Design Of Structural Dynamical Numerical Algorithms With Controllable Numerical Dissipations

Design and development of direct numerical methods for structural dynamics analysis provides a effective powerful tool for analyzing dynamic performance and solving numerical responses of structures.Therefore,This paper focuses on the analysis and development of the structural dynamical numerical algorithms with controllable numerical dissipations.First,numerical properties ans design procedure of structural dynamical numerical algorithms are analyzed detailedly based on the framework of linear multistep methods;Then,two novel direct integration algorithms with controllable numerical dissipations are proposed for the structural dynamics:The first family of algorithms is a two-step unconditionally stable methods with controllable numerical dissipations,whose algorithmic properties are determined by considering the consistent and stability analysis.In order to control its numerical dissipations well,algorithmic parameters relate to the new free parameter ρ∞(which is the spectral radius under the limit of high-frequency),which leads to that new algorithms are converted to a family of the single-parameter algorithms.By analyzing numerical properties and solving numerical examples,the superiority of new proposed methods over the explicit KR-α and traditional CH-α algorithm with regard to numerical dissipations is evident.By analyzing the advantages of the traditional implicit G-α algorithm,a new structure-dependent family of algorithms with controllable numerical dissipations is proposed by using the pole mapping method in control theory and the displacement-velocity difference scheme of CR algorithm.New algorithms consist of six sub-families of the single-parameter algorithms,where the KR-α algorithm is included as a special case.At the same time,this thesis gives the linearized nonlinear stability analysis by using the amplification matrix and Routh-Hurwitz criterion in time-domain,which successfully solve a complex problem which cannot be settled by using the root-locus plots in the frequency domain in the original paper of KR-α.In the end,the innovations of this thesis are summarized and The focus of the next research work is given.