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

: pp. 39–47
Received: October 22, 2019
Revised: January 27, 2020
Accepted: January 28, 2020
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine
Lviv National Agrarian University
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.

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