Modélisation numérique des solides par éléments finis volumiques basés sur le concept SFR (Space Fiber Rotation)

Abstract

The main objective of this thesis is to develop a new concept to enrich the 3D low-order finite elements. The major application of proposed models is the numerical modeling of solid mechanics and three-dimensional structures problems. In this context, in a first part, a new family of solid finite elements, with three translational and three rotational degrees of freedom per node has been presented. This family, named SFR, is based upon SFR (Space Fiber Rotation) concept. Using the rotation of a material fiber in 3D space, the SFR approach allows to get a more accurate displacement field, which becomes quadratic without changing the number of nodes of the linear elements. Based upon the SFR concept, eight-node brick element SFR8 and six-node wedge element SFR6 are proposed. In addition to that, a non-conforming version of SFR8, named SFR8I, is developed to overcome the Poisson’s ratio locking. The SFR8I formulation includes three incompatible modes in the natural space of the element that are then eliminated by a static condensation technique. A reduced integration technique is used to integrate the SFR solid finite elements in order to avoid locking effects and to achieve an attractive, low-cost formulation. All.....