D.H. Li

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.

Static and dynamic response analysis of functionally graded material plates with damage

ABSTRACT The typical damage pattern of functionally graded materials (FGM) is a complex three-dimensional crack with delamination and transverse cracks. The extended layerwise method (XLWM) is applied to the static, free vibration and transient response of FGM plates with typical damage pattern in this paper. In the XLWM of FGM plates, the multiple delaminations and transverse cracks are simulated by displacement assumption in thickness direction and in-plane displacement discretization of extended finite element methods (XFEM), respectively. Numerical examples are provided to validate the proposed method, and the results are compared with these of existing methods and 3D elastic models.

Extended Layerwise/Solid-Element method of composite sandwich plates with damage

ABSTRACT The truss and honeycomb sandwich plates with transverse crack and delamination in the facesheets are studied, and an Extended Layerwise/Solid-Element (XLW/SE) method is developed. The governing equations of laminated composite facesheets and cores (truss or honeycomb) are established based on the Extended Layerwise Method (XLWM) and 3D solid elements, respectively. The XLW/SE method can obtain the local stress and displacement fields accurately, considering complicated cores without any assumptions. In the numerical examples, the results obtained by the proposed method are compared with those obtained by the 3D elasticity models, and the good agreements are achieved.

Accuracy improvement of XFEM using Wilson's incompatible element technique

ABSTRACT Based on the extended finite element method (XFEM) and Wilson incompatible element technique, an incompatible extended finite element method (IXFEM) is presented to deal with the cracked bending problems in this study. The additional displacement modes of Wilsons incompatible element are introduced into the approximation of the XFEM. The internal degrees of freedom induced by additional models are condensed to improve efficiency. Derivation of the equilibrium equations of the IXFEM is performed. Several examples are employed to validate the capabilities of the proposed method. The influence of bending degree on the performance of proposed method is studied by changing the crack length. The numerical results indicate that the stress and displacement solutions of the IXFEM show a slight oscillation. The IXFEM achieves better convergence rate and computational accuracy compared with the traditional XFEM for the bending problems.

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.