水下复杂应力结构的固有频率研究

研究水下结构物的复杂应力状态对结构固有频率的影响,克服以往研究中只考虑整体均匀分布应力的局限性。水下结构因外部环境特殊常常处于复杂应力状态,复杂应力与流固耦合的共同作用使结构的固有频率求解变为一个耦合非线性特征值问题,以往求解流固耦合的方法不再适用于此类问题。有限元方法也能处理此类问题,但存在处理过程复杂、计算量大、不能明确说明结构应力与动力特性之间的本质物理联系等缺点。针对该问题用理论方法进行了分析,首先基于Flügge壳体理论、考虑流固耦合作用、利用特定模态之间的正交性建立复杂应力结构自由运动方程,然后采用多项式近似结合二次型矩阵线性化的方法对此类结构的固有频率进行求解。在数值算例中,计算了某水下圆柱壳的固有频率,并对比和分析了不同类型的复杂应力对于水下结构固有频率的影响特点。     

弱耦合算法的实现及其应用

介绍了一种求解流固耦合问题更有效的方式即弱耦合技术,将计算结构动力学(CSD)和计算流体动力学(CFD)联合起来。CSD通过计算结构位移用来指定流体域的固体边界范围,而CFD计算用来定义作用在CSD上的荷载。荷载和位移的传递分别采用守恒和非守恒插值方法,详细介绍了其插值的实现过程。这种流固耦合算法是一种对整个问题进行离散化后,采用迭代求解方法的处理复杂的流固耦合问题的数值模拟方法。最后通过对一轻柔膜结构和风荷载的流固耦合问题的求解,表明了这种方法通过耦合CFD和CSD程序,提供了一种便利的、有效的耦合问题求解方法。     

基于温度体模型的动网格生成方法及在流固耦合振动中的应用

提出温度体模型动网格生成方法,并将其应用于流固耦合算法,生成物体振动过程中的动态网格。温度体模型动网格方法将运动边界的位移映射为求解域的温度边界条件,以流体能量方程或固体导热方程作为控制方程求解得到计算域内的温度分布,将求解得到的温度分布作为网格节点的动态位移。基于温度体模型的动网格方法物理意义清晰,算法实现简单,能够快速而有效地生成高品质的动态网格,特别在边界位移大的情况下与其他网格生成方法相比有较大的优势。最后采用流固耦合有限元算法求解了定浆式轴流泵强迫振动过程中连锁特性和柱体由于旋涡脱落诱发自激振动两个工程问题。其中流场采用基于特征线方程的分离算法进行求解,固体场采用Newmark方法进行求解,在计算过程中采用温度体模型生成动态网格。结果表明该发展的算法性能优异,能有效解决流固耦合中的振动问题。     

圆柱壳在水下爆炸载荷下的流-固耦合响应分析

研究了无限域流场中两端简支圆柱壳受球形炸药爆炸冲击载荷作用的响应特性。运用Hamilton变分原理,推导出了考虑流固耦合作用圆柱壳受水下爆炸冲击载荷作用的运动方程,并分别展开成Fourier级数的形式,最后在时域上差分离散,用Galerkin方法求解,得到了在水下爆炸冲击载荷下圆柱壳的响应分析。文章着重就圆柱壳在迎爆面和背爆面的不同位置的变形位移和变形速度进行了对比分析,同时还比较了流体动压力对结构响应的影响。并将分析结果与有限元计算软件MSC.DYTRAN计算结果比较,验证了算法的可靠性。     

基于谱单元方法的平板冲击流固耦合研究

假设流体无粘且无旋,计及流体中的气穴现象,采用谱单元方法建立水下爆炸瞬态流固耦合的三维数值模型,探讨了水下爆炸瞬态流固耦合作用的机理,用经典的平板冲击问题对数值模型进行验证,数值结果与解析解吻合良好,并根据数值结果绘制了流体中的气穴区域,对气穴效应进行分析,分析显示,气穴效应会对结构响应产生很大影响,在计算中应予以考虑。基于本文建立的数值模型,在不同网格细化的条件下,分别采用谱单元方法和有限元方法对弹簧——平板模型进行水下爆炸瞬态流固耦合问题的求解,并在此基础上对谱单元方法和有限元方法进行对比研究,研究发现,谱单元方法在提高精度的同时能大量节省计算时间,可较好地应用于水下爆炸流固耦合问题的求解中。本文旨在为相关水下爆炸瞬态流固耦合的研究提供参考。     

