Abstract
This work aims to analyse the stress concentration in an infinite panel having a rounded rectangular hole reinforced with a functionally graded material layer using the extended finite element method. Young’s modulus of the functionally graded material layer varies in normal direction to the hole with a power law function. The relation of stress concentration factor with hole parameters, layer thickness, and power law index is presented for uniaxial, biaxial, and shear loads. It is noticed that the reinforcement of the functionally graded material layer around the hole has a significant influence on the stress distribution, and the controlled variation in the material properties of the layer can significantly reduce the stress concentration.
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Kirsh, G.: Infinite plate containing a circular hole (Die Theorie der Elastizitat und die Bedürfnisse der Festigkeitslehre). Zeitschrift der Vereines Deutscher Ingenieure 42, 797–807 (1898)
Muskhelishvili, N.: Some basic problems of the mathematical theory of elasticity. (Translated by Radok JRM, 1953) (Moscow, Leningrad, 1949)
Savin, G.N.: Stress Concentration Around Holes. Pergamon Press, London (1961)
Wittrick, W.: Stress concentrations for a family of uniformly reinforced square holes with rounded corners. Aeronaut. Quart. 13, 223–234 (1967)
Sobey, A.: Stress Concentration Factors for Reinforced Rounded-Square Holes in Sheets. ARC R&M 3407. H.M. Stationery Office, London (1968)
Ukadgaonker, V., Awasare, P.: A novel method of stress analysis of an infinite plate with rounded corners of a rectangular hole under uniform edge loading. Ind. J. Eng. Mater. Sci. 1, 17–25 (1994)
Louhghalam, A., Igusa, T., Park, C., Choi, S., Kim, K.: Analysis of stress concentrations in plates with rectangular openings by a combined conformal mapping—finite element approach. Int. J. Solids Struct. 48, 1991–2004 (2011)
Sharma, D.S.: Stress distribution around polygonal holes. Int. J. Mech. Sci. 65, 115–124 (2012)
Pan, Z., Cheng, Y., Liu, J.: Stress analysis of a finite plate with a rectangular hole subjected to uniaxial tension using modified stress functions. Int. J. Mech. Sci. 75, 265–277 (2013)
Kubair, D.V., Bhanu-Chandar, B.: Stress concentration factor due to a circular hole in functionally graded panels under uniaxial tension. Int. J. Mech. Sci. 50, 732–742 (2008)
Yang, Q., Gao, C., Chen, W.: Stress analysis of a functional graded material plate with a circular hole. Arch. Appl. Mech. 80, 895–907 (2010)
Mohammadi, M., Dryden, J.R., Jiang, L.: Stress concentration around a hole in a radially inhomogeneous plate. Int. J. Solids Struct. 48, 483–491 (2011)
Yang, Q.Q., Gao, C.F., Chen, W.T.: Stress concentration in a finite functionally graded material plate. Sci. China Phys. Mech. Astron. 55, 1263–1271 (2012)
Ashrafi, H., Asemi, K., Shariyat, M.: A three-dimensional boundary element stress and bending analysis of transversely/longitudinally graded plates with circular cutouts under biaxial loading. Eur. J. Mech. A Solids 42, 344–357 (2013)
Sburlati, R.: Stress concentration factor due to a functionally graded ring around a hole in an isotropic plate. Int. J. Solids Struct. 50, 3649–3658 (2013)
Sburlati, R., Atashipour, S.R., Atashipour, S.A.: Reduction of the stress concentration factor in a homogeneous panel with hole by using a functionally graded layer. Compos. Part B Eng. 61, 99–109 (2014)
Enab, T.A.: Stress concentration analysis in functionally graded plates with elliptic holes under biaxial loadings. Ain Shams Eng. J. 5, 839–850 (2014)
Gouasmi, S., Megueni, A., Bouchikhi, A.S., Zouggar, K., Sahli, A., Abbes, S.B.: On the reduction of stress concentration factor around a notch using a functionally graded layer. Mater. Res. 18, 971–977 (2015)
Yang, Q., Gao, C.F.: Reduction of the stress concentration around an elliptic hole by using a functionally graded layer. Acta Mech. 227, 2427–2437 (2016)
Hashemi, R., Avazmohammadi, R., Shodja, H.M., Weng, G.J.: Composites with superspherical inhomogeneities. Philos. Mag. Letters. 89, 439–451 (2009)
Osher, S., Sethian, J.A.: Fronts propagating with curvature dependent speed. J. Comput. Phys. 79, 12–49 (1988)
Sukumar, N., Chopp, D., Moes, N., Belytschko, T.: Modeling holes and inclusions by level sets in the extended finite-element method. Comput. Methods Appl. Mech. Eng. 190, 6183–6200 (2001)
Ding, K., Weng, G.J.: The influence of moduli slope of a linearly graded matrix on the bulk moduli of some particle- and fiber-reinforced composites. J. Elast. 53, 1–22 (1999)
Weng, G.J.: Effective bulk moduli of two functionally graded composites. Acta Mech. 166, 57–67 (2003)
Belytschko, T., Black, T.: Elastic crack growth in finite elements with minimal remeshing. Int. J. Numer. Methods Eng. 45, 601–620 (1999)
Moes, N., Dolbow, J., Belytschko, T.: A finite element method for crack growth without remeshing. Int. J. Numer. Methods Eng. 46, 131–150 (1999)
Kim, J.-H., Paulino, G.H.: Isoparametric graded finite elements for nonhomogeneous isotropic and orthotropic materials. J. Appl. Mech. 69, 502–514 (2002)
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Goyat, V., Verma, S. & Garg, R.K. Reduction of stress concentration for a rounded rectangular hole by using a functionally graded material layer. Acta Mech 228, 3695–3707 (2017). https://doi.org/10.1007/s00707-017-1907-3
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DOI: https://doi.org/10.1007/s00707-017-1907-3