Establishment of A Set of Similarity Prerequisite Conditions for Low-Cost Similitude Design of Structural System

Year : 2025 | Volume : 15 | Issue : 03 | Page : 1 15
    By

    Song Gun Kim,

  • Sol Song Pak,

  • Kwang Il Ri,

  • Yong Myong Song,

  • Jong Hyok Son,

  1. Associate Professor, Department of Mechanics, Kim Il Sung University, Pyongyang, DPR, Korea
  2. Professor, Department of Mechanics, Kim Il Sung University, Pyongyang, DPR, Korea
  3. Professor, Department of Mechanics, Kim Il Sung University, Pyongyang, DPR, Korea
  4. Associate Professor, Department of Mechanics, Kim Il Sung University, Pyongyang, DPR, Korea
  5. Professor, Department of Mechanics, Kim Il Sung University, Pyongyang, DPR, Korea

Abstract

Similitude theory and method is a branch of engineering to establish necessary and sufficient conditions for similarity among complex phenomena. It is of great significance to develop the theory and application method in a more comprehensive way so that the similitude theory can be widely applied to low-cost designs of modern complex structural systems When designing a similitude structural system with various loads and boundary conditions, including rotating machines, it is important to study the relationship between mechanical characteristics such as stress, deformation, displacement, and natural frequency at corresponding points of the prototype and similitude structure at present. This paper determined a set of similarity prerequisite conditions for low-cost similitude design of structural system with various loads and boundary conditions If these conditions are satisfied, the results are obtained that stress and deformation in similitude structure is the same as prototype, linear displacement is  (ratio of similitude) times of prototype, unknown  force is times, eigenvalue is  times, natural frequency is times, eigenvector is same, dynamic displacement is times, response time is  times of prototype And confirmed validity of suggested method through some examples. Multidisciplinary problems such as structural dynamics, structural mechanics and fluid mechanics were carefully and exactly considered to determine the similarity prerequisites This paper contributes to reducing time and cost of developing new similitude structural system on the basis of prototype.

Keywords: Similitude structure, prototype, similarity prerequisite condition, low-cost design, structural system

[This article belongs to Journal of Production Research & Management ]

How to cite this article:
Song Gun Kim, Sol Song Pak, Kwang Il Ri, Yong Myong Song, Jong Hyok Son. Establishment of A Set of Similarity Prerequisite Conditions for Low-Cost Similitude Design of Structural System. Journal of Production Research & Management. 2025; 15(03):1-15.
How to cite this URL:
Song Gun Kim, Sol Song Pak, Kwang Il Ri, Yong Myong Song, Jong Hyok Son. Establishment of A Set of Similarity Prerequisite Conditions for Low-Cost Similitude Design of Structural System. Journal of Production Research & Management. 2025; 15(03):1-15. Available from: https://journals.stmjournals.com/joprm/article=2025/view=230716


