Stress Concentration and Optimized Analysis of an Arbitrarily Shaped Hole with a Graded Layer under Anti-Plane Shear

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%.

Mechanically Induced Anisotropic Fragments in Sn-Doped In2O3 Nanoparticle Films for Flexible Strain Sensing Based on Surface Plasmons

“…Applying strain to a substrate with a circular hole (hole sample) can produce a high-stress region at the edge of the circular hole perpendicular to the loading direction . A hole sample is useful in evaluating the stress concentration around a circular hole . Simulated von Mises images show nonuniform stress distributions on the PDMS sheet with a circular hole (hole PDMS sheet) (Figures a and S9).…”

Stress Optimization of Vent Holes with Different Shapes Using Efficient Switching Delayed PSO Algorithm

“…The stress distribution around the holes has been extensively studied by analytical methods [4,5], finite element methods (FEM) [6], and experimental methods [7][8][9]. Guan et al [10] introduced a general shear-stress solution to the anti-plane problem of an arbitrarily shaped hole that was reinforced with a functionally graded layer in a homogenous plate. Shang et al [11] investigated the high-temperature tensile behavior for film-hole plates and found that the strain distribution obtained in situ by the digital image correlation technique exhibits an X-like concentration around the hole.…”

“…The results showed that the theoretical predictions agree well with the experimental results. The analytical methods mainly utilize the theory of complex variable functions and the conformal mapping technique to obtain the stress distribution of a rectangular or infinite plate with holes [10]. It may be insufficient to deal with the holes with complex shapes or particular positions in practical engineering structures with advanced materials [13,14].…”

“…: a r , b r , r r0 s.t. : (10) There are some couplings among the variation ranges of a r , b r , and r r0 in Equation (10), which will make the optimization process difficult to run. An ingenious transforma-tion in Equation ( 11) is employed to obtain a decoupled optimization model, as shown in Equation (12).…”

Out-of-Plane Bending of Functionally Graded Thin Plates with a Circular Hole

“…Shi [27] presented an analytical solution of the elastic stress fields around a circular elastic inclusion in a radial FGM plate under a uniform anti-plane shear loading at infinity. Guan and Li [28] analyzed the stress concentration around an arbitrarily shaped hole reinforced with an FGM layer in an infinite plate under anti-plane shear and performed the optimized analysis of the SCF. The above works are mainly for anti-plane problems.…”