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1.
《力学进展》2016,(0)
本文综述了线性与非线性流固耦合问题数值方法的进展及工程应用.讨论了四种数值分析方法:(1)混合有限元–子结构–子区域数值模型,以求解有限域线性流固耦合问题,如流体晃动,声腔–结构耦合,流体中的压力波,化工容器的地震响应,坝水耦合等;(2)混合有限元–边界元数值模型,以求解涉及无限域的线性流固耦合问题,如大型浮体承受飞机降落冲击,船舰的炮击回应等;(3)混合有限元–有限差分(体积)数值模型,以求解不涉及破浪和两相分离的非线性流固耦合问题;(4)混合有限元–光滑粒子数值模型,以求解涉及破浪和两相分离的非线性流固耦合问题.文中推荐分区迭代求解过程,以便应用现有的固体及流体求解器,于毎一时间步长分别求解固体及流体的方程,通过耦合迭代收敛,向前推进以达问题求解.文中选用的工程应用例子包含气–液–壳三相耦合,液化天然气船水晃动,人体步行冲击引起的声腔–建筑结构耦合,大型浮体承受飞机降落冲击的瞬态动力回应,涉及破浪和两相分离的气–翼耦合及结构于水上降落的冲击.数值分析结果与可用的实验或计算结果作了比较,以说明所述方法的精度及工程应用价值.文中列出了基于流固耦合的波能采积装置模型,以应用线性系统的共振及非线性系统的周期解原理,有效地采积波能.本文列出了231篇参考文献,以便读者进一步研讨所感兴趣方法. 相似文献
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Jing Tang XING 《力学进展》1971,46(1):201602
本文综述了线性与非线性流固耦合问题数值方法的进展及工程应用. 讨论了四种数值分析方法: (1) 混合有限元-子结构-子区域数值模型, 以求解有限域线性流固耦合问题, 如流体晃动, 声腔-结构耦合, 流体中的压力波, 化工容器的地震响应,坝水耦合等; (2) 混合有限元-边界元数值模型, 以求解涉及无限域的线性流固耦合问题, 如大型浮体承受飞机降落冲击, 船舰的炮击回应等; (3) 混合有限元-有限差分(体积) 数值模型, 以求解不涉及破浪和两相分离的非线性流固耦合问题; (4) 混合有限元-光滑粒子数值模型, 以求解涉及破浪和两相分离的非线性流固耦合问题. 文中推荐分区迭代求解过程, 以便应用现有的固体及流体求解器, 于毎一时间步长分别求解固体及流体的方程, 通过耦合迭代收敛, 向前推进以达问题求解. 文中选用的工程应用例子包含气-液-壳三相耦合, 液化天然气船水晃动, 人体步行冲击引起的声腔-建筑结构耦合, 大型浮体承受飞机降落冲击的瞬态动力回应, 涉及破浪和两相分离的气-翼耦合及结构于水上降落的冲击. 数值分析结果与可用的实验或计算结果作了比较, 以说明所述方法的精度及工程应用价值. 文中列出了基于流固耦合的波能采积装置模型, 以应用线性系统的共振及非线性系统的周期解原理, 有效地采积波能. 本文列出了231 篇参考文献, 以便读者进一步研讨所感兴趣方法. 相似文献
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二维定常不可压缩粘性流动N-S方程的数值流形方法 总被引:4,自引:4,他引:0
将流形方法应用于定常不可压缩粘性流动N-S方程的直接数值求解,建立基于Galerkin加权余量法的N-S方程数值流形格式,有限覆盖系统采用混合覆盖形式,即速度分量取1阶和压力取0阶多项式覆盖函数,非线性流形方程组采用直接线性化交替迭代方法和Nowton-Raphson迭代方法进行求解.将混合覆盖的四节点矩形流形单元用于阶梯流和方腔驱动流动的数值算例,以较少单元获得的数值解与经典数值解十分吻合.数值实验证明,流形方法是求解定常不可压缩粘性流动N-S方程有效的高精度数值方法. 相似文献
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二维边界层方程的迭代求解 总被引:2,自引:1,他引:1
针对二维边界层方程,提出了分析积分迭代法.首先将该方法应用于Blasius方程和Falkner-Skan方程的求解,数值计算结果稳定,计算精度高;然后对外部有势流不能达到自相似要求、必须二维求解的二维层流边界层问题,在分析积分迭代法中加上计算力学的松弛迭代法,形成了一套有效的算法.数值结果表明该方法用于层流边界层的计算是很有效的. 相似文献
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给出了带襟翼偏转的三维机翼绕流的一种求解N-S方程的计算方法,采用区域求解算法和对接分区网络技术相结合的方法,有效地求解了绕此外形的复杂流动,区域求解算法中提出了一种满足通量守恒的内边界耦合条件,流场求解时采用中心差分的限体积方法对空间通量顶进行离散,采用显式推进方法进行时间方向的积分,数值算例表明本方法是求解带襟翼偏转的机翼绕流的有效方法。 相似文献
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研究提高二维方腔瑞利-贝纳德对流 直接数值模拟求解方法的计算效率问题.对于非定常湍流热对流, 压力泊松方程的求解是影响整个计算效率的关键. 利用快速傅里叶变换(fast Fourier transform,FFT)解耦并结合追赶法, 可实现压力泊松方程的直接求解.通过与跳点超松弛迭代法在求解精度和计算速度对比, 可以看到, 利用FFT压力泊松方程直接方法计算热对流问题是高效的.还给出了典型状态的热对流初始羽流和大尺度环流温度场, 以及系列瑞利数(Ra)计算结果的宏观传热努塞数(Nu)变化. 相似文献
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利用全局薄板样条径向基配点法分析了功能梯度梁的弯曲问题,径向基函数的形状参数对近似精度有很大的影响,而薄板样条径向基函数的形状参数选取比其他径向基函数要容易. 利用高阶剪切变形理论推导了控制微分方程,将该文的计算结果与已有参考文献中的结果进行了对比,以验证该文方法的精度. 相似文献
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本文提出了新型带虚点的径向基函数微分求积法,并将其应用于模拟薄板弯曲问题。带虚点的径向基函数微分求积法是一种基于传统径向基函数微分求积法的新型无网格方法,传统方法只将中心点放在计算域内,而该方法扩展了中心点的区域,使其既位于计算域内又位于计算域外,在不增加计算量和存储量的基础上,显著提高计算精度。本文首次尝试将此方法应用于求解薄板弯曲问题,并与解析解和传统方法进行对比,验证了此方法的优越性 相似文献
