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Applied Mathematics and Mechanics

, Volume 9, Issue 12, pp 1183–1193 | Cite as

The convergent condition and united formula of step reduction method

  • Ji Zhen-yi
Article

Abstract

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 time 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.

Keywords

Mathematical Modeling Exact Solution Mathematical Method Industrial Mathematic Matrix Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    Yeh Kai-yuan. General solutions on certain problems of elasticity with non-homogeneity and variable thickness, IV. Bending, buckling and free vibration of non-homogeneous variable thickness beams.Journal of Lanzhou University, Special Number of Mechanics. 1 (1979), 133–157. (in Chinese)Google Scholar
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Copyright information

© Shanghai University of Technology (SUT) 1988

Authors and Affiliations

  • Ji Zhen-yi
    • 1
  1. 1.Anhui Architectural Industry InstituteHefei

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