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

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.

Quadrature element analysis of planar frameworks

“…Furthermore, it is also applicable to frameworks subject to complicated loadings. It was reported that the strong form QEM has been applied to large deformation analysis of frameworks under either static or dynamic loads [8,9]. The extension of the present weak form quadrature element technique to large deformation analysis of planar frameworks is underway and will be reported in an upcoming paper.…”

“…The strong form QEM [5] which also appeared in the name of the differential QEM [6,7] has been applied to planar frame analysis. Recently, the strong form quadrature elements have been used to deal with large deformation of planar frameworks under static or dynamic loads [8,9]. In the strong form quadrature element analysis of frames, derivatives in the governing differential equations are approximated using differential quadrature analog and all continuity conditions at framework joints are enforced.…”