Analysis And Design Of Explicit Time Integration Algorithms For Structural Dynamics

The role of transient analysis of dynamical systems has been at the forefront of computational methods of engineering mechanics in computational era.However,the performance of traditional time integration algorithms can't adapt to the requirement of analysis and design for engineering structures,and the need to discuss and improve the numerical properties.Therefore,it is critical to develop new efficient time integration algorithms for structural dynamics.This paper proposes two families of explicit time integration algorithms of structural dynamics by deeply analyzing the numerical properties of existing explicit time integration algorithms.Based on the principle of general-single-step-single-solve(GSSSS)integration algorithm,this paper introduces the integration parameter form of Chang's algorithms,analyzes the property of accuracy,overshoot,numerical damping and linear stability,and then proposes a new family of unconditionally stable explicit GSSSS algorithms for time integration of structural dynamics with controllable numerical damping.In addition,based on the separatedesign method and by introducing the concept of model-based parameters in Chang algorithms,a new explicit time integration algorithm is proposed.Then,the values or ranges of the parameters are deduced by analyzing the numerical characteristics of the time integration algorithms.At last,the parameters are converted to the function of spectral radius ?,which controls the numerical damping.Theoretical analysis indicates that the two families of new proposed explicit time integration algorithms possess the properties of second accuracy,self-starting,zero-order displacement and zero-order velocity overshooting behavior,unconditionally stable and controllable numerical damping.Moreover,the CR algorithm and KR-? method are respectively special case of the new explicit algorithm designed by new proposed framework.When solving the nonlinear dynamic response problems,the new explicit algorithms with controllable variable ? significantly improve the convergence.Numerical examples of SDOF system and MDOF system demonstrate that the accuracy of new algorithms are superior to that of ?-families algorithms.Finally,the second explicit time integration algorithm is applied to solve nonlinear dynamic response problems,which verifies the effectiveness and stability of the new algorithm.