三维弹性快速多极边界元法

将静电场多极展开法和广义极小残值法结合于三维弹性问题的边界元法,使其求解的计算量及所需内存量同节点的自由度总数成正比,变革计算结构,加快求解速度以适应大规模数值计算。两者结合的关键点在于边界元法基本解的合理分解,并用广义极小残值法(GMRES)求解方程。轧机支承辊变形场大规模数值算例的总自由度数首次达N=34008并获得成功。清晰地描述了支承辊和工作辊接触区的辊型。     

用边界元法分析轧制压力和摩擦力

本文给出了一种新的求解轧制力和摩擦力分布的方法，利用测量手段对轧制过程中的轧件进行测量，然后再利用边界元法对轧辊进行分析，从而求解出轧制中轧制力和摩擦力。这种方法避开了求解轧制力对轧件进行弹塑性分析，也解决了用测力销测量带来的困难，使轧制问题的分析求解得到了简化并提高了求解精度。     

A simple and efficient BEM algorithm for planar cavity flows

This paper presents a boundary element formulation for solution of planar Riabouchinsky cavity flow problems. An iterative procedure for adjusting the free surface position is developed and shown to be stable and convergent. Numerical results are compared with finite difference and finite element solutions, showing the superior accuracy of the BEM models.     

A parallel fast multipole BEM and its applications to large-scale analysis of 3-D fiber-reinforced composites

In this paper, an adaptive boundary element method (BEM) is presented for solving 3-D elasticity problems. The numerical scheme is accelerated by the new version of fast multipole method (FMM) and parallelized on distributed memory architectures. The resulting solver is applied to the study of representative volume element (RVE) for short fiber-reinforced composites with complex inclusion geometry. Numerical examples performed on a 32-processor cluster show that the proposed method is both accurate and efficient, and can solve problems of large size that are challenging to existing state-of-the-art domain methods.The project supported by the National Natural Science Foundation of China (10472051).The English text was polished by Yunming Chen.     

A Symmetric Galerkin BEM for Harmonic Problems and Multiconnected Bodies

A steady state harmonic solution of Navier equations of motion is presented using the symmetric Galerkin Boundary Element Method, which leads to a symmetric system of equations. For the integration, a two-step regularisation process is proposed to deal with the singularities of the involved kernels. It is also shown that the standard application of the symmetric Galerkin methodology for multiply connected bodies leads to the deterioration of the conditioning of the system for low frequencies. Two examples are presented comparing the solutions obtained with the proposed formulation with those obtained with the standard collocation method. A third example is presented to illustrate the behaviour of a simple multi-connected body.     

利用边界单元法求平面问题应力强度因子K_I的应力-位移杂交法

本文提出用裂尖附近2点或3点的应力和位移计算应力强度因子K_I的杂交方法.这种方法充分利用了边界单元法的计算结果,考虑了裂尖应力场和位移场渐近展开式的高阶项,使用远离裂尖的点算出的K_I也有较好的精度,拟合线十分平坦.用算例的结果将杂交法与一般的位移法和应力法进行了比较,同时,对常量单元和线性单元也进行了比较.     

Galerkin边界元法用于弹塑性分析的准高次元方法

提出了一种适用于Ｇａｌｅｒｋｉｎ边界元法的高次单元插值方法和半解析半数值的积分方法 准高次元法，建立了有关数值模型和将该方法应用于结构弹塑性分析的算法模型．有关算例结果表明，本文建议的方法是切实可行的．     

Element nodal computation-based radial integration BEM for non-homogeneous problems

This paper presents a new strategy of using the radial integration boundary element method （RIBEM） to solve non-homogeneous heat conduction and thermoelasticity problems. In the method, the evaluation of the radial in-tegral which is used to transform domain integrals to equivalent boundary integrals is carried out on the basis of elemental nodes. As a result, the computational time spent in evaluating domain integrals can be saved considerably in comparison with the conventional RIBEM. Three numerical examples are given to demonstrate the correctness and computational efficiency of the proposed approach.     

Analysis and calculation of stresses and displacements in layered elastic systems

The general formulae for the stresses and displacements in layered elastic systems subjected to external loads are derived in this paper. On the basis of these formulae the practical formulae for calculation of the stresses and displacements in layered elastic systems under the action of vertical, centripetal-horizontal, unidirectional-horizontal and rotational-horizontal loads distributed on circular areas and compressed by rigid circular plates are further derived, and the corresponding computer programs have been worked out.     

BEM for transient 2D elastodynamics using multiquadric functions

A new boundary element model for transient dynamic analysis of 2D structures is presented. The dual reciprocity method (DRM) is reformulated for the 2D elastodynamics by using the multiquadric radial basis functions (MQ). The required kernels for displacement and traction particular solutions are derived. Some terms of these kernels are found to be singular; therefore, a new smoothing technique is proposed to solve this problem. Hence, the limiting values of relevant kernels are computed. The validity and strength of the proposed formulation are demonstrated throughout several numerical applications. It is proven from the results that the present formulation is more stable than the traditional DRM, which uses the conical (1 + R) function, especially in predicting results in the far time zone.     

