摘要
本文从有限元基本平衡方程出发,首先导出了结构非线性稳定性分析的一般方程,在此基础上给出了一个既简单但又明瞭的临界点类型判别准则。其次,作者引用 Koiter 的渐近分析基本思想,给出了一个用有限元平衡方程形式表达的初始后临界分析的近似方程式。使用这一公式,一方面我们能判断结构在后临界状态的特性(如稳定或不稳定);另一方面我们也能把它作为在临界点处的一个有限元增量解,从而可避免在临界点处一般由于切线刚度矩阵奇异而产生的迭代收敛缓慢或发散。最后,作为本文所建议方法的应用,也给出了二个简单的分析算例。
In this paper, we start from the basic equilibrium equations expressed by finite element discrete form. The analysing equations of nonlinear stability of structures under multiple loading systems are derived, and a criterion which is used to identify the type of unstable critical points is presented.Secondly, by means of the basic idea of Koiter's asymptotic analysis, the approximate formulas of initial post-buckling analysis are derived. Applying these formulas, the behavior of post-buckling can be predicted. On the other hand, the difficulties appearing in nonlinear analysis due to the singularity of tangent stiffness matrix near the critical points can be overcome by using the present initial post-buckling analytical solutions as the incremental solutions of finite element analysis at the critical points. As the applications of present methods, two 昬xamples are also given.
出处
《力学学报》
EI
CSCD
北大核心
1991年第2期211-216,共6页
Chinese Journal of Theoretical and Applied Mechanics
基金
上海市青年科学基金
关键词
载荷作用
结构
非线性
有限元
finite element, nonlinear stability of structures
