Minimum-Weight Sandwich Structure Optimum Design Subjected to Torsional Loading

As one of the most valued structural engineering innovations developed by the composites industry, sandwich structures are now used extensively in automotive, aerospace and civil infrastructure due to the main advantage of lightweight. This paper develops a minimum weight optimization method for sandwich structure subjected to torsion load. The design process are identified for a sandwich structure required to meet the design constraint of torsion stiffness. The optimum solutions show that at optimum design the core weight accounts for 66.7% of the whole sandwich structure. To illustrate the newly developed optimum design solutions, numerical examples are presented for sandwich structures made of either isotropic face skins or orthotropic composite face skins. Agreement between the theoretical analysis and the examples results is good.     

Stress analysis of multi-layered hollow anisotropic composite cylindrical structures using the homogenization method

This paper presents a general and efficient stress analysis strategy for hollow composite cylindrical structures consisting of multiple layers of different anisotropic materials subjected to different loads. Cylindrical material anisotropy and various loading conditions are considered in the stress analysis. The general stress solutions for homogenized hollow anisotropic cylinders subjected to pressure, axial force, torsion, shear and bending are presented with explicit formulations under typical force and displacement boundary conditions. The stresses and strains in a layer of the composite cylindrical structures are obtained from the solutions of homogenized hollow cylinders with effective material properties and discontinuous layer material properties. Effective axial, torsional, bending and coupling stiffness coefficients taking into account material anisotropy are also determined from the strain solutions for the hollow composite cylindrical structures. Examples show that the material anisotropy may have significant effects on the effective stiffness coefficients in some cases. The stress analysis method is demonstrated with an example of stress analysis of a 22-layer composite riser, and the results are compared with numerical solutions. This method is efficient for stress analysis of thin-walled or moderately thick-walled hollow composite cylindrical structures with various multiple layers of different materials or arbitrary fiber angles because no explicit interfacial continuity parameters are required. It provides an efficient and easy-to-use analysis tool for assessing hollow composite cylindrical structures in engineering applications.     

复合材料蜂窝夹层板结构的多工况优化设计研究

以复合材料蜂窝夹层板结构作为研究对象,建立了多工况优化模型,对众多的材料设计变量进行必要的取舍,通过优化分析确定复合材料蜂窝夹层板面板各分层的厚度以及蜂窝芯层的厚度等,使结构满足相应的频率约束、屈曲约束,以及强度约束、位移约束和尺寸限制等,同时达到结构的重量最轻。采用序列二次规划法对某卫星的承力筒结构进行了优化设计,优化结果表明:在满足其振动特性以及静力学特性的条件下,复合材料蜂窝承力筒的各面板层厚度以及蜂窝芯层的厚度均有所减小,减重效果显著,较好地实现了复合材料蜂窝夹层板结构的多工况优化设计。     

Torsion of carbon fiber composite pyramidal core sandwich plates

A combined theoretical, experimental and numerical investigation of carbon fiber composite pyramidal core sandwich plates subjected to torsion loading is conducted. Pyramidal core sandwich plates are made from carbon fiber composite material by a hot compression molding method. Based on the Classical Laminate Plate Theory and Shear Deformation Theory, the equivalent mechanical properties of laminated face-sheet are obtained; based on a homogenization concept combined with a mechanical of materials approach, the equivalent in-plane and out-of-plane shear moduli of pyramidal core are obtained. A torsion solution is derived with Prandtl stress function and can be used in the sandwich plate with orthotropic face-sheets and orthotropic core. The influences of material properties and geometrical parameters on the equivalent torsional stiffness are explored. In order to verify the accuracy of the analytical torsion solution, experimental tests of sandwich plate samples with different face-sheet thicknesses are conducted and two types of finite element models are developed. Good agreements among analytical predictions, finite element simulations and experimental evaluations are achieved, which prove the validity of the present derivation and simulation. The proposed method could also be applied in design applications and optimization of the pyramidal core sandwich structures.     

Localized indentation of sandwich panels with metallic foam core: Analytical models for two types of indenters

Sandwich structures with metallic foam core are sensitive to local indentation because of the low strength of the core and low bending stiffness of the thin face sheets. In this paper, local indentation response of sandwich panels with metallic foam core under a flat/spherical indenter was analyzed. The composite sandwich is modeled as an infinite, isotropic, plastic membrane on a rigid-plastic foundation. For simplicity, a quadratic polynomial displacement field was employed to describe the deformation of the upper face sheet. By using the principle of minimum work, explicit solutions for the indentation force and the sizes of the deformation regions were derived. The analytical results were verified by those from simulation by using the ABAQUS code, and they are in close agreement. Distribution of radial tensile strain of the upper face sheet and the ratio of energy dissipation of foam core to that of the upper face sheet were analyzed.     

