Multiparameter Structural Optimization of Pressure Vessel with Two Nozzles

  • Martina BalacEmail author
  • Aleksandar Grbovic
Conference paper
Part of the Lecture Notes in Networks and Systems book series (LNNS, volume 54)


Structural analysis of pressure equipment (vessels) has always been a huge challenge for researchers. Pressure vessels are usually subjected to different loads in exploitation and small defects can lead to failure of the equipment, which may result in loss of life, health hazards and damage of property. Modern approach of stress and strain analysis of the influence of welded nozzles on pressure vessels involves numerical and experimental testing. In this research, 3D Digital Image Correlation (DIC) method for analyzing full field surface strain and stress, including camera system in combination with Aramis software, was used. After determination of critical areas with highest von Mises stresses and strain concentrations, numerical analysis of equivalent 3D model was performed in Ansys Workbench software. The aim of this paper is to present detailed parameter optimization of pressure vessel with two nozzles based on finite element analysis (FEA) of the structure. Several geometrical parameters were varied to obtain the optimum geometry of the pressure vessel, capable of withstanding the service load without plastic deformation. It is shown that carried out optimization gives the minimum weight of pressure vessel with optimized wall and nozzle thicknesses for the given load.


Pressure vessel Digital Image Correlation method Finite element analysis Optimization Response surface method 



Study presented in this paper is part of the Project TR 35031 financed by Ministry of Education, Science and Technological Development of Republic of Serbia.


