Linear model reduction of large scale industrial models in elastic multibody dynamics

The description of the dynamical behavior of mechanical systems is of great interest for the development process of technical products. If arbitrary rigid body movements and additional elastic deformations have to be considered, the method of elastic multibody systems (EMBS) is used. With the floating frame of reference formulation, the movement of an elastic body is separated into a large nonlinear motion of the reference frame and small elastic deformation with respect to this reference frame. In industrial applications large finite element models with millions degrees of freedom are generated to describe the elastic behavior accurately. To enable the simulation of EMBS with large models, the degrees of freedom of the elastic body have to be reduced by appropriately projecting the nodal displacements to a subspace of lower dimension. Modern reduction methods, like Krylov subspace based moment matching or Gramian matrix based reduction, are used to find optimal projection matrices by approximating the input-output behavior. The main calculation step in modern reduction methods is the solution of large sparse symmetric sets of linear equations. In the developed reduction tool Morembs, this problem is solved by using advanced numerical libraries which perform an efficient LU-decomposition. The resulting large memory consumption is a decisive challenge during the reduction of industrial systems with millions degrees of freedom. Therefore, high performance computers or out-of-core solvers are used to reduce these systems. In this contribution, numerical solvers are compared for mechanical examples of varying size. By using advanced numerical solvers for the LU-decomposition, large models with, right now, over 10 million degrees of freedom are reduced with Krylov subspace and Gramian matrix based reduction methods.