing, landing gear, etc.) or diverted (from cut-outs). This can reduce the production and maintenance cost. So it can be concluded that the sandwich concept offers great potential for multidisciplinary fuselage design. In this part the integration of structural and acoustical aspects will be discussed. First the structural aspect will be discussed followed by the acoustical aspect. Finally the possibilities to integrate these aspects are explained.     

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.     

Thermal buckling of various types of FGM sandwich plates

The sinusoidal shear deformation plate theory is used to study the thermal buckling of functionally graded material (FGM) sandwich plates. This theory includes the shear deformation and contains the higher- and first-order shear deformation theories and classical plate theory as special cases. Material properties and thermal expansion coefficient of the sandwich plate faces are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic material. Several kinds of symmetric sandwich plates are presented. Stability equations of FGM sandwich plates include the thermal effects. The thermal loads are assumed to be uniform, linear and non-linear distribution through-the-thickness. Numerical examples cover the effects of the gradient index, plate aspect ratio, side-to-thickness ratio, loading type and sandwich plate type on the critical buckling for sandwich plates.     

Elasticity, shell theory and finite element results for the buckling of long sandwich cylindrical shells under external pressure

The buckling of a sandwich cylindrical shell under uniform external hydrostatic pressure is studied in three ways. The simplifying assumption of a long shell is made (or, equivalently, ‘ring’ assumption), in which the buckling modes are assumed to be two-dimensional, i.e. no axial component of the displacement field, and no axial dependence of the radial and hoop displacement components. All constituent phases of the sandwich structure, i.e. the facings and the core, are assumed to be orthotropic. First, the structure is considered a three-dimensional (3D) elastic body, the corresponding problem is formulated and the solution is derived by solving a set of two linear homogeneous ordinary differential equations of the second-order in r (the radial coordinate), i.e. an eigenvalue problem for differential equations, with the external pressure, p the parameter/eigenvalue. A complication in the sandwich construction is due to the fact that the displacement field is continuous but has a slope discontinuity at the face-sheet/core interfaces, which necessitates imposing ‘internal’ boundary conditions at the face-sheet/core interfaces, as opposed to the traditional two-end-point boundary value problems. Second, the structure is considered a shell and shell theory results are generated with and without accounting for the transverse shear effect. Two transverse shear correction approaches are employed, one based only on the core, and the other based on an effective shear modulus that includes the face-sheets. Third, finite element results are generated by use of the ABAQUS finite element code. In this part, two types of elements are used: a shear deformable shell element and a solid 3D (brick) element. The results from all these three different approaches are compared.     

Fundamental frequency and design of the CFCF composite sandwich plate

The design efficiency of sandwich panels is often associated with the value of fundamental frequency. This paper investigates the free vibrations of rectangular sandwich plates having two adjacent edges fully clamped and the remaining two edges free (CFCF). The vibration analysis is performed by applying Hamilton’s principle in conjunction with the first-order shear deformation theory. The analytical solution determining the fundamental frequency of the plate is obtained using the generalised Galerkin method and verified by comparison with the results of finite element modal analysis. The approach developed in the paper and equations obtained are applied to the design of sandwich plates having composite facings and orthotropic core. Design charts representing the effects of the thickness of the facings and core on the mass of composite sandwich panel for a given value of the fundamental frequency are obtained.     

Buckling and postbuckling behavior of delaminated sandwich beams

An investigation was performed to study the buckling and postbuckling behavior of sandwich beams containing lengthwise and depthwise through-the-width delaminations. An analytical beam model was developed to predict the buckling load of the beam and to describe its postbuckling response for arbitrarily situated delaminations and various combinations of boundary conditions. Griffith's energy release rate model was employed to predict the stability of delamination propagation under external loading and to determine the direction of delamination growth.