Mechanical properties and design of sandwich materials

Sandwich materials consisting of a low density core with stiff skins offer considerable potential for weight saving in panel applications, where the main loads are flexural. Sandwich materials of interest for car and van body panels, seat shells, etc, include steel/plastic laminates, integral skinned plastic foams and glass fibre-reinforced polyester skins with foamed plastic cores. In this paper, basic design formulae for the flexural stiffness and strength of such sandwich materials are reviewed and a method for designing optimum sandwich structures for least weight or cost is given. Mechanical property data are presented on a range of sandwich materials of potential interest for vehicle panel applications. It is then shown how use of the least-weight design method enables core and skin thicknesses to be determined and gives a means of improving the flexural properties of existing sandwich constructions.     

Compression and bending performances of carbon fiber reinforced lattice-core sandwich composites

To restrict debonding, carbon fiber reinforced lattice-core sandwich composites with compliant skins were designed and manufactured. Compression behaviors of the lattice composites and sandwich columns with different skin thicknesses were tested. Bending performances of the sandwich panels were explored by three-point bending experiments. Two typical failure mechanisms of the lattice-core sandwich structures, delaminating and local buckling were revealed by the experiments. Failure criteria were suggested and gave consistent analytical predictions. For panels with stiff skins, delamination is the dominant failure style. Cell dimensions, fracture toughness of the adhesives and the strength of the sandwich skin decide the critical load capacity of the lattice-core sandwich structure. The mono-cell buckling and the succeeding local buckling are dominant for the sandwich structures with more compliant skin sheets. Debonding is restricted within one cell in bending and two cells in compression for lattice-core sandwich panels with compliant face sheets and softer lattice cores.     

扭弯比对SRC柱抗震性能影响的试验研究与分析

为研究扭弯比对弯曲和扭转复合作用下型钢混凝土组合（SRC）柱的受力及变形性能影响,以扭弯比为主要控制参数对7个SRC柱进行了弯矩和扭矩成比例加载的低周往复试验,研究分析了扭弯比对SRC柱的破坏特征、滞回性能、承载力以及变形等特征的影响规律,并建立了SRC柱在弯扭复合作用下的抗弯、抗扭承载能力及变形计算方法。研究结果表明:扭弯比是影响SRC柱抗震性能的主要参数,扭弯比参数决定了SRC柱的破坏类型;弯扭复合作用降低了SRC柱的抗弯、抗扭承载能力,但扭弯比对弯曲和扭转存在相反的影响;弯矩与扭矩成比例往复加载相比定扭矩弯矩往复加载,抗弯和抗扭承载力的相互影响程度减小且偏于安全。     

Characteristics of joining inserts for composite sandwich panels

Composite sandwich constructions are widely employed in various light weight structures, because composite sandwich panels have high specific stiffness and high specific bending strength compared to solid panels. Since sandwich panels are basically unsuited to carry localized loads, the sandwich structure should provide joining inserts to transfer the localized loads to other structures.In this work, the load transfer characteristics of the partial type insert for composite sandwich panels were investigated experimentally with respect to the insert shape. The static and dynamic pull out tests of the composite sandwich panels composed of an aluminum honeycomb core, two laminates of carbon fiber/epoxy composite and aluminum insert, were performed. From the experiments, the effect of the insert shape on the mechanical characteristics of composite sandwich panels was evaluated.     

多重调谐质量阻尼器控制单层非对称结构扭转振动的设计参数

研究了用两组相同的MTMD控制单层非对称结构扭转振动的最优设计参数。MTMD具有相同的刚度和 阻尼系数但不同的质量。MTMD被布置在最优位置。MTMD最优参数的设计准则定义为:结构最大扭转角位移动力放 大系数的最小值的最小化。MTMD的有效性设计准则定义为:结构最大扭转角位移动力放大系数的最小值的最小化与 无MTMD时结构最大扭转角位移动力放大系数的比值。基于定义的设计准则,研究了非对称结构的标准化偏心系数 (NER)和扭转对侧向频率比(TTFR)对处于最优位置MTMD最优设计参数和有效性的影响。     

蜂窝夹层修理结构的弯曲性能试验分析

采用四点弯加载方式研究分析了含损伤蜂窝夹层修理结构的弯曲性能,该夹层结构由碳纤维增强的聚合物面板和蜂窝芯子组成。进一步分析了挖补斜度、挖补方式、损伤程度、修理设备和修理材料对修理板弯曲性能的影响。研究表明,修理板的破坏模式可分为补片边缘折断、补片中面折断和胶层破坏三种,相同破坏模式修理板的名义弯曲强度相近,其中前两种破坏模式修理板的名义弯曲强度与完好板相近,而第三种破坏模式修理板的名义弯曲强度相对较低。所有修理板的名义弯曲强度恢复率基本处于95%以上,同时修理后抗弯刚度也满足修理准则。     