基于改进涡方法的膜结构流固耦合研究

采用改进涡方法对膜结构的流固耦合进行模拟。将非协调边界元计算势流的方法引入到传统涡方法中,即为改进涡方法。该算法可以精确计算三维粘性、不可压缩流场。采用改进涡方法可以得到每个时间步膜结构的单元节点流场压力,通过与ansys有限元模型提取出的整体刚度矩阵联合求解得到单元节点位移,并可以由单元节点位移求解出下一时间步的流场分布。由于本文引入了高效的预处理循环型广义极小残余迭代算法(GMRES),使得边界元法的优势得到了充分发挥,大幅度节省了计算时间。完成了方形平屋盖膜结构气弹模型风洞试验。采用本文算法对膜结构流固耦合效应计算得到的位移均值大部分与风洞试验吻合,计算结果表明本文提出的方法是模拟膜结构流固耦合问题的有益尝试。     

物质点法在风与膜结构耦合作用中的应用研究

为克服常用数值方法在风与膜结构的耦合计算中网格易畸变、耗费机时大的缺点,提出采用物质点法计算风与膜结构的耦合作用。结构域采用物质点法描述,流体域采用浸入边界法描述。结构对流体的作用通过对结构最边缘的网格节点施加边界条件来实现,流体对结构的作用通过在结构表面施加压力和剪力实现。分别给出了结构域、流体域和流固耦合计算的求解步骤。将该算法应用于二维膜结构的耦合计算,得到了结构响应和流体压力场等结果,与采用有限元法计算结果进行了对比,结果符合良好;同时与有限元法对比了计算效率,结果表明物质点法计算效率要高于有限元法。结果表明物质点法计算风与膜结构的流固耦合作用中可以得到准确的结果,且计算效率得到较大提升。     

基于Kriging模型的充液管道共振非概率可靠性分析

为解决传统概率可靠性在解决流固耦合问题方面的不足,研究了结构不确定参量用超椭球凸集模型和区间变量共同描述下的非概率共振可靠性问题。针对隐式极限状态函数难以求解的问题,引入Kriging模型和超立方抽样技术应用于非概率可靠性分析。该方法用Kriging模型作为近似模型描述原结构,并在计算过程中不断更新近似模型。考虑管道与液体之间的耦合作用,利用有限元软件对所建立的简单管道系统进行模态计算并且结合防共振理论进行充液管路系统的流固耦合振动非概率可靠性分析,用优化的方法计算可靠性指标。工程算例分析表明该方法的合理性,能完善流固耦合管道系统的防共振可靠性分析方法与理论。     

考虑流固耦合作用屋顶游泳池减振效应研究

某结构计划在屋顶设计标准游泳池,游泳池下部为一大跨度多功能会议室,对其进行抗振性能研究成为设计方案能否实施的关键。该文将屋顶游泳池视为调谐液体阻尼器(TLD)装置,基于位移-压力格式有限元方法,给出了TLD-结构体系流固耦合运动方程。应用ABAQUS软件建立了流固耦合实体模型,并基于TLD等效非线性调谐质量阻尼器(TMD)理论,在SAUSAGE中建立了等效调谐质量(等效TMD)模型。研究了地震荷载作用下屋顶游泳池对结构抗振性能的影响,分析了流固耦合作用的减振效率。研究结果表明：流固耦合运动方程求解与ABAQUS软件数值模拟的位移与加速度时程曲线具有较好的一致性,验证了流固耦合运动方程的准确性;大跨屋顶标准游泳池对结构在X与Y方向的地震响应均有明显的抑制作用,结构的第一阶模态振动减振效果要优于第二阶模态;流固耦合模型在地震作用下的楼层位移与基底减振率相较于不考虑流固耦合作用的等效调谐质量模型有明显提高,在设计屋顶游泳池时应充分考虑流固耦合作用的影响。     

