张拉结构找形的多坐标系力密度法

FORCE DENSITY METHOD BASED ON MULTI-COORDINATE-SYSTEM FOR FORM-FINDING OF TENSILE STRUCTURES

传统力密度法建立于统一的整体坐标系下,无法解决具有复杂斜边界的张拉结构找形问题。该文借鉴有限元法的思想提出了多坐标系力密度法。首先依据边界约束条件为各节点建立局部坐标系,由力的矢量分解关系推导出单元力密度抗力系数矩阵,然后组合成整体力密度抗力系数矩阵。依据结构抗力和外荷载合力为零的力平衡关系,建立多坐标系下的力平衡方程组,并利用固定约束方向节点坐标恒定关系修正方程组,求解该方程组可获得具有复杂斜边界的张拉结构的初始平衡形态。该文还编制了多坐标系力密度法的Matlab程序,并通过3个算例证明了该方法的有效性和正确性。

The traditional force density method can not be applied to the form-finding analysis of tensile structures with complex oblique boundaries as it is based on a unified global coordinate system.This paper presents a force density method based on multi-coordinate-system,similar to the theory of finite element method.Firstly,the local coordinate system is established for each node according to the boundary condition,and the force density reaction coefficient matrix for each element is derived according to the force vector decomposition.Then,the total force density reaction coefficient matrix is build up through the composition of the element matrixes,and the force equilibrium equation based on multi-coordinate-system is obtained from the force equilibrium between the reaction force and the load.Finally,the equilibrium equation is solved after amended by coordinate equations of the fixed nodes,and the initial equilibrium form for the tensile structure with oblique boundaries is obtained.A computer program of the proposed method is developed using Matlab,and three numerical examples are presented to illustrate the efficiency and robustness of this method.