Analytical displacement and stress fields with stress concentration factors (SCFs) are derived for linearly elastic annular regions subject to inhomogeneous boundary conditions: an infinite class of the mth order polynomial antiplane tractions or displacements. The solution of the Laplace equation governing the out-of-plane problem covers both rigid and void circular inclusions forming the core of the annulus. The results show first that the SCF and the loading order are inversely proportional. In particular, the SCF approaches value 2 when either the outer boundary of the annulus tends to infinity or the order of the polynomial loading increases. Second, the number of peculiar points on the inner contour having null stress increases with the increasing loading order. The analytical solution is confirmed and extended to noncircular enclosures via finite element analysis by exploiting the heat-stress analogy. The results show that the closed-form solution for a circular annulus can be used as an accurate approximation for noncircular enclosures. Altogether, the results shown can be exploited for analyzing complex loading conditions and/or multiple rigid or void inclusions for enhancing the design of hollow and reinforced composites materials.
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July 2018
Research-Article
Analytical Solutions and Stress Concentration Factors for Annuli With Inhomogeneous Boundary Conditions
S. Shahzad,
S. Shahzad
Department of Civil Engineering,
Aalto University,
Rakentajanaukio 4,
Espoo 02150, Finland
Aalto University,
Rakentajanaukio 4,
Espoo 02150, Finland
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J. Niiranen
J. Niiranen
Department of Civil Engineering,
Aalto University,
Rakentajanaukio 4,
Espoo 02150, Finland
Aalto University,
Rakentajanaukio 4,
Espoo 02150, Finland
Search for other works by this author on:
S. Shahzad
Department of Civil Engineering,
Aalto University,
Rakentajanaukio 4,
Espoo 02150, Finland
Aalto University,
Rakentajanaukio 4,
Espoo 02150, Finland
J. Niiranen
Department of Civil Engineering,
Aalto University,
Rakentajanaukio 4,
Espoo 02150, Finland
Aalto University,
Rakentajanaukio 4,
Espoo 02150, Finland
Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received December 20, 2017; final manuscript received April 18, 2018; published online May 10, 2018. Assoc. Editor: Thomas Siegmund.
J. Appl. Mech. Jul 2018, 85(7): 071008 (14 pages)
Published Online: May 10, 2018
Article history
Received:
December 20, 2017
Revised:
April 18, 2018
Citation
Shahzad, S., and Niiranen, J. (May 10, 2018). "Analytical Solutions and Stress Concentration Factors for Annuli With Inhomogeneous Boundary Conditions." ASME. J. Appl. Mech. July 2018; 85(7): 071008. https://doi.org/10.1115/1.4040079
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