Flexural behaviour of glue-laminated fibre composite sandwich beams

This study involved experimental investigation onto the flexural behaviour of glue-laminated fibre composite sandwich beams with a view of using this material for structural beams. Composite sandwich beams with 1, 2, 3, and 4 composite sandwich panels glued together were subjected to 4-point static bending test in the flatwise and edgewise positions to evaluate their stiffness and strength properties. The results showed that the composite sandwich beams in the edgewise position failed with 25% higher bending strength but have 7% lower bending stiffness than beams in the flatwise position. The results however indicated that the bending stiffness of flatwise specimens converges to that of the edgewise specimens with increasing laminations. More importantly, the specimens in the edgewise position failed with greater ductility due to progressive failure of the fibre composite skins while the specimens in the flatwise position failed in a brittle manner due to debonding between the skin and core. Wrapping the glue-laminated sandwich beams with one layer of tri-axial glass fibres did not prove to be effective. Overall, it has been demonstrated that the glue-laminated sandwich beams exhibited better performance than the individual composite sandwich beams.     

Fatigue analysis of unidirectional GFRP composites under combined bending and torsional loads

Fatigue behavior of unidirectional glass fiber reinforced polyester (GFRP) composites at room temperature under in-phase combined torsion/bending loading was investigated. All fatigue tests were carried out on constant-deflection fatigue machine with frequency of 25 Hz. A 30% reduction from the initial applied moments was taken as a failure criterion in the combined torsion/bending fatigue tests of the composite materials. A series of pure torsional fatigue tests were conducted to construct the failure contour of GFRP composites using different failure theories. The obtained S–N curves from combined torsion/bending tests were compared with both, pure torsion fatigue test results and published results of pure bending fatigue tests of GFRP rods. Pictures by scanning electron microscope were used to closely examine the failure mode of the tested specimens under combined torsion/bending loading.

The results showed that, the unidirectional glass fiber reinforced polyester composites have poor torsional fatigue strength compared with the published results of pure bending fatigue strength. Endurance limit value (calculated from S–N equation at N = 10⁷ cycles) of GFRP specimens tested under combined torsion/bending loading equals 8.5 times the endurance limit of pure torsion fatigue. On the other hand the endurance limit of combined torsion/bending fatigue strength approximately half the fatigue limit of pure bending fatigue strength. The predicted values of combined torsion/bending fatigue strength at different number of cycles, using the published failure theory are in good agreement with the experimental data. For the investigated range of fiber volume fractions (V_f) it was found that higher stress levels are needed to produce fatigue failure after the same number of cycles as V_f increases.     

蜂窝金属夹芯板重复冲击动态响应研究

蜂窝金属及其夹芯结构是一种物理功能与结构一体化的新型轻质高强结构,广泛应用于结构轻量化与碰撞冲击防护领域。采用ABAQUS非线性有限元软件建立了蜂窝金属夹芯板(honeycomb sandwich panel,HSP)结构动态冲击数值仿真模型,数值仿真计算结果与文献实验结果吻合较好,验证了数值仿真模型的正确性。在此基础上,开展了重复冲击载荷作用下蜂窝金属夹芯板结构动态响应研究,得到了重复冲击力时程曲线、动态变形时程曲线、冲击力位移曲线以及最终挠度,分析了冲击能量、蜂窝壁厚以及上、下面板厚度分配对蜂窝金属夹芯板结构重复冲击动态响应的影响规律。研究结果表明,重复冲击载荷作用下蜂窝金属夹芯板结构上、下面板弯曲变形以及蜂窝芯层压缩变形逐渐积累,蜂窝芯层薄壁结构逐渐达到密实化,结构抗弯刚度逐渐上升,变形增量逐渐减小,结构整体能量吸收率下降。通过调节蜂窝壁厚和上、下面板厚度分配可以显著调节蜂窝金属夹芯板结构重复冲击动态响应与能量吸收性能。     

Prediction of inter-laminar stresses in composite honeycomb sandwich panels under mechanical loading using Variational Asymptotic Method

