混合夹杂问题的边界元法

该文提出了一种求解含固体、流体和孔隙等多类型夹杂的混合夹杂问题的边界元法。混合夹杂问题实质也是多连通域问题,但内边界的位移和面力都是未知量,导致该问题因定解条件不足而无法直接求解。根据不同类型夹杂的本构关系建立了各夹杂与基体界面面力与位移之间的关联矩阵,从而形成除给定边界条件以外的补充定解条件,使问题得以解决。以平面问题为例,分别对只含固体夹杂、流体夹杂以及同时含有孔隙、固体和流体夹杂的情况进行了计算,模拟了含100个随机分布夹杂的板材的弹性模量,验证了该方法的有效性、程序的正确性和可靠性。     

非均匀材料破坏过程数值模拟的边界元法研究

用格子模型和统计分布模拟非均匀材料性质的初始分布,针对二维非均匀材料格子模型建立了重复多子域边界元法求解方程。通过把各行子域集成为亚子域,然后对链状排列的亚子域应用域转移矩阵法进行求解。由于使用的域转移矩阵法对内存的要求仅略大于一个亚子域的求解,以及重复多子域法只需要进行一次系数矩阵积分,因而可以大大提高求解的规模和效率。在此基础上,对非均匀脆性材料在简单载荷作用下的破坏过程进行了数值模拟。采用重复多子域法和域转移矩阵法,可以得到子域内高精度的连续应力分布,为进一步研究非均匀材料裂纹萌生、扩展和破坏过程提供了基础。     

求解夹杂问题的有限部积分──边界元法

利用Kelvin解及有限部积分的概念和方法,导出求解含夹杂二维有限弹性体的超奇异积分方程,继而使用有限部积分与边界元结合的方法,为其建立了数值求解方法,即有限部积分与边界元法.最后计算了若干典型数值例子夹杂端部的应力强度因子.      

随机双相介质宏观弹性模量的边界元法预报

确定多相体材料的宏观性能与其细观组织之间的关系是当今计算结构力学的一个重要课题。本文采用高效率的二次等参边界元及子域法求解了随机双相介质的宏观弹性模量。计算结果与若干常见的解析公式进行了比较,为评价这些解析公式的可靠性提供了一定的依据。可以看出:边界元法在复合材料的计算力学中具有很大的潜力。      

随机双相介质宏观弹性膜量的边界元法预报

确定多相体材料的宏观性能与其细观组织之间的关系是当今计算结构力学的一个重要课题，本文采用高效率的二次等参边界元及子域法求解了随机双相介质的宏观弹性膜量，计算结果与若干常见的解析公式进行了比较，为评价这些解析公式的可靠性提供了一定的依据，可以看出，边界元法在复合材料的计算中学中具有很大的潜力。     

随机激励下结构振动声辐射的灵敏度分析和优化设计

基于有限元法、边界元法和虚拟激励法,对随机激励下结构振动声辐射灵敏度分析及优化设计问题进行研究.有限元法用于计算结构谐振响应,边界元法用于计算结构振动声辐射,虚拟激励法结合有限元和边界元计算随机激励下结构振动声辐射问题.提出随机激励下结构振动声辐射问题的优化模型及求解算法流程,重点推导了其灵敏度分析公式.数值算例验证了灵敏度分析的准确性及优化求解算法的有效性.     

快速多极边界元法在大规模传热分析中的应用

该文将快速多极边界元法用于三维稳态传热问题的大规模数值计算。多极展开的引入使得该算法能够在单台个人电脑上完成30万自由度以上的传热边界元分析。统一展开的基本解能够处理混合边界。广义极小残差法作为快速多极边界元法的迭代求解器,数值算例分析了快速多极边界元法的计算效率。结果表明:快速多极边界元法的求解效率与常规算法相比有数量级的提高;在模拟复杂结构大规模传热问题上将具有良好的应用前景。     

快速多极与常规边界元法机群并行计算的比较

以三维弹性力学问题为例,对快速多极与常规边界元法机群并行计算进行了比较。其中常规边界元法求解方程采用高斯消去法,通过调用标准并行求解函数库ScaLAPACK实现;快速多极边界元法并行计算程序采用ANSIC++语言、调用MPI并行通信库自行编写。两种程序均运行于同一机群并行环境。数值算例表明,在同样的机群条件下,采用快速多极边界元法可使解题规模有数量级的提高,计算速度明显高于常规边界元法,并行效率也优于常规边界元法。     

