Skip to main content
SpringerLink
Log in

Static Analysis of Transversely Loaded Isotropic and Orthotropic Plates with Central Cutout

  • Original Contribution
  • Published:
Journal of The Institution of Engineers (India): Series C Aims and scope Submit manuscript

Abstract

Plate structures are an integral part of engineering and construction industry. Taking into consideration various design and functional aspects, openings are provided in these plates for access and maintenance. The presence of cutout creates stress concentration, which eventually reduces the mechanical strength of the structure and in extreme cases may lead to its failure. Therefore it is of immense practical importance to investigate these stress concentrations. In this work the deflection and induced stresses for isotropic plate and orthotropic plate with central circular and square cutout under transverse loading is studied with the help of Finite Element Method (FEM). The variation in deflection and stresses with change in d/W and b/W ratio for steel (isotropic material) as compared to e-glass/epoxy (orthotropic material) is studied. Dependence of the deflection and Stress Concentration Factor (SCF) on cutout geometry and size is also observed. The effect of orienting the square cutout with positive X-baseline is also studied. Four different boundary conditions are considered. The results so obtained are critically examined and presented in graphical form. A popular finite element package, ANSYS has been used for the analysis.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29
Fig. 30
Fig. 31
Fig. 32

Similar content being viewed by others

Abbreviations

L:

Length of rectangular plate, mm

W:

Width of rectangular plate, mm

b:

Side length of square cut out, mm

d:

Diameter of circular cut out, mm

θ:

Orientation of square cutout from the baseline in X axis, degrees

UZ :

Maximum deflection with cut out, mm

UZ*:

Maximum deflection without cut out, mm

Kt :

Stress concentration factor (SCF)

σx :

Normal stress in X-direction of plate, N/mm2

σy :

Normal stress in Y-direction of plate, N/mm2

σxy :

Shear stress in XY-direction of plate, N/mm2

References

  1. N.I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity, vol. 1 (Springer, Berlin, 1977)

    Book  Google Scholar 

  2. G.N. Savin, Stress Concentration Around Holes, vol. 1 (Pergamon Press, New York, 1961)

    Google Scholar 

  3. W.D. Pilkey, Peterson’s Stress Concentration Factors (Wiley, Hoboken, 1997)

    Book  Google Scholar 

  4. K.N. Shivakumar, J.C. Newman, Stress Concentrations for Straight-Shank and Countersunk Holes in Plates Subjected to Tension, Bending, and Pin loading, vol. 3192 (National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, Washington, 1992)

    Google Scholar 

  5. A. Tafreshi, T.E. Thorpe, Numerical analysis of stresses at oblique holes in plates subjected to tension and bending. J. Strain Anal. Eng. Des. 30(4), 317–323 (1995)

    Article  Google Scholar 

  6. Xin.-Lin. Gao, A general solution of an infinite elastic plate with an elliptic hole under biaxial loading. Int. J. Press. Vessels Pip. 67(1), 95–104 (1996)

    Article  Google Scholar 

  7. K.R.Y. Simha, S.S. Mohapatra, Stress concentration around irregular holes using complex variable method. Sadhana 23(4), 393–412 (1998)

    Article  Google Scholar 

  8. W. Hwai-Chung, M. Bin, On stress concentrations for isotropic/orthotropic plates and cylinders with a circular hole. Compos. B Eng. 34(2), 127–134 (2003)

    Article  Google Scholar 

  9. A.I. Zirka, M.P. Malezhik, I.S. Chernyshenko, Stress distribution in an orthotropic plate with circular holes under impulsive loading. Int. Appl. Mech. 40(4), 448–452 (2004)

    Article  Google Scholar 

  10. N.K. Jain, N.D. Mittal, Finite element analysis for stress concentration and deflection in isotropic, orthotropic and laminated composite plates with central circular hole under transverse static loading. Mater. Sci. Eng. A 498(1), 115–124 (2008)

    Article  Google Scholar 

  11. J.A.L.I.L. Rezaeepazhand, M. Jafari, Stress concentration in metallic plates with special shaped cutout. Int. J. Mech. Sci. 52(1), 96–102 (2010)

    Article  Google Scholar 

  12. N. Momcilovic, M. Motok, T. Maneski, Stress concentration on the contour of a plate opening: analytical, numerical and experimental approach. J. Theor. Appl. Mech. 51, 1003–1012 (2013)

    Google Scholar 

  13. F. Darwish, G. Tashtoush, M. Gharaibeh, Stress concentration analysis for countersunk rivet holes in orthotropic plates. Eur. J. Mech. A 37, 69–78 (2013)

    Article  Google Scholar 

  14. P.S. Shinde et al., Reduction in stress intensity factor of a compact tension specimen by bonding symmetrical GFRP patches. J. Inst. Eng. 94(3), 239–244 (2013)

    MathSciNet  Google Scholar 

  15. M. Madhavi, R. Venkat, Predicting structural behavior of filament wound composite pressure vessel using three dimensional shell analysis. J. Inst. Eng. 95(1), 41–50 (2014)

    Google Scholar 

  16. I.M. Daniel, O. Ishai, I.M. Daniel, I. Daniel, Engineering Mechanics of Composite Materials (Oxford university press, New York, 1994)

    Google Scholar 

  17. S. Timoshenko, J.N. Goodier, Theory of Elasticity (McGraw-Hill, New York, 1951), p. 412

    MATH  Google Scholar 

  18. W.C. Young, R.G. Budynas, Roark’s Formulas for Stress and Strain, vol. 7 (McGraw-Hill, New York, 2002)

    Google Scholar 

  19. K. Kalita, A. Dutta, S. Haldar, Stress concentration factor convergence study of a thin plate. Proceeding of 58th congress ISTAM, 2013

  20. K. Kalita, Stress concentration mitigation in clamped steel plates. Int. J. Sci. World 2(1), 21–26 (2014)

    Google Scholar 

Download references

Acknowledgments

This paper is a revised and expanded version of an article entitled, “Static Analysis of Isotropic & Orthotropic Plates with Central Cutout under Transverse Loading” presented in “National Conference on Recent Advancements in Mechanical Engineering” held at ‘North East Regional Institute of Science and Technology’, Arunachal Pradesh, India during November 8–9, 2013.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, MPSTME, SVKM’s Narsee Monjee Institute of Management Studies (NMIMS), Shirpur Campus, Dhule, 425405, Maharashtra, India

    K. Kalita

  2. Department of Aerospace Engineering & Applied Mechanics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, 711103, West Bengal, India

    S. Halder

Authors
  1. K. Kalita
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Halder
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to K. Kalita.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kalita, K., Halder, S. Static Analysis of Transversely Loaded Isotropic and Orthotropic Plates with Central Cutout. J. Inst. Eng. India Ser. C 95, 347–358 (2014). https://doi.org/10.1007/s40032-014-0138-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40032-014-0138-9

Keywords

Search

Navigation