Non linear dynamic analysis of solids using linear triangles and tetrahedra

Abstract

The basis of the FIC method is the satisfaction of the standard equations for balance of momentum (equilibrium of forces) and mass conservation in a domain of finite size and retaining higher order terms in the Taylor expansions used to express the different terms of the differential equations over the balance domain. The modified differential equations contain additional terms which introduce the necessary stability in the equations to overcome the volumetric locking problem in incompressible situations. The same ideas are applied in this paper to derive a stabilized formulation for non linear dynamic finite element analysis of quasi incompressible and fully-incompressible solids using linear triangles and tetrahedra. Examples of application of the new stabilized formulation to the semi-implicit and explicit non linear transient dynamic analysis of an impact problem and a bulk forming process are presented.