Parametric studies over a wide range of beam geometries, damage sizes and locations, composite facings and beam boundary conditions were carried out to study their effects on the overall behavior of the sandwich structure, as well as its damage tolerance. The results demonstrated that a sandwich construction is very ‘sensitive’ to the presence of delaminations situated at the core-faceplate interface. Premature buckling failure occurs at external loads which are significantly lower than the buckling load for a ‘perfect’ sandwich beam; in ‘imperfect’ beams with composite faceplates, the layup sequence affects significantly the load-carrying capacity of the beam; varying either the boundary conditions in a sandwich beam or the lengthwise location of a delamination has a small effect on the postbuckling behavior of the beam. Delaminations located within composite faceplates have less pronounced influence, and as the defect is moved outwards the limit load may reach the buckling load corresponding to that of the ‘perfect’ beam.

The proposed model is capable of analyzing the postbuckling behavior of both sandwich and composite laminated beams for arbitrary locations of the delamination, and various combinations of boundary conditions.     

Dynamic wrinkling in sandwich beams

Facings of sandwich structures employed in typical applications are often subject to parametric periodic loading. Such loading can cause local dynamic instability of the facings, i.e. large-amplitude small wavelength lateral vibrations. This phenomenon, called in the paper dynamic wrinkling, may result in fatigue damage or immediate failure. The problem of dynamic wrinkling of the facings is analyzed in the present paper for sandwich beams and for large aspect ratio wide panels that vibrate forming a cylindrical surface. The solution is obtained for the case of a relatively thick or compliant core where the Winkler elastic foundation model of the core is applicable. In addition, the problem is formulated as an extension of the Plantema core model that may be preferable for thinner and stiffer cores. In addition, a new simplified elasticity model is introduced in the paper that is based on the assumption that both facings experience simultaneous and interactive dynamic wrinkling instability. Numerical results shown for the elastic foundation model include the criterion for the onset of dynamic wrinkling and the critical value of the damping coefficient of the facing that is sufficient to prevent such wrinkling. As follows from these results, dynamic wrinkling is unlikely in most engineering applications, except for the case in which the maximum stresses in the facing approach the static wrinkling value.     

Axial buckling analysis of single-walled carbon nanotubes in thermal environments via the Rayleigh–Ritz technique

Axial buckling characteristics of single-walled carbon nanotubes (SWCNTs) including thermal environment effect are studied in this paper. Eringen’s nonlocal elasticity equations are incorporated into the classical Donnell shell theory to establish a nonlocal elastic shell model which takes small-scale effects into account. The Rayleigh–Ritz technique is implemented in conjunction with the set of beam functions as modal displacement functions to consider the four commonly used boundary conditions namely as simply supported–simply supported, clamped–clamped, clamped–simply supported, and clamped-free in the buckling analysis. Selected numerical results are presented to demonstrate the influences of small scale effect, aspect ratio, thermal environment effects and boundary conditions in detail. It is found that the value of aspect ratio has different effects on the critical axial buckling loads of SWCNTs in low and high temperature environments. Also, it is observed that the difference between the thermal axial buckling responses of SWCNTs relevant to various boundary conditions is more prominent for higher values of nonlocal elasticity constant.     

Performance evaluation of sandwich panels subjected to bending compression and thermal bowing

The engineering performance of sandwich panels with expanded polystyrene foam core and steel or aluminium faces is evaluated in this paper. Such panels are usually used in semi-structural building applications with an insulating function. Bending, compression and thermal bowing experiments are conducted on these panels in the laboratory and their results are shown to conform in general to design values determined by current building codes and commercial practices. In edge-wise compression tests failure by column buckling has never occurred and localised face wrinkling is the usual failure mode. The adhesion between the polystyrene core and the metal skin as well as the location of the polystyrene joint in the panel are shown to have significant effects on the integral performance of the sandwich panels.     

