Presenting an explicit relation for analyzing stress of plates with quasi-square holes and under tension by using multiple linear regression

Abbasnia, Ali; Jafari, Mohhamad; Rohani, Abbas

doi:10.22068/jstc.2018.81097.1417

Document Type : Research Paper

Authors

¹ Department of Mechanical Engineering, Shahrood University, Shahrood, Iran

² Department of Bio Mechanical Engineering, Ferdowsi University, Mashhad, Iran

10.22068/jstc.2018.81097.1417

Abstract

Stress concentration on the geometric discontinuities is one of the factors of structure failure. Nowadays, plates with holes are inseparable parts of designs and pieces, therefore studying the stress concentration caused by these holes is necessary to prevent structure failure. So the designer for presenting a design must be aware of the stress concentration in the hole and according to it design the basis. In this research, by using the regression method and on the basis of the mechanical properties of the materials and the radius of curvature in the corner of the hole, we try to present an explicit relation for estimating stress concentration in the orthotropic plates with quasi-square hole. This relation, in addition to easing the use and bypassing the hard and complex process of analytical solution, provides designer with the opportunity to calculate stress of perforated viscoelastic plates by using the effective module method or Boltzmann's superposition principle. At first, with analytical solution based on the Lekhnitskii method the stress values are calculated in many composite plates with quasi-square hole. Then, by using multiple linear regression and on the grounds of mechanical properties, is given an explicit relation for the stress concentration coefficient. The results show that the multiple regression model is able to predict the circumferential stress with a maximum error of 2%.

Keywords

Main Subjects

Solid mechanics - Stress analysis

References

[1] Muskhelishvili, NI., “Some Basic Problems of Mathematical Theory of Elasticity” Second ed., Netherlands, Noordhooff, 1962.

[2] Savin, GN., “Steress Concentration Around Holes” Pergamon Press, NewYork, 1961.

[3] Lekhnitskii, SG., “Anisotropic Plates” Second ed., Gordon and Breach Science Publishers, NewYork, 1968.

[4] Rezaeepazhand, J. and Jafari, M., “Stress Analysis of Perforated Composite Plates” Composite Structures, Vol. 71, pp. 463–468, 2005.

[5] Rezaeepazhand, J. and Jafari, M., “Stress Analysis of Composite Plates with Non-Circular Cutout” Key Engineering Materials, Vols. 385-387, pp. 365-368, 2008.

[6] Rezaeepazhand, J. and Jafari, M., “Stress Concentration in Metallic Plates with Special Shaped Cutout” International Journal of Mechanical Sciences, Vol. 52, pp. 96–102, 2010.

[7] Riyah, NK. and Ahmed, NE., “Stress Analysis of Composite Plates with Different Types of Cutouts” Anbar Journal of Engineering Sciences, Vol. 2, No. 1, pp. 11-29, 2009.

[8] Rezaeepazhand, J. and Jafari, M., “Stress Analysis of Composite Plateswith a Quasi-Square Cutout Subjectedto Uniaxial Tension” Journal of Reinforced Plastics and Composites, Vol. 29, No. 13, pp. 2015-2026, 2010.

[9] Batista, M., “On the Stress Concentration Around a Hole in an Infinite Plate Subject to a Uniform Load at Infinity” International Journal of Mechanical Sciences, Vol. 53, pp. 254–261, 2011.

[10] Rao, DKN. and Babu, MR. and Reddy, KRN. and Sunil D., “Stress Around Square and Rectangular Cutouts in Symmetric Laminates” Composite Structures, Vol. 92, pp. 2845–2859, 2010.

[11] Erklig, A. and Yeter, E., “The Effects of Cutouts on Buckling Behavior of Composite Plates” Science and Engineering of Composite Materials, Vol. 19, pp. 323–330, 2012.

[12] Kumar, MM. and Rajesh, S. and Yogesh, H. and Yeshaswini, BR., “Study on the Effect of Stress Concentration on Cutout Orientation of Plates with Various Cutouts and Bluntness” International Journal of Modern Engineering Research, Vol. 3, No. 3, pp. 1295-1303, 2013.

