Study On Arbitrary Boundary Conditions Of Hamilton Semi-analytical Method

Due to the need of engineering practice,the problem of solving composite laminates is of vital concern to scholars in recent years,especially the problem of complex boundary conditions.It is very difficult to deal with the problems of statics and dynamics of laminated plates under complicated boundary conditions.In engineering applications,it's very difficult to solve the statics and dynamics of laminated plate with analytic method.When dealing with laminated plates with complex boundary conditions,the semi analytical method based on the state vector equation can not only reduce the computational difficulty,but also guarantee the accuracy.In this paper,first,the Hamilton theory are introduced briefly,and then the limitation of dealing with the boundary problem of laminate by the semi analytical finite element method based on Hamilton theory system is pointed out,which is unable to deal with some complicated boundary conditions.For example,the semi analytical finite element method based on Hamilton theory requires that the boundary condition of the same side along the thickness direction is uniform.In order to overcome these difficulties,bases on Hamilton isoparametric element semi analytical method and combines with traditional finite element boundary condition processing method and transfer matrix method,establish way of dealing with complicated boundary conditions that is suitable for semi analytical method.The correctness and accuracy of the method are verified by numerical examples of a single plate and three plates.Then,the static problems of laminated plates under different boundary conditions are analyzed,and the correctness and accuracy of the boundary condition treatment methods are verified.The results of numerical examples in this paper can be used as the reference solution of other methods.