Stress Analysis Of A Functional Gradient Material's Plate With A Circular Hole

In recent years, the concept of functionally gradient materials (FGM) has been introduced and applied to engineering structures. The advantages of FGM are that the materials could resist corrosion, radiation and high temperatures effectively and, at the same time, reduce the residual and thermal stresses significantly. Thus, FGMs have found wide applications in aerospace engineering, nuclear power plants, electronics, optics, chemical engineering, biomedicine and so on.From the viewpoint of applied mechanics, FGMs are nonhomogeneous materials, and the nonhomogeneous behaviours of FGM have a great influence on their mechanical behavior. Hence, a lot of works have been done in theoretical and practical studies of the mechanical behavior of FGM. However, to the authors'knowledge, no studies can be found on the stress analysis of FGM with a circular hole, and such is the case for a finite-size plate of FGM containing a hole.In this paper, the introduction is first presented to the development of FGMs. Then, with using the method of homogenized layer, an approximate solution for the stress distribution of the FGM's plate with a circular hole is derived based on the continuous conditions of stress and displacement along the interfaces, and the use of two recursive algorithms. Furthermore, the above solutions are extended to the case of a finite functionally gradient material's plate with a circular hole under arbitrary constant loads by using Muskhelishvili's complex variable method combined with boundary collocation method. Finally, several conclusions are obtained as follows1. When the Young's modulus decreases from the hole surface to the outside, the stress concentrations around the hole obviously increase; on the contrary, as the Young's modulus increases along the radial direction, the stress concentrations decrease.2. For a finite plate, the ratio A /D (where A and D are the plate size and the radius of the hole, respectively) has a significant effect on the stress concentration around the hole. When the ratio A /D decreases, the stress concentrations around the hole obviously increase. When the ratio A /D >4, the stress concentrations have little difference between the finte paltes and the infinite plates.