| For the dynamic analysis of complex super-large degree-of-freedom systems,the explicit algorithm has significant advantages over the implicit algorithm in saving storage space and improving computational efficiency.In many cases,the explicit algorithm will become the first choice or even the only algorithm.However,the existing high-efficiency explicit algorithms are all conditional stability algorithms,which restricts the wide application of these algorithms in solving practical problems of complex engineering.Therefore,an explicit algorithm called ZXZ algorithm was studied in this work.According to design an abstractive two-degrees-of-freedom system with adjustable parameters,the ZXZ algorithm has been demonstrated an unconditional stable algorithm with the same precision and constant average acceleration method.The two-degree-of-freedom system can realize the ratio of the second-order frequency or second-order and first-order frequency of the system and the second-order mathematical damping ratio to be arbitrarily large,that is,it realizes the simulation research of any complex system.Based on the results of the two-degree-of-freedom system's research on the stability and accuracy of the algorithm,although it is theoretically possible to applied on complex super-large degree-of-freedom systems,the efficiency of the ZXZ algorithm cannot be studied based on the two-degree-of-freedom system.The resulting stability and accuracy of the algorithm may also be questioned by the engineering community.In view of this,one of the main purposes of this paper is to realize numerical simulation of a super-large degree of freedom system by designing an abstract degree-of-freedom and an adjustable uniform medium out-plane fluctuation system,and to focus on the stability,accuracy,and efficiency of the ZXZ algorithm which are simply referred to as the behavioral study of the ZXZ algorithm.By comparing the corresponding research results of the closed wave system with the previous two-degree-of-freedom system,the conclusions of the ZXZ algorithm on the stability,accuracy and computational efficiency of the closed system with complex super-large degree-of-freedom are deduced.In this paper,the fixed boundary closed system and the normal transmission boundary open system was considered for the plane wave system.Through long-term research on the normal transmission boundary of open systems,a new normal transmission boundary called the ZXZ transmission boundary has been established.The other main purpose of this paper is to study the stability,accuracy,and efficiency of the ZXZ transmission boundary by numerical simulation of the open-planar fluctuation open system described above.In view of the unconditional stable algorithm used in the closed system,the instability phenomenon in the simulation calculation is caused by the artificial boundary,which makes independent research on the behavior of the artificial boundary possible.By comparing the corresponding results of the open volatility system in this paper with the previous two-degrees of freedom system research results and combining them reasonably,we can infer the final results of the ZXZ algorithm on the stability,accuracy,and computational efficiency of complex super-large-scale freedom open systems.The behavior of the algorithm includes the accuracy,stability,and efficiency of the algorithm.This paper discusses the accuracy,stability,and efficiency of the finite element numerical simulation of the ZXZ algorithm by discussing theoretically and numerically the purpose of the algorithm's behavior.It focuses on the following aspects of research work and initially got some meaningful results:1.Numerical simulation of point source-out plane fluctuation in ZXZ algorithm in closed systemIntroducing non-dimensional space step ?_x and the discretization step size of time ?_t,and the relationship between the two parameters was ?_x=a?_t(?_x,?_t?1.0).Through theoretical research,it is concluded that the precision of the ZXZ algorithm is between the midpoint acceleration method and the linear acceleration method,ie,between the 2nd and 3rd order.The numerical simulation of out-of-plane fluctuations is compared with the LL algorithm to further confirm that the accuracy of the ZXZ algorithm is not lower than that of the LL algorithm.When a larger time step is taken,the accuracy of the algorithm also meets the requirements.The unconditional stability of the ZXZ algorithm includes stability for any a value and damping ratio.Through numerical simulation of the algorithm,it is concluded that in the case of zero damping,when a31,ZXZ algorithm and LL algorithm can maintain stability.In the case of damping,given the damping ratio,the LL algorithm gradually destabilizes as the value of a decreases,and the larger the value of a is,the sooner the algorithm loses stability;Given the value of a,the LL algorithm gradually destabilizes as the damping ratio increases,and the larger the damping ratio,the earlier the algorithm loses stability.However,for the ZXZ algorithm,the arbitrary a value and damping ratio algorithm are stable.The ZXZ algorithm is an efficient and explicit algorithm.Through theoretical analysis of the overall stiffness matrix storage and a large number of computational time-consuming statistics,it is proved that the computational time of the ZXZ algorithm is directly proportional to the first degree of freedom.2.Numerical simulation of point source-out plane fluctuation in ZXZ algorithm in open systemIn an open system,the performance of the ZXZ algorithm is similar to that of a closed system.The ZXZ transmission boundary is introduced.The accuracy of the algorithm is not lower than that of the LL algorithm by both theoretical analysis and numerical simulation.The stability of the algorithm shows unconditional and stable characteristics.The introduction of the ZXZ transmission boundary is achieved by reducing the scale of the artificial boundary,that is,greatly reducing the number of degrees of freedom of the system,thus greatly improving the efficiency of the algorithm. |
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