论文部分内容阅读
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。
In this paper, an exact non-linear finite element method is proposed for finding the shape and force of articulated semi-rigid structure, and an iterative formula for finding and finding force is established in two steps. Step 1: Based on the coordinates of the loaded node, prestressed node coordinates and the prestressing force of the prestressed state elements, a nonlinear equilibrium equation of the load structure is established. According to the matrix differential theory, Newton’s tangent method concept and the boundary conditions, the load structure nonlinearity Balance equation to obtain the prestressed state node coordinate iteration formula; Step 2: Based on the prestressed state node coordinates, zero state node coordinates and prestressed state element prestress, the establishment of nonlinear prestressed state equilibrium equations, the same based on the above theory And the concept and the boundary condition to solve the nonlinear equilibrium equation of prestressed structure, and then obtain the iteration formula of the coordinates of zero-state nodes. In each iteration step, the preconditioned configuration is first looked for by the load configuration, and then the zero configuration is taken from the prestressed configuration, alternating between two substeps. The prestressed unit prestress is determined by the difference between the pre-stressed state and the zero-state node coordinates. Through the analysis of the form-finding and the force-seeking of the one-branch dome structure, the validity of the method is verified.