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对弹性平面扇形域问题,将径向坐标模拟成时间坐标,通过适当的变换,将扇形域问题导向哈密尔顿体系,利用分离变量法及本征函数向量展开等方法,推导出裂纹尖端的应力奇性解的计算公式,结合变分原理,提出一种解决应力奇性计算的断裂分析元,将此分析元与有限元法相结合,可以进行某些断裂力学或复合材料等应力奇性问题的计算及分析,数值计算结果表明,该方法具有精度高,使用十分方便,灵活等优点,是哈密尔顿体系和辛数学优越性的一次具体体现。 相似文献
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发电机组转子轴系扭振模化系统的三重共振 总被引:9,自引:0,他引:9
建立了发电机组转子轴系扭振模化系统的数学模型,此模型具有平方非线性并受简谐激励作用.研究了系统的固有频率存在双重内共振关系ω3≈2ω2,ω2≈2ω1且Ω≈ω2时的三重共振问题.文中应用非线性振动的改进平均法,求得了系统三重共振的一次近似解,对三重共振的定常解进行了理论分析和数值计算,并进行了奇异性分析,文中指出三重共振解具有双饱和特性,对二种主要的理论分析和数值计算结果进行了实验验证,实验结果与理论结果相符. 相似文献
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直接积分法是求解动力学方程的一种有效方法。应用一种预估-校正的Generalized-α法对结构大变形动力学问题进行分析求解,并与Newmark法和Bathe法进行对比研究。首先预估当前计算步的解,然后以预估值作为起始值进行非线性迭代计算,并对解不断校正,直到满足收敛条件,进入下一时间步的计算。在保证Generalized-α法性能的基础上,简化了非线性迭代公式,便于编程实现。通过壳和实体的大变形动力学算例,证明了本文方法具有较高的稳定性和精度。 相似文献
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本文研究反应堆用石墨构件的应力分析问题。由于辐照石墨的蠕变响应是反应堆运行温度和快中子累积剂量的函数。因此使计算复杂化了。为了解决这个问题,本文提出应力变换法得到了有限元公式。对受辐照、有内热源、内外壁为放热条件的厚壁圆筒进行了求解。计算结果表明同解析解吻合得很好,并且具有简化计算和节省时间的优点。 相似文献
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基于平板小挠度弯曲波动方程,采用摄动方法具有纵向内力作用下的平板开孔弹性波的散射问题进行了研究,得么了传播稳态波时此种平板弯曲波动问题的分析解,分析了均匀纵向内力对弹性波散射结果的影响,作为算例,本文给出了平板圆形开孔的动应力集中系数的数值结果,并对计算结果进行了讨论。 相似文献
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基于Erdogan基本解边界元法计算应力强度因子 总被引:4,自引:0,他引:4
引入含裂纹问题基本解(Erdogan基本解),提出了基于Erdogan基本解的样条虚边界
元法,并阐述了该法在实施过程中的特点与具体做法. 采用该方法详细分析了若干
典型裂纹问题,全面考察了方法的计算精度和收敛情况,以及在求解复杂裂纹问题方面
的能力. 结果显示,该方法具有精度高、收敛快、计算能力强等优点,是裂纹问题分析中
一种具有竞争力的通用计算方法. 相似文献
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正交异性体反平面问题另一形式自相似解的推导 总被引:4,自引:0,他引:4
正交异性体的反平面运动方程有几种表达方式,而以自相似解表达方式尤为简单。由于在弹性动力学问题的计算中可以获得解析解,使得考虑的问题相应地简化,并具有一定的普遍性,因此对自相似形式的解的推导具有重要的意义。本文针对这一问题进行研究,利用复变函数论的方法导出另一形式自相似解的一般表达式。应用该法可以很容易地将所讨论的问题转化为Riemann—Hilbert问题,而后一问题可以用同通常的Muskhelishvili方法求解,并且可以相当简单地得到问题的闭合解。这些解在断裂动力学以及弹性动力学问题当中具有重要的应用价值。 相似文献
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《力学快报》2021,11(5):100293
A novel symplectic superposition method has been proposed and developed for plate and shell problems in recent years. The method has yielded many new analytic solutions due to its rigorousness. In this study, the first endeavor is made to further developed the symplectic superposition method for the free vibration of rectangular thin plates with mixed boundary constraints on an edge. The Hamiltonian system-based governing equation is first introduced such that the mathematical techniques in the symplectic space are applied. The solution procedure incorporates separation of variables, symplectic eigen solution and superposition. The analytic solution of an original problem is finally obtained by a set of equations via the equivalence to the superposition of some elaborated subproblems. The natural frequency and mode shape results for representative plates with both clamped and simply supported boundary constraints imposed on the same edge are reported for benchmark use. The present method can be extended to more challenging problems that cannot be solved by conventional analytic methods. 相似文献
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Rui Li Bin Wang Yifan Lv Qi Zhang Haoyang Wang Fengyu Jin Fei Teng Bo Wang 《Meccanica》2017,52(7):1593-1600
