Bending response of web-core sandwich beams

This paper presents a new analytical solution for the bending response of a web-core sandwich beam. The beam is a transverse cut from the sandwich plate. The method is based on the plane frame analysis, where the response of the beam is divided into local and global components. The Clebsch’s method is used to calculate the deflection of the face plates. The validation of the plane frame method is carried out with FE-analyses based on the shell element formulation. Also a comparison is made with the method based on homogenized beam. Periodic stress distributions in the face plates are revealed with the plane frame analysis and are supported by the FE-analysis. The existing methods based on homogenized beam are not able to predict these stresses. The plane frame analysis can benefit the development of the theory related to web-core sandwich plate.     

Bending and vibration of multilayer sandwich beams and plates

A finite element displacement analysis of multilayer sandwich beams and plates, each with n stiff layers and n?1 weak cores, is presented. Each layer of the sandwich structure may have individual orthotropic properties of its own and the bending rigidities of the stiff layers are taken into account while direct stresses in cores are neglected in the analysis. The condition of common shear angle for all cores, which has been used by several authors is not implied in the formulation. Several examples on bending problems have been solved using lower-order elements and the accuracy of the results has been shown to be excellent. Two higher-order elements have also been developed but have not been found to yield much better results. The free vibration problems of multilayer sandwich structures have also been solved, and good accuracy is demonstrated.     

Shear coupling effects of the core in curved sandwich beams

We consider a composite package formed by two curved external Euler-Bernoulli beams, which sandwich an elastic core with negligible bending strength but providing the shear coupling of the external layers. This coupling considerably affects the gross response of the composite structure. There is an extensive literature on straight sandwich beams of this type, but very little attention has been paid to the effects of curvature. Here, an analytical linear elastic model is proposed for beams with arbitrary variable curvature. Equilibrium equations and boundary conditions are obtained through a variational approach. Useful simplifications are possible for the case of moderately curved beams and beams with constant curvature.     

Vibration and damping analysis of curved sandwich beams with a visoelastic core

The energy method has been used to derive the governing equations of motion for transverse vibrations of curved sandwich beams. Assuming a series solution, the equations are solved for a simply supported curved sandwich beam with viscoelastic cores. The damping effectiveness of the beam is evaluated by application of the correspondence principle of linear viscoelasticity. Theoretical results for resonant frequencies and associated system loss factor for curved sandwich beams have been verified experimentally. The effects of curvature, core thickness, lack of symmetry and modal number on the resonant frequency parameter and associated system loss factor have been studied.     

Experimental dynamic analysis on naturally curved honeycomb sandwich beams with different damage patterns

In this study, dynamic analysis of naturally curved honeycomb sandwich beam including two surface cracks and an impact region at the facing skin is presented. Laminates of facing skin and backing skin are known as carbon fiber‐plain weave composite laminates with 1.6 mm in thickness. In the first part, in order to determine mechanical properties of both the skin with no‐crack/crack(s) and the honeycomb core of the composite beam, static tensile tests are conducted with respect to straingage measurement technique. In the second part, drop weight impact tests and vibration tests are performed to present the free vibration characteristics of the clamped‐clamped honeycomb sandwich beam including cracks and an impact‐damaged region. Corresponding to damage patterns of the sandwich beam, experimental dynamic analyses consist of six steps: (1) Vibration analysis with no‐crack and no‐impact region, (2) Vibration analysis with no‐crack and an impact region, (3) Vibration analysis with a surface crack and no‐impact region, (4) Vibration analysis with a surface crack and an impact region, (5) Vibration analysis with two surface cracks and no‐impact region, (6) Vibration analysis with two surface cracks and an impact region. For these purposes, an impact hammer with a force transducer is used to excite the undamaged or damaged naturally curved honeycomb sandwich beam through the selected points. After the excitation, the responses are obtained by an accelerometer. Resonant frequencies for the modal responses of the naturally curved honeycomb sandwich beam with different damage patterns are discussed.     

Indentation resistance of sandwich beams

High-order sandwich beam theory is used to model the local deformation under the central indentor for sandwich beams loaded under three-point bending. ‘High-order' refers to the non-linear variations of in-plane and vertical displacements through the height of the core which the model incorporates. The analysis is elastic, which is appropriate to describe the beam response up to peak load for the material combination of GFRP skins and Nomex honeycomb core which is the focus of this paper. Reasonable agreement is found between theoretical predictions of the displacement field under the indentor and experimental measurements using a beam with GFRP skins and Nomex honeycomb core. By using the model to consider the way in which different wavelengths of sinusoidal pressure loading on the top skin are transmitted to the core, a spreading length scale λ is introduced. λ, which is a function of the beam material and geometric properties, characterises the length over which a load on the top surface of a beam is spread out by the skin. Calculations of the effect of roller diameter on indentation behaviour illustrate the importance of this length scale. When λ is small compared with the roller radius R, corresponding to a flexible skin, the contact load at the roller-skin interface is transmitted relatively unchanged to the core. Conversely, when λ/R is greater than about 0.25, corresponding to a relatively rigid skin, the load from the roller is spread out by the skin and the pressure in the core is distributed over a length of the order of λ.     

