Area wise application of contact constraints in reduced mechanical systems

Solid joint contact is characterized by nonlinear contact forces inside the joint. In case of gaping no contact forces are acting on the involved surfaces while penetration is avoided by the application of proper contact forces. In the common Finite Element (FE) method such forces are typically applied at nodal degree of freedom (DOF) inside the joint. This can be done using unilateral constraint equations or nonlinear penalty stiffness's. In the frame work of modally reduced jointed structures just the penalty stiffness approach can be directly applied. In that case, the contact forces are computed based on the joint state and projected into the modal space. The problem is reduced to the question whether the mode base is capable to describe the relative displacements of the involved joint surfaces. This paper is a contribution to the more challenging problem when the contact is implemented using unilateral constraint equations. In that case the FE approach will not work in general because the number of nodal constraint equation will be higher than the number considered modes (DOF) which leads to on over constraint system. In order to overcome that problem an area wise application of the unilateral constraint equations is suggested instead of the common node wise one. After an introduction the presented idea will be outlined followed by a static example. The contribution ends with a discussion of the result and some conclusions.