References

  1. Bridgman, P. W.: Dimensional Analysis. Yale University Press, New Haven, CT (1922), rev. ed (1931)
  2. Porter, A. W.: The Method of Dimensions. Methuen, London (1933)
  3. Lanchester, F. M.: The Theory of Dimensions and Its Applications for Engineers. Crosby-Lockwood, London (1940)
  4. Stubbings, G. W.: Dimensions in Engineering Theory. Crosby-Lckwood, London (1948)
  5. Murphy, G.: Similitude in Engineering. Ronald, New York (1950)
  6. Esnault-Pelterie R.: Dimensional Analysis and Metrology. F. Rouge, Lausanne, Switzerland (1950)
  7. Goodier, J.N.: Dimensional analysis. New York: John Wiley & Sons; [chapter: Appendix II]. 1035–1070(1950)
  8. Huntley, H. E.: Dimensional Analysis, Rinehart. New York (1951)
  9. Langhaar, H. L.: Dimensional Analysis and the Theory of Models. Wiley, New York (1951)
  10. Duncan, W. J.: Physical Similarity and Dimensional Analysis. Arnold, London (1953)
  11. Focken, C. M.: Dimensional Methods and Their Applications. Ar-nold, London (1953)
  12. Sedov, L. I.: Similarity and Dimensional Methods in Mechanics. Academic, New York (1959)
  13. Ipsen, E. C.: Units, Dimensions, and Dimensionless Numbers.McGraw-Hill, New York (1960)
  14. Jupp, E. E.: An Introduction to Dimensional Methods. Cleaver Hume, London (1962)
  15. Pankhurst, R.: Dimensional Analysis and Scale Factors, Reinhold, New York (1964)
  16. Kline, S. J.: Similitude and Approximation Theory. McGraw-Hill, New York (1965)
  17. Gukhman AA. Introduction to the theory of similarity. New York: Academic Press; 1965.
  18. LeCorbeiller, P.: Dimensional Analysis. Irvington, New York (1966)
  19. De-Jong, F. J.: Dimensional Analysis for Economists. North Holland, Amsterdam (1967)
  20. Skoglund, V. J.: Similitude—Theory and Applications. International. Scranton, PA (1967)
  21. Macagno, E.O.: Historico-critical review of dimensional analysis. J. Franklin Inst.292,391–402(1971)
  22. Kurth, R.: Dimensional Analysis and Group Theory in Astrophysics. Pergamon, New York (1972)
  23. Massey, B. S.: Units, Dimensional Analysis and Physical Similarity. Van Nostrand Reinhold, New York (1971)
  24. Zierep, J.: Similarity Laws and Modeling. Dekker, New York (1971)
  25. Taylor, E. S.: Dimensional Analysis for Engineers. Clarendon Press, Oxford, England (1974)
  26. de St, E., Isaacson, Q., de St, M., Isaacson, Q.: Dimensional Methods in Engineering and Physics. Arnold, London (1975)
  27. Szucs, E.: Similitude and modeling. New York, Elsevier(1980)
  28. Barenblatt, G. I.: Dimensional Analysis. Gordon and Breach, New York (1987)
  29. Kobayashi, H., Nakamura, H.: A Scaled Teleoperation. IEEE International Workshop on Robot and Human Communication,269-274(1992)
  30. Acad, M., Sardar.:Centrifugal Fan:Similarity,Scaling Law,and Fan Doctor of Philosophy.Copyright by Bell and Howell Information and Learning Company. June(2001)
  31. Sonin, A.A.: The physical basis of dimensional analysis. Cambridge,MA. Department of Mechanical Engineering.MIT(2001)
  32. Kasivitamnuay, J., Singhatanadgid, P.: Application of an energy theorem to derive a scaling law for structural behaviors. Thammasat Int. J. Sci Technol.10,33–40(2005)
  33. Cristiano, P., Coutinho,António, J., Baptista, José. Dias. Rodrigues.: Reduced scale models based on similitude theory. A review up to 2015. Engineering Structures .119 , 81–94(2016)
  34. Simitses, G.J., Rezaeepazhand, J.: Structural similitude and scaling laws for laminated beam plates. National Aeronautics and Space Administration. Technical Report NASA CR-190585(1992)
  35. Simitses, G.J., Rezaeepazhand,J.: Structural similitude and scaling laws for cross-ply laminated plates. In: American society for composites. Cleveland,Ohio: Technomic Publishing Company. Inc, 265–339(1993)
  36. Simitses, G.J., Rezaeepazhand, J.: Structural similitude for laminated structures. Compos Eng.3,751–816(1993)
  37. Simitses, G.J., Rezaeepazhand, J., Sierakowski, R.L.: Scaled models for laminated cylindrical shells subjected to external pressure. Mech Adv Mater Struct.4,267–347(1997)
