索单元结构计算的内力全量迭代法

Internal Force Total Iterative Method in Structure Calculation for Cable Element

索结构传统的几何非线性的求解方法依赖于非常复杂而庞大的切线刚度矩阵,针对这种情况,根据几何非线性计算的基本原理,建立一种在理论上能收敛于精确解的几何非线性求解方法——内力全量迭代法,使计算结果的精度不依赖于切线刚度矩阵;根据计算方法的特点,探讨了在几何非线性计算中索单元的内力计算公式和迭代计算方法;为了保证迭代计算快速收敛于真实解,给出了迭代计算方法中索单元的切线刚度矩阵;编制了基于内力全量迭代法的有限元计算程序SUSP_CABLE。部分算例和工程实例验证了该方法的精确性与可靠性,可供广大工程技术人员参考。

Aimed at the fact that traditional methods for geometric nonlinear problems of cable structure dependent on a very complex and huge tangent stiffness matrix,a geometric nonlinear solution method,i.e.,the internal force total iterative method,whose calculation precision can theoretically converge to an exact solution was proposed according to the basic principle of geometric nonlinearity to make the calculation result independent of tangent stiffness matrix.According to the characters of this calculation method,the calculation formulas of internal force and the iterative method about cable element in calculation of geometric nonlinearity were explored.The tangent stiffness matrix of cable element in iterative method was put forward to ensure the iteration rapidly converge at true solution.The finite element calculation program SUSP_CABLE was compiled based on the internal force total iterative method.Some calculation and engineering examples proved the accuracy and reliability of this method.It is also a reference for the engineers.