DQEM for large deformation analysis of structures with discontinuity conditions and initial displacements

A nonlinear mathematical model of the large deformation analysis of beams with discontinuity conditions and initial displacements is first formulized by the arc coordinates. The differential quadrature element method (DQEM) is applied to discretize the nonlinear mathematical model, and an effective method of applying DQEM to analyse the large deformation of structures with discontinuity conditions of multivariables is presented. A set of DQEM discretization equations are obtained. Then, the Newton–Raphson method is used to solve the system of nonlinear algebraic equations. As applications, some numerical examples in engineering are presented, which include the large deformation analysis of beams, frames, piles with elastic joints. The obtained results are compared with those in the existing literatures. The numerical results show that the model and the method presented in this paper may be widely applied to solve the problems of large deformation of structures with discontinuity conditions in engineering; also the method has the advantages of little amount in computation, good stability and convergence and so on.