‘Velocity’ Finite Element Method for Dynamic Problem

‘Velocity’ finite element method for dynamic problem

After analysing the essential features of successive integration method taking displacement as variable by N. M. Newmark and E. L. Wilson et al, this paper presents a Velocity Element Method, taking velocity as variable for the solution of the initial value problem.A simplified scheme is offered for the non-damping system, and the stability is also discussed. Owing to the fact that this simplified scheme for non-damping and apparent static damping is explicit in form, it is unnecessary to solve the algebraic system of equations at every time interval, consequently the amount of computation is greatly reduced. For non-linear dynamic problems, this scheme may be used to obtain fairly good initial values for iteration.An extended form of elocity Element is presented for the arbitrary damping system. For the non-linear cases, the incremental Velocity iteration scheme is adopted and its convergence proved. Some discussions have been given on artificial damping and the effect of the parameter.Finally, the results of numerical calculatio of some typical problem are given in the appendix.