双模量矩形板的大挠度弯曲计算分析

双模量矩形板在外载荷作用下,会形成各向同性的拉伸区和压缩区,把双模量矩形板看成两种各向同性材料组成的层合板,采用弹性力学理论建立了双模量矩形板在外载荷作用下的静力平衡方程,利用静力平衡方程确定了双模量矩形板的中性面位置,推导出了双模量矩形板的大挠度弯曲变形微分方程。用加权残值法求得了双模量矩形板的大挠度弯曲变形时板中点挠度,把该方法计算结果与有限元计算结果进行了比较,说明了该计算方法是可靠的,并讨论分析了双模量对矩形板大挠度弯曲变形的影响。     

双模量面板泡沫铝芯夹层圆板的非线性弯曲

采用弹性理论建立了双模量面板泡沫铝芯圆形夹层板在均布载荷作用下的静力平衡方程,利用静力平衡方程确定了夹层板的中性面位置。在考虑剪切变形影响的基础上,采用能量法研究了双模量面板泡沫铝芯圆形夹层板的轴对称非线性弯陆问题,求得了夹层板中心挠度与均布载荷的关系式,并把该方法计算结果与有限元计算结果进行了比较,验证了该方法是可靠...     

高阶剪切变形板理论下FG-GRC板的屈曲和弯曲分析

基于三阶剪切变形板理论(TSDPT)和正弦剪切变形板理论(SSDPT),研究了功能梯度石墨烯增强复合材料(FG-GRC)板的屈曲和弯曲行为,并通过与一阶剪切变形板理论(FSDPT)计算结果的比较,分析了TSDPT、SSDPT与FSDPT在FG-GRC板屈曲和弯曲力学行为研究过程中的差异。材料的有效杨氏模量通过修正的Halpin-Tsai微观力学模型估算,有效泊松比通过混合律确定。利用最小势能原理推导出了包含五个未知量的控制方程,并获得了简支FG-GRC矩形板弯曲挠度和临界屈曲载荷Navier形式的解析解。数值结果表明：与TSDPT和SSDPT相比,FSDPT明显高估了FG-X型FG-GRC板的临界屈曲载荷而明显低估了其弯曲挠度,且略微低估了FG-O型FG-GRC板的临界屈曲载荷而略微高估了其弯曲挠度,而UD型和FG-A型FG-GRC板在三种理论下的计算结果几乎完全一致;TSDPT和SSDPT在计算FG-GRC板的弯曲挠度和临界屈曲载荷时结果十分相近;当板的总层数NL小于10层～15层时,弯曲载荷比率和临界屈曲载荷比率的变化非常显著,当总层数NL超过10层～15层时,弯曲载荷比率和临界屈...     

考虑剪切效应时双模量梁的自由振动

研究了考虑剪切效应时双模量梁自由振动问题。利用双模量材料纯剪切应力状态单元体,推导出双模量材料剪切弹性模量表达式。在考虑剪切效应的基础上,建立双模量梁振动的微分方程,推导出了双模量梁振动问题的振型表达式,并讨论分析了剪切效应对双模量梁自由振动固有频率的影响。算例分析表明,对于某些双模量梁自由振动问题,剪切效应的影响是不能忽略的。得到了双模量梁自由振动时,奇数波型与波型振型是不连续的存在间断点的结论。     

点阵材料夹芯简支梁在冲击载荷下的动力响应

首先给出了两端可移点阵材料夹芯简支梁受到均布冲击载荷时的刚塑性动力响应分析,然后将理论预测的夹芯梁中点的最大挠度和结构响应时间与有限元结果进行了比较,理论预测结果与有限元计算结果一致性较好。通过与质量和材料相同的单层实心梁进行对比分析,证实了点阵材料夹芯简支梁具有很好的抗冲击性能。通过对四棱锥夹芯简支梁进行拓扑构型设计,发现两端可移夹芯简支梁的最大挠度和结构响应时间对芯层的相对密度和相对厚度、面板与杆元的夹角十分敏感。随着夹芯梁所承受的单位面积冲量增大 , 夹芯梁中点的挠度增大。通过对由应变率敏感的304不锈钢制成的四棱锥桁架夹芯梁进行精细有限元分析,发现当考虑应变率效应时,梁的最大挠度小于不考虑应变率时的最大挠度。     

