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

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Abstract

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 discontinuity 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.

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Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics, Department of Mechanics, Shanghai University, Shanghai, 200072, P. R. China

    Yu-jia Hu  (胡育佳) & Chang-jun Cheng  (程昌钧)

  2. Department of Computer Science and Technology, Shanghai Normal University, Shanghai, 200234, P. R. China

    Yuan-yuan Zhu  (朱媛媛)

  3. Department of Mechanics, Shanghai University, Shanghai, 200444, P. R. China

    Chang-jun Cheng  (程昌钧)

Authors
  1. Yu-jia Hu  (胡育佳)
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  2. Yuan-yuan Zhu  (朱媛媛)
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  3. Chang-jun Cheng  (程昌钧)
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Corresponding author

Correspondence to Chang-jun Cheng  (程昌钧).

Additional information

Contributed by CHENG Chang-jun

Project supported by Shanghai Pujiang Program (No. 07pj14073), and Shanghai Leading Academic Discipline Project (No. Y0103)

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Hu, Yj., Zhu, Yy. & Cheng, Cj. Differential-algebraic approach to large deformation analysis of frame structures subjected to dynamic loads. Appl. Math. Mech.-Engl. Ed. 29, 441–452 (2008). https://doi.org/10.1007/s10483-008-0403-7

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  • DOI: https://doi.org/10.1007/s10483-008-0403-7

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Chinese Library Classification

2000 Mathematics Subject Classification

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