考虑脱粘的复合材料加筋板屈曲后屈曲及承载能力数值分析

建立了复合材料层合加筋壁板的屈曲后屈曲有限元分析模型。该模型采用界面单元以有效模拟筋条和壁板之间的连接界面, 连接界面和复合材料层板分别采用Quads和Hashin失效准则作为失效判据, 引入材料刚度退化模型, 采用非线性有限元方法, 研究了复合材料加筋壁板在压缩载荷下的前后屈曲平衡路径及破坏过程。数值分析结果与实验结果吻合良好, 证明了该方法的合理有效性。详细探讨了筋条尺寸及界面单元强度等参数对加筋壁板屈曲后屈曲行为及承载能力的影响规律, 研究表明增加筋条截面惯性矩及筋条密度在一定程度上能有效提高加筋板的屈曲载荷与极限强度, 筋条密度增加到一定程度会引起结构破坏形式由失稳破坏?湮顾跗苹? 界面强度与铺层方式对极限强度有重要影响, 界面脱粘是引起加筋板最终破坏的重要因素。      

Failure analysis of FRP sandwich bus panels by finite element method

The weakest part of fiber reinforced polymer composites (FRP) sandwich structures is commonly the interfacial zone between layers. Under service loading, delamination failure will be most likely to initiate from these interfaces. Typical failure analysis for such sandwich structures usually depends on the modeling details of the interface. In this paper, the sandwich panel was modeled as separated layers with appropriate constrains imposed between them. These constrains guaranteed a smooth stress transfer from the skins to the core. The proposed FEM model was applied to simulate the failure behavior of a FRP sandwich panel that is used in bus body. The simulation results were compared with other numerical predictions and the experiment. It was concluded that this model is very efficient computationally for analyzing the failure issues of FRP sandwich structures.     

Buckling failure modes of FRP thin-walled beams

A study on buckling phenomena in pultruded Fiber Reinforced Polymer (FRP) beams, based on two mechanical models recently formulated by the authors with regard to composite thin-walled beams, is presented in this paper. Global buckling behavior is analyzed by means of a one-dimensional model in which cross-section torsional rotation is divided into two parts: the first one, associated with Vlasov’s axial warping, the second one, associated entirely with shear strains. The study of local behavior is based on the individual buckling analysis of the components of FRP profile, assumed as elastically restrained transversely isotropic plates. Both mechanical models take into account, within the field of small strains and moderate rotations, the contribution of shear deformation in the kinematic hypotheses. Design charts suitable to evaluate the buckling load of FRP “I” beams with either narrow or wide flanges are obtained and presented in this paper.     

Buckling and postbuckling response of sandwich panels under non-uniform mechanical edge loadings

The buckling and postbuckling responses of cylindrical sandwich panels, subjected to non-uniform in-plane loadings are investigates in this paper by analytical method. A fourth and fifth order expansions are used respectively for the transverse and tangential displacement of the core to model the core compressibility effect. The stress distribution within the panels due to the applied non-uniform in-plane edge loadings are determined by prebuckling analysis. The governing partial differential equations describing the buckling and postbuckling behavior of cylindrical sandwich panels are derived using the principle of minimum total potential energy. Galerkin’s method is used to reduce the governing partial differential equations to a set of non-linear algebraic equations. Newton–Raphson method in conjunction with Riks approach is employed to solve the algebraic equations. Numerical results are presented for both flat and cylindrical sandwich panels subjected to various non-uniform in-plane edge loadings. The sandwich panels used in the present investigation are made up of isotropic and composite materials.     

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.     

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。      

Buckling analysis of anisotropic variable-curvature panels and shells

A buckling formulation for anisotropic variable-curvature panels is presented in this paper. The variable-curvature panel is assumed to consist of two or more panels of constant curvature where each panel may have a different curvature. Bezier functions are used as Ritz functions. Displacement (C⁰), and slope (C¹) continuities between segments are imposed by manipulation of the Bezier control points. A first-order shear-deformation theory is used in the buckling formulation. Results obtained from the present formulation are compared with those from finite element simulations and are found to be in good agreement.     