圆孔对GLARE层合板抗冲击性能的影响

为获得圆孔对玻璃纤维增强铝合金（GLARE）层合板抗冲击性能的影响规律,采用40 J的冲击能量对无孔和含圆孔GLARE层合板进行了落锤低速冲击试验,获得了冲击载荷、挠度和能量-时间曲线。应用ABAQUS/Explicit有限元分析软件对试验进行模拟,并预测了圆孔直径对GLARE层合板抗冲击性能的影响。结果显示:在低速冲击下,GLARE层合板纤维层的失效模式以分层损伤和纤维断裂为主;随着圆孔边缘至冲击中心距离的增加,层合板的冲击载荷峰值提高,而挠度峰值减小;数值模拟结果与试验结果的比较验证了模型的合理性;随着圆孔直径的增大,GLARE层合板的抗冲击性能逐步劣化。      

犬挠度层合板的拟协调罚单元

本文将考虑耦合和剪切效应的三角形拟协调罚单元推广到对层合板的大挠度分析。数值计算证明:该单元具有良好的收敛性和足够的精度.文中用大量图表显示了边界条件,纤维铺设角,铺层数和材料弹性模量出等因素对层合板大挠度解的影响。      

横向载荷作用下复合材料层板的铺层优化设计

本文讨论了双向增强层合板在横向载荷作用下的铺层优化分析。文中首先证明了具有最高固有频率及最小挠度的最优结构必定是对称铺设结构,进一步还说明了上述优化问题可化为单设计变量优化问题,本中导出了相应的极其简单的计算公式。      

集中载荷下四边固支正交各向异性矩形板的线性弯曲问题

采用载荷叠加法将集中载荷下四边固支正交各向异性矩形板线性弯曲的挠度分为3个部分:集中载荷下四边简支板的挠度、上下边简支左右边受弯矩的板的挠度、左右边简支上下边受弯矩的板的挠度,3个挠度之和在满足固支边界条件的情况下即为所要求的挠度的解。采用MATLAB软件编写程序进行计算,并将相同长宽的板在4种不同的厚度和载荷情况下的挠度计算结果与有限元分析结果进行比较,验证了解析解的正确性。最后讨论了经典的Kirchhoff薄板假设对于集中载荷的适用性问题。     

磁致伸缩层合悬臂梁式作动器的振动分析

为了分析磁致伸缩薄膜型层合悬臂梁式作动器的振动问题,应用磁致伸缩材料的非线性本构关系,由哈密尔顿原理导出了双层悬臂梁的振动微分方程。采用分离变量方法和常微分方程组的解析解法对磁致伸缩薄膜型层合悬臂梁的自由振动和受迫振动进行了理论分析。数值算例表明本文计算结果与有限元结果吻合较好,从而佐证了本文理论模型和求解方法的正确性,并讨论了几何参数、材料参数对层合梁固有频率的影响。还分析了在周期输入磁场激励下悬臂梁的挠度响应,且挠度响应呈现出倍频效应的动态特性。      

A perturbation solution of von-Kármán circular plates with different moduli in tension and compression under concentrated force

By modifying classical von-Kármán equations, we established bimodular von-Kármán equations of thin plates with different moduli in tension and compression. Adopting central deflection as a perturbation parameter, we used a perturbation method to solve the equations under various boundary conditions, including rigidly clamped, loosely clamped, simply hinged, and simply supported. The relation of load versus central deflection and stress formulas were derived via the perturbation solution obtained. The numerical simulation also shows that the perturbation solution based on central deflection is overall valid. The results indicate that when the compressive modulus of materials is greater than the tensile one, the bearing capacity of the plate will be further strengthened, which should be considered in the analysis and design of plate-like structures with obvious bimodular effect. Moreover, by comparing with the case under uniformly distributed load, the plate-membrane transition under centrally concentrated force presents discontinuity to some extent.     

