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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 is based on a unified global coordinate system, which can not solve the problem of the form-finding of tension structures with complicated oblique boundaries. In this paper, the idea of finite element method proposed multi-coordinate force density method. Firstly, a local coordinate system is established for each node according to the boundary constraints, and the matrix of unit force density resistance coefficients is deduced from the vector decomposition relationship of the forces, and then the matrix is formed into a unit of total force density resistance coefficients. According to the force balance relationship between structural resistance and zero load of external load, the force equilibrium equations in multi-coordinate system are established and the equations are corrected by the constant coordinate of fixed constrained direction nodes. Solving the equations can obtain the images with complicated oblique boundary The initial equilibrium shape of the pull structure. The paper also prepared Matlab program of multi-coordinate system force density method, and proved the effectiveness and correctness of the method through three examples.