求解平面固体几何大变形问题的有限质点法

有限质点法是基于向量式力学提出的一种新兴的数值计算方法。它采用物理计算模式,将分析域定义成一组质点的集合,并根据牛顿第二定律描述质点的运动,从而取代了传统数值方法中数学连续体的概念。该方法通过虚拟逆向运动分离刚体位移和变形位移,并采用变形坐标的形式来计算内力,再利用显式时间积分逐步求解质点运动方程。分析中可以通过描述各质点的轨迹来追踪整体的运动行为。该文阐述了有限质点法的基本概念和原理,推导了平面固体的内力求解公式,并将其应用于平面固体几何大变形问题的数值计算,通过自编程序对实例计算的结果表明,该方法有良好的精度和收敛性,对于求解平面固体的大位移、大转动问题是有效的、可行的。     

Wave radiation by a submerged source undergoing large amplitude periodic motion

Equations are derived to calculate the water waves radiation at infinity bya submerged source undergoing large amplitude motion. These equations do not require the full solution of the velocity potential itself, as demonstrated by a number of two- and three-dimensional examples. The results obtained are used to derive a far field equation for calculating the steady force (the drift force) on a submerged body undergoing large amplitude motion. It is concluded that the equations derived are useful to cases such as a deeply submerged body for which the source distribution may be taken as those obtained in an unbounded fluid domain.     

简支梁在无限大不可压缩流体和声学流体中的固有振动问题

本文用边界积分方程描述无限大声学流体,从而得到了控制圆截面简支梁在该流体中固有振动的积分-微分方程。在此方程基础上,分别用摄动法和有限元与摄动展开相结合的方法,计算了简支梁在无限大声学流体中的固有频率。当声速趋于无穷大时,得到了无限大不可压缩流体中简支梁的固有频率。本文的方法可推广到较为复杂的结构声辐射系统的固有频率的计算上。     

轴对称声振耦合的边界子波谱与有限元耦合方法及应用

在轴对称结构有限元和轴对称Helmholtz积分方程的基础上,建立了轴对称弹性结构构声振耦合的边界 子波谱有限元耦合方法,该方法能处理任意边界条件。采用提出的耦合方法研究了含有壳、肋、板复杂结构的水下航行 器的声辐射,给出了轴对称圆环肋的刚度矩阵和质量矩阵。进行了声振耦合的模态分析,研究了航行器的轴向激励、侧 向激励的声辐射;计算了0～2kHz的频率响应。结果对水下航行器的研究设计有一定的参考价值。     

向量式有限元在索穹顶静力分析中的应用

索穹顶结构是一种由预应力拉索与竖杆组成的高效柔性空间结构,易发生较大位移,拉索可能出现松弛现象。该文采用向量式有限元进行了索穹顶的静力分析。向量式有限元是一种向量力学与数值计算相结合的分析方法,不同于传统分析力学方法和其他数值计算方法。向量式有限元基于运动方程求解,不需求解非线性方程组及刚度矩阵,尤其适合于发生刚体位移和几何大变形的结构或机构求解。该文首先介绍了向量式有限元的基本原理,推导了预应力索单元的求解公式,最后采用自编向量式有限元程序,分析了一个单摆模型和一个索穹顶结构模型。结果表明:向量式有限元应用于索穹顶静力分析是可行而且可靠的,在传统有限元计算难以收敛的情况下仍然可以对结构进行精确的非线性分析,为索穹顶的非线性分析提供了一种新的方法和手段。     

A fast elastostatic solver based on fast Fourier transform on multipoles (FFTM)

In this paper, we present a fast algorithm to solve elasticity problems, governed by the Navier equation, using the boundary element method (BEM). This fast algorithm is based on the fast Fourier transform on multipoles (FFTM) method that has been developed for the Laplace equation. The FFTM method uses multipole moments and their kernel functions, together with the fast Fourier transform (FFT), to accelerate the far field computation. The memory requirement of the original FFTM tends to be high, especially when the method is extended to the Navier equation that involves vector quantities. In this paper, we used a compact representation of the translation matrices for the Navier equation based on solid harmonics. This reduces the memory usage significantly, allowing large elasticity problems to be solved efficiently. The improved FFTM is compared with the commonly used FMM, revealing that the FFTM requires shorter computational time but more memory than the FMM to achieve comparable accuracy. Finally, the method is applied to calculate the effective Young's modulus of a material containing numerous voids of various shapes, sizes and orientations. Copyright © 2008 John Wiley & Sons, Ltd.     

