Issue 40

Ch. F. Markideset alii, Frattura ed Integrità Strutturale, 40 (2017) 108-128; DOI: 10.3221/IGF-ESIS.40.10 108 Focussed on Recent advances in “Experimental Mechanics of Materials” in Greece The multi-layered ring under parabolic distribution of radial stresses combined with uniform internal and external pressure Christos F. Markides, Ermioni D. Pasiou, Stavros K. Kourkoulis National Technical University of Athens, School of Applied Mathematical and Physical Sciences, Department of Mechanics, 5 Heroes of Polytechnion Avenue, Theocaris Bld., Zografou Campus, 157 73 Athens, Greece A BSTRACT . A recently introduced solution for the stress- and displacement- fields, developed in a multi-layered circular ring, composed of a finite number of linearly elastic concentric layers, subjected to a parabolic distribution of radial stresses, is here extended to encompass a more general loading scheme, closer to actual conditions. The loading scheme includes, besides the parabolic radial stresses, a combination of uniform pressures acting along the outer- and inner- most boundaries of the layered ring. The analytic solution of the problem is achieved by adopting Savin’s pioneering approach for an infinite plate with a hole strengthened by rings. Taking advantage of the results provided by the analytic solution, a numerical model, simulating the configuration of a three- layered ring (quite commonly encountered in practical applications) is validated. The numerical model is then used for a parametric analysis enlightening some crucial aspects of the overall response of the ring. K EYWORDS . Multi-layered ring; Parabolic pressure; Stress and displacement fields; Uniform pressure; Complex potentials. Citation: Markides Ch.F., Pasiou E.D., Kour- koulis S.K., The multi-layered ring under para- bolic distribution of radial stresses combined with uniform internal and external pressure, Frattura ed Integrità Strutturale, 40 (2017) 108-128. Received: 12.02.2017 Accepted: 12.03.2017 Published: 01.04.2017 Copyright: © 2017 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. I NTRODUCTION n a recently published paper [1] the stress- and displacement-fields developed in a circular multi-layered ring were con- sidered both analytically and numerically. The ring was composed by a finite number of concentric layers made of different linearly elastic materials and it was loaded by a parabolic distribution of radial stresses acting along two finite arcs of the outer boundary of the outer-most layer. In general, the configuration of multi-layered rings is common in quite a few engineering applications of increased interest, ranging from Biomechanics (human aorta) to Fluid Mechanics (insulated pipes). Such composite rings are usually loaded either by uniformly distributed internal or external pressure or by a combination of them. In the study by Markides et al. [1] a more complicated loading scheme was considered consisting of radial stresses acting along two finite arcs of the external boundary of the outer-most layer (antisymmetric with respect to the geometric centre of the ring) distributed according to a parabolic law. Such a loading scheme appears in case a circular ring is compressed between either plane or curved jaws (as it is for example the jaws of the device introduced by the International Society for Rock Mechanics (ISRM) [2] for the standardized implementation of the Brazilian-disc test). The solution by Markides et al. [1] is here generalized to confront a more general loading scheme including, besides the parabolic radial stresses, a combination of uniform pressures acting along the outer- and inner-most boundaries of the I