本文關(guān)鍵詞：一種提高四邊形四節(jié)點平面殼單元計算精度的新方法　出處：《計算力學(xué)學(xué)報》2017年02期 　論文類型：期刊論文

  更多相關(guān)文章： 平面殼單元 高斯積分點 單元局部坐標系 形函數(shù)對局部坐標的導(dǎo)數(shù) 曲面殼體

【摘要】：平面殼單元是由平面應(yīng)力單元和平板彎曲單元疊加組合而成,具有簡單的理論表達,但是它在計算曲面殼體結(jié)構(gòu)時誤差較大。為了進一步提高平面殼單元的計算精度,本文提出了一種計算平面殼單元剛度矩陣的新方法。通過該方法在高斯積分點建立多個單元局部坐標系,并保證每個局部坐標系都位于單元在高斯點處的切平面上,從而可以有效適應(yīng)曲面殼體形狀,達到進一步提高平面殼單元計算精度的目的。為了在這種新坐標系下計算單元剛度矩陣,給出了求解形函數(shù)對局部坐標的導(dǎo)數(shù)、局部到自然坐標系積分轉(zhuǎn)換的雅可比、以及局部到整體坐標系的轉(zhuǎn)換矩陣的新型計算方法。通過將這些新坐標系以及新計算方法運用到平面殼單元DKQ24中,可以有效提高平面殼單元尤其是在計算曲面殼體時的精度。計算結(jié)果表明,本文方法和平面殼單元相結(jié)合,不僅具有平面殼單元簡單的理論表達式,還能得到滿意的精度。另外,本文方法還可以應(yīng)用到其他類型的平面殼單元,為提高其他類型平面殼單元的計算精度提供了一種新的途徑和思路,具有廣闊的應(yīng)用前景。
[Abstract]:The planar shell element is composed of planar stress element and plate bending element. It has a simple theoretical expression, but it has large error when calculating the shell structure. In order to further improve the calculation precision of the plane shell element, a new method for calculating the stiffness matrix of the plane shell element is proposed in this paper. By means of this method, multiple element local coordinate systems are established at Gauss integration points, and each local coordinate system is located at the tangent plane at the Gauss point, so that it can effectively adapt to the shape of the surface shell, and further improve the accuracy of the calculation of the shell element. In order to calculate the element stiffness matrix in the new coordinate system, gives the derivative, solving the shape functions of the local coordinates to local natural coordinates conversion, Jacobi integral and local to the new calculation method of the transfer matrix in the global coordinate system. Through these new coordinates and a new calculation method is applied to the plane shell element in DKQ24, can effectively improve the plane shell element especially in the calculation of the precision of curved surface shell. The calculation results show that the combination of this method and the plane shell element not only has a simple theoretical expression of the plane shell element, but also has a satisfactory precision. Besides, this method can also be applied to other types of shell elements. It provides a new way and idea for improving the accuracy of other types of shell elements, and has broad application prospects.
【作者單位】： 大連理工大學(xué)工業(yè)裝備結(jié)構(gòu)分析國家重點實驗室航空航天學(xué)院;
【基金】：國家自然科學(xué)基金(11172055,11202045,11302040) 大連科技之星(2014年稱號)資助項目
【分類號】：O302
【正文快照】： 1 引言 目前工程中提出了很多種殼體單元[1-6],應(yīng)用到三維空間的殼單元,一般分為平面殼元和曲面殼元[7]。曲面殼元可以很好地描述殼體形狀,并且在單元內(nèi)考慮了膜彎耦合,具有較好的計算精度,但是由于難以恰當(dāng)表達剛體運動來避免剪切和膜閉鎖,使得曲面殼元的構(gòu)造變得困難和復(fù)雜，

本文編號：1340464