Free vibration analysis of coplanar sandwich panels

A comprehensive vibration study of simple three-layer sandwich plates, based on the h-p version of the finite element method, is presented. The methodology incorporates a new set of trigonometric functions to provide the element p-enrichment—these functions exhibit good convergence characteristics, and enable the medium frequency regime to be explored at minimum computational expense. Elements may be joined together to model more general coplanar assemblies, and the trade-off between h-division and p-enrichment is discussed. Excellent agreement has been found with the work of other investigators, and new results are presented for (i) a completely free, symmetric section, rectangular sandwich panel whose core thickness is varied as a function of the overall plate thickness whilst the mass per unit area is maintained constant, and (ii) a cantilevered, T-planform, asymmetric section, sandwich plate. The results from this latter case are compared with those forthcoming from a proprietary finite element package; outstanding agreement is obtained, and a reduction of over 30% in the total number of degrees of freedom is demonstrated.     

含面芯界面缺陷的蜂窝夹芯板侧向压缩破坏模式

为了对含面芯层间脱胶缺陷的蜂窝夹芯板在侧向压缩载荷作用下的典型破坏模式进行数值预报, 建立了基于蔡-希尔破坏准则和粘结模型的计算模型。该计算模型是建立在对蜂窝夹芯板的双悬臂梁(DCB)和单臂梁(SLB) 试验中所发现的一种新的破坏模式的分析基础之上的。对蜂窝夹芯板的侧向压缩破坏行为的数值预报中, 发现一种新的破坏模式: 位于脱胶区域的面板首先发生局部屈曲失稳, 随后面板内部靠近芯子的45°/0°层间出现分层, 与此同时最靠近芯子的45°铺层发生断裂, 伴随着45°/0°层间分层的扩展, 面板发展成为对称性整体屈曲失稳。与侧向压缩试验测试结果对比发现, 计算模型模拟中所预报的破坏模式在实验测试中也得到了很好的验证。      

Precise bending stress analysis of corrugated-core,honeycomb-core and X-core sandwich panels

A semi-analytical method for bending analysis of corrugated-core, honeycomb-core and X-core sandwich panels is presented. The real displacement of sandwich panels is divided into the global displacement field and local displacement field. The discrete geometric nature of the core is taken into account by treating the core sheets as beams and the sandwich panel as composite structure of plates and beams with proper displacement compatibility. In the global displacement field, the governing equations of these sandwich panels are derived using energy variation principle and solved by employing Fourier series and the Galerkin approach. In the local displacement field, the face sheets under external loads are taken as a multi-span thin plate and the local bending response are then computed. Then the real bending responses are obtained by superposing these bending responses calculated in the two displacement fields and the structural stress fluctuation can be captured. Results from the proposed method agree well with available results in the literature and those from detailed finite element analysis. Furthermore, the mechanical properties of the three kinds of sandwich panels have been compared.     

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.     

Assessment of models for analysis of singly-curved sandwich panels

Overall behaviour of a simply-supported singly-curved shallow sandwich panel under lateral loading is considered. Three types of linear models — general shell, shallow shell and curved plate theories — are employed to describe a static overall behaviour of such a panel. The shallow panel with a constant curvature loaded by a uniform pressure is used as a trial case to assess the accuracy of the models. A nonlinear model for a panel of arbitrary shape under an arbitrary loading is developed on the basis of the curved plate theory. A closed-form nonlinear analytic solution for the panel of constant curvature under a uniform lateral pressure is obtained, and its accuracy is estimated. An experimental investigation of a sandwich beam under a uniform lateral loading is carried out, and the data obtained are compared with the theoretical calculations.     

Buckling analysis of cross-ply laminated conical panels using GDQ method

The buckling analysis of cross-ply laminated conical shell panels with simply supported boundary conditions at all edges and subjected to axial compression is studied. The conical shell panel is a very interesting problem as it can be considered as the general case for conical shells when the subtended angle is set to 2π and also cylindrical panels and shells when the semi-vertex angle is equal to zero. Equations were derived using classical shell theory of Donnell type and solved using generalized differential quadrature method. The results are compared and validated with the known results in the literature. The effects of subtended angle, semi-vertex angle, length, thickness and radius of the panel on the buckling load and mode are investigated.     

