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桁架结构大都具有较强的几何非线性,受荷载后易出现较大的几何变形。提出一种基于力密度的针对桁架结构几何大变形问题的解法;引入杆件单元的力密度矩阵,推导出相应非线性方程的Jacobi矩阵;与有限单元法集成求解的思想相同,采用力密度矩阵建立结构变形后整体的精确非线性平衡方程。研究结果表明:应用Newton-Raphson迭代法求解,采用适当的迭代收敛精度可得到较精确的桁架结构位移解。
Most of the truss structure has a strong geometric nonlinearity, prone to large geometric deformation after loading. A new method for solving the large geometric deformation of truss structure based on force density is proposed. By introducing the force density matrix of rod element and deriving the Jacobi matrix of the corresponding nonlinear equation, the idea of integrating finite element method is the same. Establish the overall nonlinear accurate balance equation after structural deformation. The results show that the Newton-Raphson iterative method can solve the truss structure displacement accurately with the appropriate iterative convergence accuracy.