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Complex variable sensitivity methods for finite element analysis.

機譯：用于有限元分析的復(fù)雜可變靈敏度方法。

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摘要

Complex variable differentiation methods offer many advantages over traditional finite differencing. These advantages include higher accuracy and greater stability. Numerical differentiation can be used to perform sensitivity analyses for engineering design problems. Shape sensitivity analysis of finite element models has become very common, since it can be used to perform design optimization. Finite differencing methods can be very difficult to implement in conjunction with finite element analysis due to the meshing problems it can create. For this reason, the complex variable differentiation methods, complex Taylor series expansion and Fourier differentiation, may be better suited than finite differencing for shape sensitivity analysis. One-dimensional and two-dimensional finite element codes have been written in Matlab, and shape sensitivity analysis using both complex variable methods and traditional finite differencing have been conducted. It was observed that for almost all cases, the accuracy of the numerical solution limits the accuracy of the numerical derivatives. This means that the increased accuracy of the complex variable methods is limited by the error in the solution. Complex Taylor series expansion still has several advantages over finite differencing, including a reduced number of sample points, and no re-meshing requirements.
機譯：與傳統(tǒng)的有限差分法相比，復(fù)雜的變量差分法具有許多優(yōu)勢。這些優(yōu)點包括更高的準(zhǔn)確性和更高的穩(wěn)定性。數(shù)值微分可用于對工程設(shè)計問題進(jìn)行敏感性分析。有限元模型的形狀敏感性分析已變得非常普遍，因為它可用于執(zhí)行設(shè)計優(yōu)化。有限差分方法可能會產(chǎn)生網(wǎng)格問題，因此很難與有限元分析結(jié)合起來實施。因此，復(fù)雜的變量微分方法，復(fù)雜的泰勒級數(shù)展開和傅立葉微分可能比有限差分更適合形狀敏感性分析。用Matlab編寫了一維和二維有限元代碼，并使用復(fù)變量方法和傳統(tǒng)的有限差分方法進(jìn)行了形狀敏感性分析。據(jù)觀察，在幾乎所有情況下，數(shù)值解的精度都限制了數(shù)值導(dǎo)數(shù)的精度。這意味著復(fù)雜變量方法提高的準(zhǔn)確性受到解決方案中誤差的限制。與有限差分相比，復(fù)雜的泰勒級數(shù)展開式仍具有多個優(yōu)勢，包括減少了采樣點數(shù)量，并且沒有重新劃分網(wǎng)格的要求。

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  • 作者

    Voorhees, Andrew.;

  • 作者單位

    The University of Texas at San Antonio.;

  • 授予單位 The University of Texas at San Antonio.;
  • 學(xué)科 Engineering Mechanical.
  • 學(xué)位 M.S.
  • 年度 2009
  • 頁碼 106 p.
  • 總頁數(shù) 106
  • 原文格式 PDF
  • 正文語種 eng
  • 中圖分類 機械、儀表工業(yè);
  • 關(guān)鍵詞

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