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基于径向基函数强形式的无单元(RBFS)法是真正意义上的无单元方法,但为了追求精度要求却未达到稀疏化。本文对RBFS进行了改进,通过构造具有δ函数性质的形函数,得到了具有稀疏带状性的系数矩阵,提高了计算效率,同时具有RBFS方法的优点。通过求解微分方程,得到节点均布时影响域半径与求解精度的关系曲线,验证了基函数中自由参数最佳取值的计算公式的适用性;并把节点均布下得到的影响域半径和自由参数的规律应用到节点任意排列的情况下,求解结果变化不大,均满足精度要求,由此得出这些规律仍然适用,这种无单元法对节点位置不敏感。 相似文献
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A stress function-based approach is proposed to analyze the free-edge interlaminar stresses of piezo-bonded symmetric laminates. The proposed method satisfies the traction free boundary conditions, as well as surface free conditions. The symmetric laminated structure was excited under electric fields that can generate induced strain, resulting in pure extension in the laminated plate. The governing equations were obtained by taking the principle of complementary virtual work. To verify the proposed method, cross-ply, angle-ply and quasi-isotropic laminates were analyzed. The stress concentrations predicted by the present method were compared with those analyzed by the finite element method. The results show that the stress function-based analysis of piezo-bonded laminated composite structures is an efficient and accurate method for the initial design stage of piezo-bonded composite structures. 相似文献
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轴对称横观各向同性层状弹性半空间问题受力分析 总被引:6,自引:0,他引:6
本文从柱坐标系弹性力学基本方程出发,将位移场和应力场在径向进行Hankel变换,利用常微分主程求解原理,直接得出在轴对称荷载作用下横观各向同性半无限弹性空间的位移场,利用此结果推导出单层元的刚度矩阵。 相似文献
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Based on the local discontinuous Galerkin methods for time-dependent convection-diffusion systems newly developed by Corkburn and Shu, according to the form of the generalized convection-diffusion equations which model the radial porous flow with dispersion and adsorption, a local discontinuous Galerkin method for radial porous flow with dispersion and adsorption was developed, a high order accurary new scheme for radial porous flow is obtained. The presented method was applied to the numerical tests of two cases of radial porous, i. e. , the convection-dispersion flow and the convection-dispersion-adsorption flow, the corresponding parts of the numerical results are in good agreement with the published solutions, so the presented method is reliable. Reckoning of the computational cost also shows that the method is practicable. 相似文献
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F. Motaman G. R. Rakhshandehroo M. R. Hashemi M. Niazkar 《Transport in Porous Media》2018,125(3):543-564
Richards’ equation is a nonlinear partial differential equation governing unsteady seepage flow through unsaturated porous media. This paper investigates applicability of radial basis function-based differential quadrature (RBF-DQ), as a meshless method, to simulate one-dimensional flow processes in the unsaturated zone under different initial and boundary conditions. Fourth-order Runge–Kutta scheme has been adopted for time integration. Results of solving three numerical examples using RBF-DQ are compared with those of analytical, numerical, and experimental solutions presented in the literature. The comparison indicates that RBF-DQ can provide more accurate results