Design And Application Of New Model-Based Integration Algorithms

As a new type of direct integration algorithm,model-based integration algorithm is favored by researchers because of its explicit algorithm format and unconditionally stable numerical characteristics.However,because the existing model-based integration algorithms have the problems of lower-order of accuracy and complex introduction of numerical damping,therefore,this paper focuses on the design and development of model-based integration algorithm with higher-order accuracy and model-based integration algorithm with controllable numerical damping.Firstly,through the discretization of continuous domain in discrete control theory,two new model-based integration algorithms with fourth-order accuracy,namely NDE(New Dual-Explicit)-4th(Fourth)algorithm and NSE(New Semi-Explicit)-4th(Fourth)algorithm,are proposed by using dual-explicit and semi-explicit format with pole mapping rules of second-order Padéapproximation.The numerical characteristics of NDE-4th algorithm and NSE-4th algorithm is comprehensively analyzed and verified by two classical numerical examples.The results show that the two new algorithms can achieve fourth-order accuracy in the case of single-degree-of-freedom undamped free vibration.In other cases,the numerical accuracy of the new algorithm will be reduced to the thirds or second order,but because the period elongation of the two new algorithms is extremely small,the actual calculation error of the two new algorithms is still much smaller than that of the existing second-order accuracy algorithms.and can maintain the same level as the fourth-order Runge-Kutta algorithm.Then,using the eigenvalue matching method of amplification matrix,using dual-explicit and semi-explicit format respectively,two model-based integration algorithms with controllable numerical damping,namely NDE-ρ_∞algorithm and NSE-ρ_∞algorithm,are proposed.The eigenvalues of the two new algorithms are equal to those of the traditional implicitρ_∞-Bathe algorithm,so the numerical characteristics of the new algorithm are basically the same as those of theρ_∞-Bathe algorithm.Both the NDE-ρ_∞algorithm and the NSE-ρ_∞algorithm have two free parameters to control the numerical damping,and the structural equations of motion do not need to be weighted,so they are more flexible and controllable.Two classical numerical examples show that compared with KR-αalgorithm and Chang-αalgorithm,NDE-ρ_∞algorithm and NSE-ρ_∞algorithm have larger maximum numerical damping,more controllable numerical damping and more convenient to use.Finally,on the basis of the research of Lages,we deeply study the influence of the parameters in the DHC(Displacement History Curvature)strategy on the adaptive time step,and apply it to the model-based integration algorithm to explore whether it is necessary to update the integration parameters in real time with the change of time step.Through two classical numerical examples,it is verified that the time step adaptive strategy can successfully achieve a balance between accuracy and efficiency,and that the higher-order accuracy algorithm is more suitable for the time step adaptive strategy than the lower-order accuracy algorithm.