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Computation of stresses in non-homogeneous elastic solids by local integral equation method: a comparative study

COMPUTATIONAL MECHANICS 2008年第6期41卷 827-845页

作者： Sladek, Vladimir Sladek, Jan Zhang, Chuanzeng Slovak Acad Sci Inst Construct & Architecture Bratislava Slovakia Univ Siegen Dept Civil Engn Siegen Germany

The paper deals with the numerical implementation of local integral equations for solution of boundary value problems and interior computations of displacements and their gradients in functionally graded elastic solids. Two kinds of meshless approximations and one element based approximation are employed in various formulations. The numerical stability, accuracy, convergence of accuracy and cost efficiency are investigated in numerous test examples with exact benchmark solutions.

关键词： elasticity local integral equations point interpolation method MLS-approximation accuracy numerical stability convergence CPU-time

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Computation of stresses in non-homogeneous elastic solids by local integral equation method: a comparative study

Computation of stresses in non-homogeneous elastic solids by...

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Symposium of the International-Association-for-Boundary-Element-methods

作者： Sladek, Vladimir Sladek, Jan Zhang, Chuanzeng Slovak Acad Sci Inst Construct & Architecture Bratislava Slovakia Univ Siegen Dept Civil Engn Siegen Germany

关键词： elasticity local integral equations point interpolation method MLS-approximation accuracy numerical stability convergence CPU-time

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Upper and Lower Bounds for Numerical Solutions of Elasticity Problems using LC-PIM and FEM

Upper and Lower Bounds for Numerical Solutions of Elasticity...

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2007国际计算力学研讨会

作者： G.R.Liu~(1,2*),G.Y.Zhang~(1,2) 1 Center for Advanced Computations in Engineering Science(ACES),Department of Mechanical Engineering, National University of Singapore,117576,Singapore 2 The Singapore-MIT Alliance(SMA),E4-04-10,4 Engineering Drive 3,117576,Singapore

It is well known that the finite element method(FEM) provides a lower bound in energy norm for the exact solution to elasticity ***,it is much more difficult to bound the solution from above for general problems in elasticity,and it has been a dream of many decades to find a systematical way to obtain such an upper *** paper presents a very important and unique property of the linearly conforming point interpolation method(LC-PIM):it provides a general means to obtain an upper bound solution in energy norm for elasticity *** paper conducts first a thorough theoretical study on the LC-PIM:we derive its weak form based on variational principles,study a number of properties of the LC-PIM,and prove that LC-PIM is variationally consistent and that it produces upper bound *** then demonstrate these properties through numerical studies via examples of 1D,2D and 3D *** the LC-PIM together with the FEM,we now have a systematically way to numerically obtain both upper and lower bounds of the exact solution to elasticity problems.

关键词： linearly conforming point interpolation method upper and lower bounds in energy norm

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A comparative study of meshless approximations in local integral equation method

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CMC-COMPUTERS MATERIALS & CONTINUA 2006年第3期4卷 177-188页

作者： Sladek, Vladimir Sladek, Jan Zhang, Chuanzeng Slovak Acad Sci Inst Construct & Arcihitecture Bratislava 84503 Slovakia Univ Siegen Dept Civil Engn D-57068 Siegen Germany

This paper concerns the stability, convergence of accuracy and cost efficiency of four various formulations for solution of boundary value problems in non-homogeneous elastic solids with functionally graded Young's modulus. The meshless point interpolation method is employed with using various basis functions. The interaction among the elastic continuum constituents is considered in the discretized formulation either by collocation of the governing equations or by integral satisfaction of the force equilibrium on local sub-domains. The exact benchmark solutions are used in numerical tests.

关键词： integral equation method integral force equilibrium collocation method point interpolation method radial basis functions elasticity Functionally Graded Materials (FGMs)

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Eigenvalue analysis of doubly connected plates with different configurations

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JOURNAL OF SOUND AND VIBRATION 2006年第1-2期295卷 76-93页

作者： Singh, Anand V. Tanveer, Muhammad Univ Western Ontario Dept Mech & Mat Engn London ON N6A 5B9 Canada

This paper deals with the vibration and buckling analyses of the first-order shear deformable rhombic and square plates using a p-type variational method. The formulation includes rotary inertia and transverse shear terms. The full plate is modeled with a single domain defined by a set of geometric points in the plane of the plate. Square and rectangular plates with a circular hole at the center are treated as the numerical example for the doubly connected plate and are modeled using one quarter of the geometry and only two elements. The symmetry about x and y axes with regards to load and boundary conditions are exploited. Buckling coefficients and natural frequencies are calculated and compared with results from the published sources and the finite element method. (c) 2006 Elsevier Ltd. All rights reserved.

关键词： SHEAR-DEFORMABLE PLATES point interpolation method RECTANGULAR-PLATES SKEWPLATES QUADRATURE method BUCKLING ANALYSIS FREE-VIBRATION LOADED PLATES HOLES

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Buckling and free vibration analyses of stiffened plates using the FSDT mesh-free method

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JOURNAL OF SOUND AND VIBRATION 2006年第3期289卷 421-449页

作者： Peng, LX Liew, KM Kitipornchai, S City Univ Hong Kong Dept Bldg & Construct Kowloon Hong Kong Peoples R China Nanyang Technol Univ Nanyang Ctr Supercomp & Visualisat Singapore 639798 Singapore Nanyang Technol Univ Sch Mech & Aerosp Engn Singapore 639798 Singapore

This paper presents a mesh-free Galerkin method for the free vibration and stability analyses of stiffened plates via the first-order shear deformable theory (FSDT). The model of a stiffened plate is formed by (1) regarding the plate and the stiffener separately, (2) imposing displacement compatible conditions between the plate and the stiffener so that displacement fields of the stiffener can be expressed in terms of the midsurface displacement of the plate, and (3) superimposing the strain energy of plate and stiffener. Because there are no meshes used in this method, the stiffeners can be placed anywhere on the plate and need not be placed along the mesh lines. Several numerical examples are computed by this method to show its accuracy and convergence. The present results demonstrate good agreement with the existing solutions given by other researchers and the ANSYS. Influences of support size and order of the complete basis functions on the numerical accuracy are also investigated. (c) 2005 Elsevier Ltd. All rights reserved.

