A new analysis based on Airy stress function method is presented for a functionally graded piezoelectric material cantilever beam. Assuming that the mechanical and electric properties of the material have the same variations along the thickness direction, a two-dimensional plane elasticity solution is obtained for the coupling electroelastic fields of the beam under different loadings. This solution will be useful in analyzing FGPM beam with arbitrary variations of material properties. The influences of the functionally graded material properties on the structural response of the beam subjected to different loads are also studied through numerical examples.
In a homogeneous plate, Rayleigh waves will have a symmetric and anti-symmetric mode regarding to the mid-plane with different phase velocities. If plate properties vary along the thickness, or the plate is of functionally graded material (FGM), the symmetry of modes and frequency behavior will be modified, thus producing dif-ferent features for engineering applications such as amplifying or reducing the velocity and deformation. This kind of effect can also be easily realized by utilizing a layered structure with desired material properties that can produce these effects in terms of velocity and displacements, since Rayleigh waves in a solid with gen-eral material property grading schemes are difficult to analyze with known methods. Solutions from layered structures with exponential and polynomial property grad-ing schemes are obtained from the layered model and comparisons with known analytical results are made to validate the method and examine possible applica-tions of such structures in engineering.
In this paper the plane elasticity problem for a functionally graded interfacial zone containing a crack between two dissimilar homogeneous materials has been considered. It is assumed that in the interfacial zone the reciprocal of the shear modulus is a linear function of the coordinate, while Possion’s ratio keeps constant. By utilizing the Fourier transformation technique and the transfer matrix method, the mixed boundary problem is reduced to a system of singular integral equations that are solved numerically. The influences of the geometric parameters and the graded parameter on the stress intensity factors are investigated. The numerical results show that the graded parameters, the thickness of interfacial zone, the crack size and location have significant effects on the stress intensity factors.
CHENG Zhanqi1,2 & ZHONG Zheng1 1. School of Aerospace Engineering and Applied mechanics, Tongji University, Shanghai 200092, China
