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娄路亮,曾攀.影响无网格方法求解精度的因素分析[J].计算力学学报,2003,20(3):313~319
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影响无网格方法求解精度的因素分析
Factors affecting computational precision of MLS-based meshless method
修订日期：2001-07-06
DOI：10.7511/jslx20033061
中文关键词: 无网格方法影响因素权函数计算精度移动最小二乘法分布密度基底函数计算力学
英文关键词:meshless method,weight function,compact support,computational precision,MLS
基金项目:国家杰出青年科学基金(59825117)资助项目.
娄路亮曾攀
清华大学机械工程系，清华大学机械工程系北京100084，北京100084
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中文摘要:
基于移动最小二乘法的无网格方法的计算精度除受到节点的分布密度和基底函数的阶次影响外，还受到其它因素的影响，其中权函数的选取、权函数影响域的大小及位移边界条件的引入对计算精度影响较大。本文分析了几种常用权函数在数值计算时的特点，包括计算精度、收敛情况、计算效率等，同时分析了影响域大小及边界条件的引入对计算精度的影响。通过分析给出了确定权函数及其影响域大小的方法。当受约束的自由度较多时，通过配点法引入位移边界条件会引起计算结果的振荡，通过施加稳定项可以消除振荡现象，通过对带孔方板的受力分析证明了其可行性。应用以上结论对J23—10曲柄压力机机身进行了受力分析，应力集中部位的计算结果得到了较高的精度。
英文摘要:
The computational precision of MLS\\|based meshless method is affected by many factors besides the nodal distribution density and the order of the basis, some of which are the weight functions, the compact support's size, and how to enforce the essential boundary conditions. In this paper three commonly used weight functions, exponential function, spline function, and circular function, were analyzed including the approximation precision, the convergence behavior, and the computational efficiency. At the same time the effect of the compact support and the enforcement of essential boundary conditions on the computational precision was studied. Through analysis how to choose the weight function and the compact support was given. When the constrained DOF was relatively more, the enforcement of the essential boundary conditions by collocation method would cause the results oscillation. A stabilization term was introduced to improve the precision on the boundary, which was validated by the example of a rectangular plate with centered hole under uniform tensile loading. This paper concludes with a sample stress analysis of J23\\|10 press's body, and the numerical results are in good agreement with the experimental results.
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