The Convergent Condition and United Formula of Step Reduction Method

The step reduction method was first suggested by Prof. Yeh Kai-yuan^[1]. This method has more advantages than other numerical methods. By this method, the analytic expression of solution can he obtained for solving nonuniform elastic mechanics. At the same time, its calculating lime is very short and convergent speed very fast. In this paper, the convergent condition and united formula of step reduction method are given by mathematical method. It is proved that the solution of displacement and stress resultants obtained by this method can converge to exact solution uniformly, when the convergent condition is satisfied. By united formula, the analytic solution can be expressed as matrix form, and therefore the former complicated expression can be avoided. Two numerical examples are given at the end of this paper which indicate that, by the theory in this paper, a right model can be obtained for step reduction method.