Research On High-accuracy Frame And Cable Elements For Dynamic Calculation

The structural dynamic analysis plays a very important role in the structural analysis. The results obtained from conventional finite element method are often not accurate enough in the higher frequency range. The dynamic stiffness matrix method (DSM) is a very powerful means of solving vibrating problems in the structural engineering field, particularly when higher frequency and accuracy are required. This method is often referred to as an exact method for all assumptions for the method coming from the classical theory of the differential equations of motion of any studied element. The Dynamic Element Method is an approximate method based on polynomial matrix approximations to DSM for the free vibration analysis of structure, which gives results more accurate than those from a conventional finite element model with the same number of degrees of freedom. In this thesis, the dynamic stiffness matrix and dynamic element matrices for the bar, beam, and cable which can be widely used in dynamic calculation of structures, i.e., the truss structures and the strut-tensile structures under different static load are closely studied.First, the application and research history of the dynamic stiffness matrix and the dynamic element matrix are reviewed. Then the methods of obtaining the dynamic stiffness matrix and dynamic element matrix for different elements are discussed. Also, a method presented by He Guojing based on vibration principle in linear elastodynamics is extended to obtain higher-order dynamic items in dynamic element method.The dynamic stiffness matrix and the corresponding dynamic element matrices for an Euler-Bernoulli bar element with the inclusion of axial forces are derived, so it can be widely used in dynamic calculation of structures which must consider the effect of prestress. The dynamic element matrices for beam element with the inclusion of axial forces are also deduced so that their ranges of use are expanded. The dynamic stiffness matrix and dynamic element matrices for cable element are briefly introduced in order to calculate dynamic characteristic of the strut-tensile structures. The algorithms to solve the nonlinear eigenvalue problems evoked by the dynamic stiffness matrix method and the dynamic element matrix method are summarized and programmed.Based on the dynamic stiffness matrix and dynamic element matrix above, the dynamic characteristic of the truss structures, beam structures, guyed mast structures and strut-tensile structures are closely studied. The numericalexamples demonstrate that the results from using the dynamic stiffness matrix and dynamic element matrices are more efficient in the truss structures than other structures, while both methods are show great improvement in the precision of all the structure systems.At last, after summarizing the result of this thesis, the future research work was presented.