实心矩形截面杆的初始塑性后屈曲<sup>*</sup>

实心矩形截面杆的初始塑性后屈曲^*

基金项目: * 国家自然科学基金

1.
College of Struciural Engineering, Tongji Universtiy, Shanghai 200092, P. R. China;
2.
Department of Mechanical Engineering, East China University of Technology, Shanghai 200093, P. R. China

摘要: 文中用一种新的方法分析了简支受压矩形截面杆的塑性初始后屈曲问题,求出了后屈曲摄动展开式中的高阶项。所用的方法在某些方面类似于Hutchinson的方法,但是由于避免了一般奇异摄动中所必需的坐标伸长,因此大大简化了分析过程。从整个求解过程可以看出,本文所提出的方法可用于分析一般板壳结构的塑性初始后屈曲问题。
- 塑性后屈曲 /
- 摄动 /
- 矩形截面杆
Abstract: The plastic post-buckling of a simply supported column with a solid rectangular cross section is analysed by a new approach. High order terms in the asymptotic post-buckling expansions are carried out. In some aspects, the method proposed in this paper is similar io Hutchinson's. However, the computation is simple since the introduction is avoided of stretched coordinates. The method can be used to analyse initial post-bifurcation of plates and shells in the plastic range.
- plastic post-buckling /
- perturbation /
- columns of rectangular cross section

[1]	S. Akel, Q. S. Nguyen and C. Stolz, Instabilite's Plastiques, Seminaire CEA/EDF/INRIA. Paris (1985).
[2]	R. Hill, A general theory of uniqueness and stability in elastic/plastic solids, J.Meth. Phys. Solids,7(1958), 209-225.
[3]	J. W. Hutchinson, Post-bifurcation behaviour in plastic range, J. Mech. Phys. Solids, 21 (1973), 163-190.
[4]	J. W. Hutchinson, Plastic buckling, Adrarrces in Appl. Mech., 14(1974), 67-144.
[5]	Q. S. Nguyen, Bifurcation and post-bifurcation analysis in plasticity and brittle fracture, J. Mech. Phys. Solids, 35(1987), 303-324.
[6]	Q. S. Nguyen and N. Triantafyllidis, Plastic bifurcation and post-bifurcation analysis for generalized standard continua, J. Mech. Phrs. Solids, 37(1989), 545-566.
[7]	F. R. Shanley, Inelastic column theory, J. Aero. Sci., 14(1947), 261-267.
[8]	苏旭明，塑性后屈曲理论及缺陷敏感分析，上海工业大学博士论文(1998)
[9]	X. M. Su and W. D. Lu, Postbuckling and imperfection sensitivity analysis of structures in the plastic range Part II: Shallow shell analysis, Thin-Walled Struct, 11(1991),203-217.