Abstract
The aim of this paper is to study the problem of stress concentration in an infinite plate with an elliptic hole reinforced by a functionally graded layer based on the complex variable method combined with the technique of conformal mapping. With using the method of piece-wise homogeneous layers, the general solution for the functionally graded layer having normal arbitrary elastic properties is derived when the plate is subjected to arbitrary constant loads at infinity, and then numerical results are presented for several special examples. It is found that the existence of the functionally graded layer can influence the stress distribution in the plate, and thus choosing proper variations of the normal elastic properties and proper thicknesses of the layer can effectively reduce the stress concentration around the elliptic hole.
Similar content being viewed by others
References
Afsar, A.M., Sekine, H.: Inverse problems of material distributions for prescribed apparent fracture toughness in FGM coatings around a circular hole in infinite elastic media. Compos. Sci. Technol. 62(7–8), 1063–1077 (2002)
Zhang, X.Z., Kitipornchai, S., Liew, K.M., Lim, C.W., Peng, L.X.: Thermal stresses around a circular hole in a functionally graded plate. J. Therm. Stress. 26(4), 379–390 (2003)
Huang, J., Venkataraman, S., Rapoff, A.J., Haftka, R.T.: Optimization of axisymmetric elastic modulus distributions around a hole for increased strength. Struct. Multidiscip. Optim. 25(4), 225–236 (2003)
Venkataraman, S., Haftka, R.T., Rapoff, A.J.: Structural optimization using biological variables to help understand how bones design holes. Struct. Multidiscip. Optim. 25(1), 19–34 (2003)
Cardenas-Garcia, J.F., Shabana, Y.M., Medina, R.A.: Thermal loading and material property characterization of a functionally graded plate with a hole using an inverse problem methodology. J. Therm. Stress. 29(1), 1–20 (2006)
Theotokoglou, E.E., Stampouloglou, I.H.: The radially nonhomogeneous elastic axisymmetric problem. Int. J. Solids Struct. 45(25–26), 6535–6552 (2008)
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(4), 732–742 (2008)
Yang, Q.Q., Gao, C.F., Chen, W.T.: Stress analysis of a functional graded material plate with a circular hole. Arch. Appl. Mech. 80(8), 895–907 (2010)
Yang, Q.Q., Gao, C.F.: Non-axisymmetric thermal stress around a circular hole in a functionally graded infinite plate. J. Therm. Stress. 33(4), 318–334 (2010)
Yang, Q.Q., Gao, C.F., Chen, W.T.: Stress concentration in a finite functionally graded material plate. Sci. China-Phys. Mech. Astron. 55(7), 1263–1271 (2012)
Mohammadi, M., Dryden, J.R., Jiang, L.Y.: Stress concentration around a hole in a radially inhomogeneous plate. Int. J. Solids Struct. 48, 483–491 (2011)
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-Solid. 42, 344–357 (2013)
Kubair, D.V.: Stress concentration factors and stress-gradients due to circular holes in radially functionally graded panels subjected to anti-plane shear loading. Acta Mech. 224(11), 2845–2862 (2013)
Kubair, D.V.: Stress concentration factor in functionally graded plates with circular holes subjected to anti-plane shear loading. J. Elast. 114, 179–196 (2014)
Yang, B., Chen, W.Q., Ding, H.J.: 3D elasticity solutions for equilibrium problems of transversely isotropic FGM plates with holes. Acta Mech. 226, 1571–1590 (2015)
Sburlati, R.: Stress concentration factor due to a functionally graded ring around a hole in an isotropic plate. Int. J. Solids Struct. 50(22–23), 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 61, 99–109 (2014)
Chao, C.K., Lu, L.M., Chen, C.K., Chen, F.M.: Analytical solution for a reinforcement layer bonded to an elliptic hole under a remote uniform load. Int. J. Solids Struct. 46, 2959–2965 (2009)
Chen, F.M., Chao, C.K.: Stress analysis of an infinite plate with a coated elliptic hole under a remote uniform heat flow. J. Therm. Stress. 31, 599–613 (2008)
Muskhelishvili, N.I.: Some Basic Problems of Mathematical Theory of Elasticity. Noordhoof, Leyden (1975)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yang, Q., Gao, CF. Reduction of the stress concentration around an elliptic hole by using a functionally graded layer. Acta Mech 227, 2427–2437 (2016). https://doi.org/10.1007/s00707-016-1620-7
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-016-1620-7