Dynamic And Static Analyses Of Timoshenko Composite Beams Using Weak Form Differential Quadrature Method

The displacement-based finite element method(FEM),as one of the most popular structural analysis methods,has been widely accepted in the engineering,however,there is still much potential to improve its analysis efficiency.As a result,the weak form differential quadrature element method(WQEM)is used in the present paper,seeking to raise the efficiency of interpolation in the conventional FEM formulation,thus to reduce the computational scale and improve the computational efficiency.The two-layer composite beam structure,which is common in use in the bridge engineering,is analyzed herein to study the performance of WQEM.Firstly,the background of the composite beams and their applications in the engineering are reviewed,and the principle of differential quadrature discretization is introduced in the first two chapters.Then,it is carried out the detailed weak-form differential quadrature element formulation for the dynamic characteristics and static response analyses of the partial interaction Timoshenko composite beams.In the quadrature element analysis,the derivatives of the primary unknowns of the composite beams are discretized by the differential quadrature method,then the DOF-adaptive weak-form differential quadrature element equations are formulated,using the principle of virtual work of the composite beams' dynamic problem.For the convenience of comparison on the analysis efficiency of the proposed WQEM and FEM,the parabolic interpolation finite element equations are also provided,thus 1)the predicted deflections and natural frequencies of the composite beams are verified;2)the smoothness of the internal forces and stresses results generated by WQEM and FEM are compared,and 3)the convergence rates of higher order free vibration modes are also examined.Numerical results show that the efficiency of the proposed WQEM has,on the one hand,significantly triumphs over that of FEM on analyses including static response,natural frequencies and higher order dynamic modes,on the other hand,the smoothness of results,including internal forces and stresses,is greatly refined.