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.
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References
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)
Yeh Kai-yuan and Xu Jian-yun. General solution on certain problems of elasticity with non-homogeneity and variable thickness, I. Elastic and plastic stress analyses of high speed rotating disc with non-homogeneity and variable thickness under non-homogeneous steady temperature field.Journal of Lanzhou University, Special Number of Mechanics. 1 (1979), 60–74. (in Chinese)
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Communicated by Yeh Kai-yuan
Project Supported by Science and Technic Fund of the National Education Committee.
The author would like to thank Prof. Yeh Kai-yuan for his directing.
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Zhen-yi, J. The convergent condition and united formula of step reduction method. Appl Math Mech 9, 1183–1193 (1988). https://doi.org/10.1007/BF02014473
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DOI: https://doi.org/10.1007/BF02014473