An analytical solution for long-wave scattering by a submerged circular truncated shoal

An analytical solution of the long-wave (or shallow-water) equation in closed-form is obtained for simple harmonic waves scattered by a submerged circular truncated shoal. This analytical solution is firstly validated against Longuet-Higgins’s classical analytical solution for a submerged cylinder, and then validated against numerical solutions obtained by using the DRBEM (dual reciprocity boundary-element method) model for a submerged circular truncated cone. Finally, the analytical solution is used to investigate the changing trend of maximum wave amplification, the trace pattern of focal position of wave-energy versus the wave period and the influence of shoal submergence on wave-energy trapping.     

Stochastic Finite Element Method for Mechanical Vibration Based on Conjugate Gradient(CG)

When material properties, geometry parameters and applied loads are assumed to be stochastic, the vibration equation of a system is transformed to static problem by using Newmark method. In order to improve the computational efficiency and to save storage, the Conjugate Gradient (CG) method is presented. The CG is an effective method for solving a large system of linear equations and belongs to the method of iteration with rapid convergence and high precision. An example is given and calculated results are compared to validate the proposed methods.     

A dual-reciprocity method for acoustic radiation in a subsonic non-uniform flow

In this paper, the dual-reciprocity boundary-element method is used to model acoustic radiation in a subsonic non-uniform-flow field. The boundary-integral formulation is based on a direct boundary-integral equation developed very recently by the authors for acoustic radiation in a subsonic uniform flow. All the terms due to the non-uniform-flow effect are taken to the right-hand side and treated as source terms. The source terms result in a domain integral in the standard boundary-integral formulation. The dual-reciprocity method is then used to transform the resulting domain integral into boundary integrals. Numerical tests show reasonably good agreement with an analytical soution for a pulsating sphere submerged in a potential-flow field.     

A Lie-Group Adaptive Method for Imaging a Space-Dependent Rigidity Coefficient in an Inverse Scattering Problem of Wave Propagation

We are concerned with the reconstruction of an unknown space-dependent rigidity coefficient in a wave equation. This problem is known as one of the inverse scattering problems. Based on a two-point Lie-group equation we develop a Lie-group adaptive method (LGAM) to solve this inverse scattering problem through iterations, which possesses a special character that by using onlytwo boundary conditions and two initial conditions, as those used in the direct problem, we can effectively reconstruct the unknown rigidity function by aself-adaption between the local in time differential governing equation and the global in time algebraic Lie-group equation. The accuracy and efficiency of the present LGAM are assessed by comparing the imaged results with some postulated exact solutions. By means of LGAM, it is quite versatile to handle the wave inverse scattering problem for the image of the rigidity coefficient without needing any extra information from the wave motion.     

A Fictitious Time Integration Method for Multi-Dimensional Backward Wave Problems

We address a new numerical approach to deal with these multi-dimensional backward wave problems (BWPs) in this study. A fictitious time τ is utilized to transform the dependent variable u(x, y, z, t) into a new one by (1+τ)u(x, y, z, t)=: v(x, y, z, t, τ), such that the original wave equation is written as a new hyperbolic type partial differential equation in the space of (x, y, z, t, τ). Besides, a fictitious viscous damping coefficient can be employed to strengthen the stability of numerical integration of the discretized equations by using a group preserving scheme. Several numerical instances demonstrate that the present scheme can be utilized to retrieve the initial wave very well. Even though the noisy final data are very large, the fictitious time integration method is also robust against disturbance.