The spline finite point method (SFPM) that is based on the classical laminated plate theory is introduced to investigate the natural vibration of smart FGM plate, which is integrated with piezoelectric layers. The spline basic function that meets different boundary conditions is constructed by the generalized parameter method, and a new dynamic computational scheme for smart FGM plate is established to analysis the natural frequency that considering influence of the axial force, which is generated by the electric field. To demonstrate the less computational cost and higher accuracy of the SFPM, several numerical examples are calculated. The effects of the electric field and the influence of the thickness ratio of piezoelectric layer and substrate on the fundamental frequency are also discussed.

To study the crack repair performance of shape memory alloy to the concrete beam, the SMA wire with a certain initial strain at room temperature is placed eccentrically in the concrete beam. Because of its constrained recovery stress produced during the phase transition, the driving force is exerted on the beam by energizing the SMA. In this paper, the constrained recovery stress of SMA was calculated based on the Brinson constitutive model and would be equivalent to the unit stress of reinforcement. The repair performance of SMA was analyzed by ANSYS. According to the study, it can be concluded that the cracks in concrete beam can be effectively controlled by SMA. Increasing the diameter of SMA is a effective measure to enhance its driving force. When the excitation temperature is, the diameter of SMA are 2mm and 4mm, the response rates of crack width are 4.1% and 16.5%. Under certain conditions, the smaller the reinforcement ratio is, the better repair performance.

The element-free spline method is proposed to analyze the vibration of the functionally graded material (FGM) plate with various boundaries. The field functions are constructed by using the linear combination of double B-spline basis functions together with mixed displacement parameters and then an equation based on Reddy's third order plate theory is developed for the vibration analysis of the FGM plate. The validity of the proposed method is illustrated by some numerical examples. Six lower vibration frequencies of FGM plate are calculated under various boundaries and the influence of boundary condition and material gradient on vibration frequencies are also discussed. The proposed method needs less computational cost and has high accuracy.

A fit-to-data technique was proposed to identify the mechanical and piezoelectric parameters of a model involving a piezoelectric laminated composite beam. Analytical solutions for displacement of the model were derived for parameter identification. The parameter identification problem was formulated as the problem of minimizing the objective function defined as a square sum of differences between the measured displacement and the computed displacement by the analytical solutions. Levenberg-Marquardt method was used to solve the minimization problem. The sensitivities of displacements with respect to the parameters were based on the finite difference approximation method. Numerical example shows that the proposed technique for parameter identification is effective.

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