Computation of super-convergent nodal stresses of timoshenko beam elements by EEP method

The newly proposed element energy projection (EEP) method has been applied to the computation of super-convergent nodal stresses of Timoshenko beam elements. Generalformul as based on element projection theorem were derived and illustrative numerical examples using two typical elements were given. Both the analysis and examples show that EEP method also works very well for the problems with vector function solutions. The EEP method gives super-convergent nodal stresses, which are well comparable to the nodal displacements in terms of both convergence rate and error magnitude. And in addition, it can overcome the “ shear locking“ difficulty for stresses even when the displacements are badly affected. This research paves the way for application of the EEP method to general onedimensional systems of ordinary differential equations.     

基于等几何边界元法的声学敏感度分析

基于非均匀有理B样条(NURBS)曲面建模技术,边界物理量同样用NURBS基函数插值,推导出三维声场等几何边界积分方程。进一步以控制点为设计变量,用直接微分法推导出等几何敏感度边界积分方程,给出声场声压对形状参量的敏感度。针对边界积分方程中的超奇异积分,使用奇异相消技术并结合Cauchy主值积分和Hadamard有限部分积分处理,给出了超奇异积分的NURBS插值半解析表达式。数值算例验证了本文算法求解声学结构形状敏感度的有效性,为声学结构的整体形状优化打下基础。     

Frequency– and Time-domain BEM Analysis of Rigid Track on a Half-Space with Vibration Barriers

The rapid development of high-speed trains like the TGV or the ICE in recent years results in high dynamic loads causing vibrations which propagate from the train-track structure into the ground and further into nearby buildings. In this context it is important to develop rigid tracks with improved dynamic behaviour and to investigate possible means of vibration reduction. The boundary element method in frequency and time domain is used to simulate train-track structures subjected to dynamic loading and the reduction of vibrations which for instance can be achieved via a trench running parallel to the rigid track. In this context the non-causality error, which arises when the time-domain BEM algorithm is applied to mathematically concave domains, is discussed and the substructure method is proposed as a solution to this problem. A two-layered cylindrical elastic structure on a half-space with a trench is added as an example of a possible application.     

Boundary contour analysis for surface stress recovery in 2-D elasticity and Stokes flow

Summary A variant of the boundary element method, called the boundary contour method, offers a further reduction in dimensionality. Consequently, boundary contour analysis of 2-D problems does not require any numerical integration at all. In a boundary contour analysis, boundary stresses can be accurately computed using the approach proposed in Ref. [1]. However, due to singularity, this approach can be used only to calculate boundary stresses at points that do not lie at an end of a boundary element. Herein, it is shown that a technique based on the displacement/velocity shape functions can overcome this drawback. Further, the approach is much simpler to apply, requires less computational effort, and provides competitive accuracy. Numerical solutions and convergence study for some well-known problems in linear elasticity and Stokes flow are presented to show the effectiveness of the proposed approach. This research was supported in part by the 2004 Ralph E. Powe Junior Faculty Enhancement Award from Oak Ridge Associated Universities and by the University of South Alabama Research Council.     

The effect of initial stress and inhomogeneity on the thermoelastic stresses in a rotating anisotropic solid

The present paper presents a general treatment of the transient thermoelastic stresses in a rotating nonhomogeneous anisotropic solid under compressive initial stress. The system of fundamental equations is solved by means of a boundary element method (BEM) and the numerical calculations are carried out for the temperature, displacement components and stress components. The results indicate that the effects of inhomogeneity and initial stress are very pronounced.     

边界元法求解瞬态弹性动力学问题的一种新解法

本文首次将Newmark法引入到边界元法之中,从而使得边界元法与有限元法有机地结合起来,使边界元法的通用性在求解瞬态弹性动力学问题上大大加强,在程序的实现过程中应用一定的技巧,提出了多重子单元划分法,解决了时间步长与单元网格之间的耦合关系。提高了计算精度,缩短了计算时间,从所给出的算例可知,此算法是可行的,程序也是可靠的。     

BEM for modal analysis of 3-D anisotropic structures

The boundary element method for the modal anlysis of free vibration for 3-D anisotropic structures using particular solutions has been developed. The complete polynomials of order two are used to construct the particular solutions for general anisotropic materials. The numerical results for 3-D free vibration analysis of an isotropic cantilever beam by the method presented is in good agreement with the results using the Ritz technique. For anisotropic materials, the numerical results calculated from the proposed method are in good agreement with the results from MSC.NASTRAN. Project supported by the National Natural Science Foundation of China (No. 19872011).     

复合材料层合板在加工固化后期降温速率对残余热应力的影响

本文采用非线性有限元方法，对材料性质与温度有关的复合材料层合板在加工固化后期降温过程中的温度速场和热应力场进行了分析，对降温度速率对板中固化残余热应力的影响进行了研究，获得一些对层合板固化成型工艺和固化残余热应力分析模型的选取均有意义的结果。     

等参管单元及其在热传导问题边界元法中的应用Isoparametric tube elements and their application in heat conduction BEM analysis

采用边界元法（BEM ）求解实际工程问题时,很大一部分误差来自于离散误差。为此,本文基于Lagrange插值原理,提出了一种三维等参管单元边界元算法,该单元能很好地模拟管状结构的几何外形并对物理量进行高阶插值,大大地消除了离散误差。另外,当在边界元法中使用等参管单元时,提出了一种在等参平面内消除积分奇异性的方法。算例表明,本文算法具有划分网格少,求解精度高的优点。