State Space Based Mixed Finite Element-Differential Quadrature Method And Its Applications

Composite structures have been widely used in bridge and tunnel engineering.And the state space method has unique advantages when analyzing composite structures.Therefore,this paper proposes a Mixed Finite Element – Differential Quadrature Method(MFE-DQM)based on the state space method,which is verified with various engineering examples of composite structures.Firstly,the mixed energy functional is derived in the Hamiltonian system.Then,while reserving the continuity in the thickness direction of the composite structure,mixed elements with nodal displacements and their energy-conjugated stresses as nodal variables are introduced in other directions.Thus,state equations with element nodal variables as state vectors are established.Finally,DQM is introduced in the thickness direction to solve the equations.Due to the use of element nodal displacements and stresses as fundamental variables in the state equations,various transfer characteristics at the interlayer interfaces of composite structures can be conveniently handled.The introduction of DQM,on the other hand,gives this method the ability to deal with various types of boundary conditions in order to simulate different support conditions in practical engineering.The main work of this paper is as follows:Firstly,a two-dimensional analytical model of composite beam is established using cross section equivalent transformation.And the static and dynamic MFE-DQM solutions is achieved.Numerical examples under different boundary conditions,load distributions and span combinations show that this method can conveniently analyze the interlayer slip of composite beams and the anisotropic characteristics of the corrugated steel webs.Owing to the use of a two-dimensional analytical model,this method can analyze the pullout resistance of shear connectors and provide benchmarks for displacement and stress assumptions as well as reference standards for various onedimensional simplified beam theories.Secondly,this paper establishes a two-dimensional static MFE-DQM solution in the polar coordinate system.Through the analyses of tunnel lining,it is shown that the present method is able to consider multiple connecting stiffnesses of joints,to deal with complex interface relations between double lining layers,and to consider the interaction between lining and the surrounding groud.Finally,this paper establishes a three-dimensional static MFE-DQM solution of the laminated plates in the space rectangular coordinate system.Studies of laminated plates under different boundary conditions,load distribution and those with notches in the plate plane shows that the present method can effectively deal with irregular geometries in the plate and analyze the two-dimensional slips between layers.Taking the track slab as an example,its interaction with the foundation and the influences of the foundation on its interlayer slip and stress distribution are analyzed.A large number of numerical examples and analyses show that this MFE-DQM method is applicable to a wide range of objects and could give accurate stress results.This method retains the advantages of the state-space method for composite structures and takes advantage of the FEM for handling non-uniform materials and complex boundary conditions,and can provide benchmarks for various simplified theories.