Consideration of nonlinear multipoint constraints in finite element analyses based on a master-slave elimination scheme operating at the global level

A method to consider nonlinear multipoint constraints in finite element analysis based on a master-slave elimination scheme operating at the global level is presented. We focus on systems with nonlinear constraints in which the number of constraints is of the same order of magnitude as the number of degrees of freedom. Therefore, we rely on the master-slave elimination which gives us the huge benefit of drastically reducing the problem size. In the literature the presented master-slave elimination schemes for linear constraints are based on the manipulation of the system equations (global level), but the master-slave elimination schemes for nonlinear constraints are based on manipulation of the element formulation (local level). In contrast to that we use a global approach for which the nonlinear constraints are applied directly on the system equations in analogy to linear constraints. Thus, the method is independent of the underlying element formulation and the type of constraints which makes it more flexible.