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复合材料纤维张力缠绕技术通过提高纤维的张力水平可充分发挥纤维高强、高模优势,在成型过程中对结构进行预紧,成为解决高速转动部件径向变形大、界面强度低等问题新的有效途径。将每一层纤维的张力缠绕等效为一个含预应力复合材料薄环的叠加,基于正交各向异性复合材料缠绕层和各向同性金属芯模弹性变形理论,建立了纤维张力缠绕力学解析模型,得到芯模和缠绕层预应力场随缠绕层数及缠绕张力的变化规律,并通过复合材料纤维张力工艺试验验证了力学解析模型的正确性。研究发现了纤维张力缠绕中预应力“饱和”现象,并确定了影响张力缠绕预应力场的两个主要参数:缠绕层环径向刚度比Eθ/Er和张力大小T(r),为复合材料纤维张力缠绕成型工艺提供理论支撑。 相似文献
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泡沫金属的力学性能强烈依赖于内部结构。当构件特征尺寸与胞孔特征尺寸d处于相同数量级时,表现出明显的尺度效应。为了揭示这种尺度效应的力学机理,研究了泡沫金属试件的剪切和纯弯曲试验。一方面,利用应变梯度弹性理论给出解析解,其中包含了材料内禀尺寸lc这一关键模型参数。另一方面,把每段胞壁视为铁木辛柯梁,从而建立梁链网作为泡沫金属的微观力学模型。通过应变能等效原理建立应变梯度连续体和基体金属材料弹性参数之间的关系。发现,边界层的约束条件对泡沫金属的力学响应有重要影响。弯曲问题中,只有对离散模型上下表面施加恰当的附加转角约束后,应变梯度理论解与链网模型数值解才能够吻合。这为理解应变梯度理论中的非传统边界条件提供了一个直观的实例。通过数据拟合,得到了内禀尺寸lc与胞孔特征尺寸d之间的关系,与文献结论相符。 相似文献
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解析型Winkler弹性地基梁单元构造 总被引:1,自引:0,他引:1
该文采用Winkler弹性地基梁理论确定了弹性地基梁的挠度方程解析通解; 根据最小势能原理建立了解析型Winkler弹性地基欧拉梁及铁摩辛柯梁的单元刚度及等效节点荷载; 得到了解析型弹性地基欧拉梁单元AWFB-E及铁摩辛柯梁单元AWFB-T。同时,论文还采用传统里兹法求得了相应的Winkler弹性地基欧拉梁及铁摩辛柯梁单元刚度矩阵,得到了里兹法弹性地基欧拉梁单元RWFB-E及铁摩辛柯梁单元RWFB-T。对该文构建的两类单元与一般梁-基体系有限元分析结果及理论解析解进行了对比。对比结果表明,传统里兹法由于其多项式形函数无法精确模拟弹性地基梁变形,因此其结果与理论解析解有误差,但随着单元数量增多其误差减小; 采用解析型单元进行计算时,无论单元数量多少,得到的均为“真实”解,说明解析试函数法求得的位移形函数比一般的多项式形函数精确,得到的弹性地基梁单元具备解析型、精确性的特点,可应用于解决实际工程问题。 相似文献
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基于弹性核法的曲梁有限梁段法,在求解曲梁单元刚度矩阵时,因柔度矩阵的表达式繁琐,难以直接求逆得到单元刚度矩阵的解析表达式.相关文献及曲梁的梁段有限元程序均采用数值方法求逆,得其刚度矩阵.该文提出一个矩阵求逆理论,并证明之.依此理论推导出曲梁单元刚度矩阵的解析解,并提出对曲梁有限梁段法的改进.算例验证了公式的正确性和可靠... 相似文献
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该文基于弹性动力学理论,采用复变函数与保角映射方法,研究了指数梯度材料中任意形孔洞对弹性波的散射与动应力集中,给出了问题的解析解.并以求解椭圆孔动应力集中系数为例,分析了入射波数和材料非均匀参数等对椭圆孔动应力分布的影响. 相似文献
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该文运用Green函数法求解了Timoshenko曲梁在强迫振动下的解析解,通过分析曲梁截面的力学平衡,建立了Timoshenko曲梁的振动方程。依次采用分离变量法和Laplace变换法,对不同边界的Timoshenko曲梁求解出了相应的Green函数。并且通过引入两个特征参数来考虑阻尼对强迫振动的影响。数值计算中,验证了该解析解的有效性,并对其中涉及的各种重要物理参数的影响进行了研究。研究结果表明:通过将半径R设置为无穷大,可以简化为Timoshenko直梁振动模型,在此基础上,将剪切修正因子κ设置为无穷大,可以退化为Prescott直梁振动模型,最后再把转动惯量γ设置为0,可退化为Euler-Bernoulli直梁振动模型。该文给出的数值结果验证了所得解的有效性。 相似文献
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The main objective of this work is to obtain analytical solutions for thick-walled cylinders subjected to internal and external pressure in which the entire wall is made of functionally graded material or of only a thin functionally graded coating present on the internal homogeneous wall. We assume that the materials are isotropic with constant Poisson’s ratio; as far as the Young modulus is concerned, we consider a power and an exponential. The proposed analytical solutions show the effects of the different profiles describing the graded properties of the materials on the stress and displacement fields; in addition, comparisons between graded coating and conventional homogeneous coating highlight the advantage of the graded material on the interface stress reduction. Furthermore, we show how even a thin graded coating can be useful to satisfy the requirements of a specific application without having to make an entire wall with graded properties. This investigation permits us to optimize the elastic response of cylinders under pressure by tailoring the thickness variation of the elastic properties and to reduce manufacturing costs given by the technological limitations that occur to produce entire functionally graded walls. 相似文献
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《Composites Science and Technology》2007,67(3-4):481-488
The problem of a cantilever functionally graded beam subjected to different loads is studied. In terms of Airy stress function a general two-dimensional solution is presented for a cantilever functionally graded beam, assuming that all the elastic moduli of the material have the same variations along the beam-thickness direction. Explicit expressions of analytical solutions to some specific examples under different boundary conditions are obtained to demonstrate the usefulness of the proposed general solution technique. This solution will be useful in analyzing functionally graded beam with arbitrary variations of material properties and it can serve as a basis for establishing simplified functionally graded beam theories. 相似文献
