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一些新型空间结构的施工分析模型可以简化为铰接板机构,如Pantadome。利用三角形形状稳定性特点,将三条边长变化为零来表征三角形板单元的刚体位移。进而基于杆单元的协调方程,建立了一个简便的顶点铰接三角形板单元的机构位移协调方程,且给出了1阶和2阶协调矩阵。将四边形板单元划分为2个三角形板单元,通过引入单元四顶点共面条件,推导出平面四边形板单元的协调矩阵。理论上,利用该思路可构建任意平面多边形板单元的协调矩阵。针对该简便协调方程,进一步给出了求解铰接板机构运动路径的计算策略。对1个顶升施工的Pantadome和1个顶推施工的双坡网架的成形过程进行了数值模拟,结果表明该方法对于此类铰接板机构的运动路径分析有很高的精度。
Some of the new spatial structure of the construction analysis model can be simplified as a hinge plate mechanism, such as the Pantadome. Using the characteristics of triangular shape stability, the three side lengths are changed to zero to characterize the rigid body displacement of the triangular plate element. Based on the coordination equation of the rod element, a simplified coordinate displacement equation of the apex hinged triangular plate element is established, and the first order and the second order coordination matrix are given. The quadrilateral plate element is divided into two triangular plate elements. By introducing the four-vertex coplanar condition of the element, the coordination matrix of the planar quadrilateral plate element is deduced. In theory, this idea can be used to construct a coordination matrix of any planar polygon plate element. Aiming at the simple coordination equation, the calculation method for solving the motion path of hinge plate mechanism is given. The numerical simulation of the forming process of a Pantadome with a jacking construction and a double-slope grid with a jacking construction shows that the proposed method has high precision for the analysis of the movement path of such hinge plate mechanism.