Differentiai-algebraic approach to large deformation analysis of frame structures subjected to dynamic loads  

作　　者：胡育佳 朱媛媛 程昌钧 

机构地区：[1]Shanghai Institute of Applied Mathematics and Mechanics,Department of Mechanics,Shanghai University [2]Department of Computer Science and Technology,Shanghai Normal University [3]Department of Mechanics,Shanghai University,Shanghai 200444,P.R.China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2008年第4期441-452,共12页应用数学和力学（英文版）

基　　金：Project supported by Shanghai Pujiang Program(No.07pj14073);and Shanghai Leading Academic Discipline Project(No.Y0103)

摘　　要：A nonlinear mathematical model for the analysis of large deformation of frame structures with discontinuity conditions and initial displacements, subject to dynamic loads is formulated with arc-coordinates. The differential quadrature element method （DQEM） is then applied to discretize the nonlinear mathematical model in the spatial domain, An effective method is presented to deal with discontinuity conditions of multivariables in the application of DQEM. A set of DQEM discretization equations are obtained, which are a set of nonlinear differential-algebraic equations with singularity in the time domain. This paper also presents a method to solve nonlinear differential-algebra equations. As application, static and dynamical analyses of large deformation of frames and combined frame structures, subjected to concentrated and distributed forces, are presented. The obtained results are compared with those in the literatures. Numerical results show that the proposed method is general, and effective in dealing with disconti- nuity conditions of multi-variables and solving differential-algebraic equations. It requires only a small number of nodes and has low computation complexity with high precision and a good convergence property.A nonlinear mathematical model for the analysis of large deformation of frame structures with discontinuity conditions and initial displacements, subject to dynamic loads is formulated with arc-coordinates. The differential quadrature element method （DQEM） is then applied to discretize the nonlinear mathematical model in the spatial domain, An effective method is presented to deal with discontinuity conditions of multivariables in the application of DQEM. A set of DQEM discretization equations are obtained, which are a set of nonlinear differential-algebraic equations with singularity in the time domain. This paper also presents a method to solve nonlinear differential-algebra equations. As application, static and dynamical analyses of large deformation of frames and combined frame structures, subjected to concentrated and distributed forces, are presented. The obtained results are compared with those in the literatures. Numerical results show that the proposed method is general, and effective in dealing with disconti- nuity conditions of multi-variables and solving differential-algebraic equations. It requires only a small number of nodes and has low computation complexity with high precision and a good convergence property.

关 键 词：FRAME large deformation discontinuity condition differential quadrature element method （DQEM） differential-algebraic system 

分 类 号：O344.3[理学—固体力学]