ON THE COMPLETENESS OF MESHFREE PARTICLE METHODS
ON THE COMPLETENESS OF MESHFREE PARTICLE METHODS
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DOI：
10.1002/(sici)1097-0207(19981115)43:5
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发表时间：
1998-11
影响因子：
2.9
通讯作者：
T. Belytschko;Y. Krongauz;J. Dolbow;C. Gerlach
中科院分区：
文献类型：
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作者：
T. Belytschko;Y. Krongauz;J. Dolbow;C. Gerlach
研究了光滑粒子流体动力学（SPH）及其修正的完备性。Galerkin近似中的完备性或再生条件与微分近似中的一致性起着相同的作用。几种技术，恢复不同程度的完整性，通过满足再现条件的近似或衍生物的近似进行检查。一个粒子方法的彼得罗夫-伽辽金制定使用近似校正导数。它是一个归一化的SPH制定基于核近似和Galerkin方法的基础上移动最小二乘近似。结果表明，在SPH离散化中，起检验作用的函数是不可积的。数值结果表明，不满足完备性和可积性条件的近似不收敛的线性弹性静力学，因此收敛非线性连续介质力学。
The completeness of smoothed particle hydrodynamics (SPH) and its modiications is investigated. Completeness, or the reproducing conditions, in Galerkin approximations play the same role as consistency in nite diierence approximations. Several techniques which restore various levels of completeness by satisfying reproducing conditions on the approximation or the derivatives of the approximation are examined. A Petrov-Galerkin formulation for a particle method is developed using approximations with corrected derivatives. It is compared to a normalized SPH formulation based on kernel approximations and a Galerkin method based on moving least square approximations. It is shown that the major diierence is that in the SPH discretization the function which plays the role of the test function is not integrable. Numerical results show that approximations which do not satisfy the completeness and integrability conditions fail to converge for linear elastostatics, so convergence is not expected in nonlinear continuum mechanics.