Some Problems in Nonlinear Dynamic Instability and Bifurcation Theory for Engineering Structures

• Published in: Journal of Shanghai University Vol. 9; no. 1; pp. 29 - 34
• Main Author: 彭妙娟 程玉民
• Format: Journal Article
• Language: English; Chinese
• Published: 01.02.2005
• Subjects: 分叉理论; 土木工程; 工程结构; 非稳定非线性系统; 非线性动态失稳
• ISSN: 1007-6417; 1863-236X
• DOI: 10.1007/s11741-005-0100-4

In civil engineering, the nonlinear dynamic instability of structures occurs at a bifurcation point or a limit point. The instability at a bifurcation point can be analyzed with the theory of nonlinear dynamics, and that at a limit point can be discussed with the theory of elastoplasticity. In this paper, the nonlinear dynamic instability of structures was treated with mathematical and mechanical theories. The research methods for the problems of structural nonlinear dynamic stability were discussed first, and then the criterion of stability or instability of structures, the method to obtain the bifurcation point and the limit point, and the formulae of the directions of the branch solutions at a bifurcation point were elucidated. These methods can be applied to the problems of nonlinear dynamic instability of structures such as reticulated shells, space grid structures, and so on.