铰接板机构运动分析的简便协调方程

SIMPLE COMPATIBILITY EQUATIONS FOR KINEMATIC ANALYSIS OF PIN-JOINTED PLATE MECHANISMS

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。

The erection analysis models of some new spatial structures, such as Pantadome, can be simplified as pin-jointed plate mechanisms. The rigid body displacement of a triangular plate element is characterized by the un-elongation of its three sides due to the shape stability of a triangle. Based on the compatibility equation of a bar element, a simple compatibility equation of a triangular plate element with pin-jointed vertices is established. Its first- and second- order compatibility matrices are presented. By introducing four-vertex coplanar conditions, the compatibility matrices of a quadrangular plate element, which is divided into two triangular plate elements, are further deduced. Theoretically, the compatibility matrix of a planar arbitrarily polygonous plate element can be established by this way. As for the simple compatibility equations, a computational strategy is adopted to track the kinematic path of pin-jointed plate mechanisms. The erection processes of an up-jacked Pandadome and an incrementally-launched gable space frame are numerically simulated. The results indicate that the method presented possesses a high accuracy for solving the kinematic path of pin-jointed plate mechanisms.