有曲率突变的轴对称壳(波纹壳)的有限元解
Finite Element Method of Axial Symmetrical Shell with Abrupt Change of Curvature (Corrugated Tubes)
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摘要: 本文指出了在一般用直线单元的轴对称壳的有限元法中,由于忽视了曲率对斜度变形的影响,并不能用以处理曲率突变的轴对称壳问题.本文提出了考虑曲率影响的、以壳的斜度变形为连续参数的直线单元有限元法,并用以处理C型波纹壳的计算.和Turner-Ford的实验结果比较,以及和钱伟长教授的解析解比较,都证明这个理论是正确的.Abstract: It is shown in this paper that due to the neglecting of curvature effect in the calculation of deformation of slope, the ordinary straight line finite elements are not suitable for the calculation of axile symmetrical shells with abrupt change of curvature.A new straight line finite element is proposed by considering the curvature effect on the deformation of slope, and regarding the deformation of slope as a continuously varied parameter. This new straight-line element is used for the calculation of semi-circular arc type corrugated tubes. The computed results are compared with Turner-Ford Experiments and also with computed results by analytical solution of slender ring theory given by Prof, Chien Wei-zang (1979).
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[1] 钱伟长,半圆弧波纹管的计算—细环壳理论的应用,清华大学基础课力学教研组,1978.9. [2] 钱伟长,郑思樑 半圆弧波纹管的计算—环壳一般解的应用,应用数学和力学,3 (1980). [3] Crafton,Analysis of axisymmetrical shells by direct stiffness method.A.I.A.A.J.1,10,(1963). [4] Stricklin,J.A.,Novaratna,D.R.& Pian,T.H.H.,Improvements on the analysis of shells of revolution by the matrix displacement method,A.I.A.A.J.,4,11,(1966). [5] Jones,R.E.& Strome,D.R.,Direct stiffness method analysis of shells of revolution utilizing curved elements,A.I.A.A.J.,14. 9,(1966). [6] Cook,R.D.,Concepts and Applications of Finite Element Analysis,(1974). [7] Zienkiewicz,O.C.,The Finite Element Method in Engineering Science,(1971). [8] Witmer,E.A.& Kotanchik,J.J.,Progress report on discrete-element elastic and elastic-plastic analysis of shells of revolution subjected to axisymmetric and asymmetric loading,Proceedings of the Second Conference on Matrix Methods in Structural Mechanics. [9] Turner,C.E.& Ford,H.,Stress and deflection studies of pipeline expansions bellow,Proceedings of the Institute of Mechanical Engineers,171,(1957). [10] 谢大吉等,C型波纹壳应力分布及变形测定(未发表). -
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