Ji Zhen-yi. The Convergent Condition and United Formula of Step Reduction Method[J]. Applied Mathematics and Mechanics, 1988, 9(12): 1117-1127.
 Citation: Ji Zhen-yi. The Convergent Condition and United Formula of Step Reduction Method[J]. Applied Mathematics and Mechanics, 1988, 9(12): 1117-1127.

# The Convergent Condition and United Formula of Step Reduction Method

• Publish Date: 1988-12-15
• 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.
•  [1] 叶开沅,非均匀变厚度弹性力学的若干问题的一般解,Ⅳ.非均匀变厚度梁的弯曲,稳定和自由振动,兰州义学学报,力学专号,1 (1979), 133-157. [2] 叶开沅、许剑云,非均匀变厚度弹性体力学的若干问题的一般解,Ⅰ.在非均匀定常温度场下的非均匀变厚度高速旋转圆盘的弹塑性应力分析,兰州大学学报,力学专号,1 (1979),60-74. [3] 叶开沅、郭建虎,非均匀变草度弹性体力学的若干问题的一般解,在任意定常温度场和任意分布载荷下的任意轴对称非均匀、变厚度环形板的弯曲问题,兰州大学学报,力学专号,1 (1979),75-114 [4] 叶开沅、李金荣、李进潮,非均匀变厚度弹性叶力学的若干问题一般解,任意分布载荷下两对边简支单向非均匀变厚度矩形板的弯曲问题,兰州大学学报,力学专号,1 (1979),115-132. [5] 叶开沅、尚新春,任意分布载荷下两对边简支单向非均匀变厚度矩形板的弯曲问题的一般解—折线折算法,兰州大学学报,力学专号,19 (1983), 58-75. [6] 叶开沅、汤任基、甄继庆,非均匀变截面弹性圆环在任意载荷下的弯曲问题,应用数学和力学,2, 1 (1982), 1-12. [7] Reltorys, Karel, lrariational Methods in Mathematics, Science and Engineering, D.Reidel Publishing Company Press, Holland, sec, ed,(1980).

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