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Analytical solution for cylindrical thin shells with normally intersecting nozzles due to external moments on the ends of shells

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Abstract

The stress analysis based on the theory of a thin shell is carried out for cylindrical shells with normally intersecting nozzles subjected to external moment loads on the ends of shells with a large diameter ratio(ρ 0 «0. 8). Instead of the Donnell shallow shell equation, the modified Morley equation, which is applicable toρ 0(R/T)1/2 »1, is used for the analysis of the shell with cutout. The solution in terms of displacement function for the nozzle with a nonplanar end is based on the Goldenveizer equation. The boundary forces and displacements at the intersection are all transformed from Gaussian coordinates (α, β) on the shell, or Gaussian coordinates (ζ, θ) on the nozzle into three-di-mensional cylindrical coordinates(ρ,θ, z). Their expressions on the intersecting curve are periodic functions ofθ and expanded in Fourier series. Every harmonic of Fourier coefficients of boundary forces and displacements are obtained by numerical quadrature. The results obtained are in agreement with those from the three-dimensional finite element method and experiments.

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References

  1. Eringen, A. C., Naghdi, A. K., Thief, C. C. et al., Stress distribution at two normally intersecting cylindrical shells,Nuclear Structural Eng., 1965,2: 235.

    Google Scholar 

  2. Bijlaard, P. P., Stresses from local loading in cylindrical pressure vessels,Trans. ASME, 1955, 77:805.

    Google Scholar 

  3. Qian, L. X., Tan, X. J., Zhong, W. X. et al., General solution of cylindrical shells with a cut-out,J. Dalian Inst. Technol. (in Chinese), 1965,3(4):1.

    Google Scholar 

  4. Lekerkerker, J. G., The determination of elastic stresses near cylinder-to-cylinder intersection,Nuclear Eng. Des., 1972, 20: 57.

    Article  Google Scholar 

  5. Steele, C. R., Steele, M. L., Stress analysis of nozzle in cylindrical vessels with external load,ASME J. Pres. Ves. Tech., 1983,105:191.

    Article  Google Scholar 

  6. Moffat, D. G., Mwenifumbow, J. A. M., Xu, S. H. et al., Effective stress factors for piping branch junctions due to internal pressure and external moment loads,J.of Strain Analysis, 1991,26(2): 85.

    Article  Google Scholar 

  7. Amran, B. A., Moffat, D.G., Mistry, J., Interaction of pressure and moment loads on a piping branch junction using finite element analysis,Proc. 8th Int. Conf. on Pres. Ves. Technology, Vol. 2, Design and Analysis, Montreal, ASME, 1996, 185—196.

    Google Scholar 

  8. Afshari,|P., Widera, G. E. O., Analysis of shell intersections,Int. Conf. of Pres. Ves. Tech., 1991, 378.

  9. Xue, M. D., Deng, Y., Hwang, K.C., Some results on analytical solution of cylindrical shells with large opening,ASME J.Pres. Ves. Tech., 1991, 113: 297.

    Article  Google Scholar 

  10. Deng,|Y., Hwang, K. C., Xue, M.D., The stress analysis of cylindrical shells with rigid inclusions having a large ratio of radii,SMiRT 11 Transactions F, F05/2, Tokyo, 1991, 85—90.

  11. Xue, M. D., Chen, W., Deng, Y. et al., The thin shell theoretical solution for cylindrical shells with large openings,Acta Mechanica Sinca (in Chinese), 1995, 27(4): 482.

    Google Scholar 

  12. Xue, M. D., Chen, W., Hwang, K. C, Stresses at the intersection of two cylindrical shells,Nuclear Engineering and Design, 1995, 154: 231.

    Article  Google Scholar 

  13. Xue, M. D., Hwang, K. C., Lu, W. et al., A reinforcement design method based on analysis of large openings in cylindrical pressure vessels,ASME]. Pres. Ves. Tech., 1996, 118: 502.

    Article  Google Scholar 

  14. Timoshenko, S., Woinowsky-Krieger, S.,Theory of Plates and Shells, New York: Mc Graw-Hill Book Company, 1959.

    Google Scholar 

  15. Goldenveizer, A. L.,Theory of Elastic Thin Shells, New York: Pergamon Press, 1961.

    Google Scholar 

  16. Hwang, K. C., Lu, M. W., Xue, M. D.,Theory of Thin Shells (in Chinese), Beijing: Higher Education Press, 1988.

    Google Scholar 

  17. Corum,J. M., Bolt, S. E., Greenstreet, W. L. et al., Theoretical and experimential stress analysis of ORNL thin shell cylinder to cylinder Model-1,ORNL Report 4553, 1974.

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Authors and Affiliations

  1. Department of Engineering Mechanics, Tsinghua University, 100084, Beijing, China

    Xue Mingde, Wang Hehui, Chen Wei & Huang Kezhi

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  1. Xue Mingde
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  2. Wang Hehui
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  3. Chen Wei
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  4. Huang Kezhi
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Mingde, X., Hehui, W., Wei, C. et al. Analytical solution for cylindrical thin shells with normally intersecting nozzles due to external moments on the ends of shells. Sci. China Ser. A-Math. 42, 293–304 (1999). https://doi.org/10.1007/BF02879064

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  • DOI: https://doi.org/10.1007/BF02879064

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