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《Composites Part B》2013,45(1):274-282
The plane stress problem of an orthotropic functionally graded beam with arbitrary graded material properties along the thickness direction is investigated by the displacement function approach for the first time. A general two-dimensional solution is obtained for a functionally graded beam subjected to normal and shear tractions of arbitrary form on the top and bottom surfaces and under various end boundary conditions. For isotropic case explicit solutions are given to some specific through-the-thickness variations of Young’s modulus such as exponential model, linear model and reciprocal model. The influence of different grade models on the stress and displacement fields are illustrated in numerical examples. These analytical solutions can serve as a basis for establishing simplified theories and evaluating numerical solutions of functionally graded beams. 相似文献
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Static deformations, and free and forced vibrations of a thick rectangular functionally graded elastic plate are analyzed by using a higher-order shear and normal deformable plate theory (HOSNDPT) and a meshless local Petrov–Galerkin (MLPG) method. All components of the stress tensor are computed from equations of the plate theory. The plate material, made of two isotropic constituents, is assumed to be macroscopically isotropic with material properties varying in the thickness direction only. Effective material moduli are computed by using the Mori–Tanaka homogenization technique. Computed results for static and free vibration problems are found to agree well with their analytical solutions. The response of the plate to impulse loads is also computed for different volume fractions of the two constituents. Contributions of the work include the use of the HOSNDPT and the MLPG method for the analysis of functionally graded plates. 相似文献
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Analytical modelling of thermal residual stresses in exponential functionally graded material system
Ali Bouchafa Abdelnour Benzair Abdelouahed Tounsi Kada Draiche Ismail Mechab El Abbas Adda Bedia 《Materials & Design》2010,31(1):560-563
An analytical model is developed for prediction of thermal residual stresses, arising from the fabrication of exponential functionally graded material (simply called E-FGM) systems. The thermomechanical properties of functionally graded layers are assumed to vary exponentially through the thickness. Residual stresses were found to increase when fully ceramic and/or fully metal regions are included in the structure, adjoining the graded zone. The effects of temperature dependent elastic and thermal expansion characteristics of constituents on residual stress were found to be small. 相似文献
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Exact solutions for functionally graded thick plates are presented based on the three-dimensional theory of elasticity. The plate is assumed isotropic at any point, while material properties to vary exponentially through the thickness. The system of governing partial differential equations is reduced to an ordinary one about the thickness coordinate by expanding the state variables into infinite dual series of trigonometric functions. Interactions between the Winkler–Pasternak elastic foundation and the plate are treated as boundary conditions. The problem is finally solved using the state space method. Effects of stiffness of the foundation, loading cases, and gradient index on mechanical responses of the plates are discussed. It is established that elastic foundations affects significantly the mechanical behavior of functionally graded thick plates. Numerical results presented in the paper can serve as benchmarks for future analyses of functionally graded thick plates on elastic foundations. 相似文献
