Abstract
The out-of-plane bending problems of functionally graded thin plates with a circular hole are studied for two-dimensional deformations. The thin plates have arbitrary variations of elastic properties along the radial direction. The general solutions of the stresses and moments are presented for the plates subjected to remote bending moments based on the theory of complex variable functions. Two different cases—a whole functionally graded plate with a circular hole and a functionally graded ring reinforced in a homogeneous perforated plate—are considered by numerical examples. The influence of parameters like Young’s modulus and Poisson’s ratio, function types of these elastic properties, and width of the reinforcing ring on the moments around the hole is presented. It is shown that the moment concentration, caused by the geometric discontinuity of the hole in the traditional homogeneous plate, can be well relieved or even eliminated by careful selection of the above parameters. The results for some special cases are compared with previous literatures and are found in good agreement.
Highlights
Holes exist widely in engineering structures for either design or manufacture reasons, and the high stress concentration around them has been a serious issue to the engineers and designers for many years
The stress concentrations in an functionally graded material (FGM) plate with a center circular hole or elliptical hole were numerically analyzed by Kubair and Bhanu-Chandar [17] and Wang et al [18], respectively, based on the finite element method
Numerical examples are given to discuss the effect of different radial variations of elastic parameters on the distribution of the moments for two different cases: a whole FGM plate with a circular hole and an FGM ring reinforced in a homogeneous perforated plate
Summary
Holes exist widely in engineering structures for either design or manufacture reasons, and the high stress concentration around them has been a serious issue to the engineers and designers for many years. The stress concentrations in an FGM plate with a center circular hole or elliptical hole were numerically analyzed by Kubair and Bhanu-Chandar [17] and Wang et al [18], respectively, based on the finite element method They both considered the variations of Young’s modulus along three different directions: radial direction, x direction, and Y direction. Goyat et al [22] analyzed the effects of different radial variations of Young’s modulus on the stress concentration factor (SCF) around the hole in FGM plate with the method of extended finite element. Nie et al [24] derived the analytical SCF in an FGM plate with a circular hole as Young’s modulus and Poisson’s ratio change along the radial direction with exponential function or power function, and they laid emphasis on the tailoring problem of the material.
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