Study On Statics Of Laminated Plates And Shells With Complicated Boundary

Based on the theory of elasticity in Hamilton system,this paper studied static problems of the laminated plates and shells with complicated boundary by using the double trigonometric series method and the semi-analytical finite element method of B-spline wavelet on the interval(BSWI),the detailed achievements are summarized as follows:The Hamilton canonical equation of elastic materials and piezoelectric materials was derived from the modified Hellinger-Reissner(H-R) variational principle for such materials,and then,the non-homogeneous state equation of the laminated plates and shells with clamped edges was established by employing the double trigonometric series method after assuming boundary stress function.Finally the non-homogeneous state equation was transformed into the homogeneous state equation by employing the dimensional expanding method.This study presented a new method to get the analytical solution of the laminated plates and shells with clamped edges.The method not only benefits programming,but also avoids the calculation of inverse matrix,and improves the computing efficiency and the numerical stability.The scaling function of BSWI was employed to discretize the domain in-plane of plates and shells,the BSWI element formula of the Hamilton canonical equation for the plates and the elastic shells was established by employing the modified H-R variational principle for elastic materials and piezoelectric materials.One of the main characteristics of BSWI element is analytical form in the direction with respect to the thickness of the structure.In order for the solution of the laminated plates and shells to ensure interlaminar continuity of the physical variables,the transfer matrix technique was used.This method combined the advantages of the wavelet-based finite element method with the advantages of the semi-analytical solution of the Hamilton canonical equation.The study proposed a new method for studying the mechanical property of the laminated plates and shells.