Abstract
In the paper, the solution for square notch problem with small round corners in plane elasticity under remote loading is studied. Based on the two obtained particular solutions and the extrapolation technique, the general relation between the stress concentration and the small radius at the corner point is obtainable. It is emphasized here that this relation can be used to the arbitrary small radius case.
This is a preview of subscription content, log in via an institution to check access.
References
Muskhelishvili, N.I.: Some Basic Problem of the Mathematical Theory of Elasticity. Noordhoof, The Netherlands (1963)
Savin, G.N.: Stress Distribution around h=Nole (English translation edition) Pergamon Press, Oxford (1961)
Florence, A.L., Goodier, G.N.: Thermal stresses due do disturbance of uniform heat flow by an insolated ovaloid hole. ASME J. Appl. Mech. 27, 835–839 (1960)
Chen, Y.Z.: A special boundary element formulation for multiple circular hole problems in an infinite plate. Comp. Meth. Appl. Mech. Eng. 50, 263–273 (1985)
Xu, X.W., Sun, L.G., Fan, X.Q.: Stress concentration of finite composites laminates weakened by multiple elliptical holes. Int. J. Solids Struct. 32, 3001–3014 (1995)
Ting, K., Chen, K.T., Yang, W.S.: Applied alternating method to analyze the stress concentration around interacting multiple circular holes in an infinite domain. Int. J. Solids Struct. 36, 533–556 (1999)
Mogilevskaya, S.G., Crouch, S.L.: A Galerkin boundary integral method for multiple circular elastic inclusions with homogeneously imperfect interfaces. Int. J. Solids Struct. 39, 4723–4746 (2002)
Legros, B., Mogilevskaya, S.G., Crouch, S.L.: A boundary integral method for multiple circular inclusions in an elastic half-plane. Eng. Anal. Boun. Elem. 28, 1083–1098 (2004)
Troyani, N., Hernández, S.I., Villarroel, G., Pollonais, Y., Gomes, C.: Theoretical stress concentration factors for short flat bars with opposite U-shaped notches subjected to in-plane bending. Int. J. Fatigue 26, 1303–1310 (2005)
She, C.M., Guo, W.L.: Three-dimensional stress concentrations at elliptic holes in elastic isotropic plates subjected to tensile stress. Int. J. Fatigue 29, 330–335 (2007)
Savruk, M.P., Kazberuk, A.: Two-dimensional fracture mechanics problems for solids with sharp and rounded V-notches. Int. J. Fract. 161, 79–95 (2010)
Zappalorto, M., Lazzarin, P.: In-plane and out-of-plane stress field solutions for V-notches with end holes. Int. J. Fract. 168, 167–180 (2011)
Yang, Z., Kim, C.B., Cho, C.D., Beom, H.G.: The concentration of stress and strain in finite thickness elastic plate containing a circular hole. Int. J. Solids Struct. 45, 713–731 (2008)
Vigdergauz, S.: Shape optimization in an elastic plane under remote shear: from single to interfacing holes. J. Mech. Mater. Struct. 3, 1341–1363 (2008)
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Chen, Y.Z. Solution for square notch problem with small round corners in plane elasticity under remote loading (technical note). Arch Appl Mech 91, 2943–2947 (2021). https://doi.org/10.1007/s00419-021-01952-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00419-021-01952-y