Deflection of thick beams of multimodular materials

A transfer-matrix analysis is presented for determining the static behaviour of thick beams of ‘multimodular materials’ (i.e. materials which have different elastic behaviour in tension and compression, with nonlinear stress–strain curves approximated as piecewise linear, with four or more segments). To validate the transfer-matrix method results, a closed-form solution is also presented for cases in which the neutral-surface location is constant along the beam axis. Numerical results for axial displacement, transverse deflection, bending slope, bending moment, transverse shear, axial force and location of neutral surface are presented for multimodular and bimodular models of unidirectional aramid cordrubber. The transfer-matrix method results agree very well with the closed-form solutions.     

Levy-type piezothermoelastic solution for hybrid plate by using first-order shear deformation theory

A Levy-type solution is presented for hybrid rectangular plates, with two opposite edges simply supported, made of a cross-ply composite laminate with attached piezoelectric layers, and subjected to thermoelectromechanical load. First-order shear deformation and classical lamination theories are used. A mixed formulation is employed for the solution. The effect of the width-to-depth ratio and aspect ratio on deflection and force resultants has been illustrated for a uniform load on plates with various boundary conditions. The effect of shear deformation on deflection and force resultants for moderately thick plates is generally more pronounced for the mechanical load case than for the self-straining cases of thermal and electric loads.     

Nonlinear bending of thick beams laminated from bimodular composite materials

A higher-order shear deformation beam theory is presented to analyze geometrically nonliner bending of thick, rectangular beams made from bimodular materials. This is performed by using a mixed finite element model. Results are reported for maximum deflections of simply-supported and clamped-clamped beams under a uniformly distributed load. The effect of material bimodularity on the nonlinear transverse deflection is investigated.     

Nonlinear large deflection buckling analysis of compression rod with different moduli

Many novel materials exhibit a property of different elastic moduli in tension and compression. One such material is graphene, a wonder material, which has the highest strength yet measured. Investigations on buckling problems for structures with different moduli are scarce. To address this new problem, first, the nondimensional expression of the relation between offset of neutral axis and deflection curve is derived based on the phased integration method, and then using the energy method, load–deflection relation of the rod is determined; second, based on the improved constitutive model for different moduli, large deformation finite element formulations are developed, and combined with the arc-length method, finite element iterative program for rods with different moduli is established to obtain buckling critical loads; third, material mechanical properties testing of graphite, which is the raw material of graphene, is performed to measure the tensile and compressive elastic moduli; moreover, buckling tests are also conducted to investigate the buckling behavior of this kind of graphite rod. By comparing the calculation results of the energy method and finite element method with those of laboratory tests, the analytical model and finite element numerical model are demonstrated to be accurate and reliable. The results show that it may lead to unsafe results if the classic theory was still adopted to determine the buckling loads of those rods composed of a material having different moduli. The proposed models could provide a novel approach for further investigation of nonlinear mechanical behavior for other structures with different moduli.     

Optimum laminate design by using singular value decomposition

In practice, a structure is subjected to given loads and boundary conditions, and a multitude of stress and strain states may exist in the structure; hence, optimal construction of a laminate in a structure cannot be sought by considering only a limited number of stress resultants in the existence of multiple load cases. Then, another design objective based on optimization of a laminate for the worst possible load case emerges which is formulated as a minimax problem whose solution is shown to be equivalent to singular value minimization problem. As the squares of singular values are the bounds of power, energy and power spectral density ratios between the input and output vectors, shaping the singular values of a composite material is equivalent to shaping the response of the material. As a novel approach, singular values are used for the layout optimization of laminate. In this method, the main idea is minimization of the largest singular value of the transfer function matrix between force/moment resultants and outputs stress/strain. Thus the overall optimization problem is reduced to a simple minimization problem. Numerical examples and finite element simulations are presented for several test problems. In particular, it is shown that the use of singular values and singular vectors is computationally advantageous in case of multiple load case.     

