A time domain FEM approach based on implicit Greenʹs functions for non-linear dynamic analysis

The present paper describes an unconditionally stable algorithm to integrate the equations of motion in time. The standard FEM displacement model is employed to perform space discretization, and the time-marching process is carried out through an algorithm based on the Green’s function of the mechanical system in nodal co-ordinates. In the present ‘implicit Green’s function approach’ (ImGA), mechanical system Green’s functions are not explicitly computed; rather they are implicitly considered through an iterative pseudo-forces process. Under certain simplifying hypothesis, iterations are not necessary and the ImGA becomes cheaper than standard Newmark/Newton–Raphson algorithm. At the end of the paper numerical examples are presented in order to illustrate the accuracy of the present approach