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potential problems with random parameters by the generalized perturbation-based stochastic finite element method

COMPUTERS & STRUCTURES 2010年第7-8期88卷 437-445页

作者： Kaminski, Marcin Tech Univ Lodz Dept Steel Struct Fac Civil Engn Architecture & Environm Engn PL-90924 Lodz Poland

The main aim of this paper is to present the new version and the application of the generalized nth order stochastic perturbation technique to the solution of the field problems with random coefficients. The variational stochastic nth order principles are proposed here using Taylor expansions with random parameters together with the additional stochastic finite element method discretization of the problem, a derivation of up to the fourth probabilistic moments and the coefficients of the potential function are also provided. The formulation is dual in the sense that both Direct Differentiation Method and the Response Function Method in its local version are proposed and implemented using the symbolic computer system MAPLE to determine numerically the random system response and to make the additional visualization. This methodology is illustrated with two examples - 1D viscous irrotational and incompressible fluid flow and 2D torsion of the prismatic rectangular beam with random transverse modulus (C) 2009 Elsevier Ltd All rights reserved

关键词： Stochastic finite element method potential problems Stochastic perturbation method Response Function Method

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potential problems and Possible Solutions for Electronic Information Industry Development in Chongqing

Potential Problems and Possible Solutions for Electronic Inf...

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2nd International Conference on Civil Engineering, Architecture and Building Materials (CEABM 2012)

作者： Zhang, Meihua Xiang, Xinyi Wu, Qiang Southwest Univ Sch Geog Sci Chongqing 400715 Peoples R China Chongqing Communist Youth League School Chongqing 400715 Peoples R China

ISBN: (纸本)9783037854235

Under the context of improving the world's ecological standards, the developed countries are making higher standards, which may lead to the traditional "high end" industry transferring to China and other developing countries, especially the industry which takes more subtle pollution or longer incubation period. In China, reflection after three decades of development in Guangdong and other pre-open areas may lead to these "high end" industries transfer to the developing area, such as Chongqing. From the example of four confrontations between Greenpeace and Hewlett-Packard, it can be found that the electronic information industry development may bring long-term worries. In this context, in order to avoid the "high end" industries development's pitfalls, the electronic information industry in Chongqing must be conducted with a comprehensive system of research about its concealed or latent ecological and environmental worries of electronics industry.

关键词： Electronic information industry Chongqing the industrial development potential problems scientific development

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The complex variable meshless local Petrov-Galerkin method of solving two-dimensional potential problems

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Chinese Physics B 2012年第10期21卷 49-55页

作者：杨秀丽戴保东张伟伟 Department of Engineering Mechanics Taiyuan University of Science&Technology

Based on the complex variable moving least-square（CVMLS） approximation and a local symmetric weak form,the complex variable meshless local Petrov-Galerkin（CVMLPG） method of solving two-dimensional potential problems is presented in this *** the present formulation,the trial function of a two-dimensional problem is formed with a one-dimensional basis *** number of unknown coefficients in the trial function of the CVMLS approximation is less than that in the trial function of the moving least-square（MLS） *** essential boundary conditions are imposed by the penalty *** main advantage of this approach over the conventional meshless local Petrov-Galerkin（MLPG） method is its computational *** numerical examples are presented to illustrate the implementation and performance of the present CVMLPG method.

关键词： meshless method complex variable moving least-square method complex variable meshless local Petrov-Galerkin method potential problems

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Overhauser triangular elements for three-dimensional potential problems using boundary element methods

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 1996年第24期39卷 4183-4198页

作者： Durodola, JF Fenner, RT UNIV LONDON IMPERIAL COLL SCI TECHNOL & MED DEPT MECH ENGNLONDON SW7 2BXENGLAND

Interpolation to boundary data and one-dimensional Overhauser parabola blending methods are used to derive Overhauser triangular elements. The elements are C-1-continuous at inter-element nodes and no functional derivatives are required as nodal parameters. These efficient parametric representation elements are used to solve three-dimensional potential problems using the Boundary Element Method (BEM). Results obtained are generally as accurate as those obtained using Overhauser quadrilateral elements.

关键词： Overhauser triangular elements boundary element three-dimensional potential problems

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A coupled finite element and meshless local Petrov-Galerkin method for two-dimensional potential problems

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2003年第41-42期192卷 4533-4550页

作者： Chen, T Raju, IS NASA Langley Res Ctr Hampton VA 23681 USA

A coupled finite element (FE) and meshless local Petrov-Galerkin (MLPG) method for analyzing two-dimensional potential problems is presented in this paper. A transition region is created between the FE and MLPG regions. The transition region blends the trial and test functions of the FE and MLPG regions. The trial function blending is achieved using a new coupling technique similar to the 'Coons patch' method that is widely used in computer aided geometric design. By using the technique, trial functions, which are similar to the isoparametric "serendipity" element, of the transition element can be constructed. The test function blending is achieved by using either the FE or MLPG test functions on the nodes. Several potential problems are used to establish the validity of the coupled method. 2003 Elsevier B.V. All rights reserved.

关键词： finite element method meshless local Petrov-Galerkin (MLPG) method coupling method blending functions potential problems

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Local integral equation method for potential problems in functionally graded anisotropic materials

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ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2005年第9期29卷 829-843页

作者： Sladek, V Sladek, J Tanaka, M Zhang, C Slovak Acad Sci Inst Construct & Architecture Bratislava 84503 Slovakia Shinshu Univ Dept Mech Syst Engn Nagano 3808553 Japan Univ Siegen Dept Civil Engn D-57068 Siegen Germany

Efficient computational techniques are developed for 2D potential problems in anisotropic media with continuously variable material coefficients. The method is based on integral relationships considered on local sub-domains and domain-type approximations of the field variable. Three different kinds of integral equations are combined with either a domain element interpolation or a meshless point interpolation. The physical background of the formulation is discussed briefly. The accuracy and the convergence of the proposed techniques are tested by several examples and compared with benchmark analytical solutions. (C) 2005 Elsevier Ltd. All rights reserved.

