| 黄斌.随机结构有限元分析的递推求解方法的改进[J].计算力学学报,2010,27(2):202~206 |
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| 随机结构有限元分析的递推求解方法的改进 |
| Improvement on recursive stochastic finite element method |
| 投稿时间：2008-05-23 |
| DOI：10.7511/jslx20102005 |
| 中文关键词: 随机结构 非正交多项式展开 随机有限元 伽辽金投影 计算精度 |
| 英文关键词:random structures non-orthogonal polynomial expansion stochastic finite element method galerkin project scheme calculation precision |
| 基金项目:国家自然科学基金(50208016)资助项目. |
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| 摘要点击次数: 1561 |
| 全文下载次数: 1164 |
| 中文摘要: |
| 将随机结构有限元分析的递推求解方法和伽辽金投影方法相结合,提出了求解随机静力响应的改进的递推求解方法。利用随机收敛的非正交多项式展开表示由于材料、外部荷载或构件几何尺寸的随机性导致的结构随机响应。采用递推求解方法得到响应多项式展开的初始系数,并运用定义的数学算子显式地表达出来。然后,通过定义修正系数,应用伽辽金方法对随机力平衡方程在非正交多项式基上进行投影,得到了和响应展开阶次个数相同的确定的有限元方程,并进行求解得到了修正系数。数值算例表明,通过对递推求解方法中响应表达式系数的修正,以很小的计算代价较大地提高了随机响应的计算精度;与基于正交多项式展开的随机有限元方法相比,在精度相当的前提下新方法耗费的计算时间大大降低。 |
| 英文摘要: |
| Combining recursive stochastic finite element method and Galerkin project scheme, an improving method on solving random problem with finite elements was presented. Convergent non-orthogonal polynomial expansion in random space was used to express random structural response because of randomness of material characteristics, external load and sectional geometric shape and so on. After modification coefficients were defined, Galerkin method was utilized to project random equilibrium equation on non-orthogonal polynomial basis and determinate finite element equations which number is equal to the order number of polynomial expansion are obtained. Through solving the determinate equations, the modification coefficients can be got. Numerical examples show that result precision of the new improved method is much better than that of original recursive stochastic finite element method. Compared with spectral stochastic finite element method, the calculation cost of the present method is significantly reduced when the two methods have the same calculation precision. |
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