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功能梯度热释电材料矩形板的三维精确分析 总被引:17,自引:2,他引:17
对四边简支、接地、等温的功能梯度热释电材料矩形板进行精确三维分析.根据正交各向异性热释电材料基本方程,导出了功能梯度热释电材料的状态方程.假定材料的机械、电学和热学性质沿板厚方向按统一的指数函数形式梯度分布,获得了四边简支、接地和等温的矩形板,在上下表面作用任意的机械荷载、电荷载和热荷载情况下的三维精确解.通过算例,分析了在机械荷载、电荷载和热荷载分别作用下,材料性质的不同梯度变化对平板结构响应的影响.所获得的精确结果可作为评价其他近似方法的标准解答或者作为建立简化的功能梯度热释电材料平板理论的基础。 相似文献
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讨论螺旋细杆的特殊形式扭转振动,即均匀扭转振动.以非圆截面杆和有原始曲率的圆截面杆为研究对象.杆作均匀扭转振动时各截面有相同的扭角变化规律,且杆中心线的几何形状不受振动过程的影响.研究表明,扭振来源于杆截面的非对称性及杆的原始曲率.杆的扭振规律与单摆运动相似,其动力学方程存在精确解.圆环杆的均匀扭振为螺旋杆的倾角为零时的特例. 相似文献
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基于柱坐标系下的三维弹性力学基本方程,采用状态空间法得到两端固支单层与叠层圆柱厚壳轴对称问题的精确解析解。为严格满足固支端的边界条件,将固支端的边界位移函数作为状态变量引入状态方程,采用增维方法把非齐次状态方程变为齐次状态方程,并通过层合渐近技术将变系数状态矩阵转为常系数矩阵进行求解。所得到的解不仅严格满足三维弹性力学基本方程,而且严格满足固支边界条件,是真正意义上的三维精确解。算例表明,本研究解与有限元解吻合,具有很高的精度,且关于级数项数和分层数具有很好的收敛性。另外,通过圆柱厚壳各力学量沿径向和轴向的精确分布规律分析了厚径比和跨径比变化对位移和应力分布的影响。 相似文献
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瞬变流摩阻计算及摩阻对水力瞬变的影响 总被引:2,自引:0,他引:2
摩阻损失的精确计算对于长输管道的水力瞬变分析是很重要的一个环节、过去为减少计算工作量,采用固定摩阻系数和流量一阶近似法计算瞬交流摩阻,精度有限.本跟踪液流流态变化,采用变摩阻系数和流量二阶插值法计算瞬交流摩阻,提高了摩阻计算精度.同时,从理论上分析了管道摩阻对水力瞬变的影响,澄清了一些模糊认识. 相似文献
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求解水下纵向加肋无限长非圆柱壳声辐射问题的一种新的半解析方法 总被引:3,自引:3,他引:3
基于齐次扩容精细积分法和复数矢径虚拟边界谱方法,利用Fourier积分变换和稳相法,提出了一种具有较高效率和精度的新的求解水下纵向加肋无限长非圆柱壳声辐射问题的半解析方法.考虑了非圆柱壳和肋骨之间同时存在多种相互作用力和力偶矩,较已往很多学者仅计及法向相互作用力更加符合实际.不仅比较了该文方法和精确解计算纵向加肋圆柱壳在集中点力激励下的声辐射计算结果,同时还研究了肋骨数量、大小以及椭圆柱壳横截面椭圆度对声辐射特性的影响.数值计算结果表明该文方法较已有的混合FE-BE法更为有效. 相似文献
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D.THUNG 《应用数学和力学(英文版)》2011,32(11):1407-1422
The spline finite strip method(PSM) is one of the most popular numerical methods for analyzing prismatic structures.Efficacy and convergence of the method have been demonstrated in previous studies by comparing only numerical results with analytical results of some benchmark problems.To date,no exact solutions of the method or its explicit forms of error terms have been derived to show its convergence analytically. As such,in this paper,the mathematical exact solutions of spline finite strips in the plat... 相似文献
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ANALYTICAL SOLUTIONS TO STRESS CONCENTRATION PROBLEM IN PLATES CONTAINING RECTANGULAR HOLE UNDER BIAXIAL TENSIONS 总被引:3,自引:0,他引:3
The stress concentration problem in structures with a circular or elliptic hole can be investigated by analytical methods. For the problem with a rectangular hole, only approximate results are derived. This paper deduces the analytical solutions to the stress concentration problem in plates with a rectangular hole under biaxial tensions. By using the U-transformation technique and the finite element method, the analytical displacement solutions of the finite element equations are derived in the series form. Therefore, the stress concentration can then be discussed easily and conveniently. For plate problem the bilinear rectangular element with four nodes is taken as an example to demonstrate the applicability of the proposed method. The stress concentration factors for various ratios of height to width of the hole are obtained. 相似文献
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研究高次杆单元和梁单元的节点位移精度问题.首先求出一端固支均匀杆和悬臂梁在任意次多项式形式分布载荷作用下的位移精确解,然后用二次杆单元、五次欧拉梁单元和三次铁木辛柯梁单元求得了节点位移.通过比较有限元解与精确解以及利用静力凝聚方法,发现一次以上杆单元、三次以上欧拉梁单元以及三次以上铁木辛柯梁单元都可以给出精确的端点位移. 相似文献
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《International Journal of Solids and Structures》2007,44(22-23):7564-7576
Non-local viscoelastic beam models are used to analyse the dynamics of beams with different boundary conditions using the finite element method. Unlike local damping models the internal force of the non-local model is obtained as weighted average of state variables over a spatial domain via convolution integrals with spatial kernel functions that depend on a distance measure. In the finite element analysis, the interpolating shape functions of the element displacement field are identical to those of standard two-node beam elements. However, for non-local damping, nodes remote from the element do have an effect on the energy expressions, and hence on the damping matrix. The expressions of these direct and cross damping matrices may be obtained explicitly for some common spatial kernel functions and Euler–Bernoulli beam theory. Alternatively numerical integration may be applied to obtain solutions. Examples are given where the eigenvalues are compared to the exact solution for a pinned–pinned beam to demonstrate the convergence of the finite element method. The results for beams with other boundary conditions are used to demonstrate the versatility of the finite element technique. 相似文献
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平面理性元的收敛性证明 总被引:5,自引:0,他引:5
理性元直接在物理面内列式,并用微分方程的解插值,不用等参技术而在计算面内用多项式插值.由于其解析的特性,即使是不协调元也可证明其收敛性.本文的证明采用力学方法,故易于为力学工作者所接受,且可用于多种单元的结构.收敛性证明可给理性有限元以坚实的理论基础. 相似文献