This work focuses on the formulation of an asymptotically correct theory for symmetric composite honeycomb sandwich plate structures. In these panels, transverse stresses tremendously influence design. The conventional 2-D finite elements cannot predict the thickness-wise distributions of transverse shear or normal stresses and 3-D displacements. Unfortunately, the use of the more accurate three-dimensional finite elements is computationally prohibitive. The development of the present theory is based on the Variational Asymptotic Method (VAM). Its unique features are the identification and utilization of additional small parameters associated with the anisotropy and non-homogeneity of composite sandwich plate structures. These parameters are ratios of smallness of the thickness of both facial layers to that of the core and smallness of 3-D stiffness coefficients of the core to that of the face sheets. Finally, anisotropy in the core and face sheets is addressed by the small parameters within the 3-D stiffness matrices. Numerical results are illustrated for several sample problems. The 3-D responses recovered using VAM-based model are obtained in a much more computationally efficient manner than, and are in agreement with, those of available 3-D elasticity solutions and 3-D FE solutions of MSC NASTRAN.     

Multi-scale modeling of time-dependent response of smart sandwich constructions

Polymer and polymer based composite structures exhibit time-dependent response, leading to their being described as viscoelastic bodies. The rate of creep (or stress relaxation) in viscoelastic bodies increases with increasing the temperature of the bodies. In this study, we are interested in analyzing the time-dependent response of smart sandwich composites comprising of glass fiber reinforced polymer (GFRP) skins, polyurethane foam core, and lead zirconate titanate (PZT) wafers embedded in the GFRP skins. The PZT is used to monitor lifetime performance of sandwich composites. A multi-scale model is developed to integrate different constitutive models of the constituents in the sandwich structures. Quasi-static and creep tests are conducted for bulk epoxy, GFRP, polyurethane foam, and sandwich specimens under uniaxial tension and bending. The tests were done at room temperature and at 80 °C. The experimental data are used for material characterization and model verification. The multi-scale model that is developed can be used to understand the effect of different responses of the constituents on the overall time-dependent behavior of sandwich structures and examine the feasibility of using PZT wafers for monitoring lifetime performance of sandwich structures.     

A C1 finite element including transverse shear and torsion warping for rectangular sandwich beams

A new three‐noded C¹ beam finite element is derived for the analysis of sandwich beams. The formulation includes transverse shear and warping due to torsion. It also accounts for the interlaminar continuity conditions at the interfaces between the layers, and the boundary conditions at the upper and lower surfaces of the beam. The transverse shear deformation is represented by a cosine function of a higher order. This allows us to avoid using shear correction factors. A warping function obtained from a three‐dimensional elasticity solution is used in the present model. Since the field consistency approach is accounted for interpolating the transverse strain and torsional strain, an exact integration scheme is employed in evaluating the strain energy terms. Performance of the element is tested by comparing the present results with exact three‐dimensional solu‐tions available for laminates under bending, and the elasticity three‐dimensional solution deduced from the de Saint‐Venant solution including both torsion with warping and bending. In addition, three‐dimensional solid finite elements using 27 noded‐brick elements have been used to bring out a reference solution not available for sandwich structures having high shear modular ratio between skins and core. A detailed parametric study is carried out to show the effects of various parameters such as length‐to‐thickness ratio, shear modular ratio, boundary conditions, free (de Saint‐Venant) and constrained torsion. Copyright © 1999 John Wiley & Sons, Ltd.     

Design and Optimization of Composite Automotive Hatchback Using Integrated Material-Structure-Process-Performance Method

The application of polymer composites as a substitution of metal is an effective approach to reduce vehicle weight. However, the final performance of composite structures is determined not only by the material types, structural designs and manufacturing process, but also by their mutual restrict. Hence, an integrated “material-structure-process-performance” method is proposed for the conceptual and detail design of composite components. The material selection is based on the principle of composite mechanics such as rule of mixture for laminate. The design of component geometry, dimension and stacking sequence is determined by parametric modeling and size optimization. The selection of process parameters are based on multi-physical field simulation. The stiffness and modal constraint conditions were obtained from the numerical analysis of metal benchmark under typical load conditions. The optimal design was found by multi-discipline optimization. Finally, the proposed method was validated by an application case of automotive hatchback using carbon fiber reinforced polymer. Compared with the metal benchmark, the weight of composite one reduces 38.8%, simultaneously, its torsion and bending stiffness increases 3.75% and 33.23%, respectively, and the first frequency also increases 44.78%.     

高速列车及其用复合材料的发展

介绍了国内外高速列车及其用复合材料的发展,分析了列车高速化带来的问题以及实现列车高速化的主要途径,阐述了夹芯结构复合材料的性能特点及取代传统层合板结构复合材料的趋势,并提出了将三维整体复合材料夹芯结构用于制造高速列车车体结构件,从而弥补传统泡沫夹芯结构制造大尺寸构件刚度不足的缺点。