BENDING OF FUNCTIONALLY GRADED PIEZOELECTRIC RECTANGULAR PLATES

By introducing two displacement functions as well as two stressfunctions, two independent state equations with variable coefficientsare derived from the three-dimensional theory equations of piezo-elasticity for transverse isotropy. A laminated approximation is usedto transform the state equations to those with constant coefficientsin each sub-layer. The bending problem of a functionally gradedrectangular plate is then analyzed based on the state equations.Numerical results are presented and the effect of material gradi- entindex is discussed.

SOLUTION OF GENERALIZED COORDINATE FOR WARPING FOR NATURALLY CURVED AND TWISTED BEAMS

A theoretical method for static analysis of naturally curved and twisted beams under complicated loads was presented, with special attention devoted to the solving process of governing equations which take into account the effects of torsion-related warping as well as transverse shear deformations. These governing equations, in special cases, can be readily solved and yield the solutions to the problem. The solutions can be used for the analysis of the beams, including the calculation of various internal forces, stresses, strains and displacements. The present theory will be used to investigate the stresses and displacements of a plane curved beam subjected to the action of horizontal and vertical distributed loads. The numerical results obtained by the present theory are found to be in very good agreement with the results of the FEM results. Besides, the present theory is not limited to the beams with a double symmetric cross-section, it can also be extended to those with arbitrary cross-sectional shape.

ON THE FREE VIBRATION OF A SUBMERGED FGM HOLLOW SPHERE

The free vibration of a functionally graded material hollow spheresubmerged in a compress- ible fluid medium is exactly analyzed. Thesphere is assumed to be spherically isotropic with material consta-nts being inhomogeneous along the radial direction. By employing aseparation technique as well as the spherical harmonics expansionmethod, the governing equations are simplified to an uncoupledsecond-order ordinary differential equation, and a coupled system oftwo such equations. Solutions to these equations are given when theelastic constants and the mass density are power functions of theradial coordinate. Numerical examples are finally given to show theeffect of the material gradient on the natural frequencies.

AN INVESTIGATION OF RANDOM FATIGUE STRENGTH OF K-TYPE TUBULAR JOINTS AND CRACK PROPAGATION BEHAVIORS

Random fatigue of welded K-type tubular joints subjected to axial or out-of-plane bending load is analyzed. By considering the sizes of initial surface cracks and material constants as random variables with some probabilistic distributions, incorporating the effect of the weld, five hundred random samples are generated. Statistical computational results of life of crack propagation and effect of change of crack shape are finally obtained and compared with experimental data available based on a regression analysis. Meanwhile, crack propagation behaviors are also investigated.

ANALYSIS OF A PARTIALLY DEBONDED ELLIPTIC INHOMOGENEITY IN PIEZOELECTRIC MATERIALS

A generalized solution was obtained for the partially debonded elliptic inhomogeneity problem in piezoelectric materials under antiplane shear and inplane electric loading using the complex variable method. It was assumed that the interfacial debonding induced an electrically impermeable crack at the interface. The principle of conformal transformation and analytical continuation were employed to reduce the formulation into two Riemann-Hilbert problems. This enabled the determination of the complex potentials in the inhomogeneity and the matrix by means of series of expressions. The resulting solution was then used to obtain the electroelastic fields and the energy release rate involving the debonding at the inhomogeneity-matrix interface. The validity and versatility of the current general solution have been demonstrated through some specific examples such as the problems of perfectly bonded elliptic inhomogeneity, totally debonded elliptic inhomogeneity, partially debonded rigid and conducting elliptic inhomogeneity, and partially debonded circular inhomogeneity.

THE DISCRETE MODELS ON A FRICTIONAL SINGLE DEGREE OF FREEDOM SYSTEM

Two stochastic models on simple random system with friction were developed. One of them was a discrete model by a two-dimensional mean map applied to describe random stick-slip motion. The numerical examples show, that external noise can reduce the complexity of the system behavior. Secondly, a probability model described was established with coexistence of stick-slip and slip motions. The numerical results point out that this model possesses pure stochastic behavior.

EQUIVALENT LINEARIZATION METHOD BASED ON ENERGY-TO-cTH-POWER DIFFERENCE CRITERION IN NON- LINEAR STOCHASTIC VIBRATION ANALYSIS OF MULTI-DEGREE-OF-FREEDOM SYSTEMS

Basic equations of energy-to-cth-power difference criterion were derived for multi-degree-of-freedom (MDOF) systems subjected to stationary Gaussian excitations with non-zero mean. Modal transform technique was used in order to reduce the unknowns. Main computational formulae were presented and suggested values of c were given. Numerical results show that the method of this paper prevails over equation difference criterion both in accuracy and in simplicity.