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

• Published in: Applied mathematics and mechanics Vol. 29; no. 4; pp. 441 - 452
• Main Author: 胡育佳 朱媛媛 程昌钧
• Format: Journal Article
• Language: English
• Published: Heidelberg Shanghai University Press 01.04.2008; Shanghai Institute of Applied Mathematics and Mechanics,Department of Mechanics,Shanghai University,Shanghai 200072,P.R.China%Department of Computer Science and Technology,Shanghai Normal University,Shanghai 200234,P.R.China%Shanghai Institute of Applied Mathematics and Mechanics,Department of Mechanics,Shanghai University,Shanghai 200072,P.R.China; Department of Mechanics,Shanghai University,Shanghai 200444,P.R.China
• Subjects: Applications of Mathematics; Classical Mechanics; Convergence; Deformation; Discontinuity; Dynamic loads; Fluid- and Aerodynamics; Frame structures; Mathematical analysis; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Mathematics and Statistics; Nonlinearity; Partial Differential Equations; 大变形; 微分代数; 微分面积求解方法; 标架; 非连续性条件; differential-algebraic system; 74K30; differential quadrature element method (DQEM); discontinuity condition; large deformation; O344.3; frame; differential quadrature element method(DQEM)
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-008-0403-7

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.