Several Static And Dynamic Problems And Structure Design On Functionally Graded Materials

As a class of new advanced composite materials, functionally graded materials whose material properties continuously vary along one or multi spatial directions can be tailored to satisfy particular engineering application by technologically manufacturing process. In recent years, functionally graded materials have been widely used in nuclear energy reactor, turbine motors, aerospace engineering, and civil engineering etc. However, its continuous material properties bring out some difficulties in analyzing their mechanical behaviors. From a more practical point of view, we do not need to assume the gradient to be special functions and the integral equation method is presented to treat static and dynamic mechanical problems of functionally graded materials with any gradient. This thesis mainly includes the following items:(1) Firstly, for functionally graded axisymmetrical structures with arbitrarily varying material properties, a simple and efficient approach is put forward to study the elastic problem of functionally graded circular disk, cylinder, sphere and sandwich rotating disk. The associated elastic problem is reduced to a Fredholm integral equation. By solving the resulting equation, the distribution of the stress components and displacement can be determined. As examples, some typically varying material properties are considered. The obtained results indicate that change in the gradient of the functionally graded axisymmetrical structure does not induce a substantial variation of the radial stress, but strongly affects the circumferential stress. And for some special gradient parameters, the distribution curves of circumferential stress become more gently and maximum value of circumferential stress occurs at an interior position of the structure, not at the surfaces like homogeneous materials. Thus, in practical design, the method presented in this thesis may help engineering designers to choose appropriate gradients and materials to acquire an optimal state and to ensure the structure to be safer in the service-environment. (2) With above-mentioned method we study the elastic problem of rotating functionally graded hollow polar orthotropic circular disks whose relevant material properties arbitrarily varying along the radial direction. Emphasis is placed on the influence of orthotropy and gradient on the elastic field in particular the circumferential stress. Numerical results are presented for two particular cases:free boundaries and clamped-free boundaries. The numerical results show that, for different boundary conditions, the circumferential stress is not always larger than radial stress, and the influences of gradient parameter on circumferential stress are different, too. So, during the design of functionally graded orthotropic rotating disk, for different boundary conditions, individual failure criterion needs to be established. The obtained results are helpful for the optimization on design of functionally graded orthotropic rotating disk for the purpose of optimal design.(3) Furthermore, some coupling problems of functionally graded axisymmetrical structures are investigated such as thermoelastic and electroelastic problems. For the gradient of a power-law behavior, a closed form solution is derived. For general gradient, an integral equation method is suggested to reduce the problem to a Fredholm integral equation, and the response of the coupling field can be determined. The obtained results show that choosing appropriate materials and gradient parameters can make not only the stresses more gently, but also the functionally graded piezoelectric devices to achieve the best performance, and then enhance the reliability and service life of devices.(4) The transient response of the dynamic fracture parameters for an interfacial crack of functionally graded piezoelectric or magnetoelectric material coated by a homogeneous piezoelectric or magnetoelectric material substrate on the surface is analyzed. Two different loading situations are mainly considered:one is a realistic situation when impacts are suddenly applied on the material surface; and the other is on the crack surfaces. With the integral transform method, the problem is reduced to solving singular integral equations, and four different dynamic fracture parameters are obtained. It is found that when applied electromechanical impacts are exerted on the material surface, the gradient index causes the transient response to be significantly amplified or reduced depending on negative or positive gradient index. At the same time, by comparing the four dynamic fracture parameters, dynamic stress intensity factor, strain intensity factor, energy release rate and energy density factor, it is found that the stain intensity factor seems to be an efficient fracture parameter for smart materials, due to its consistency with some experimental observations.