Abstract
This paper provides a general solution to the anti-plane problem of an arbitrarily shaped hole reinforced with a functionally graded (FG) layer in a homogenous plate. By using the piece-wise homogeneous layers method and the conformal mapping technique, the complex potentials in the form of series in the FG layer are derived based on the theory of complex variable functions. The influence of the FG layer on the shear stress distributions around some typically shaped holes are discussed by numerical examples, and then the optimized analysis of the stress concentration factor (SCF) is performed. The results showed that the SCF of various shaped holes can be noticeably reduced by the optimum design of the material variations in the layer, and the most significant one in this paper is the triangular hole, whose SCF can be decreased by more than 50%.
Highlights
Graded materials (FGMs) are increasingly used in many fields due to their continuous change of material properties and functions in spatial locations
A general solution is presented for calculating the stress concentration in a homogeneous plate with an arbitrarily shaped hole reinforced with an functionally graded (FG) layer under anti-plane shear loads
We considered an infinite homogenous plate with an arbitrarily shaped hole subjected to anti-plane shear loads at infinity
Summary
Graded materials (FGMs) are increasingly used in many fields due to their continuous change of material properties and functions in spatial locations. Dave and Sharma [23] derived the solution for stress and moments around a circular or elliptical hole in an infinite FGMs plate, where the material properties change with the plate thickness. Sharma and Dave [36,37] presented a general solution to calculate stresses around hypocycloidal and hypotrochoidal holes in an infinite plate using Muskhelishvili’s complex variable method. A general solution is presented for calculating the stress concentration in a homogeneous plate with an arbitrarily shaped hole reinforced with an FG layer under anti-plane shear loads. The theoretical method in the paper can be used to derive the stress magnitudes and distribution around the arbitrarily shaped holes in FGM plates, and the stress concentration can be further optimized and reduced through analysis of the effect of material variations in the FG layer
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