各向异性外问题的非均匀网格的自然边界元法及其耦合法

本文对于无界区域上各向异性外问题提出了在椭圆边界非均匀网格上的自然边界元法及其与有限元法的耦合法,证明相应的收敛定理和误差估计式,并且在这两种方法中引入基于等分布原理的移动网格技巧.最后,通过数值结果表明了误差收敛理论的正确性以及所提方法和技巧的有效性.     

On subsurface box-shaped lined tunnel under incident SH-wave propagation

In this paper, a half-plane time-domain boundary element method is applied to obtain the seismic ground response, including a subsurface box-shaped lined tunnel deployed in a linear homogenous elastic medium exposed to obliquely incident SH-waves. Only the boundary around the tunnel is required to be discretized. To prepare an appropriate model by quadratic elements, a double-node procedure is used to receive dual boundary fields at corners as well as change the direction of the normal vector. After encoding the method in a previously confirmed computer program, a numerical study is carried out to sensitize some effective parameters, including frequency content and incident wave angle for obtaining a surface response. The depth and impedance ratio of the lining are assumed to be unvaried. The responses are illustrated in the time and frequency domains as two/three-dimensional graphs. The results showed that subsurface openings with sharp corners distorted the propagation path of the anti-plane waves to achieve the critical states on the ground surface. The present approach can be proposed to civil engineers for preparing simple underground box-shaped models with angular boundaries.     

CMRH method as iterative solver for boundary element acoustic systems

Disceretization of boundary integral equations leads to complex and fully populated linear systems. One inherent drawback of the boundary element method (BEM) is that, the dense linear system has to be constructed and solved for each frequency. For large-scale problems, BEM can be more efficient by improving the construction and solution phases of the linear system. For these problems, the application of common direct solver is inefficient. In this paper, the corresponding linear systems are solved more efficiently than common direct solvers by using the iterative technique called CMRH (Changing Minimal Residual method based on Hessenberg process). In this method, the generation of the basis vectors of the Krylov subspace is based on the Hessenberg process instead of Arnoldi's one that the most known GMRES (Generalized Minimal RESidual) solver uses. Compared to GMRES, the storage requirements are considerably reduced in CMRH.     

Multiple pole residue approach for 3D BEM analysis of mathematical degenerate and non‐degenerate materials

In this paper we develop an alternative boundary element method (BEM) formulation for the analysis of anisotropic three‐dimensional (3D) elastic solids. Our implementation is based on the derivation of explicit expressions for the fundamental solution displacements and tractions, of general validity for any class of anisotropic materials, by means of Stroh formalism and Cauchy's residue theory. The resulting fundamental solution remains valid for mathematical degenerate cases when Stroh's eigenvalues are coincident, meanwhile it does not exhibit numerical instabilities for quasi‐degenerate cases when Stroh's eigenvalues are nearly equal. A multiple pole residue approach is followed, leading to general explicit expressions to evaluate the traction fundamental solution for poles of m‐multiplicity. Despite the existence of general displacement solutions in the literature, and for the sake of completeness, the same approach as for the traction solution is considered to derive the displacement fundamental solution as well. Based on these solutions, an explicit BEM approach for the numerical solution of 3D linear elastic problems for solids with general anisotropic behavior is presented. The analysis of cracked anisotropic solids is also considered. Details on the numerical implementation and its validation for degenerate cases are discussed. Copyright © 2010 John Wiley & Sons, Ltd.     