双腔结构消声器声学性能计算子域耦合方法

提出基于子域划分的耦合方法求解双腔结构消声器声学性能。据结构特点或材料属性将消声器分为不同子域,用数值模态匹配法或三维解析方法求解规则等截面子域结构传递矩阵,用三维数值方法求解非规则渐变截面子域结构传递矩阵,用子域连续条件求得消声器整体矩阵,进而获得消声器传递损失。分别用基于子域划分的耦合方法、三维有限元方法及数值模态匹配法计算典型双腔结构消声器的传递损失。结果表明,基于子域划分的耦合方法适用预测双腔结构消声器声学特性,与数值模态匹配法相比计算效率较高。     

超弹性柔性结构与流体耦合运动的浸入边界法研究

浸入边界法是模拟大变形柔性弹性结构和粘性流体相互作用的重要数值方法之一。该文有效结合传统的反馈力方法和混合有限元浸入边界方法,对圆柱和方柱绕流后柔性悬臂梁流固耦合振动问题进行数值模拟。其中,固体采用超弹性材料,利用有限单元法求解,流体为不可压缩牛顿流体,使用笛卡尔自适应加密网格,利用有限差分法进行求解。通过数值计算,得到柔性超弹性结构的耦合振动特性和流场动态分布特性,并将计算结果同其他文献计算结果进行比较,验证了该耦合计算方法的可靠性。     

An analysis of solidification problems by the boundary element method

The problem of interest in this paper is the calculation of the motion of the solid–liquid interface and the time-dependent temperature field during solidification of a pure metal. An iterative implicit algorithm has been developed for this purpose using the boundary element method (BEM) with time-dependent Green's functions and convolution integrals. The BEM approach requires discretization of only the surface of the solidifying body. Thus, the numerical method closely follows the physics of the problems and is intuitively very appealing. The formulation and the numerical scheme presented here are general and can be applied to a broad range of moving boundary problems. Emphasis is given to two-dimensional problems. Comparison with existing semi-analytical solutions and other numerical solutions from the literature reveals that the method is fast, accurate and without major time step limitations.     

An overlapping domain decomposition approach for coupling the finite and boundary element methods

An overlapping iterative domain decomposition approach for the coupling of the finite element method (FEM) and the boundary element method (BEM) is presented in this paper. In this proposed method, the domain of the original problem is subdivided into a FEM sub-domain and a BEM sub-domain, such that the two sub-domains partially overlap over a common region. The common region is modeled by both methods. A brief discussion on the existing iterative coupling methods and their limitations are given in the first part of this paper. In the second part, the proposed overlapping method is described and the convergence conditions are presented. Two numerical examples are given to demonstrate the capability of the proposed method for handling cases where the Neumann boundary conditions are specified on the entire external boundary of the FEM or BEM sub-domains.     

Dynamic analysis of interfacial crack problems in anisotropic bi-materials by a time-domain BEM

A time-domain boundary element method (BEM) together with the sub-domain technique is applied to study dynamic interfacial crack problems in two-dimensional (2D), piecewise homogeneous, anisotropic and linear elastic bi-materials. The bi-material system is divided into two homogeneous sub-domains along the interface and the traditional displacement boundary integral equations (BIEs) are applied on the boundary of each sub-domain. The present time-domain BEM uses a quadrature formula for the temporal discretization to approximate the convolution integrals and a collocation method for the spatial discretization. Quadratic quarter-point elements are implemented at the tips of the interface cracks. A displacement extrapolation technique is used to determine the complex dynamic stress intensity factors (SIFs). Numerical examples for computing the complex dynamic SIFs are presented and discussed to demonstrate the accuracy and the efficiency of the present time-domain BEM.     

A fast multipole boundary element method for 2D multi-domain elastostatic problems based on a dual BIE formulation

A new fast multipole formulation for the hypersingular BIE (HBIE) for 2D elasticity is presented in this paper based on a complex-variable representation of the kernels, similar to the formulation developed earlier for the conventional BIE (CBIE). A dual BIE formulation using a linear combination of the developed CBIE and HBIE is applied to analyze multi-domain problems with thin inclusions or open cracks. Two pre-conditioners for the fast multipole boundary element method (BEM) are devised and their effectiveness and efficiencies in solving large-scale problems are discussed. Several numerical examples are presented to study the accuracy and efficiency of the developed fast multipole BEM using the dual BIE formulation. The numerical results clearly demonstrate the potentials of the fast multipole BEM for solving large-scale 2D multi-domain elasticity problems. The method can be applied to study composite materials, functionally-graded materials, and micro-electro-mechanical-systems with coupled fields, all of which often involve thin shapes or thin inclusions.     

