Variationally consistent inertia templates for speed-up and customization in explicit dynamics

Abstract

The present work deals with innovative numerical methods for the computer simulation of dynamic problems with explicit time integration. The proposed methods aim to increase accuracy as well as reduce the calculation effort. The basis for the development are variationally consistent inertia templates. The term ‘inertia template‘ covers both alternatives to the commonly used diagonal mass matrices and novel reciprocal mass matrices. Reciprocal mass matrices result directly from the variational formulation and are sparse, assemblable, inverse mass matrices, which allow a trivial computation of the acceleration from Newton‘s second law. In the first part of the work, the focus is on the variational consistency of reciprocal mass matrices and the therewith associated minimum requirements on the ansatz spaces. In the second part, the approach is systematically exploited not only to increase the critical time step but also to customize the inertia template to specific needs, like improved low-frequency accuracy. The third part aims at further development and investigation of reciprocal mass matrices to increase their usability for practical applications. The focus is therefore on the development of an efficient time step estimate and the treatment of contact.