非线性杆单元荷载矩阵积分算子直接集成算法

Method of directly integrating nonlinear frame load matrix based on integration factors

在文献 [1]的基础上 ,将积分算子直接集成单元刚度矩阵的方法扩展应用于非线性杆单元的荷载矩阵集成。该方法将分布荷载产生的内力函数分解为由未知参数表示的线形项 ,和与分布荷载特性相关的已知函数项的组合 ,计算积分算子 ,由积分算子的线形组合得到分布荷载产生的杆件内力函数 ,从而得到荷载矩阵。该方法没有采用任何假定 ,具有广泛的普适性 ,能用于求解任意刚度分布杆件上作用任意分布荷载或集中荷载的单元荷载矩阵。对于刚度非连续、荷载分布非连续的情况 ,该方法避免了高斯数值积分的误差 ,具有更高的计算精度。

Method directly based on integration factors is now developed to form the load matrix of nonlinear beam. The method expresses the inner force of nonlinear beam excited by distributing load as the combination of two parts; the one is a linear function with unknown constants of the nodal moment, and the other is a known function just determined by the distributing load itself. Both functions can be separately integrated as many constant factors. With the boundary conditions of two nodes, the unknown constants of the first linear function can be expressed by those integration factors, and so far the whole function of inner force and the load matrix of nonlinear beam are gained. The method never adopts any hypothesis and is analytic and accurate. It is to fit for all kind of nonlinear frame with the arbitrary distributing load to gain load matrix. The results are more accurate than that the Gauss numerical integration for beams with the un-continual nonlinear stiffness or un-continual distributing load.