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《Journal of Earthquake Engineering and Engineering Vibration》 2009-01
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An explicit time integration method for structural dynamic equations

LIU Heng1,LIAO Zhenpeng1,2(1.Institute of Engineering Mechanics,China Earthquake Administration,Harbin 150080,China;2.Department of Shipbuilding and Ocean Engineering,Harbin Engineering University,Harbin 150001,China)  
Starting from the spacial decoupling finite element ordinary differential equations,this paper explores the explicit time integration method for structural dynamic equations.A group of explicit schemes for the numerical simulation of wave motion are derived via the Lagrange polynomial interpolation and integration by parts;the schemes are decoupling both in time and space,which mean that the motion of a discrete nodal point at a time can be computed explicitly by the schemes in term of the data of motion of the point and its neighboring nodal points at n+1 moments before the time.The schemes have the following features.Firsty,their truncation error is limited to O(Δtn+3),where Δt is time step and n is a non-negative integer.Seconly,they are not only suitable for the numerical simulation of linear wave motion,but also applicable for the numerical simulation of nonlinear constitutive equations.Finally,the schemes can be generalized to solve a series of transient mathematic-physical problems.The stability of the schemes are investigated preliminary by a simple time-invariant system,however,the stability should be further researched.
【Fund】: 国家重点基础研究(973)项目(2007CB714201)
【CateGory Index】: TU311.3
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