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.     

Shock waves in curved beams

Summary The paper investigates the propagation of shock waves in linearly elastic curved beams. The propagation of conditions are determined and the equations which govern their growth and decay are determined. We treat in detail shock waves in an orthotropic, simple curved beam.     

Thermal buckling of bimodular sandwich beams

This paper presents a model that explores the thermal buckling of three-layer sandwich beams possessing thick facings and moderately stiff cores. Bimodular facings and core material are used. In contrast to conventional theory, the effects of transverse shear deformation in the facings as well as the effect of the stretching and bending action in the core on thermal buckling are considered. The governing equations are derived using the principle of minimum total potential energy and the fact that its second derivative is zero. The finite-element results are presented in order to investigate the effects of important parameters such as thickness, thermal expansion coefficients and moduli ratio on critical buckling temperatures.     

Fatigue analysis of honeycomb-composite sandwich beams

The fatigue behaviour of honeycomb sandwich beams is experimentally investigated through four-point bending tests. Two kinds of specimens, initially undamaged and damaged by interface debonding, have been tested. The fatigue tests results are presented in standard SN diagrams with a best curve fit of the experimental data, while the fatigue limit is evaluated through a stair-case procedure. Two different failure mechanisms were found: undamaged specimen failure is due to collapse of the compressed face, while damaged specimen failure occurs due to the collapse of the honeycomb cell walls at the tip of the debonded portion.     

Nonlinear closed-form high-order analysis of curved sandwich panels

Closed-form high-order theory of sandwich panels, including transverse flexibility and shear rigidity of a core, as well as geometrical nonlinearity of unsymmetric faces is generalized for sandwich panels of constant curvature. Variational calculus is used to derive the set of governing equations describing a stress-deformation response of the panel to arbitrary loads. Boundary conditions are presented both in the local and global formulations. The procedure for the numerical solution of the governing nonlinear differential equations is based on the finite-difference method with deferred corrections. The solution technique is illustrated through numerical examples. Influence of the geometrical nonlinearity on the overall behaviour of the sandwich panel and localized effects are demonstrated.     

基于钢板屈曲分析的双钢板-混凝土组合剪力墙轴压承载力计算方法

双钢板混凝土组合结构结合了钢与混凝土两种材料的优势、力学性能以及耐久性优越,且施工快速便捷,正越来越广泛地应用于核电工程中。双钢板混凝土组合墙与钢筋混凝土筏板基础的锚固节点是其优越性能充分发挥的关键之一。插筋式节点相较于传统嵌入式节点和埋件式节点可以显著提高施工效率,从而得到更多青睐,但是目前关于该类节点锚固性能的研究较少。该文设计了4个1∶2缩尺的双钢板混凝土组合墙-钢筋混凝土基础插筋锚固节点,对其进行静力单调拉伸试验。通过对试件承载力、刚度、裂缝形态、钢筋及钢板应变等开展分析,探究了搭接钢筋布置方式以及对拉钢筋配置对于节点锚固性能的影响规律,并针对可能的破坏模式提出了相应的设计方法。试验结果表明：该类节点可以实现等强连接,且延性较好;对拉钢筋对控制裂缝发展,提高节点整体性具有重要作用,且沿长度方向对拉钢筋应变呈非线性分布;随着搭接钢筋与钢板距离的增大,钢筋与钢板间的不平衡力矩增加,导致对拉钢筋应变增大,但搭接钢筋的滑移有所降低。该文研究结果为插筋式节点的锚固设计提供了重要依据。     

Damping characteristics of electro-rheological fluid sandwich beams

Summary This paper presents experiments aimed to critically examine the damping mechanisms in sandwich beams filled with electro-rheological (ER) fluids. ER fluids made from silicone oil and with different concentrations of starch are used in the present study. It is observed that loss factors increase with increase in the applied electric field and concentration of starch. It is also observed that the complex hysteresis behavior of ER fluids is less dominant in sandwich structures.     