Domain decomposition boundary element method with overlapping sub-domains

A numerical approach based on the domain decomposition boundary element method (BEM) with overlapping sub-domains has been developed. The approach simplifies the assembly of the equations arising from the BEM sub-domain methods, reduces the size of the system matrix, produces a closed system of equations when continuous elements are used, and reduces any problems arising from near-singular or singular integrals which otherwise may appear in the integral equations. The overlapping numerical approach is tested on three different problems, i.e., the Poisson equation, and a one-dimensional and two-dimensional convection–diffusion problems. The approach is implemented in combination with the dual reciprocity method (DRM) with two different radial basis functions (RBFs), though the approach is general and can be applied with other BEM formulations. The results are compared with the previous results obtained using the dual reciprocity method–multi domain (DRM–MD) approach, showing comparable accuracy and convergence.     

Vector and multithread computation of silencer performance prediction on a dual-processor PC workstation

Silencers used in industry usually contain complex internal components such as thin baffles, internal tubes, perforated tubes, and bulk-reacting sound absorbing materials. The direct mixed-body boundary element method (BEM) is an ideal analysis tool because each component has its own surface attribute and can be meshed independently. A model can be easily created by assembling individual components together. However, the BEM computation over a broad frequency range is very time consuming, especially at high frequencies. To speed up the computation, a dynamic meshing scheme is adopted and the BEM computation at each frequency is vectorized as well as parallelized. The multi-processor x86architecture running Windows NT/2000 is selected as the computational platform mainly because of its popularity and low cost. Evaluation of the fundamental solutions is vectorized to speed up numerical integration. At the same time, parallelization is achieved via the multithread implementation. Both the matrix generation part and the matrix solution part are parallelized. Numerical results show that an overall parallel efficiency of around 0.9 can be achieved on a dual-processor PC workstation.     

A hybrid micro–macro BEM formulation for micro-crack clusters in elastic components

Local analysis schemes capable of detailed representations of the micro-features of a problem are integrated with a macro-scale BEM technique capable of handling complex finite geometries and realistic boundary conditions. The micro-scale effects are introduced into the macro-scale BEM analysis through an augmented fundamental solution obtained from an integral equation representation of the micro-scale features. The proposed hybrid micro-macro BEM formulation allows decomposition of the complete problem into two sub-problems, one residing entirely at the micro-level and the other at the macro-level. This allows for investigations of the effects of the micro-structural attributes while retaining the macro-scale geometric features and actual boundary conditions for the component or structure under consideration. As a first attempt, elastic fracture mechanics problems with interacting cracks at close spacings are considered. The numerical results obtained from the hybrid BEM analysis establish the accuracy and effectiveness of the proposed micro–macro computational scheme for this class of problems. The proposed micro–macro BEM formulation can easily be extended to investigate the effects of other micro-features (e.g. interfaces, short or continuous fibre reinforcements, voids and inclusions, in the context of linear elasticity) on macroscopic failure modes observed in structural components.     

Boundary element method for band gap calculations of two-dimensional solid phononic crystals

A boundary element method (BEM) is developed to calculate the elastic band gaps of two-dimensional (2D) phononic crystals which are composed of square or triangular lattices of solid cylinders in a solid matrix. In a unit cell, the boundary integral equations of the matrix and the scatterer are derived, the former of which involves integrals over the boundary of the scatterer and the periodic boundary of the matrix, while the latter only involves the boundary of the scatterer. Constant boundary elements are adopted to discretize the boundary integral equations. Substituting the periodic boundary conditions and the interface conditions, a linear eigenvalue equation dependent on the Bloch wave vector is derived. Some numerical examples are illustrated to discuss the accuracy, efficiency, convergence and the computing speed of the presented method.     

Numerical simulation of crack deflection and penetration at an interface in a bi-material under dynamic loading by time-domain boundary element method

The hybrid time-domain boundary element method (BEM), together with the multi-region technique, is applied to simulate the dynamic process of crack deflection/ penetration at an interface in a bi-material. The whole bi-material is divided into two regions along the interface. The traditional displacement boundary integral equations (BIEs) are employed with respect to the exterior boundaries; meanwhile, the non-hypersingular traction BIEs are used with respect to the part of the crack in the matrix. Crack propagation along the interface is numerically modelled by releasing the nodes in the front of the moving crack tip and crack propagation in the matrix is modeled by adding new elements of constant length to the moving crack tip. The dynamic behaviours of the crack deflection/penetration at an interface, propagation in the matrix or along the interface and kinking out off the interface, are controlled by criteria developed from the quasi-static ones. The numerical results of the crack growth trajectory for different inclined interface and bonded strength are computed and compared with the corresponding experimental results. Agreement between numerical and experimental results implies that the present time-domain BEM can provide a simulation for the dynamic propagation and deflection of a crack in a bi-material.