Advances in dynamic relaxation techniques for non-linear finite element analysis

Traditionally the finite element technique has been applied to static and steady state problems using implicit methods. When non-linearities exist, equilibrium iterations must be performed using Newton-Raphson or quasi-Newton techniques at each load level. In the presence of complex geometry, nonlinear material behaviour and large relative sliding of material interfaces, solutions using implicit methods often become intractable. A dynamic relaxation algorithm is developed for inclusion in finite element codes. The explicit nature of the method avoids large computer memory requirements and makes possible the solution of large scale problems. The method described approaches the steady state solution with no overshoot, a problem which has plagued researchers in the past. The method is included in a general non-linear finite element code. A description of the method along with a number of new applications involving geometric and material nonlinearities are presented.