A closed-form solution for thermal buckling of piezoelectric FGM rectangular plates with temperature-dependent properties

A thermal buckling analysis is presented for functionally graded rectangular plates that are integrated with surface-bonded piezoelectric actuators and are subjected to the combined action of thermal load and constant applied actuator voltage. The temperature-dependent material properties of the functionally graded plate are assumed to vary as a power form of the thickness coordinate. Derivation of the equations is based on the third-order shear deformation plate theory. Results for the critical buckling temperatures are obtained in closed-form solution, which are convenient to be used in engineering design applications. The effects of the applied actuator voltage, plate geometry, and volume fraction exponent of the functionally graded material on the buckling temperature are investigated.     

Numerical investigation of the response of sandwich-type panels using thin-walled tubes subject to blast loads

The response of a novel lightweight panel design under blast loading is numerically investigated. The sandwich-type panel uses thin-walled square tubes as the core material with mild steel outer plates. A parametric study is carried out with ABAQUS/Explicit to examine the effects and interaction between design variables in three different tube layouts. Tube position, thickness and aspect ratio as well as top plate thickness are varied. Buckling stability and absorption performance are shown to be highly sensitive to tube placement due to interaction effects between the top plate and tubes. For each panel an optimal tube positioning is obtained corresponding to nearly perfect axial progressive symmetric tube buckling. Tube thickness is shown to influence the onset of buckling and hence affects the stability of the core, while energy absorption performance is also highly configurable. Tube aspect ratio shows only a small effect on core buckling stability and energy absorption. Top plate thickness influences absorber performance significantly while having a small effect on buckling stability. A simple theoretical analysis is presented and shows reasonable agreement with the numerical simulations.     

The Effect of Load and Geometry on the Failure Modes of Sandwich Beams

Facing compressive failure, facing wrinkling and core shear failure are the most commonly encountered failure modes in sandwich beams with facings made of composite materials. The occurrence and sequence of these failure modes depends on the geometrical dimensions, the form of loading and type of support of the beam. In this paper the above three failure modes in sandwich beams with facings made of carbon/epoxy composites and cores made of aluminum honeycomb and two types of foam have been investigated. Two types of beams, the simply supported and the cantilever have been considered. Loading included concentrated, uniform and triangular. It was found that in beams with foam core facing wrinkling and core shear failure occur, whereas in beams with honeycomb core facing compressive failure and core shear crimping take place. Results were obtained for the dependence of failure mode on the geometry of the beam and the type of loading. The critical beam spans for failure mode transition from core shear to wrinkling failure were established. It was found that initiation of a particular failure mode depends on the properties of the facing and core materials, the geometrical configuration, the type of support and loading of sandwich beams.     

Thermal buckling of a nanoplate with small-scale effects

In this paper, thermal buckling properties of a nanoplate with small-scale effects are studied. Based on the nonlocal continuum theory, critical temperatures for the nonlocal Kirchhoff and Mindlin plate theories are derived. The thermal buckling characteristics are presented with different models. The influences of the scale coefficients, half-wave numbers, width ratios, and the ratios of the width to the thickness are discussed. From this work, it can be observed that the small-scale effects are significant for the thermal buckling properties. Both the half-wave number and width ratio have influence. The nonlocal Kirchhoff plate theory is valid for the thin nanoplate, and the nonlocal Mindlin plate theory is more appropriate for simulating the mechanical behaviors of the thick nanoplate.     

木质蜂窝夹芯包装材料抗弯性能研究

根据夹层结构原理,就木质蜂窝夹芯材料抗弯性能进行研究,同时根据三点外伸梁和简支梁原理对夹芯结构的抗弯刚度进行了理论分析.结果表明:木质蜂窝夹芯材料的抗弯性能较原蜂窝纸板大大提高,给出的木质蜂窝夹芯材料抗弯刚度的近似公式可以预测夹芯结构的刚度.木质蜂窝夹芯材料作为一种具有良好性能的绿色包装材料,将会有很好的应用前景.     