关键词： DIFFERENTIAL QUADRATURE method SHEAR-DEFORMABLE PLATES KERNEL PARTICLEmethod FREE GALERKIN method LAMINATED COMPOSITE PLATES point interpolation method FINITE-ELEMENTANALYSIS ANNULAR MINDLIN PLATES RITZ method SHELLS

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A Radial interpolation Meshless methods with point Polynomial Basis

A Radial Interpolation Meshless Methods with Point Polynomia...

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The second Asia-Pacific International Conference on Computational methods in Engineering（ICOME2006）

作者： Maohui Xia , Yan Jia, Jin Li College of science, Yanshan University, Qinghuangdao, Heibei, 066004 China

point interpolation method which bases on the basis function is a new meshless method. It solves the limitation of point interpolation method (PIM), which coefficient matrix may be singular. In addition, the formulated shape function has the property of delta function, which is convenient to implement essential condition. This paper introduces point interpolation method simply and presents the basis principle of radial point interpolation method, then gives some examples to show the advantages of Mfree methods: high efficiency and accuracy. So it becomes wide development in project.

关键词： Mfree methods point interpolation method Radial point interpolation methods

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Assessment and applications of point interpolation methods for computational mechanics

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INTERNATIONAL JOURNAL FOR NUMERICAL methodS IN ENGINEERING 2004年第10期59卷 1373-1397页

作者： Liu, GR Gu, YT Dai, KY Natl Univ Singapore Dept Mech Engn Ctr Adv Computat Engn Sci Singapore 119260 Singapore

Two meshfree point interpolation methods (PIMs), which are based on the polynomial and the radial basis functions, have been proposed recently in addition to the earlier work with the moving least-squares (MLS) approximation for the field function approximation. However, it is found that PIMs cannot automatically ensure the compatibility of the solution when they are used together with the energy principles. In this paper, issues related to the compatibility of PIMs are studied. A technique of background cell-based nodal selections and a penalty method are proposed to enforce the compatibility of the solution of PIMs. The patch test is studied in great detail. The convergences and performances are investigated for both conforming and non-conforming PIMs. It is found that those methods of the PIM family are very easy to implement, and are very efficient in obtaining numerical solutions for problems of computational mechanics. Copyright (C) 2004 John Wiley Sons, Ltd.

关键词： Computational mechanics meshfree method point interpolation method compatibility

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Comparison between the radial point interpolation and the Kriging interpolation used in meshfree methods

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COMPUTATIONAL MECHANICS 2003年第1-2期32卷 60-70页

作者： Dai, KY Liu, GR Lim, KM Gu, YT Natl Univ Singapore Dept Mech Engn Ctr Adv Computat Engn Sci Singapore 119260 Singapore

The radial point interpolation method (RPIM) based on local supported radial basis function (RBF) and the Galerkin weak form has been developed and successfully applied to many engineering problems. Recently, a new meshfree method was proposed based on the universal moving Kriging interpolation. This paper studies the difference between the meshfree shape functions created based on the point interpolation and the Kriging interpolation. It is found that both the two methods yield the same shape function as long as the same radial basis function or semivariograin is adopted for interpolation. Although the two methods lead to the same shape function, the theorem in Kriging formulation may provide an alternative theoretical support for the RPIM. Some common semivariograms used in Kriging may also be incorporated in the RPIM. in addition, in order to satisfy the conformability requirements, a penalty technique is introduced in this paper to form a conforming Kriging, which can pass the standard patch test exactly.

关键词： point interpolation method Kriging method radial basis functions meshfree method

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A radial boundary node method for two-dimensional elastic analysis

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ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2003年第8期27卷 853-862页

作者： Xie, H Nogami, T Wang, JG Natl Univ Singapore Trop Marine Sci Inst Singapore 119260 Singapore Natl Univ Singapore Dept Civil Engn Singapore 119260 Singapore

The boundary node method (BNM) takes the advantages of both the boundary integral equation in dimension reduction and the moving least-square (MLS) approximation in elements elimination. However, the BNM inherits the deficiency of the MLS approximation, in which the shape functions lack the delta function property. As a result boundary conditions could not be exactly implemented for the BNM. In this paper, a radial boundary node method (RBNM) is proposed. The RBNM uses radial basis functions (RBFs) instead of the MLS to construct its interpolation. Consequently, the interpolation function could pass through nodes exactly, and the shape functions are of the delta function property. The exponential (EXP) and the multiquadric (MQ) RBFs are used in the current RBNM, and their shape parameters are studied in detail through some analyses of two-dimensional elastic problems. The suitable ranges of the shape parameters are proposed for both the EXP and the MQ basis functions. It is found that the RBNM is as accurate as or even more precise than the BEM. This suggests that the current RBNM could be robust and applicable. (C) 2003 Published by Elsevier Ltd.

关键词： boundary integral equation boundary node method point interpolation method radial basis function shape parameter

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