铰接半刚性结构找形与找力分析的非线性有限元方法  

A Nonlinear Finite Element Method for the Form-Finding and Force-Finding of Semi-Rigid Structures with Pin Connections

作　　者：刘树堂[1] 

机构地区：[1]广州大学土木工程学院,广州510006

出　　处：《建筑钢结构进展》2015年第3期13-18,共6页Progress in Steel Building Structures

摘　　要：对铰接半刚性结构找形、找力分析,提出一种精确的非线性有限元方法.分两步建立找形与找力分析迭代公式。第1步:基于荷载态节点坐标、预应力态节点坐标及预应力态单元预应力,建立荷载态结构非线性平衡方程,根据矩阵微分理论、Newton切线法概念和边界条件求解荷载态结构非线性平衡方程,从而得到预应力态节点坐标迭代公式;第2步:基于预应力态节点坐标、零态节点坐标和预应力态单元预应力,建立预应力态结构非线性平衡方程,同样根据上述理论和概念以及边界条件求解预应力态结构非线性平衡方程,从而得到零态节点坐标迭代公式。在每个迭代步中,首先由荷载态构形去找预应力态构形,然后由预应力态构形去找零态构形,两个子步交替进行。预应力态单元预应力由预应力态与零态的节点坐标之差确定。通过一弦支穹顶结构的找形与找力分析,验证了该方法的有效性。This paper proposes a nonlinear finite element method for the form finding and force finding of semi-rigid structures with pin connections. The iteration formulas are developed in two steps. Firstly, the structural nonlinear equilibrium equations of load state are established in terms of the node coordinates of load state and prestress-state as well as the internal forces of elements at prestress-state. The equations are solved based on the matrix differentiation theory, Newton＇s tangent method and the boundary conditions. Then the iteration formulas for the node coordinates of prestress-state are established. In the second step,the structural nonlinear equilibrium equations of prestress-state are developed in terms of the node coordinates of prestress-state and zero-state as well as the internal forces of elements at prestress-state. These equations are solved using similar theories mentioned above. Eventually the iteration formulas are built for the node coordinates of zero state. The internal forces of elements at prestress-state are determined from the difference of the node coordinates between prestress-state and zero-state. The validity of present method is established through form-finding and force-finding of a suspendome.

关 键 词：半刚性结构 找形 找力 非线性 节点坐标 弦支穹顶 预应力 

分 类 号：TU393.3[建筑科学—结构工程]