Nonlinear analysis of sandwich plates with FGM face sheets resting on elastic foundations

Nonlinear vibration, nonlinear bending and postbuckling analyses are presented for a sandwich plate with FGM face sheets resting on an elastic foundation in thermal environments. The material properties of FGM face sheets are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The governing equation of the plate that includes plate-foundation interaction is solved by a two-step perturbation technique. The thermal effects are also included and the material properties of both FGM face sheets and homogeneous core layer are assumed to be temperature-dependent. The numerical results reveal that the foundation stiffness and temperature rise have a significant effect on the natural frequency, buckling load, postbuckling and nonlinear bending behaviors of sandwich plates. The results also reveal that the core-to-face sheet thickness ratio and the volume fraction distribution of FGM face sheets have a significant effect on the natural frequency, buckling load and postbuckling behavior of the sandwich plate, whereas this effect is less pronounced for the nonlinear bending, and is marginal for the nonlinear to linear frequency ratios of the same sandwich plate.     

Thermal buckling of cross-ply laminated composite beams

Summary Thermal buckling of thick, moderately thick and thin cross-ply laminated beams subjected to uniform temperature distribution are analyzed. Exact analytical solutions of refined beam theories are developed to obtain the critical buckling temperature of cross-ply beams with various boundary conditions. The state space concept in conjunction with Jordan canonical form will be used to solve exactly the governing equations of the thermal buckling problems. The effects of length to thickness ratio, modulus ratio, thermal expansion coefficients ratio, various boundary conditions and number of layers on the critical buckling temperature are investigated.     

复合材料夹芯梁屈曲破坏模式及极限承载

为研究复合材料夹芯梁在轴压作用下的屈曲、后屈曲特性及承载能力,进行了试验研究与有限元仿真。首先,开展了系列复合材料夹芯梁屈曲特性试验,研究了铺层比例、梁长度、表层厚度及芯层厚度等因素对其屈曲、后屈曲破坏模式及极限承载的影响;然后,基于非线性屈曲理论,采用三维内聚力界面单元模拟面芯脱粘,并引入初始预变形及材料损伤准则对复合材料夹芯梁在轴压下的屈曲特性及极限承载进行仿真研究。结果显示:界面脱粘是屈曲破坏的重要模式;仿真计算的极限承载与试验结果相比,误差控制在10%以内。所得结论表明该方法可有效预报复合材料夹芯梁的后屈曲路径、破坏模式及极限承载。      

格构腹板增强型泡沫复合材料夹层结构腹板平面内屈曲分析

利用有限元数值模拟研究了在平面内荷载作用下,腹板间距、腹板高度、泡沫芯材弹性模量等因素对格构腹板增强型泡沫夹层结构腹板屈曲性能的影响。结合有限元分析结果提出半波数基床系数,采用文克尔地基模型模拟泡沫芯材对格构腹板增强型泡沫复合材料夹层结构腹板的弹性支撑作用,基于Ritz法提出腹板平面内荷载作用下屈曲荷载理论分析方法和计算公式。分析表明:泡沫芯材的存在使得腹板的屈曲特性不同于无芯材时屈曲特性,随腹板高度增加屈曲荷载表现出平稳增加的趋势,屈曲形态呈现出多峰特征的褶皱;腹板间距和高度较大时,泡沫芯材的支撑对腹板的稳定起到主导作用;理论方法分析结果、有限元结果以及试验数据总体上一致。     

Thermal buckling of shallow/nonshallow piezoelectric-composite cylindrical shells

A thermal buckling analysis is presented for laminated cylindrical shells with surface mounted piezoelectric actuators under combined action of thermal and electrical loads. Derivations of the equations are based on the classical laminated shell theory, using the Sanders nonlinear kinematic relations. The analysis uses the Galerkin method to obtain closed form solutions for the buckling loads of shallow and nonshallow piezolaminated cylindrical shells. Temperature dependency of material properties is taken into account. Illustrative examples are presented to verify the accuracy of the proposed formulation. The effects of the various design parameters on thermal buckling loads are investigated.