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[A. 数学/物理基础] 【讨论】Arguments to Finite Element: theoretical basement

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发表于 2004-2-17 03:41:12 | 显示全部楼层 |阅读模式 来自 加拿大
1)Direct physical argument. for example, the matrix method in structural analysis. But this approach is limited to simple problems and simple elements.
  
2)Virtual work argument: powerful and has physical appeal, but doesn’t provide a framework for producing general FE approximation.
  
3)Rayleigh-Ritz variational arguments applied to functionals. This method requires that only a functional be available. A functional is an integral expression that implicitly contains the governing equation, such as potential energy. It includes two forms: classical form and FE form.
  
4)Galerkin argument(weighted residual).
   
In Zienkiewicz's Finite Element book, 1)Galerkin procedure in method of residuals and 2)variational functionals are called two distinct procedures for obtaining the approximation in the integral form(weak form).
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