开口薄壁结构声固耦合问题的计算方法

对于开口薄壁结构的声辐射问题,很难用解析法直接计算,可采用多种数值方法进行仿真分析。文中研究了有限元法、边界元法与无限元法几种数值方法及其耦合的理论基础,研究了求解不封闭声腔声辐射问题的几种数值方法。在考虑声固耦合的前提下,分析了间接边界元法、直接边界元内外声场耦合法、有限元与边界元耦合法、有限元与无限元耦合法4种方法求解开口结构声场问题的系统方程及求解过程,以具体开口薄壁结构为实例采用4种方法进行了模拟计算,并对结果进行了分析比较,得出相关结论。     

基于改进叶素动量理论的水平轴风电机组气动性能计算

综合考虑到风剪切、塔影效应、三维旋转效应的影响,本文对传统的叶素动量理论（bladeelementmomentum,BEM）进行改进,建立风电机组气动性能计算模型,基于该模型编制计算程序,以商用1．5MW风电机组为计算实例,计算出其在不同的风速、转速和桨距角配置下的轴向和切向气动荷载分布,以及推力、功率和风能利用系数,与传统BEM模型及风电设计分析软件FOCUS5计算值对比,验证了该模型的正确性和优越性。     

声呐导流罩内声场特性研究

为研究机械激励下声呐导流罩壳内噪声预报问题,采用数值计算(有限元法-边界元法)结合实验的方法对一导流罩模型的壳内声场进行研究。首先依据实际导流罩模型建模,并加载机械激励进行数值计算,得到壳内声场的均方声压,然后进行湖内实验测量,最后对比了数值计算和实验的结果。研究表明:有限元法加间接边界元法是分析导流罩内声场这种封闭结构流-固-声耦合问题的有效方法;导流罩壳内声场的数值计算结果与实验测量结果吻合较好;声场均方声压与结构均方振速之比反映了罩壳结构内平均声场特性,可用来对比分析数值计算和实验的结果。     

Dynamic crack propagation in matrix involving inclusions by a time-domain BEM

The dynamic crack propagation in composites with inclusions is analyzed by a time-domain boundary element method (BEM) in conjunction with the sub-region technique. The crack-growth direction and the crack-tip instantaneous velocity are determined by the maximum circumferential stress criterion. The instantaneous velocity is well smoothed by a bisection technique. New crack-tip elements of inconstant length are added to the active crack-tip to simulate the fast crack growth. Square root shape functions are adopted as to describe the proper asymptotic behavior in the vicinity of the crack-tips. The computation time for the dynamic fracture problems in composites with multiple inclusions is reduced by a numerical method. The influences of the inclusions on the shielding ratio, the crack growing path and the crack-tip instantaneous speed are well investigated.     

A fast dual boundary element method for 3D anisotropic crack problems

In the present paper a fast solver for dual boundary element analysis of 3D anisotropic crack problems is formulated, implemented and tested. The fast solver is based on the use of hierarchical matrices for the representation of the collocation matrix. The admissible low rank blocks are computed by adaptive cross approximation (ACA). The performance of ACA against the accuracy of the adopted computational scheme for the evaluation of the anisotropic kernels is investigated, focusing on the balance between the kernel representation accuracy and the accuracy required for ACA. The system solution is computed by a preconditioned GMRES and the preconditioner is built exploiting the hierarchical arithmetic and taking full advantage of the hierarchical format. The effectiveness of the proposed technique for anisotropic crack problems has been numerically demonstrated, highlighting the accuracy as well as the significant reduction in memory storage and analysis time. In particular, it has been numerically shown that the computational cost grows almost linearly with the number of degrees of freedom, obtaining up to solution speedups of order 10 for systems of order 10⁴. Moreover, the sensitivity of the performance of the numerical scheme to materials with different degrees of anisotropy has been assessed. Copyright © 2009 John Wiley & Sons, Ltd.     

Steady-State Module of Cooling Analysis in Injection Molding

Cooling system in injection molding is of great importance because it cannot only reduce molding cycle time efficiently but also can improve part quality. Current cooling analysis method is based on boundary element method (BEM). Because the cooling analysis module is so complex, with the same BEM, the equations of the item calculation of coefficient matrix are variable. Different calculation equations cause different problems, which influence its practicability. This article presents a practicable analysis model. Many tests show its result is reasonable.