Buckling of sandwich panels with different boundary conditions — A comparison between FE-analysis and analytical solutions

Buckling loads of sandwich panels obtained by analytical calculations and FE-analysis are compared. Approximate buckling loads for panels with different boundary conditions have been derived using an energy method with deflection functions satisfying the boundary conditions. The comparison shows good agreement for panels with simply supported edges. In other cases the agreement is acceptable for panels with a length/ breadth ratio of 1 or greater. The approximate solutions can thus be used to estimate buckling loads of panels when designing sandwich structures.     

Buckling of open-section bead-stiffened composite panels

Stiffened panels are structures that can be designed to efficiently support in-plane compression, bending, and shear loads. Although the stiffeners are usually discrete elements which are fastened or bonded to a flat or continuously curved plate, manufacturing methods such as thermoforming allow integral formation of the stiffeners in a panel. Such a configuration offers potential advantages in terms of a reduced number of parts and manufacturing operations. For thermoplastic composite panels stiffened by integrally formed open-section beads, the effects of bead spacing and bend cross-section geometry on the initiation of buckling under uniaxial compression and uniform shear loading were investigated. Finite elements results for a range of stiffened panel sizes and bead geometries are presented and compared with approximate closed-form solutions based on an effective flat plate size. Experimental verification of analytical predictions for one of the shear panels and one of the compression panels is described. Compensation of the forming tool to reduce the degree of initial curvature of the panels was found to be necessary.     

Competition between brittle fracture and plastic collapse in the failure of thin rectangular panels

A centre-cracked panel of elastic-plastic material of unit thickness is loaded remotely by an uniaxial traction acting along its longitudinal axis. Making use of the Dugdale-Barenblatt model, the size of the plastic zones ahead of the crack tips can be obtained by equilibrium considerations. Connected to , a generalised elastic-plastic stress intensity factor K is defined which, as 0, approaches the ordinary elastic one. Once the critical values W _c or K _c at the onset of the unstable propagation of the crack have been specified, the residual-strength curves for plane stress state can be easily deduced. Moreover, conditions are sought for which ductile fracture, brittle fracture or plastic collapse takes place.     

Micro and macro analysis of sisal fibre composites hollow core sandwich panels

In the view of the growing environmental concerns, hollow cores from recyclable natural fibre composites were manufactured to reduce the undesirable impact on the environment. To evaluate the feasibility of using short sisal fibres as reinforcements in the composites, existing micromechanical models have been used to predict properties starting from the intrinsic properties of its constituents. The stress relaxation behaviour of the composites was examined experimentally by performing tensile stress relaxation tests and to understand the process, it was modelled using variations of Maxwell’s model. A steady-state finite element analysis in the linear range was performed in ANSYS environment to examine flexural properties of the panels, and the shear strength of the hollow cores was experimentally determined by subjecting them to flexural loads in a four-point bending scheme. The micromechanics models indicated that the fibres had failed to provide effective reinforcements with their existing lengths, acting as fillers rather than reinforcements. The stress relaxation models indicated that the formed part needs to be cooled to room temperature within the die under suitable forming loads to avoid local deformations due to warping. The mid-span deflections of the sandwich panels predicted by the FE model agree well with the experimental results, the analysis predicted facing buckling as a mode of failure when wood veneers facings of modulus 4.5 GPa and thickness 1.7 mm were used. The specific shear strengths of the reinforced core are more than twice than those of the unreinforced polypropylene cores, increasing the scope of such panels as structural members in various engineering facets.     

Wrinkling of corrugated skin sandwich panels

Compression wrinkling of composite sandwich panels with corrugated skins was investigated numerically, analytically and experimentally. Semi-circular and sine-wave shaped corrugations were studied. The corrugations significantly increased wrinkling strength when compared with equal mass flat panels. Semi-circular corrugations proved to be highly preferable to sine-wave shaped corrugations due to localized buckling in the latter. Over 40 fiberglass and foam core sandwich specimens were manufactured with semi-circular skin corrugations. These specimens were tested to failure, providing confirmation of the numerical and analytical results.     

Buckling analysis of trapezoidal composite sandwich plate subjected to in-plane compression

The results of the stability analysis of simply supported layered isosceles trapezoidal plate subjected to axial in-plane compression are presented. The layup configuration is confined to symmetric laminates. The solution has been obtained by means of the Galerkin orthogonalisation method combined with the proposed method of the coordinate system transformation. The results of the analytical solution are compared with the verifying FEM calculation. The computed results in the form of graphs of the buckling force as a function of material and geometrical parameters of the panel are included.