Guanghui Qing

Free Vibration Analysis of Composite Laminates with Delamination Based on State Space Theory

A semi-analytical solution based on the modified H-R (Hellinger-Reissner) variational principle and a nonlinear spring-layer model is presented to analyze the free vibration problem of laminates with a delamination in the Hamilton system. This nonlinear spring-layer model between the upper and lower sub-laminates ensures the exact continuous transverse stresses and displacements in the un-delaminated region by specifying the infinite values of springs and avoids the possibility of penetration phenomenon in the delaminated region. As an application of this method, the influence of the delamination size, depth, and boundary conditions on the first three natural frequencies of delaminated composite laminates is investigated.

B-Spline Wavelet on the Interval Element for the Solution of Hamilton Canonical Equation

Based on the modified Hellinger-Reissner (H-R) variational principle for the elastic material, the formulation of B-spline wavelet on the interval (BSWI) element of the Hamilton canonical equation was derived through the use of the interpolation scaling function of BSWI. To demonstrate the excellent predictive capability of the formulation, numerical studies were conducted on a thick plate and a three-layer plate with various common boundary conditions. The basic steps from which the formulation of the BSWI element of the Hamilton canonical equation was derived can also be extended to deduce the expressions of other wavelet elements in the Hamiltonian system, such as Daubechies orthogonal wavelet, biorthogonal wavelet based on lifting scheme, and so on.