共查询到19条相似文献,搜索用时 47 毫秒
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本文讨论了动力边界元法中的奇异积分问题,对其中的强奇异积分提出了一个有效的计算方法.该方法从合非零初始态的边界积分方程出发,利用动力方程的特解间接地确定了主系数(即所谓强奇异积分),从而避免了直接计算强奇异积分的困难.根据该方法编制了计算程序,并给出了一个简单算例。 相似文献
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将重构核粒子法(RKPM)和边界积分方程方法结合,提出了一种新的边界积分方程无网格方法——重构核粒子边界无单元法(RKP-BEFM).对弹性力学问题,推导了其重构核粒子边界无单元法的公式,研究其数值积分方案,建立了重构核粒子边界无单元法离散化边界积分方程,并推导了重构核粒子边界无单元法的内点位移和应力积分公式.重构核粒子法形成的形函数具有重构核函数的光滑性,且能再现多项式在插值点的精确值,所以本方法具有更高的精度.最后给出了数值算例,验证了本方法的有效性和正确性.
关键词:
重构核粒子法
弹性力学
边界无单元法 相似文献
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弹性波散射问题的边界元解法 总被引:1,自引:0,他引:1
采用边界单元法求解弹性波对孔口的散射问题,给出了弹性波散射问题的边界积分方程,针对数值中出现的奇异积分,提出了一种改进的把动力基本解分解为正则部分和奇异部分分别计算的方法。最后讨论了P波和SV波对圆孔和椭圆孔的散射而引起的动应力集中。 相似文献
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基于热传导及热弹性力学的基本关系式,建立了激光辐照锗透镜的热力耦合数学物理模型,对瞬态热传导方程和应力平衡方程进行有限元数值求解,得到了锗透镜的温度场和应力场分布,并利用波长1.06 μm,脉冲宽度10 ns的Nd∶YAG脉冲激光对锗透镜进行了热冲击实验研究.数值分析表明,热应力损伤在锗透镜的脉冲强激光损伤中占据主导地位,在短脉冲激光辐照下,锗透镜出现热应力损伤的激光能量密度小于出现熔融损伤的激光能量密度,热应力损伤主要集中在光斑中心区域并体现为压应力损伤,将使材料表面出现裂纹或剥落,实验结果与数值分析基本相符. 相似文献
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一、前言 边界元法是近年来兴起的一种新的基于边界积分方程的数值计算方法.Brebbia将其归之为加权剩余法的一个分支,但该法比有限元和有限差分法更具有解析——数值计算特点.有别于区域计算法,边界元法通过引入一个满足场方程的奇异函数作为权函数,将问题的区域计算转化为边界计算.由于所获得的一组边界积分方程仅联系边界上各个 相似文献
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传统外部声学Helmholtz边界积分方程无法在个人计算机上求解大规模工程问题. 为了有效解决这个问题, 将快速多极方法引入到边界积分方程中, 加速系统矩阵方程组的迭代求解. 由于在边界积分方程中引入基本解的对角形式多极扩展, 新的快速多极边界元法的计算效率与传统边界元相比显著提高, 计算量和存储量减少到O(N)量级(N为问题的自由度数). 包括含有420000个自由度的大型潜艇模型数值算例验证了快速多极边界元法的准确性和高效性, 清楚表明新算法在求解大规模声学问题中的优势, 相似文献
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传统外部声学Helmholtz边界积分方程无法在个人计算机上求解大规模工程问题. 为了有效解决这个问题, 将快速多极方法引入到边界积分方程中, 加速系统矩阵方程组的迭代求解. 由于在边界积分方程中引入基本解的对角形式多极扩展, 新的快速多极边界元法的计算效率与传统边界元相比显著提高, 计算量和存储量减少到O(N)量级(N为问题的自由度数). 包括含有420000个自由度的大型潜艇模型数值算例验证了快速多极边界元法的准确性和高效性, 清楚表明新算法在求解大规模声学问题中的优势, 具有良好的工程应用前景. 相似文献
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In the conformal near-field acoustic holography (NAH) using the boundary element method (BEM), the transfer matrix relating the vibro-acoustic properties of source and field depends solely on the geometrical condition of the problem. This kind of NAH is known to be very powerful in dealing with the sources having irregular shaped boundaries. When the vibro-acoustic source field is reconstructed by using this conformal NAH, one tends to position the sensors as close as possible to the source surface in order to get rich information on the nonpropagating wave components. The conventional acoustic BEM based on the Kirchhoff-Helmholtz integral equation has the singularity problem in the close near field of the source surface. This problem stems from the singular kernel of the Green function of the boundary integral equation (BIE) and the singularity can influence the reconstruction accuracy greatly. In this paper, the nonsingular BIE is introduced to the NAH calculation and the holographic BIE is reformulated. The effectiveness of nonsingular BEM has been investigated for the reduction of reconstruction error. Through interior and exterior examples, it is shown that the resolution of predicted field pressure could be improved in the close near field by employing the nonsingular BIE. Because the BEM-based NAH inevitably requires the field pressure measured in the close proximity to the source surface, the present approach is recommended for improving the resolution of the reconstructed source field. 相似文献
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A moving Kriging interpolation-based boundary node method for two-dimensional potential problems 下载免费PDF全文
In this paper,a meshfree boundary integral equation(BIE) method,called the moving Kriging interpolationbased boundary node method(MKIBNM),is developed for solving two-dimensional potential problems.This study combines the BIE method with the moving Kriging interpolation to present a boundary-type meshfree method,and the corresponding formulae of the MKIBNM are derived.In the present method,the moving Kriging interpolation is applied instead of the traditional moving least-square approximation to overcome Kronecker’s delta property,then the boundary conditions can be imposed directly and easily.To verify the accuracy and stability of the present formulation,three selected numerical examples are presented to demonstrate the efficiency of MKIBNM numerically. 相似文献
