高速碰撞的三维欧拉数值模拟方法

介绍一种可用于高速碰撞问题数值模拟的三维弹塑性流体动力学数值计算方法，以及应用该方法研制的应用软件ＭＥＰＨ３Ｄ，并给出了一些高速碰撞问题的数值计算结果，计算结果表明该程序具有计算三维高速碰撞问题的能力。     

用粘性体力方法计算轴流叶轮机械内部流场

阐述了一种用于叶轮机械内部三维粘性流场计算程序。该程序以有限体积显式时间推进方法为基础，用Baldwin-Lomax模型模拟湍流流动，用局部时间步长和多重网格方法提高计算效率。使用上述方法计算了NASA 37^#跨音速压气机转子流场，并与实验结果进行了比较，从而证明文中提出的方法能够快速、准确地模拟轴流叶轮机械内部复杂三维流场，该方法具有较强的工程实用意义。     

三维势流场的比例边界有限元求解方法

比例边界有限元法(SBFEM)是线性偏微分方程的一种新的数值求解方法。该方法只对计算域边界利用Galerkin方法进行数值离散,相对于有限元方法(FEM)减少了一个空间坐标的维数,而在减少的空间坐标方向利用解析方法进行求解;相对于边界元法(BEM),比例边界有限元方法不需要基本解,避免了奇异积分的计算,所以它结合了有限元和边界元方法的优点。本文建立了利用比例边界有限元法求解三维Laplace方程的数值模型并用于计算三维物体周围的水流场,将计算结果与解析解和边界元方法进行了对比,结果表明此方法可以很好地模拟水流场,且具有较高的计算精度。     

弹性力学中一种新的边界轮廓法

利用基本解的特性，将面力积分方程化成仅含有Ｃａｕｃｈｙ主值积分的形式，基于这种边界积分方程，提出了一种新的边界轮廓法，对于三维问题，该方法只须计算沿边界单元界线的线积分，对二维问题，则只需计算边界单元两点的热函数之差，无须进行数值积分计算，实例计算说明该方法是有效的。     

弹性力学平面问题中一类无奇异边界积分方程

从理论上提出一种新的方法，归化出间接变量无奇异边界积分方 程. 采用Lagrange二次单元，建立一个数值求解框架系统. 此外，基于问题的计算区域的 特殊性，给出一种边界近似方法. 数值算例表明该方法所取得的数值结果与精确解相当接 近，特别是边界量的数值结果. 此外，该方法容易被推广到三维问题. 和已有的直接变量的情形相比较，具有优点：1)无需处理HFP积分. 大大降低处理问 题的复杂性，并提高了计算效率和解的精度；2)摆脱了问题的具体形式，进入纯代数操作. 这样做的好处是从理论上建立一种普遍适用的方法，不仅适用于弹性力学问题，同样可应用 于其它问题，如位势问题, Stokes问题等. 3)提供了一种计算CPV积分的方法.     

三维相移电子散斑干涉法在柴油机机身中的应用

本文通过一新的三维电子散斑干涉方法，结合四步相移技术和图象处理技术，从三幅全场散斑位相条纹图分离出独立的u、υ、w场位移。测量系统的特点是用三个激光器作为光源，一个PZT相移器推动三个反射镜产生参考光并实现相移以及CCD摄像机前放置大错位剪切镜。将该测量系统应用到柴油机机身部件测量上，得到了机身主轴承孔周的三维位移场，并将此结果作为有限元计算的边界条件，得到了精确的柴油机机身计算结果，证明这一新技术可为柴油机零部件的强度和刚度分析评价提供一种十分有效的方法。     

卵形杆弹对铝靶的斜侵彻

在Lagrange有限元基础上，扼要介绍了一种适用于三维斜侵彻数值模拟计算的滑移面处理技术。该方法放弃了传统滑移计算中从单元的设置，而代之以预设从节点，从而避免三维斜侵彻数值计算中主从单元的相交、滑移面的识别、修正与再定义的困难。在确保计算精度的同时，有效地提高了计算效率。卵形杆弹对铝靶侵彻的系列数值模拟计算表明，无论对于正撞击或斜撞击，本文中所获结果与实验结果都有良好的一致性，这说明本文中所述方法和所建程序的合理性和有效性，为侵彻贯穿过程的数值分析提供了一种实用和有效的手段。     

