Further insights of a composite implicit time integration scheme and its performance on linear seismic response analysis

Abstract In this work, some further insights of a composite implicit time integration scheme proposed by Wen et al. are presented. The local truncation error of the proposed scheme is first derived, and analytical accuracy solution is thus acquired as well as the optimal value of algorithmic parameter. The influence of approximate loads on computation accuracy of the proposed scheme is quantified by local truncation errors. More detailed analysis is conducted to demonstrate the desirable performance of the proposed scheme on accuracy, stability and numerical dissipation properties. The calculation procedure of the presented scheme for seismic response is proposed. Numerical examples demonstrate the presented scheme possesses desirable accuracy and efficiency for seismic response analysis when compared with other representative schemes.

[1]  Y. Wen.  Method for Random Vibration of Hysteretic Systems , 1976 .

[2]  Salvatore Sessa,et al.  Nonlinear dynamic analysis of hysteretic mechanical systems by combining a novel rate-independent model and an explicit time integration method , 2019, Nonlinear Dynamics.

[3]  Donghuan Liu,et al.  Accuracy of a composite implicit time integration scheme for structural dynamics , 2017 .

[4]  Yi Ji,et al.  An optimized three-sub-step composite time integration method with controllable numerical dissipation , 2020 .

[5]  Lidija Zdravković,et al.  An assessment of time integration schemes for dynamic geotechnical problems , 2008 .

[6]  Fabrizio Greco,et al.  A mixed explicit–implicit time integration approach for nonlinear analysis of base-isolated structures , 2018 .

[7]  Oreste S. Bursi,et al.  Generalized‐α methods for seismic structural testing , 2004 .

[8]  K. Bathe,et al.  On a composite implicit time integration procedure for nonlinear dynamics , 2005 .

[9]  D. Fang,et al.  An improved time integration scheme based on uniform cubic B-splines and its application in structural dynamics , 2017 .

[10]  M. Dokainish,et al.  A survey of direct time-integration methods in computational structural dynamics—I. Explicit methods , 1989 .

[11]  Shuenn-Yih Chang,et al.  Family of Structure-Dependent Explicit Methods for Structural Dynamics , 2014 .

[12]  Nathan M. Newmark,et al.  A Method of Computation for Structural Dynamics , 1959 .

[13]  K. Bathe,et al.  Performance of an implicit time integration scheme in the analysis of wave propagations , 2013 .

[14]  Roberto Villaverde,et al.  Fundamental Concepts of Earthquake Engineering , 2009 .

[15]  D. Fang,et al.  A comparative study of three composite implicit schemes on structural dynamic and wave propagation analysis , 2017 .

[16]  Suchuan Dong,et al.  BDF-like methods for nonlinear dynamic analysis , 2010, J. Comput. Phys..

[17]  K. Tamma,et al.  Time Discretization of Equations of Motion: Recent Advances , 2012 .

[18]  H. M. Zhang,et al.  Optimization of a class of composite method for structural dynamics , 2018, Computers & Structures.

[19]  Thomas J. R. Hughes,et al.  Improved numerical dissipation for time integration algorithms in structural dynamics , 1977 .

[20]  Jie Zhang,et al.  A‐stable two‐step time integration methods with controllable numerical dissipation for structural dynamics , 2019, International Journal for Numerical Methods in Engineering.

[21]  Jintai Chung,et al.  Explicit time integration algorithms for structural dynamics with optimal numerical dissipation , 1996 .

[22]  S. M. Spottswood,et al.  A robust composite time integration scheme for snap-through problems , 2015 .

[23]  Yi Min Xie,et al.  AN ASSESSMENT OF TIME INTEGRATION SCHEMES FOR NON-LINEAR DYNAMIC EQUATIONS , 1996 .

[24]  A. Kaveh,et al.  A DISCRETE BIG BANG - BIG CRUNCH ALGORITHM FOR OPTIMAL DESIGN OF SKELETAL STRUCTURES , 2010 .

[25]  K. Bathe,et al.  The Bathe time integration method with controllable spectral radius: The ρ∞-Bathe method , 2019, Computers & Structures.

[26]  D. Fang,et al.  A quadratic b-spline based isogeometric analysis of transient wave propagation problems with implicit time integration method , 2018, Applied Mathematical Modelling.

[27]  Ningbo Wang,et al.  An improved sub-step time-marching procedure for linear and nonlinear dynamics with high-order accuracy and high-efficient energy conservation , 2021 .

[28]  Jintai Chung,et al.  A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method , 1993 .

[29]  Edward L. Wilson,et al.  Nonlinear dynamic analysis of complex structures , 1972 .

[30]  Yi Ji,et al.  On the construction of a type of composite time integration methods , 2019, Computers & Structures.

[31]  Wooram Kim,et al.  An improved implicit time integration algorithm: The generalized composite time integration algorithm , 2018 .

[32]  P. J. Pahl,et al.  Development of an implicit method with numerical dissipation from a generalized ingle-step algorithm for structural dynamics , 1988 .

[33]  K. Jian,et al.  An explicit time integration method for structural dynamics using septuple B‐spline functions , 2014 .

[34]  Jinze Li,et al.  A novel family of controllably dissipative composite integration algorithms for structural dynamic analysis , 2019, Nonlinear Dynamics.

[35]  Randolph E. Bank,et al.  Transient simulation of silicon devices and circuits , 1985, IEEE Transactions on Electron Devices.

[36]  Pui-Shum B. Shing,et al.  Implicit time integration for pseudodynamic tests , 1991 .

[37]  Mohammad Rezaiee-Pajand,et al.  A novel time integration formulation for nonlinear dynamic analysis , 2017 .

[38]  D. Fang,et al.  Improved quadratic isogeometric element simulation of one-dimensional elastic wave propagation with central difference method , 2018 .

[39]  Anil K. Chopra,et al.  Dynamics of Structures: Theory and Applications to Earthquake Engineering , 1995 .

[40]  Huanzi Wang,et al.  An analytical study of bond strength associated with splitting of concrete cover , 2009 .

[41]  Daining Fang,et al.  A novel sub-step composite implicit time integration scheme for structural dynamics , 2017 .

[42]  Salvatore Sessa,et al.  A class of uniaxial phenomenological models for simulating hysteretic phenomena in rate-independent mechanical systems and materials , 2018 .

[43]  Salvatore Sessa,et al.  A generalized class of uniaxial rate-independent models for simulating asymmetric mechanical hysteresis phenomena , 2021 .

[44]  Stephen A. Mahin,et al.  Pseudodynamic Method for Seismic Testing , 1985 .