Friction finite elements for numerical analysis of piping systems: Theory and applications

Contact problems are often encounteted in civil engineering applications and specially in nuclear piping systems: pipe whip, impact on supports in case of seismic analysis, non linear calculations of thermal expansions, etc... Most of the time, the geometrical non linearity of the contact problems is coupled with a material non linearity due to the nature of the contact associated with the state of the surfaces in contact. For the sake of simplicity, the classical Coulomb friction model has been assumed, which leads to frictional sliding when the tangential force modulus reaches a fraction of the normal compression force. In order to account for such a model in a beam type finite element program, a special element has been developped. It is formulated in terms of generalized stresses: axial forces and shear forces in two orthogonal directions. Below the sliding threshold, the element has only axial and shear elastic rigidities in compression. When the sliding threshold is reached, a perfectly plastic behavior is assumed. The element can be used together with unilateral conditions for example in order to calculate the pipe whip impact on a structure. This element has been implemented in the piping analysis TEDEL program of the CEASEMT finite element system. In the second part of this paper, simple tests are presented. (orig.)