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Vibration analysis of a functionally graded rectangular plate resting on two parameter elastic foundation is presented here. The displacement filed based on the third order shear deformation plate theory is used. By considering the in-plane displacement components of an arbitrary material point on the mid-plane of the plate and using Hamilton’s principle, the governing equations of motion are obtained which are five highly coupled partial differential equations. An analytical approach is employed to decouple these partial differential equations. The decoupled equations of functionally graded rectangular plate resting on elastic foundation are solved analytically for levy type of boundary conditions. The numerical results are presented and discussed for a wide range of plate and foundation parameters. The results show that the Pasternak (shear) elastic foundation drastically changes the natural frequency. It is also observed that in some boundary conditions, the in-plane displacements have significant effects on natural frequency of thick functionally graded plates and they cannot be ignored. 相似文献
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《International Journal of Engineering Science》2007,45(2-8):467-485
This paper investigates the plane stress problem of generally anisotropic magneto-electro-elastic beams with the coefficients of elastic compliance, piezoelectricity, dielectric impermeability, piezomagnetism, magnetoelectricity, and magnetic permeability being arbitrary functions of the thickness coordinate. Firstly, partial differential equations governing stress function, electric displacement function and magnetic induction function are derived for plane problems of anisotropic functionally graded magneto-electro-elastic materials. Secondly, these functions are assumed in forms of polynomials in the longitudinal coordinate and can be acquired through a successive integral approach. The analytical expressions of axial force, bending moment, shear force, average electric displacement, average magnetic induction, displacements, electric potential and magnetic potential are then deduced. Thirdly, problems of functionally graded magneto-electro-elastic plane beams are considered, with integral constants being completely determinable from boundary conditions. A series of analytical solutions are thus obtained, including the solutions for beams under tension and pure bending, for cantilever beams subjected to shear force applied at the free end, and for cantilever beams subjected to uniform load. These solutions can be easily degenerated into the solutions for homogenous anisotropic magneto-electro-elastic beams. Finally, a numerical example is presented to show the application of the proposed method. 相似文献
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C. F. Lü C. W. Lim W. Q. Chen 《International journal for numerical methods in engineering》2009,79(1):25-44
Semi‐analytical 3‐D elasticity solutions are presented for orthotropic multi‐directional functionally graded plates using the differential quadrature method (DQM) based on the state‐space formalism. Material properties are assumed to vary not only through the thickness but also in the in‐plane directions following an exponential law. The graded in‐plane domain is solved numerically via the DQM, while exact solutions are sought for the thickness domain using the state‐space method. Convergence studies are performed, and the present hybrid semi‐analytical method is validated by comparing numerical results with the exact solutions for a conventional unidirectional functionally graded plate. Finally, effects of material gradient indices on the displacement and stress fields of the plates are investigated and discussed. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
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覆盖层为功能梯度材料弹性半平面中的Love波 总被引:1,自引:0,他引:1
对均匀各向同性弹性半平面上覆盖一层功能梯度材料中存在的Love波的频散问题进行了研究,给出了Love波频散方程的一般形式。利用WKBJ近似理论,给出了功能梯度材料层的位移、应力近似解析解,导出了Love波WKBJ近似频散方程的一般形式。该文以功能梯度材料层的剪切弹性模量和质量密度沿厚度方向均为指数函数变化为例,进行了实例计算和分析,给出了频散曲线,讨论了Love波在功能梯度材料覆盖层弹性半平面中传播的一般性质。这些结论对无损检测和反问题分析方法的改进提供理论依据。 相似文献