Performance Improvement And Engineering Application Of Explicit Structure-dependent Time Integration Algorithms

The damage and nonlinear dynamic behavior of structures caused by strong earthquake action imposes high requirements for dynamic analysis and seismic design of large-scale structures.Real-time dynamic hybrid testing can be used to investigate the dynamic performance,response process and failure mechanism of structures under earthquake action by using the large scale experimental model.To achieve high accuracy for the real-time dynamic hybrid testing,it is imperative to develop the time integration algorithms with good stability and high efficiency.Furthermore,to ensure the accuracy of dynamic response in buildings,dams,bridges,aerospace aircrafts and other engineering structures,the degree of freedom of computational model is very more.The computational cost of dynamic analysis increases dramatically with the increasing degree of freedom.As a result,it is urgent to study the computational efficiency,accuracy and stability of time integration algorithms in the dynamic analysis of large-scale structures.The structures are sometimes subjected to the stochastic excitation from service environment.The nonlinear explicit time history analysis and random vibration analysis possess academic theoretical significance and engineering application value for structural design.Recently,some time integration algorithms have been proposed.Conventional explicit time integration algorithms are conditionally stable.The implicit algorithms require iteration for nonlinear system,which leads to low computational efficiency in dynamic analysis of largescale structures.The structure-dependent time integration algorithm can effectively overcome these disadvantages,but it has the unusual amplitude growth phenomenon for structures with high natural frequencies.Moreover,the accuracy is not enough in long-term simulation of structural dynamics.There are few studies on dynamic analysis and random vibration analysis of large-scale structures.Accordingly,this dissertation aims to improve the performance of structure-dependent integration algorithm and improve its accuracy and study its application in deterministic and stochastic dynamic analysis of large-scale structures.The main contents are presented as follows:(1)An unusual amplitude growth phenomenon of explicit structure-dependent integration algorithms was studied,and a general displacement modification method for eliminating the unusual amplitude growth phenomenon was presented.An unusual amplitude growth phenomenon of the steady-state response for structures with high natural frequencies was found in explicit or semi-explicit structure-dependent integration algorithms with unconditional stability,second-order accuracy and no overshoot.A general displacement modification method for eliminating such an unusual amplitude growth phenomenon is proposed,by incorporating the load-dependent term into the displacement recursive formula without changing the numerical properties of the structure-dependent integration algorithm.Compared with the existing formulation using the local truncation error for deriving the load-dependent term,the proposed method has the advantages of less symbolic operations,while naturally including the existing formulation.In addition,it is observed that the coefficients of the loaddependent term are proportional to the limit values of the displacement coefficients in the displacement recursive formula as the natural frequency of the system tends to infinity.Then,the general displacement modification method is tested for 15 structure-dependent integration algorithms to verify its correctness.Finally,numerical examples of linear and nonlinear multiple-degrees-of-freedom systems illustrate that the general displacement modification method can effectively and conveniently remove the unusual amplitude growth phenomenon for dynamic response analyses.(2)In order to improve the accuracy of time integration algorithms for long-term simulation of structural dynamics,a new method of reducing the period elongation(numerical dispersion)was proposed by utilizing the mass scaling matrix for the first time.Firstly,the mass scaling method was used to modify the mass matrix,which is weighted by the original mass matrix and stiffness matrix.As a result,the numerical frequency of the time integration algorithms is changed,and the period elongation was reduced.Then,the bisection method is utilized to determine the parameter according to the formulation of period elongation.Finally,the original mass matrix is replaced by the modified mass matrix.The convergence rate of original time integration algorithm remains unchanged and the proposed mass scaling method imposes little influence on the stability condition of original algorithm.Moreover,this method only modifies the mass matrix of time integration algorithm and is easy to implement.Both linear and nonlinear long-term dynamic response analyses for multiple-degree-of-freedom systems indicated that,the proposed mass scaling method is effective and convenient to reduce the period elongation for time integration algorithms.(3)There is a lack of comprehensive comparison and analysis on the numerical performance of structure-dependent integration algorithms for solving the dynamic problems of large-scale structures.As a contrast,the stability,computational accuracy and efficiency of some representative conventional algorithms are also considered.Firstly,the stability,accuracy and efficiency of the algorithm were examined,and the relationship between two structure dependence algorithms and the conventional time integration algorithms were found.Subsequently,these algorithms were applied to compute the dynamic responses of three engineering examples with more than 10,000 degrees of freedom,i.e.,Kirchhoff plate,threedimensional dam and the elastoplastic gravity dam.Moreover,the influences of mass scaling method,consistent mass and lumped mass on the computational efficiency and accuracy of time integration algorithms were analyzed.Finally,the results indicated that the explicit structuredependent DY algorithm can be employed for dynamic analysis of large-scale structure with high accuracy and efficiency.The mass scaling method can significantly increase the critical time step of explicit algorithms and suppress spurious high-frequency mode response.The seismic responses of elastoplastic dam strongly correlate with peak ground acceleration of nearfault ground motions.(4)Based on direct probability integration method and explicit structure-dependent integration algorithm,random vibration analysis of large gravity dam and arch dam is performed.The random vibration analysis also requires structural dynamic analysis,and largescale structure dynamic analysis needs a large amount of computational cost.The direct probability integration method can solve the differential equation of motion and the probability density integral equation in turn to achieve the random vibration analysis.The DY algorithm with better performance is combined with the direct probability integration method for random vibration analysis of large structures with more than 10000 degrees of freedom.Finally,the probability distribution and dynamic reliability of the elastoplastic gravity dam model and the elastic three-dimensional arch dam under stochastic near-fault impulsive ground motions were calculated,and the random vibration analysis of the gravity dam under stochastic structural parameters and excitation was also performed.The results show that the high efficiency random vibration analysis of large structures can be realized by combining DY algorithm with direct probability integration method,and its computational cost mainly depends on the efficiency of the time integration algorithm.Furthermore,it is significant to decrease the coefficient of variant of elastic modulus for enhancing the dynamic reliability of the dam.