一种变厚度的精化壳体理论及其应用

在Reddy型高阶壳体理论的基础上，采用沿壳体厚度方向的剪切应变呈抛物线分布并且能够满足在壳体的上下表面为零的假设，发展出了一种适合于对变厚度壳体进行非线性分析的方法。该方法利用Ritz原理得到问题的控制方程。通过对一种典型的变厚度壳体结构（子午线轮胎）的结构分析，该方法的计算结果与商用有限元软件的三维分析结果能够很好的吻合。表明了该方法的适用性和有效性。     

功能梯度材料板件三维分析的半解析梯度有限元法

将半解析有限元与梯度有限元相结合,形成一种半解析梯度有限元来求解功能梯度材料板件问题。该方法兼有有限元法的适应性强、程序统一,半解析有限元法的节省单元与计算工作量,梯度有限元法的适应构件内部材料性能任意梯度分布等特点,并实现用一维数值计算给出构件三维分析结果。算例分析表明了方法的精度、功能与上述特点,充分揭示了功能梯度材料板件力学响应的三维形态。半解析梯度有限元法可推广应用到其他功能梯度材料面结构的各类分析中。     

层合板三维—二维混合分区有限元法研究

本文提出了一种三维－二维混合分区有限元方法分析复合材料层合结构。构造了三维－二维过渡元素和三维的十七节点复合元素。本方法在大大地减少了自由度，缩短了计算时间。算例表明，计算结果令人满意。本方法是可靠的并同样适用于其它结构。     

A new method for obtaining the exact solutions of the Navier-Stokes (NS) equations and its applications

In this paper we propose a new method for obtaining the exact solutions of the Mavier-Stokes (NS) equations for incompressible viscous fluid in the light of the theory of simplified Navier-Stokes (SNS) equations developed by the first author^[1,2], Using the present method we can find some new exact solutions as well as the well-known exact solutions of the NS equations. In illustration of its applications, we give a variety of exact solutions of incompressible viscous fluid flows for which NS equations of fluid motion are written in Cartesian coordinates, or in cylindrical polar coordinates, or in spherical coordinates. The project supported by National Natural Science Foundation of China.     

On the Stokes entry flow into a semi-infinite circular cylindrical tube

The problem of Stokes entry flow into a semi-infinite circular cylindrical tube was studied in this paper. A new kind of series solutions was derived. Their evident difference from the solutions in References [1,2] is that the present solutions don ’t involve infinite integral. So they are favourable for calculation. We calculated an example by allocated method and obtained satisfied results.     

A high accurate time-domain-advance integration method for transient elastodynamic problems

All step-by-step integration methods available at present for structural dynamic analysis use the displacement, velocity, and acceleration vectors computed at a previous interval for evaluating those at an advanced time step. Hence, an accumulated error will be definitely introduced after such integration. This paper presents a novel time-domain-advance integration method for transient elastodynamic problems in which the exact initial conditions are strictly satisfied for the solutions for each time step. In this way, the accumulated error can be eliminated and the approximate solutions will converge to the exact ones uniformly on the whole time domain. Therefore, the new method is more accurate. When applying to a structural dynamic problem, the present mehtod does not have to use the initial acceleration as is required by most other algorithms and the corresponding computation can be avoided. The present method is simple in representation, easy to be programmed, and especially suitable for accurate analyses of long-time problems. The comparison of numerical results with exact ones shows that the present method is much more accurate than some most widely used algorithms.     

STUDY ON EXACT ANALYTICAL SOLUTIONS FOR TWO SYSTEMS OF NONLINEAR EVOLUTION EQUATIONS

ＩｎｔｒｏｄｕｃｔｉｏｎＤｕｒｉｎｇｔｈｅｃｏｕｒｓｅｏｆｓｔｕｄｙｉｎｇｔｈｅｗａｔｅｒｗａｖｅ,ｍａｎｙｃｏｍｐｌｅｔｅｌｙｉｎｔｅｇｒａｂｌｅｍｏｄｅｌｓｗｅｒｅｏｂｔａｉｎｅｄ ,ｓｕｃｈａｓＫｄＶｅｑｕａｔｉｏｎ ,ｍＫｄＶｅｑｕａｔｉｏｎ ,(2 1 )＿ｄｉｍｅｎｓｉｏｎａｌＫＰｅｑｕａｔｉｏｎ ,ｃｏｕｐｌｅｄＫｄＶｅｑｕａｔｉｏｎｓ,ｖａｒｉａｎｔＢｏｕｓｓｉｎｅｓｑｅｑｕａｔｉｏｎｓ ,ＷＫＢｅｑｕａｔｉｏｎｓｅｔｃ .[1- 13 ].Ｉｎｏｒｄｅｒｔｏｆｉｎｄｅｘｐｌｉｔｉｃｅｘａｃｔｓｏｌｕｔｉｏ…     

