随机变量的变分原理及有限元法
The Random Variational Principle and Finite Element Method
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摘要: 本文将材料的随机性,结构几何形状的随机性,力的边界条件和位移边界条件的随机性,直接引入泛函变分表达式中,应用小参数摄动法,提出了统一的随机变量的变分原理及有限元法.从算例表明,应用此方法处理随机变量的力学问题,具有程序实施简便,计算效率高等优点.Abstract: In this paper, we introduced the random materials, geometrical shapes, force and displacement boundary condition directly into the functional variational formulations and developed a unified random variational principle and finite element method with the small parameter perturbation method.Numerical examples showed that the methods have the advantages of the simple and convenient program implementation, and are effective for the random mechanics problems.
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Key words:
- variational principle /
- flnite element method /
- perturbation method
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[1] 中桐滋、久田俊明.《确率有限要素法入门》,培风馆(1985). [2] 钱伟长,《广义变分原理》,知识出版社(1985). [3] Vanmarcke E.,et al.,Random fields and stochastic finite elements,Structural Safety,3(1986) 143-166. [4] Liu W.K.,T.Belytschko,and A.Mani,Random field finite elements,Int.J.Numer.Methods Engrg.,23,10 (1985). [5] Contreras H.,The stochastic finite element method,Comput.Struct.,12,(1980),341-384. [6] Lawrence,M.A.,Basis random variables in finite element anylysis,Int.J.Numer.Methods Engrg.,24,(1987),1849-1863． -
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