Configurational forces induced by finite-element discretization

In: Proceedings of the Estonian Academy of Sciences. Physics - Mathematics, Jg. 46 (1997) ; 1/2, S. 24-31
ISSN: 1406-0086
Zeitschriftenaufsatz / Fach: Maschinenbau
Abstract:
In standard finite-element analysis a fixed mesh is prescribed in the undeformed body and the strain energy is considered as a function of nodal displacements. Since the strain energy also depends inherently on the prescribed nodal coordinates of the mesh, any shift of a node in the undeformed body will cause a change of strain energy in the deformed state. This gives rise to the definition of configurational forces acting on the nodes in the undeformed body. The forces are represented in terms of the Eshelby stress tensor. The undeformed finite-element mesh can be modified such as to make the inner configurational forces vanish. Only the boundary nodes have to sustain configurational forces normal to the boundary, to preserve the shape of the body.