多层地基的弹塑性分析

提出了多层地基的弹塑性力学分析方法，该方法建立在严格的数学、力学基础上，所推得的泛函求解式子具有可靠、明了的特点。通过有限元离散后，归结出一个求自由变量的二次规划问题，用所设计的算法进行求解，可避开传统迭代法中反复迭代的过程，具有高效、优化等特点。此方法可用于多层地基的路面设计以及对地基工作状态进行分析。     

交错网格上应用有限谱QUICK法计算方腔流动

王健平教授提出的有限谱方法是一种局域化谱方法，具有精度高、无相位差、应用灵活等特点，在以往的实践中取得了很大成功。本文在交错网格上对二维驱动方腔流问题进行计算，求解了二维不可压缩流动的涡流流函数方程。其中微分部分采用有限谱法进行处理，对流项的处理则应用了QUICK格式。本文计算了雷诺数为1000、5000、10000、20000等多种情况，将所得的结果进行分析，并将中线上的速度分别同已有的文献数据进行对比，从而，验证有限谱微分的正确性和其在实际应用中的可行性。     

Elastic Equilibrium of the Half-Space Revisited. Mindlin and Boussinesq Problems

The displacement caused in an isotropic elastic half-space by a point force localized on or beneath its surface is calculated here by a new method. These classical problems are known as Boussinesq and, respectively, Mindlin problems. The motivation for the present work resides in the fact that the original solutions involve some particular procedures, required by the complexity of the boundary conditions, which may limit their general application. The solutions presented here are obtained by including in a generalized Poisson equation the values of the function and its derivatives on the boundary, and by using in-plane Fourier transforms. This method is general and can be extended to other, similar problems.     

A boundary-type finite element model for water surface wave problems

A new combinative method of boundary-type finite elements and boundary solutions is presented to study wave diffraction-refraction and harbour oscillation problems. The numerical model is based on the mild-slope equation. The key feature of this method is that the discretized matrix equation can be formulated only by the calculation of a line integral, since the interpolation equation which satisfies the governing equation in each element is used. The numerical solutions are compared with existing analytical, experimental, observed and other numerical results. The present method is shown to be an effective and accurate method for water surface wave problems.     

A New Method for Experimentally Quantifying Dynamic Deflection of a Cylindrical Structure

There is a present desire to experimentally acquire resolved strain and deflection along long, slender cylinders using non-visible and minimally invasive instrument techniques. This desire supports present safety related activities within the nuclear power industry. At present, no relevant technology has been demonstrated to support this function while satisfying the above requirements. This study presents and details a new method for experimentally quantifying the deflection of a cylinder experiencing both static and dynamic loads. The method applies a distributed strain fiber-optic sensor which is helically wrapped along the axial length of the cylinder. An analytic correlation is developed and detailed herein which decomposes the helical strain into both axial strain as well as transverse deflection. This newly developed experimental method is compared against analytic solutions using ideal beam theory as well as independent and proven optical methods for the purpose of verifying the new method. The outcome of this study results in a new and verified method that quantifies the deflection profile of a cylindrical structure.     

Characterization of strongly interacted multiple cracks in an infinite plate

Based on the Kachanov method and the alternating iteration technique, a new method is proposed to deal with the problem of the strongly interacted multiple cracks in an infinite plate. Unlike the Kachanov method which neglects the interaction of the tractions of the non-uniform components, the tractions of the non-uniform components on the surfaces of cracks are considered through the alternating technique. The accuracy and efficiency of present method are validated by comparing the results of two collinear and two parallel overlapped open the cracks obtained by the present method with those of the exact solutions, the results of the Kachanov method and the alternating iteration technique. Applications of present method in solving sliding close crack problems and evaluating the plastic zones demonstrate the versatility of present method.