Buckling & post-buckling analysis of arches based on rigid body rule and GDC method
Li Yunfei1 Chen Zhaohui1,2 Yang Yongbin1,2 Chen Feng1 Liao Minmao1,2
1. School of Civil Engineering, Chongqing University, Chongqing 400045, China;
2. The Key Laboratory of New Technology for Construction of Cities in Mountain Area of the Ministry of Education, Chongqing University, Chongqing 400045, China
Abstract：The principal and disadvantage of the commonly used incremental-iteration method of non-linear analysis is discussed in the present paper. The theory of rigid body rule and the generalized displacement control method (GDC) are presented. The nonlinear analysis method for bar structure is produced based on rigid body rule and the GDC method. The initial forces acting on the balanced rigid body would keep the force magnitudes constants with the force directions being changed with the rigid motion of the body. This is the so called rigid body rule which should also be satisfied by the deformed body. The generalized stiffness parameter (GSP) is introduced in the GDC method to determine the incremental step, by which the iteration direction near limit point and snap-back point is identified effectively. The GSP has clear physical meaning and is suitable for solving nonlinear problems with multiple limit points for its self-adaptive in changing the loading directions. By using the above method, a practical circular arch and space shallow-arch are analyzed. The results compared with the analytical solution and that obtained by ANSYS software have shown that the rigid body rule and the GDC method can solve the geometric nonlinear problem effectively and accurately, and is generally applicable for geometric nonlinear analysis in engineering practice.
