In this paper, the specific solutions of orthotropic plane problems with body forces are derived. Then, based on the general solution in the case of distinct eigenvalues and the specific solution for density functionally graded orthotropic media, a series of beam problem, including the problems of cantilever beam with body forces depending only on z or on x coordinate and expressed by z or x polynomial is solved by the principle of superposition and the trial-and-error method.
<正>In this paper,the wave propagation in a functionally graded piezoelectric coating on a cylinder is studied....
Yong-dong PAN Institute of Acoustics,Tongji University,1239 Siping Road,Shanghai 200092,China Zheng ZHONG School of Aerospace Engineering and Applied Mechanics,Tongji University,1239 Siping Road,Shanghai 200092,China
Two-dimensional thermoelasticity analysis of functionally graded thick beams is presented using the state space method coupled with the technique of differential quadrature. Material properties vary continuously and smoothly through the beam thickness, leading to variable coefficients in the state equation derived from the elasticity equations. Approximate laminate model is employed to translate the state equation into the one with constant coefficients in each layer. To avoid numerical instability, joint coupling matrices are introduced according to the continuity conditions at interfaces in the approximate model. The differential quadrature procedure is applied to discretizing the beam in the axial direction to make easy the treatment of arbitrary end conditions. A simply-supported beam with exponentially varying material properties is considered to validate the present method. Numerical examples are performed to investigate the influences of relative parameters.
Lü Chaofeng1, CHEN Weiqiu1 & ZHONG Zheng2 1. Department of Civil Engineering, Zhejiang University, Hangzhou 310027, China
The time-dependent behavior of a simply-supported functionally graded beam bonded with piezoelectric sensors and actuators is studied using the state-space method. The creep behavior of bonding adhesives between piezoelectric layers and beam is characterized by a Kelvin-Voigt viscoelastic model, which is practical in a high temperature circumstance. Both the host elastic functionally graded beam and the piezoelectric layers are orthotropic and in a state of plane stress, with the former being inhomogeneous along the thickness direction. A laminate model is employed to approximate the host beam. Moreover, the coupling effect between the elastic deformation and electric field in piezoelectric layers is considered. Results indicate that the viscoelastic property of interfacial adhesives has a significant effect on the function of bonded actuators and sensors with time elapsing.
YAN Wei1 & CHEN Weiqiu1,2 1. Department of Civil Engineering, Zhejiang University, Hangzhou 310027, China
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
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.