缠绕肋缠绕过程试验及力学行为分析

首先通过单向拉伸试验测试和理论计算两种方法得到4层(45?/?45?/45?/?45?)铺设碳纤维复合材料的弹性模量,作为文中数值计算及弯矩分析的材料参数。通过4层(45?/?45?/45?/?45?)铺设碳纤维复合材料肋进行整体缠绕过程试验,得到肋整体缠绕过程肋表层应变和缠绕弯矩。利用ABAQUS分别建立了复合材料肋整体缠绕精细有限元模型,实现了缠绕一周过程强几何非线性数值模拟分析,得到各层应力、应变特征和缠绕弯矩,并与试验结果比较分析。进而给出缠绕弯矩解析表达式,并对材料铺设与厚度进行分析,得到缠绕过程最优材料铺设机理与最大厚度分析方法。该文对缠绕肋设计和深入研究具有重要参考价值。     

分布式连接全装配RC楼盖竖向承载力与变形分析

在分布式连接新型全装配RC楼盖中,板与板之间通过连接件连接实现横板向传力。为研究新型楼盖竖向承载力计算方法,进行了新型楼盖在竖向荷载作用下的内力与变形分析。结果表明:基于正交各向异性弹性薄板小挠度理论和单三角级数法得到四边简支新型楼盖在竖向均布荷载作用下的弯矩与挠度表达式,提出了新型楼盖横板向刚度计算方法,并通过与试验和有限元结果对比,验证了所提方法的准确性;新型楼盖的挠度在两个方向呈空间抛物面分布,表明新型楼盖具有良好横板向传力性能;板缝连接可有效传递板内弯矩,但正交的两个方向弯矩传递效果存在差异,表现为顺板向弯矩的传递效果优于横板向。研究成果可为分布式连接全装配RC楼盖的研究和应用提供参考。     

金属裂纹板复合材料单面胶接修补结构应力分析

考虑金属裂纹板复合材料单面胶接修补结构的几何非线性和边界条件,建立了考虑弯曲变形单面修补结构力学分析模型,计算出承受面内载荷时修补结构的弯矩和挠度,将补片自由端和金属板裂纹处的弯矩作为胶层应力控制微分方程的边界条件,推导出剪应力和剥离应力的解析解,及裂纹张开位移的表达式,并与有限元数值结果进行对比。分析结果表明,胶接修补结构应力分析理论模型和相关简化假设合理、正确。利用所建立的解析模型研究了金属裂纹复合材料单面胶接修补结构的应力分布特点及胶层主导破坏模式的失效机制,为胶接修补结构的承载能力分析以及结构改进设计提供了一定的理论依据。     

Effect of the interface stiffness and skin–core adhesion efficiency on the interfacial stress distribution of sandwich structures

This paper investigates the load distribution along the skin–core interface length of FRP-metal laminates subjected to in-plane tension, using an improved shear lag model. The model elucidates the significance of the interface stiffness concept on the skin–core interface load distribution in FRP-metal laminate beams and introduces a basic hypothesis according which, the interface stiffness depends on the difference in shear moduli of the constituent materials as well as on the degree of adhesion which, in turn, depends on the abrupt jump in shear moduli at the skin–core boundary. Details of an experimental procedure carried out and of experimental results obtained are also presented. From the combined experimental and theoretical investigation it can be concluded that for a given FRP-metal laminate structure with known core and facing properties, it is possible to evaluate the skin–core degree of adhesion as well as the interface stiffness and predict the interfacial stress distribution by simply conducting a single tensile test. Thus, the proposed method can be considered as a tool for the structural performance and reliability control of FRP-metal laminate structures.