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Cellular solids are usually treated as homogeneous continuums with effective properties. Nevertheless, these mechanical properties depend strongly on the ratio of the specimen size to the cell size. These size effects may be accounted for according to preliminary static analysis of effective continuums based on couple-stress theory. In this paper an effective dynamic continuum model, based on couple-stress theory, is proposed to analyze the behavior of free vibrations of periodic cellular solids. In this continuum model, the effective mechanical constants of the effective continuum are deduced by an equivalent energy method. The cellular solid structure is then replaced with the equivalent couple-stress continuum with same overall dimension and shape. Moreover, the finite element formulation of the couple-stress continuum for the generalized eigenvalue analysis is developed to implement the free vibration analysis. The eigenfrequencies of the effective continuum are then obtained via the shear beam theory or the finite element method. A conventional finite element analysis by discretizing each cell of the cellular solids is also carried out to serve as an exact solution. Several structural cases are calculated to demonstrate the accuracy and effectiveness of the proposed continuum model. Good agreement on structural eigenfrequencies between the effective continuum solutions and the exact solutions shows that the proposed continuum model can accurately simulate the dynamic behavior of the cellular solids. 相似文献
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The correspondence principle is an important mathematical technique to compute the non-ageing linear viscoelastic problem as it allows to take advantage of the computational methods originally developed for the elastic case. However, the correspondence principle becomes invalid when the materials exhibit ageing. To deal with this problem, a second-order two-scale (SOTS) computational method in the time domain is presented to predict the ageing linear viscoelastic performance of composite materials with a periodic structure. First, in the time domain, the SOTS formulation for calculating the effective relaxation modulus and displacement approximate solutions of the ageing viscoelastic problem is formally derived. Error estimates of the displacement approximate solutions for SOTS method are then given. Numerical results obtained by the SOTS method are shown and compared with those by the finite element method in a very fine mesh. Both the analytical and numerical results show that the SOTS computational method is feasible and efficient to predict the ageing linear viscoelastic performance of composite materials with a periodic structure. 相似文献
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《International Journal of Solids and Structures》2014,51(19-20):3361-3371
Within this paper, an analytical formulation is provided and used to determine the natural frequencies and mode shapes of a planar beam with initial pre-stress and large variable curvature. The static configuration, mode shapes, and natural frequencies of the pre-stressed beam are obtained by using geometrically exact, Euler–Bernoulli beam theory. The beam is assumed to be not shear deformable and inextensible because of its slenderness and uniform, closed cross-section, as well as the boundary conditions under consideration. The static configuration and the modal information are validated with experimental data and compared to results obtained from nonlinear finite-element analysis software. In addition to the modal analysis about general static configurations, special consideration is given to an initially straight beam that is deformed into semi-circular and circular static configurations. For these special circular cases, the partial differential equation of motion is reduced to a sixth-order differential equation with constant coefficients, and solutions of this system are examined. This work can serve as a basis for studying slender structures with large curvatures. 相似文献
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Scott E. Stapleton Evan J. Pineda Thomas Gries Anthony M. Waas 《International Journal of Solids and Structures》2014
Macroscopic finite elements are elements with an embedded analytical solution that can capture detailed local fields, enabling more efficient, mesh independent finite element analysis. The shape functions are determined based on the analytical model rather than prescribed. This method was applied to adhesively bonded joints to model joint behavior with one element through the thickness. This study demonstrates two methods of maintaining the fidelity of such elements during adhesive non-linearity and cracking without increasing the mesh needed for an accurate solution. The first method uses adaptive shape functions, where the shape functions are recalculated at each load step based on the softening of the adhesive. The second method is internal mesh adaption, where cracking of the adhesive within an element is captured by further discretizing the element internally to represent the partially cracked geometry. By keeping mesh adaptations within an element, a finer mesh can be used during the analysis without affecting the global finite element model mesh. Examples are shown which highlight when each method is most effective in reducing the number of elements needed to capture adhesive nonlinearity and cracking. These methods are validated against analogous finite element models utilizing cohesive zone elements. 相似文献
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随机梁式结构静力损伤识别的一种改进方法 总被引:1,自引:1,他引:0
针对已有的损伤识别方法会出现损伤误识别的问题,本文在已有方法的基础上发展了一种随机梁式结构静力损伤识别的改进方法。假定静力荷载下梁式结构初始模型参数(如弹性模量和几何尺寸等)及测量误差为随机量,给出已有的基于随机有限元模型的梁式结构静力损伤识别方法,并进一步提出了一种改进方法。该方法通过设定损伤概率指标的阈值和反复迭代对结构损伤识别进行改进。数值算例和简支梁静力试验表明,考虑初始模型的不确定性以及静力响应测量误差,本文方法相较已有方法可以更有效地识别梁式结构的损伤。 相似文献