comparing with traditional FDM or FEM without the need to discretize the computational domain. Moreover, the merit of mesh-free characteristic in RBF-DQ makes it suitable not only for solving nonlinear problems but also for dealing with multidimensional problems since meshless methods are not restricted to dimensional limitations. A key parameter in utilizing multiquadratic approximation in RBF-DQ method is the user-defined shape parameter C, which may significantly affect solution accuracy. Thus, a sensitivity analysis has been conducted to study possible effects of shape parameter on achieved results. 相似文献
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《Acta Mechanica Solida Sinica》2017,(5)
The Non-uniform rational B-spline(NURBS)enhanced scaled boundary finite element method in combination with the modified precise integration method is proposed for the transient heat conduction problems in this paper.The scaled boundary finite element method is a semi-analytical technique,which weakens the governing differential equations along the circumferential direction and solves those analytically in the radial direction.In this method,only the boundary is discretized in the finite element sense leading to a reduction of the spatial dimension by one with no fundamental solution required.Nevertheless,in case of the complex geometry,a huge number of elements are generally required to properly approximate the exact shape of the domain and distorted meshes are often unavoidable in the conventional finite element approach,which leads to huge computational efforts and loss of accuracy.NURBS are the most popular mathematical tool in CAD industry due to its flexibility to fit any free-form shape.In the proposed methodology,the arbitrary curved boundary of problem domain is exactly represented with NURBS basis functions,while the straight part of the boundary is discretized by the conventional Lagrange shape functions.Both the concepts of isogeometric analysis and scaled boundary finite element method are combined to form the governing equations of transient heat conduction analysis and the solution is obtained using the modified precise integration method.The stiffness matrix is obtained from a standard quadratic eigenvalue problem and the mass matrix is determined from the low-frequency expansion.Finally the governing equations become a system of first-order ordinary differential equations and the time domain response is solved numerically by the modified precise integration method.The accuracy and stability of the proposed method to deal with the transient heat conduction problems are demonstrated by numerical examples. 相似文献
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借鉴流形方法思想,引入广义节点的概念,对传统的无网格法进行了改进,建立了可具有任意高阶多项式插值函数的广义节点无网格方法。同时采用径向插值函数构造具有插值特性的逼近函数;采用配点法建立系统的离散方程。在阐述了这种方法基本原理的同时,针对线弹性力学问题给出了这种方法的数值计算列式。与传统无网格方法相比,这种方法更具有一般性;同时由于采用了配点法而不需要背景积分网格,所以可以认为这种方法是某种真正意义上的无网格法。当选取0阶广义节点位移插值函数时便可得到传统的无网格法;在不增加支持域内节点数目的条件下,通过选取高阶广义节点位移插值函数可以提高计算精度。最后通过算例分析,对0阶、1阶及2阶广义节点无网格法与现有的有关解答进行了对比,论证了其合理性。 相似文献