关键词： potential problems anisotropic and non-homogeneous media integral equation methods fundamental solutions integral balance equation domain-type approximations meshless interpolation accuracy convergence

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A new global and direct integral formulation for 2D potential problems

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ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2021年 125卷 233-240页

作者： Zhang, Chao Fu, Zhuojia Zhang, Yaoming Hohai Univ Coll Mech & Mat Nanjing 211100 Peoples R China Nanjing Univ Aeronaut & Astronaut State Key Lab Mech & Control Mech Struct Nanjing 210016 Peoples R China Shandong Univ Technol Inst Appl Math Zibo 255049 Shandong Peoples R China

A new global and direct integral formulation (GDIF) is presented for 2D potential problems. The 'global' and 'direct' mean that Gaussian quadrature can be applied directly to the entire body surface if its geometry description is mathematically available. This concept is simple and time-honored. The method has been long pursued by several researchers thanks to its accuracy and efficiency. However, the GDIF is based on the boundary integral equations (BIEs). The most crucial but difficult part in this method is to eliminate the singularities in BIEs, especially the source singularity. In this study, new non-singular boundary integral equations (NSBIEs) with indirect unknowns are developed in association with the average source technique without using the equi-potential method for source singularity. The integrands of all integrals in the NSBIEs are finite at any point on the body surface, which allows them to be considered as a normal function for computation. Based on this, with collocation points chosen in the NSBIEs being exactly the same as Gaussian points, an arbitrary order Gaussian quadrature can be directly applied to evaluate the integrals over the global elements. Three benchmark examples are tested to verify the efficiency and convergence of the proposed scheme.

关键词： Global element Direct integration Non-singular boundary integral equation potential problems

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A simple formula for obtaining OIFs on Neumann boundary in 2D potential problems and its applications

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ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2022年 134卷 581-590页

作者： Chen, Bin Qu, Wenzhen Shu, Kaiou Zhang, Lei Jiujiang Univ Sch Civil Engn & Urban Construct Jiujiang 332005 Jiangxi Peoples R China Qingdao Univ Sch Math & Stat Qingdao 266071 Peoples R China

Prior to this study, an empirical formula has been proposed to evaluate origin intensity factors on the Dirichlet boundary. In this work, a simple empirical formula for obtaining origin intensity factors on the Neumann boundary is provided. As a result, origin intensity factors both on Dirichlet boundary and Neumann boundary could be directly achieved. It makes the numerical implementation of the singular boundary method easier. Numerical results are carried out to verify the accuracy and stability of the present scheme.

关键词： Singular boundary method Fundamental solutions Origin intensity factors Neumann boundary potential problems

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An isogeometric boundary element method for three dimensional potential problems

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2017年 313卷 454-468页

作者： Gong, Y. P. Dong, C. Y. Qin, X. C. Beijing Inst Technol Sch Aerosp Engn Dept Mech Beijing 100081 Peoples R China

Isogeometric analysis (IGA) coupled with boundary element method, i.e. IGABEM, received a lot of attention in recent years. In this paper, we extend the IGABEM to solve 3D potential problems. This method offers a number of key improvements compared with conventional piecewise polynomial formulations. Firstly, the models for analysis in the IGABEM are exact geometrical representation no matter how coarse the discretization of the studied bodies is, thus the IGABEM ensures that no geometrical errors are produced in the analysis process. Secondly, a meshing process is no longer required, which means redundant computations are eliminated to allow analysis to be carried out with greatly reduced pre-processing. To accurately evaluate the singular integrals appearing in our method, the power series expansion method is employed. The integration surface is on the real surface of the model, rather than the interpolation surface, i.e. no geometrical errors. Thus, the value of integral is more accurate than the traditional boundary element method, which can improve the computation accuracy of the IGABEM. Some numerical examples for 3D potential problems are used to validate the solutions of the present method with analytical and numerical solutions available. (C) 2016 Elsevier B.V. All rights reserved.

关键词： potential problems 3D IGABEM Singular integrals Power series expansion method

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EXTRACTING SINGULARITIES OF CAUCHY INTEGRALS - A KEY POINT OF A FAST SOLVER FOR PLANE potential problems WITH MIXED BOUNDARY-CONDITIONS

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 1992年第2期44卷 167-185页

作者： HAAS, R BRAUCHLI, H SWISS FED INST TECHNOL INST MECHCH-8092 ZURICHSWITZERLAND

The authors (1991) proposed an algorithm for solving plane potential problems with mixed boundary conditions. The method is based on a corresponding Riemann-Hilbert problem on the unit disc, onto which the problem has been transformed conformally. Numerically the evaluation of the solution reduces to the computation of Cauchy integrals on the unit, circle, operating on singular functions. Explicit extraction and analytical integration of these singularities up to a certain order is possible by the Schwarz formula. The remaining integral can then be treated accurately applying fast Fourier techniques. Where Haas and Brauchli (1991) focus on a more general description including computed examples, this paper gives the mathematical details concerning the construction of the singular extraction functions. Explicit expressions for their coefficients are derived.

关键词： EXTRACTION OF SINGULARITIES potential problems MIXED BOUNDARY CONDITIONS RIEMANN-HILBERT PROBLEM NUMERICAL CONFORMAL MAPPING

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