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Research Papers

Investigation of Stress Behavior in the Vicinity of Singular Points of Elastic Bodies Made of Functionally Graded Materials

[+] Author and Article Information
Andrey Yu. Fedorov

Laboratory of Simulation,
Department of Complex Problems
of Mechanics of Deformable Solid,
Institute of Continuous Media Mechanics,
Ural Branch Russian Academy of Sciences,
Perm 614013, Perm Krai, Russian Federation
e-mail: fedorov@icmm.ru

Valerii P. Matveenko

Professor
Head of the Department of Complex Problems
of Mechanics of Deformable Solid,
Institute of Continuous Media Mechanics,
Ural Branch Russian Academy of Sciences,
Perm 614013, Perm Krai, Russian Federation
e-mail: mvp@icmm.ru

1Corresponding author.

Manuscript received November 8, 2017; final manuscript received March 11, 2018; published online April 4, 2018. Assoc. Editor: A. Amine Benzerga.

J. Appl. Mech 85(6), 061008 (Apr 04, 2018) (7 pages) Paper No: JAM-17-1624; doi: 10.1115/1.4039619 History: Received November 08, 2017; Revised March 11, 2018

This paper presents the results of analytical and numerical investigations into stress behavior in the vicinity of different types of singular points on two-dimensional (2D) elastic bodies made of functionally graded materials (FGMs). A variant of constructing eigensolutions for plane FGM wedges, where the elastic properties are represented as a series expansion with respect to the radial coordinates, was considered. It was shown that, in the vicinity of singular points, the stress behavior is determined by solving the problem for the corresponding homogeneous wedge, where the elastic characteristics coincide with the characteristics of FGMs at the wedge vertex. Numerical investigations were carried out to evaluate the stress state of elastic bodies containing FGM elements at singular points, where the type of boundary conditions changes or where dissimilar materials come into contact. The results of the calculations showed that the behavior of stresses in FGMs in the vicinity of singular points can also be determined from an analysis of the eigensolutions for the corresponding homogeneous wedges, where the elastic properties coincide with the elastic constants of FGMs at singular points and that the functionally graded properties are dependent on one or two polar coordinates.

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Figures

Grahic Jump Location
Fig. 2

The example of finite element mesh with gradual refinement near singular point

Grahic Jump Location
Fig. 3

Computational schemes for a trapezoidal plate (dashed areas are the FGM regions)

Grahic Jump Location
Fig. 4

The regions of solutions with and without stress singularity for a wedge in the plane-strain state, where one face is fixed and the other is free of stress

Grahic Jump Location
Fig. 5

Three-layer plate with a sublayer containing an FGM subzone

Grahic Jump Location
Fig. 6

The curve separating, in the space of parameters E2/E1 and ν2, the regions of solutions with and without stress singularity at γ1=γ2=π/2, ν1=0.3

Grahic Jump Location
Fig. 7

Distribution of stresses σy over the surface of perfect bonding of a glue and glued material at b/a=2, c/a=0.2, d/a=0.1 and under linear variation of E20, ν20 over the range (a−d)≤|x|≤a: (a) point I, (b) point II, and (c) point III

Grahic Jump Location
Fig. 1

Plane wedge in the polar coordinate system (r, φ)

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