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A complex variable meshless method for fracture problems

Science china(Physics,mechanics & Astronomy) 2006年第1期49卷 46-59页

作者： cheng yumin1 & li jiuhong2.1. shanghai institute of applied mathematics and mechanics, shanghai university, shanghai 2.0072. china 2. Department of Building Engineering, Xi’an university of Technology, Xi’an 710048, china shanghai institute of applied mathematics and mechanics Shanghai University Shanghai China Department of Building Engineering Xi’an University of Technology Xi’an China

Based on the moving least-square (MLS) approximation, the complex variable moving least-square approximation (CVMLS) is discussed in this paper. The complex variable moving least-square approximation cannot form ill-conditioned equations, and has greater precision and computational efficiency. Using the analytical solution near the tip of a crack, the trial functions in the complex variable moving least-square approxi- mation are extended, and the corresponding approximation function is obtained. And from the minimum potential energy principle, a complex variable meshless method for fracture problems is presented, and the formulae of the complex variable meshless method are obtained. The complex variable meshless method in this paper has greater precision and computational efficiency than the conventional meshless method. Some examples are given.

关键词： moving least-square approximation, complex variable moving least-square approximation, meshless method, complex variable meshless method, fracture.

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The complex variable reproducing kernel particle method for elasto-plasticity problems

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Science china(Physics,mechanics & Astronomy) 2010年第5期53卷 954-965页

作者： CHEN li1 & cheng yumin2.1 Department of Engineering mechanics,Chang’an university,Xi’an 710064,china 2 shanghai institute of applied mathematics and mechanics,shanghai university,shanghai 2.0072.china Department of Engineering mechanics Chang’an University Xi’an China shanghai institute of applied mathematics and mechanics Shanghai University Shanghai China

On the basis of reproducing kernel particle method(RKPM),using complex variable theory,the complex variable reproducing kernel particle method(CVRKPM) is discussed in this *** advantage of the CVRKPM is that the correction function of a two-dimensional problem is formed with one-dimensional basis function when the shape function is *** the CVRKPM is applied to solve two-dimensional elasto-plasticity *** Galerkin weak form is employed to obtain the discretized system equation,the penalty method is used to apply the essential boundary *** then,the CVRKPM for two-dimensional elasto-plasticity problems is formed,the corresponding formulae are obtained,and the Newton-Raphson method is used in the numerical *** numerical examples are given to show that this method in this paper is effective for elasto-plasticity analysis.

关键词： meshless method reproducing kernel particle method(RKPM) complex variable reproducing kernel particle method(CVRKPM) correction function elasto-plasticity

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