Updating component reduction bases of static and vibration modes using preconditioned iterative techniques

Abstract

Although component mode synthesis (CMS) methods for structural dynamic analysis were introduced in the 1960s, one of the current challenges is to apply the methodology in a practical design process in which (parametric) modifications are applied to the component(s). For every design change, these components need to be remodeled and their reduction bases recomputed, thereby seriously hindering the effectiveness of the CMS approach. To overcome this, we propose in this work an approach based on preconditioned iterative methods to efficiently update the reduction basis.For the updating of the static modes, we use the well known preconditioned conjugate gradient (CG) method applied in a block form and combined with the projection and reconjugation technique. The updating of vibration modes is achieved using the recent inverse-free preconditioned Krylov subspace (IFPKS) method, while techniques for extending its preconditioning and enhancing its initial guess are also proposed. Both algorithms are started from the nominal solutions and preconditioned using the factorization of the nominal stiffness matrix. As a result, no factorization of the modified stiffness matrix is needed and optimal use is made of the available information. The effectiveness of the proposed updating strategy will be illustrated by an industrial case study.