[13] Patil, RD. and Kumar, B., “Stress Analysis of Perforated Tube Sheet Used for Pressure Vessel having Square Pitch Hole Pattern” International Journal of Innovative Research in Science, Engineering and Technology, Vol. 4, No. 1, pp. 18899-18906, 2015.

[14] Miao, C. and Wei, Y. and Yan, X., “Stress Concentration of Periodic Collinear Square Holes in an Infinite Plate in Tension” Journal of Pressure Vessel Technology, Vol. 137, pp. 51201-51208, 2015.

[15] Jafari, M. and Moussavian, M., “Optimum Design of Laminated Composite Plates Containing a Quasi-Square Cutout” Structural and Multidisciplinary Optimization, Vol. 55, No. 1, pp. 141–154, 2016.

[16] Jafari, M. and Rezaeepazhand, J., “ Investigation of the Effect of Different Parameters on Stress Distribution of Non-Axial Plate with Central and Traction Shear” 17th Annual (International) Conference on Mechanical Engineering, 2009. (In Persian)

[17] Rohani, A. and Jafari, M., “Determination of Optimum Parameters Effect on Stress Distribution in Orthotropic Plates with Quasi-Square Cut out Using Genetic Algorithm” Journal of Solid and Fluid Mechanics, Vol. 4, No. 4, pp. 87-99, 2015. (In Persian)

[18] Jafari, M. and Rahimi-Petroudi, A., “A Study of the Effect of Various Parameters on the Stress Analysis of Isotropic and Anisotropic Plates Containing a Central Rectangular Hole Subjected to Shear Stress” Journal of Solid and Fluid Mechanics, Vol. 5, No. 1, pp. 101-114, 2015. (In Persian)

[19] Malekzadeh Fard, K. and Bayati Chaleshtari, MH. and Jafari, M. and Pourmoayed, AR., “Determination of Optimal Parameters for Orthotropic Plates with Pentagonal Cutout by Imperialist Competitive Algorithm” Journal of Science and Technology of Composites, Vol. 4, No. 2, pp. 161-170, 2017. (In Persian)

[20] Mohammadi, B. and Kazemi, A. and Ghasemi, R., “Damage Analysis of Holed Composite Laminates Using Continuum Damage Mechanics” Journal of Science and Technology of Composites, Vol. 2, No. 3, pp. 23-34, 2015. (In Persian)

[21] Eslami-Farsani, R. and Sari, A. and Khosravi, H., “Mechanical Properties of Carbon Fibers/Epoxy Composite Containing Anhydride Self-Healing Material under Transverse Loading” Journal of Science and Technology of Composites, Vol. 3, No. 3, pp. 285-290, 2016. (In Persian)

[22] Eslami-Farsani, R. and Khosravi, H. and Ebrahimnezhad-Khaljiri, H., “An Experimental Study on Mechanical Properties of Epoxy/Basalt/Carbon Nanotube Composites under Tensile and Flexural Loadings” Journal of Science and Technology of Composites, Vol. 3, No. 2, pp. 187-194, 2016. (In Persian)

[23] I. M. Daniel, O.Ishai, “Engineering Mechanics of Composite Materials” pp. 34-35, 1994.

[24] Abuelfoutouh, NM., “Preliminary Design of Unstiffend Composite Shells” Symposium of 7th Technical Conference of ASC: 693-786, 1993.

[25] Jafari, M., “Stress Analysis of Isotropic and Orthotropic Plates with the Non-Circular Opening under Uniaxial Tension, PhD Thesis, Department of Mechanical Engineering” Iran University of Ferdowsi, Mashhad, 2009. (In Persian)

[26] Asmar, GH. and Jabbour, TG., “Stress Analysis of Anisotropic Plates Containing Rectangular Holes” International journal of mechanics and solids, Vol. 2, No. 1, pp. 59-84, 2007.‏

Presenting an explicit relation for analyzing stress of plates with quasi-square holes and under tension by using multiple linear regression

References

Volume 6, Issue 1June 2019Pages 21-30

Volume 6, Issue 1
June 2019
Pages 21-30