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The layerwise/solid element method（ LW/SE） was used to study the static and free vibration problems of lattice sandwich structure under different boundary conditions. First,the layerwise theory was used to analyze the behavior of the shell of composite face sheets,and the three-dimensional solid elements were employed to obtain the governing equations of the core. And then,based on the governing equations of the face sheets and core,the finial governing equation of sandwich structure was assembled by using the compatibility conditions,which was used to ensure the compatibility of displacements at the interface between face sheets and core. The numerical results of the proposed method were compared with those obtained from the 3 D elastic model developed in finite element software,and good agreements are achieved. Furthermore,a series of numerical analyses are conducted to further explore the effects of the thickness of the face sheets on the static responses and free vibration responses of composite lattice sandwich structures.

A semi-analytical solution theory is presented by combining the separable Hamilton canonical equation and finite element method. The problem of free-edge effect of orthotropic laminates is studied in symplectic system. First, the separable Hamilton canonical equations are established with modified Hellinger-Reissner variational principle. And the state equations are established with finite element method. Then, an example analysis of the distribution of interlaminar stresses in composite laminates is calculated. The numerical results show the efficiency of the proposed method.