This paper deals with the bending of rectangular thin plates point-supported at three corners using an analytic symplectic superposition method. The problems are of fundamental importance in both civil and mechanical engineering, but there were no accurate analytic solutions reported in the literature. This is attributed to the difficulty in seeking the solutions that satisfy the governing fourth-order partial differential equation with the free boundary conditions at all the edges as well as the support conditions at the corners. In the following, the Hamiltonian system-based equation for plate bending is formulated, and two types of fundamental problems are analytically solved by the symplectic method. The analytic solutions of the plates point-supported at three corners are then obtained by superposition, where the constants are obtained by a set of linear equations. The solution procedure presented in this paper offers a rigorous way to yield analytic solutions of similar problems. Some numerical results, validated by the finite element method, are shown to provide useful benchmarks for comparison and validation of other solution methods. 相似文献
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角点支承矩形薄板的屈曲问题是板壳力学的一类重要课题,控制方程和边界条件的复杂性导致寻求该类问题的解析解十分困难。虽然各类近似/数值方法可用于解决此类难题,但作为基准的精确解析解在公开文献中鲜有报道。本文基于近年来提出的辛叠加方法,解析求解了四角点支承四边自由矩形薄板的屈曲问题。首先将问题拆分为两个子问题,接着利用分离变量与辛本征展开推导出子问题的解析解,最后通过叠加获得原问题的解。由于求解过程从基本控制方程出发,逐步严格推导,无需假定解的形式,因此本文解法是一种理性的解析方法。数值算例给出了不同长宽比和不同面内载荷比情况下,四角点支承四边自由矩形薄板的屈曲载荷和典型屈曲模态,并经有限元方法验证,确认了解析解的正确性。 相似文献
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The two-dimensional (2D) transient heat conduction problems with/without heat sources in a rectangular domain under different combinations of temperature and heat flux boundary conditions are studied by a novel symplectic superposition method (SSM). The solution process is within the Hamiltonian system framework such that the mathematical procedures in the symplectic space can be implemented, which provides an exceptional direct rigorous derivation without any assumptions or predetermination of the solution forms compared with the conventional inverse/semi-inverse methods. The distinctive advantage of the SSM offers an access to new analytic heat conduction solutions. The results obtained by the SSM agree well with those obtained from the finite element method (FEM), which confirms the accuracy of the SSM. 相似文献
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基于YNS层合格理论,建立反对称铺设层合板动力问题的Hamilton正则方程,并采用共轭辛正交归一关系给出一对边简支,另一对边为任意支承层合板自振频率的精确解,数值算例讨论了长宽比,铺设角,层数及剪切修正系数的影响。 相似文献
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SOLVINGTHEFREEBOUNDARYPROBLEMINCONTINUOUSCASTINGBYUSINGBOUNDARYELEMENTMETHODLiYaoyong(李耀勇);ZhangZhili(张自立)(ReceivedJune,18,19... 相似文献
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In this paper, a new analytical method of symplectic system, Hamiltonian system, is introduced for solving the problem of the Stokes flow in a two-dimensional rectangular domain. In the system, the fundamental problem is reduced to an eigenvalue and eigensolution problem. The solution and boundary conditions can be expanded by eigensolutions using adjoint relationships of the symplectic ortho-normalization between the eigensolutions. A closed method of the symplectic eigensolution is presented based on completeness of the symplectic eigensolution space. The results show that fundamental flows can be described by zero eigenvalue eigensolutions, and local effects by nonzero eigenvalue eigensolutions. Numerical examples give various flows in a rectangular domain and show effectiveness of the method for solving a variety of problems. Meanwhile, the method can be used in solving other problems. 相似文献