双钢板-混凝土组合结构在沉管隧道中的发展与应用

深中通道沉管管节采用钢壳-混凝土组合结构形式,通过向空钢壳浇筑混凝土预制而成。为评估沉管管节施工后的整体变形,建立了热-结构顺序耦合的分析框架,基于ANSYS APDL及UFPs二次开发模块,分别建立了考虑水化度、日照辐射、大气温度变化的精细温度场模型和考虑混凝土硬化及收缩特性的结构分析模型。通过对足尺管节的温度及应变模拟结果与监测数据的对比,验证了有限元模型的可靠性。在此基础上,分析了日照辐射、大气温度变化等对于管节温度场的影响,同时分析了管节的整体变形模式,以及温度效应、混凝土收缩及自重三种因素对管节整体横向、纵向及竖向变形的影响。结果表明：管节施工过程的温度场表现为时变和空间分布的特征,格仓边部温度受外界气温变化和日照辐射的影响存在周期性波动,而格仓中部温度峰值主要受混凝土自身水化放热特性的控制;管节最终表现为顶板横向及纵向内收,竖向下挠,底板横向及竖向变形不显著;太阳辐射对于结构温度场影响较日气温变化更显著,建议在混凝土温度峰值预测中予以考虑,而日气温变化可采用日平均气温值予以简化;温度效应及材料收缩对管节横向及纵向整体变形影响显著,自重因素导致的变形在横向及纵向的比例为44.3%、11.7%,而在竖向所占比例达92.5%,因而温度效应及材料收缩在管节横向及纵向变形分析中不可忽视;该分析方法可适用于大体积混凝土等结构的温度效应的预测和评估。

     

Strength of sandwich beams with interface debondings

The adhesive joint bonding the faces to the core material in a sandwich structure ensures that the loads are transferred between the components. However, debondings may arise either during the manufacturing process or due to overloading. These will reduce both the stiffness and the load bearing capacity of the structure. In the present paper, debondings in foam core sandwich beams are investigated assuming that cracks in the interface between the face and core are present. Stress intensity factors are found from an analytical model and compared to solutions from several finite element calculations. Fracture toughness values, determined from simple specimens, are used to predict the fracture loads for beams with simulated debondings subjected to four-point bending.     

Free in-plane vibrations of curved nonuniform beams

Summary By introducing two physical parameters, the analysis of free in-plane vibrations of curved non-uniform beams is simplified. The explicit relations between the flexural displacement and the longitudinal displacement are derived. With these explicit relations, the two coupled governing differential equations are reduced to a complete sixth-order ordinary differential equation with variable coefficients in the longitudinal displacement, and a limiting study from the curved beam theory to the straight beam theory is successfully revealed. Finally, the influence of taper ratio, center angle and arc length on the first two natural frequencies of the beams is illustrated.     

Bending and vibration of CFRP-faced rectangular sandwich plates

A linear analysis is presented for bending and vibration of sandwich plates consisting of an orthotropic core and unbalanced laminated face plates. A solution method is proposed through the principle of minimum total potential energy, and a double Fourier series approach is used for the displacement functions. Analytical and experimental investigations are performed for fully clamped boundary conditions, and the results show reasonable correlation. Holographic techniques were used to obtain the deflection and vibration modes.     

Bending response of inhomogeneous fiber-reinforced viscoelastic sandwich plates

The static response of an inhomogeneous fiber-reinforced viscoelastic sandwich plate is investigated by using the first-order shear deformation theory. Several types of sandwich plates are considered taking into account the symmetry of the plate and the thickness of each layer. In addition, two cases are considered depending on the viscoelastic material which are included in the core or the faces of the sandwich plates. The method of effective moduli and Illyushin’s approximation method are used to solve the equations governing the bending of simply supported inhomogeneous fiber-reinforced viscoelastic sandwich plates. Numerical computations were carried out to study the effect of the time parameter on deflections and stresses at different values of the aspect ratio, side-to-thickness ratio and constitutive parameter.     

Experiments on curved sandwich panels under blast loading

In this paper curved sandwich panels with two aluminium face sheets and an aluminium foam core under air blast loadings were investigated experimentally. Specimens with two values of radius of curvature and different core/face sheet configurations were tested for three blast intensities. All the four edges of the panels were fully clamped. The experiments were carried out by a four-cable ballistic pendulum with corresponding sensors. Impulse acting on the front face of the assembly, deflection history at the centre of back face sheet, and strain history at some characteristic points on the back face were obtained. Then the deformation/failure modes of specimens were classified and analysed systematically. The experimental data show that the initial curvature of a curved sandwich panel may change the deformation/collapse mode with an extended range for bending dominated deformation, which suggests that the performance of the sandwich shell structures may exceed that of both their equivalent solid counterpart and a flat sandwich plate.