多跨弹性支座圆弧梁计算的传递矩阵法

以圆弧梁初参数方程的通解为基础,求得承受任意分布载荷的圆弧梁段的载荷函数,推得反映状态向量变化的传递矩阵式。根据变形协调条件和力的平衡条件推得圆弧梁在弹性支座作用处和集中载荷作用处的点矩阵,解决在这些截面两侧某些状态变量突变的问题。将多跨弹性支座圆弧梁的复杂计算变成一个利用一维矩阵连续相乘的简单问题。通过验证表明,这种方法的计算结果和理论解一致。通过对多跨弹性支座圆弧梁实例的计算表明,其结果与其他方法求得的结果也十分吻合。

The Transfer Matrix Method for Calculating Circular Beam with Several Elastic Supports

Based on the general solution of the elementary parameter equation of circular beam, the load function receiving random distributed load was deduced to gain the transfer matrix reflecting the change of state vectors. The dot matrix was deduced according to the condition of deformation harmony and static equilibrium to solve the problem that the state variable variety of each side of sections where the elastic supports or concentrated loads existed. Then the complex calculating of circular beam with several elastic supports was turned into a simple problem by multiplying one dimension matrix by matrix. The result calculated by circular beam transfer matrix method was correct in comparison with the theoretic result and result calculated by other method.