等截面梁有限变形的传递函数解法

Distributed Transfer Function Method for Finite Deformation of Uniform beam

本文应用传递函数方法对等截面梁的有限变形进行了分析。对于等截面梁的有限变形问题,该方法从变分方程出发把问题表述为状态空间的形式,然后利用Gauss积分对轴力进行加速迭代求解,不需要进行增量迭代即可取得具有良好计算精度的数值结果,对简单受力的等截面梁情况该解可以看作是所讨论问题的精确解。对于受力比较复杂或者阶梯变截面梁情况,为减少运算量,可以和有限元法类似,采用多个单元进行拼接,从而得到问题的解。数值算例表明,本方法具有半解析、精度高、收敛快等特点。

Distributed transfer function method is applied to calculate the finite deformation of uniform beam. In this method, the problem of uniform beam was first analyzed in variational form, then the equation was transformed to state space form, at last, it was solved through accelerated iteration on axial force by use of Gausian quaduature formulas. This method avoids large-scale calculatoin in increment iteration and the solution is of high numerical precision. For the simple beam, this solution is an exact result. Meanwhile, for a complex beam, the solution can be obtained by synthesizing the transfer functions of sub-segments like FEM. The numerical examples show that this method has the characteristics of semi-analytical, high precision and good convergence.