In this paper, the mixed-mode fracture problem of two parallel cracks in a functionally graded piezoelectric material (FGPM) strip is considered. It is assumed that the electroelastic properties of the strip vary continuously along the thickness of the strip, and that the strip is under a uniform electric loading. The crack faces are supposed to be insulated electrically. Fourier transform techniques are used to reduce the mixed boundary value problems to a system of singular integral equations. The singular integral equations are solved by using the Gauss-Jacobi integration formula. Numerical calculations are carried out, and the stress and electric displacement intensity factors are presented for various values of dimensionless parameters representing the crack size, the crack location, and the material nonhomogeneity.
Characteristics of inverse problem analysis techniques on structural system identification based on filtering theory using as iterative calculation algorithm were studied computationally. The projection filter which is given as simple formula was adopted as an example of some filtering algorithm. Our study focused on the engineering quantity related sensitivity matrix, difference technique and setting method of initial values were proposed to calculate stably the iterative calculations.
System identification was performed for five-story frame models to estimate lateral stiffness of every story at once in engineering field of inverse problem. In this study filtering algorithm based on variable parametric projection filter (VPPF) was used for the structural system identification adopted natural frequencies as observations. Identification results based on VPPF were compared with the results of Kalman filtering algorithm, the effectiveness of algorithm are made clear through the results on inverse analysis of various case from points of view on institution procedures of initial values and regularization parameter.
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