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  4. The stress singularity order in a composite wedge of functionally graded materials under antiplane deformation

The stress singularity order in a composite wedge of functionally graded materials under antiplane deformation

MMC.
2020;
Volume 7, Number 1
: pp. 39–47
https://doi.org/10.23939/mmc2020.01.039
Received: October 22, 2019
Revised: January 27, 2020
Accepted: January 28, 2020

Mathematical Modeling and Computing, Vol. 7, No. 1, pp. 39–47 (2020)

Authors:
  1. M. I. Makhorkin
  2. T. A. Skrypochka
  3. A. R. Torskyy
1
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine
2
Lviv National Agrarian University
3
Centre of Mathematical Modelling of IAPMM NASU named after Ya. S. Pidstryhach

In this paper, finding the order of singularity in multi-wedge systems containing elements made of functionally gradient material (FGM) with an angular gradient under antiplane deformation is studied.  These elements are proposed to be modeled by means of multi-wedge composite, where the shear modulus changes from wedge to wedge according to a certain functional dependence (in this article we consider the linear, quadratic, and exponential dependencies).  It is found that the model region composed of 20 elements provides a relative error in the calculation of the stress field singularity order, which does not exceed 5%.  Using the simulation of FGM by a multi-wedge system, the influence of an insert made of functionally graded material with an angular gradient on the singularity order in a three-component composite wedge has been studied. A number of regularities have been established.

antiplane problem
multi-wedge system
stress singularity
functionally graded material
angular gradient
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