半解析有限元法分析圆柱壳外压稳定性问题的研究

Research on the Semi-analytical Finite Element Method in Analyzing Stability of Cylindrical Shell under External Pressure

圆柱壳外压稳定性问题,采用半解析有限元法,周向使用解析型的三角函数,轴向使用离散型的插值多项式,使问题得到了简化,减小了自由度,提高了精度.

In this paper,the stability of cylindrical shell under external pressure is analyzed by use of the semianalytical finite element method which adopts analytical trigonometric functions in the circumferential direction and discrete interpolating polynomials in the axial direction. In the process of analysis, all the displacements u, v and w of an arbitrary point in the middle curved plane are considered. u and v, functions of w , are derived on the basis of the conditions of non-extension in the circumferential direction and with no shear strain in the middle curved plane established by Lord Rayleigh. Thus this method simplifies the problem , reduces the numbers of freedom, improves the accuracy and makes the solving of various complicated problems easier. Finally, the results of calculation coincide well with the solution of Mises.