  1. 1.
    Sang, Z.F., Xue, L.P., Lin, Y.J., Widera, G.E.O.: Limit and burst pressures for a cylindrical shell intersection with intermediate diameter ratio. Int. J. Press. Vessels Pip. 79, 341–349 (2002). Scholar
  2. 2.
    Petrovic, A., Balac, M., Jovovic, A., Dedic, A.: Oblique nozzle loaded by the torque moment: stress state in cylindrical shells on the pressure vessel. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 226(3), 567–575 (2012). Scholar
  3. 3.
    Bajic, D., Momcilovic, N., Maneski, T., Balac, M., Kozak, D., Culafic, S.: Numerical and experimental determination of stress concentration factor for a pipe branch model. Tehnickivjesnik Tech. Gaz. 24(3), 687–692 (2017). Scholar
  4. 4.
    Mitrovic, N., Petrovic, A., Milosevic, M., Momcilovic, N., Miskovic, Z., Maneski, T., Popovic, P.: Experimental and numerical study of globe valve housing. Chem. Ind. 71(3), 251–257 (2017). Scholar
  5. 5.
    Maneski, T., Bajic, B., Momcilovic, N., Milosevic, M.V., Balac, M.: Determination of internal pressure value causing pipe branch model to plastically deform. FME Trans. 46(2), 218–223 (2018). Scholar
  6. 6.
    Balac, M., Grbovic, A., Petrovic, A., Popovic, V.: Fem analysis of pressure vessel with an investigation of crack growth on cylindrical surface. Eksploatacjai Niezawodnosc Maint. Reliab. 20(3), 378–386 (2018). Scholar
  7. 7.
    Lu, M.H., Yu, J.S., Chen, J.J.: The effect of analysis model on the stress intensity calculation for the nozzle attached to pressure vessel under internal pressure loading. Int. J. Press. Vessels Pip. 117–118, 9–16 (2014). Scholar
  8. 8.
    Sathe, A.A., Maurya, V.R., Tamhane, S.V., Save, A.P., Nikam, P.V.: Design and analysis of pressure vessel components as per ASME Sec. VIII Div. III. Int. J. Eng. Dev. Res. 6(1), 834–840 (2018)Google Scholar
  9. 9.
    Sahu, Y.K., Nagpal, S.: Design and optimization of a low pressure vessel. Res. J. Eng. 6(7), 1–6 (2017)Google Scholar
  10. 10.
    Carbonari, R.C., Muñoz-Rojas, P.A., Andrade, E.Q., Paulino, G.H., Nishimoto, K., Silva, E.C.N.: Design of pressure vessels using shape optimization: an integrated approach. Int. J. Press. Vessels Pip. 88, 198–212 (2011). Scholar
  11. 11.
    Kulkarni, A.A., Jatkar, K.H.: A review on optimization of finite element modelling for structural analysis of pressure vessel. Int. J. Eng. Trends Technol. (IJETT) 12(1), 20–22 (2014)CrossRefGoogle Scholar
  12. 12.
    Javed Hyder, M., Asif, M.: Optimization of location and size of opening in a pressure vessel cylinder using ANSYS. Eng. Fail. Anal. 15, 1–19 (2008). ISSN 2231-5381CrossRefGoogle Scholar
  13. 13.
    Widiharso, H.S., Tauviqirrahman, M., Jamari, M.J.: Thickness optimization of pressure vessel for minimum weight using finite element method (FEM). Int. J. Eng. Technol. 8(6), 2676–2682 (2017). Scholar
  14. 14.
    Zhang, C., Yang, F.: Pressure vessel optimization design based on the finite element analysis. Appl. Mech. Mater. 65, 281–284 (2011). Scholar
  15. 15.
    Bochare, S.: Optimization of location and size of opening in a pressure vessel cylinder for spherical and elliptical head. Int. J. Emerg. Technol. 6(2), 229–234 (2015)Google Scholar
  16. 16.
    Gupta, S.R., Desai, A., Vora, C.P.: Optimize nozzle location for minimization of stress in pressure vessel. Int. J. Adv. Eng. Res. Dev. (IJAERD) 1(6), 1–14 (2014)Google Scholar
  17. 17.
    Digvijay, K., Jewargi, S.S.: Stress analysis of pressure vessel with different type of end connections by FEA. Int. J. Innov. Res. Sci. Eng. Technol. 4(5), 2769–2775 (2015). Scholar
  18. 18.
    Lawate, S., Deshmukh, B.B.: Analysis of heads of pressure vessel. Int. J. Innov. Res. Sci. Eng. Technol. 4(2), 759–765 (2015). Scholar
  19. 19.
    Orteu, J.J.: 3-D computer vision in experimental mechanics. Opt. Lasers Eng. 47, 282–291 (2009). Scholar
  20. 20.
    Sedmak, A., Milosevic, M., Mitrovic, N., Petrovic, A., Maneski, T.: Digital image correlation in experimental mechanical analysis. Struct. Integr. Life 12, 39–42 (2012)Google Scholar
  21. 21.
    Kawabayashi, H., Matsuda, H., Zhao, C., Konzuma, H., Yamashita, T.: Modeling cylindrical shell with initial imperfections by using optical method. In: The Fifth China: Japan Joint Seminar for the Graduate Students in Civil Engineering, Shanghai, China, pp. 181–186 (2008)Google Scholar
  22. 22.
    Peters, W.H., Ranson, W.F.: Digital imaging techniques in experimental stress analysis. Opt. Eng. 21(3), 427–431 (1982). Scholar
  23. 23.
    Rodrigues, L.D., Freire, J.L., Vieira, R.D., Castro, J.T.P.: Strain analysis of thin pipe pressure vessels using digital image correlation. J. Mech. Eng. Autom. 4(2), 63–72 (2014). Scholar
  24. 24.
    Chen, F., Chen, X., Xie, X., Feng, X., Yang, L.: Full-field 3D measurement using multi-camera digital image correlation system. Opt. Lasers Eng. 51, 1044–1052 (2013). Scholar
  25. 25.
    Revilock, D.M., Thesken, J.C., Schmidt, T.E., Forsythe, B.S.: 3D digital image correlation of a composite overwrapped pressure vessel during hydrostatic pressure tests. In: Proceedings of the 2007 SEM Annual Conference and Exposition on Experimental and Applied Mechanics, Springfield, MA, pp. 1–15 (2007)Google Scholar
  26. 26. Accessed 21 Nov 2016
  27. 27.
    Balać, M., Grbović, A., Petrović, A.: A numerical predictions of crack growth in a pressure vessel with welded nozzles. Struct. Integr. Life 15(1), 55–61 (2015)Google Scholar
  28. 28.
    Balac, M.: Nozzles interaction influence on stress state and strains on cylindrical shell of the pressure vessel. Ph.D. thesis, University of Belgrade, Faculty of Mechanical Engineering (2014)Google Scholar
  29. 29. Accessed 15 Apr 2018
  30. 30.

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Faculty of Mechanical EngineeringUniversity of BelgradeBelgradeSerbia

Personalised recommendations