  38. Simitses, G.J.: Structural similitude for flat laminated surfaces Compos Struct.51,191–195(2001)
  39. Rezaeepazhand, J., Simitses, G.J., Starnes, J.H.J.: Scale models for Laminated cylindrical shells subjected to axial compression.Compos Struct.34,371–380(1996)
  40. Chouchaoui, C.S., Ochoa, O.O.: Similitude study for laminated cylindrical tube under tension, torsion, bending, internal and external pressure Part i:Governing equations. Compos Struct.44,221–230(1999)
  41. Chouchaoui, C.S., Parks, P., Ochoa, O.O.: Similitude study for a Laminated cylindrical tube under tension, torsion, bending, internal and external pressure – Part ii: Scale models. Compos Struct. 44,231–237(1999)
  42. Crawford, H., Greenewalt.: The Significant Dimensions, Their Departure from the Requirements for Dimensional Similarity, and the Effect on Flight Aerodynamics of That Departure. Transactions of the American Philosophical Society. Vol. 65, No. 4, 1-67.American Philosophical Society(1975)
  43. Jackson, K.E.: Workshop on scaling effects in composite materials and structures. National Aeronautics and Space Administration. 1994. Technical Report NASA CP-3271(1994)
  44. Jackson, K.E., Fasanella, E.L.: Scaling effects in the static large deflection response of graphite-epoxy composite beams. National Aeronautics and Space Administration. Technical Report NASA TM-101619(1989)
  45. McKown, S., Cantwell, W.J., Jones, N.: Investigation of scaling effects in fiber- metal laminates. J. Compos Mater.42,865–88(2008)
  46. Jackson KE. Scaling effects in the static and dynamic response of graphite-epoxy beam-columns Ph.d.. Virginia Polytechnic Institute and State University(1990)
  47. Hamada H, Ramakrishna S. Scaling effects in the energy absorption of carbonfiber/peek composite tubes. Compos Sci Technol.55,211–232(1995)
  48. Kellas S, Morton J. Scaling effects in angle-ply laminates. National Aeronautics and Space Administration. Technical Report NASA CR-4423(1992)
  49. Nettles AT, Douglas MJ, Estes EE. Scaling effects in carbon/epoxy laminates under transverse quasi-static loading. National Aeronautics and Space Administration.Technical Report NASA TM-1999-209103(1999)
  50. Tarfaoui M, Gning PB, Davies P, Collombet F. Scale and size effects on dynamic response and damage of glass/epoxy tubular structures. J Compos Mater. 41,547–505(2007)
  51. Anthony,, Atkins and Robert, M., Caddell.: The Laws of Similitude and Crack Propagation, Int. J. mech. Scl. Pergamon Press. Vol. 16, 541-548(1974)
  52. Sousaa, R.A., Figueiredo, F.P.: The principle of similitude analysed from plastic zones estimates ahead crack tips, International Journal of Mechanical Sciences.89,403–412(2014)
  53. Dutson,A.J.,Wood,K.,Beaman,J.J.,Crawford,R.H.,Bourell,D.L.:Application of similitude techniques to functional testing of rapid prototypes. Rapid Prototyp J. 9,6–13(2003)
  54. Gang,X.,Wang,D.,Su,X.: A new similitude analysis method for a scale model test. Key Eng Mater.704–713(2010)
  55. Apatay, T.,Arslan, E.,Mack, W.: Elastic–plastic design of a rotating shrink fit with functionally graded hub. Arch Appl Mech.87,1829–1843(2017)
  56. Maël Couchaux., Mohammed Hjiaj., Ivor Ryan.: Enriched beam model for slender prismatic solids in contact with a rigid foundation. Int J Mech Sci. 93,181-190(2015)
  57. Jedari Salami, M. Sadighi, M. Shakeri.:Improved high order analysis of sandwich beams by considering a bilinear elasto-plastic behavior of core: An analytical and experimental investigation. International Journal of Mechanical Sciences 93, 270–289 (2015)
  58. Zamanian, A. Karimiyan.:Analysis of the mechanical behavior of a doubled microbeam configuration under electrostatic actuationInternational Journal of Mechanical Sciences 93 ,82–92(2015)
  59. Victor Rizov, Angel Mladensky.:Elastic–plastic analysis of Asymmetric Double Cantilever Beam specimen. International Journal of Mechanical Sciences 92, 44–51(2015)

Regular Issue Subscription Review Article
Volume 15
Issue 03
Received 04/07/2025
Accepted 06/09/2025
Published 17/09/2025
Publication Time 75 Days


Login


My IP

PlumX Metrics