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Honggang Jia Yufeng Nie & Junlin Li 《advances in applied mathematics and mechanics.》2015,7(6):780-795
In this paper, a method for extracting stress intensity factors (SIFs) in orthotropic
thermoelasticity fracture by the extended finite element method (XFEM) and
interaction integral method is presented. The proposed method is utilized in linear elastic
crack problems. The numerical results of the SIFs are presented and compared with
those obtained using boundary element method (BEM). The good accordance among
these two methods proves the applicability of the proposed approach and conforms its
capability of efficiently extracting thermoelasticity fracture parameters in orthotropic
material. 相似文献
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In this paper, we present an efficient and accurate numerical algorithm for calculating the electrostatic interactions in biomolecular systems. In our scheme, a boundary integral equation (BIE) approach is applied to discretize the linearized Poisson-Boltzmann (PB) equation. The resulting integral formulas are well conditioned for single molecule cases as well as for systems with more than one macromolecule, and are solved efficiently using Krylov subspace based iterative methods such as generalized minimal residual (GMRES) or bi-conjugate gradients stabilized (BiCGStab) methods. In each iteration, the convolution type matrix-vector multiplications are accelerated by a new version of the fast multipole method (FMM). The implemented algorithm is asymptotically optimal O(N) both in CPU time and memory usage with optimized prefactors. Our approach enhances the present computational ability to treat electrostatics of large scale systems in protein-protein interactions and nano particle assembly processes. Applications including calculating the electrostatics of the nicotinic acetylcholine receptor (nAChR) and interactions between protein Sso7d and DNA are presented. 相似文献
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Rao SM 《The Journal of the Acoustical Society of America》2011,130(4):1792-1798
In this work, a simple iterative method to solve the acoustic scattering/radiation problems using the boundary integral equation (BIE) formulation is presented. The operator equation obtained in the BIE formulation is converted into a matrix equation using the well-known method of moments solution procedure. The present method requires much fewer mathematical operations per iteration when compared to other available iterative methods. Further, the present iterative method can easily handle multiple incident fields, a highly desirable feature not available in any other iterative method, much the same way as direct solution techniques. Several numerical examples are presented to illustrate the efficiency and accuracy of the method. 相似文献
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This study deals with elastic-wave identification of discrete heterogeneities (inclusions) in an otherwise homogeneous “reference” solid from limited-aperture waveform measurements taken on its surface. On adopting the boundary integral equation (BIE) framework for elastodynamic scattering, the inverse query is cast as a minimization problem involving experimental observations and their simulations for a trial inclusion that is defined through its boundary, elastic moduli, and mass density. For an optimal performance of the gradient-based search methods suited to solve the problem, explicit expressions for the shape (i.e. boundary) and material sensitivities of the misfit functional are obtained via the adjoint field approach and direct differentiation of the governing BIEs. Making use of the message-passing interface, the proposed sensitivity formulas are implemented in a data-parallel code and integrated into a nonlinear optimization framework based on the direct BIE method and an augmented Lagrangian whose inequality constraints are employed to avoid solving forward scattering problems for physically inadmissible (or overly distorted) trial inclusion configurations. Numerical results for the reconstruction of an ellipsoidal defect in a semi-infinite solid show the effectiveness of the proposed shape-material sensitivity formulation, which constitutes an essential computational component of the defect identification algorithm. 相似文献