基于刚体准则和广义位移控制法的拱结构屈曲与后屈曲分析

论述了常用非线性分析增量迭代法的基本思想及不足，阐述了刚体准则及广义位移控制法的基本原理，将刚体准则和广义位移控制法结合，建立了杆系结构的几何非线性分析方法。初始受力平衡的刚体单元在经历刚体位移时其作用力只发生方向的改变而不会发生大小的改变，用于大变形大位移几何非线性分析的单元应满足这一刚体准则；广义位移控制法通过广义刚度参数来控制增量步，弥补了传统几何非线性分析方法中极值点和回弹点附近迭代方向不能有效确定的难题，且广义刚度参数物理意义明确，能有效调整加卸载方向，适用于多临界点的计算。将上述方法应用于实际工程，对平面和空间拱结构进行屈曲与后屈曲分析，与理论解、ANSYS数值解的对比表明，刚体准则和广义位移控制法结合，具有结构几何非线性分析的普适性，能准确高效地进行结构几何非线性分析，适于工程应用。

Buckling & post-buckling analysis of arches based on rigid body rule and GDC method

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.