Abstract
On the basis of the stepped reduction method suggested in [1], we investigate the problem of the bending of elastic circular ring of non-homogeneous and variable cross section under the actions of arbitrary loads. The general solution of this problem is obtained so that it can be used for the calculations of strength and rigidity of practical problems such as arch, tunnel etc. In order to examine results of this paper and explain the application of this new method, an example is brought out at the end of this paper.
Circular ring and arch are commonly used structures in engineering. Timoshenko, S.[2], Barber, J. R.[3], Tsumura Rimitsu[4] et al. have studied these problems of bending, but, so far as we know, it has been solely restricted to the general solution of homogeneous uniform cross section ring. The only known solution for the problems with variable cross section ones has been solely restricted to the solution of special case of flexural rigidity in linear function of coordinates. On account of fundamental equations of the non-homogeneous variable cross section problem being variable coefficients, it is very difficult to solve them. In this paper, we use the stepped reduction method suggested in [1] to transform the variable coefficient differential equation into equivalent constant coefficient one. After introducing virtual internal forces, we obtain general solution of an elastic circular ring with non-homogeneity and variable cross section under the actions of arbitrary loads.
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References
Yeh Kai-yuan, General solutions on certain problems of clasticity 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
Timoshenko, S.,Strength of Materials, Part II, D Van Nostrand Company, (1957)
Barber, J. R., Force and displacement influence functions for the circular ring,Journal of Strain Analysis for Engineering Design, 13(2), (Apr. 1978) 77–81
Tang Ren-ji, Initial parameter method for the calculation of elastic foundation circular ring,Journal of Lanzhou University, 1, (1961), 25–42
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Kai-yuan, Y., Ren-ji, T. & Ji-qing, Z. The bending of elastic circular ring of non-homogeneous and variable cross section under the actions of arbitrary loads. Appl Math Mech 2, 1–14 (1981). https://doi.org/10.1007/BF02432049
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DOI: https://doi.org/10.1007/BF02432049