Variational methods for mass scaling

• Applicant: Professor Dr.-Ing. Manfred Bischoff
• Subject Area: Applied Mechanics, Statics and Dynamics
• Term: from 2015 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 279006948

The subject of the proposed research project is the development of new variational methods for selective mass scaling in the context of explicit dynamic finite element analysis with the aim to achieve substantial speed-up for modern industrial applications. There are three fundamental innovations which we seek to develop and advance: First, a method for direct and sparse construction of consistent inverse mass matrices will be developed. Such matrices allow trivial computation of the nodal accelerations from the global force vector, i. e. no cost-intensive matrix inversion is required. Preliminary work has shown that application of selective mass scaling onto these inverse mass matrices allows to increase the critical time step by a factor of two while keeping accuracy of thecomputational results close to the ones obtained with a diagonalized mass matrix. Here, further effort is needed to extend the method for a broader range of solid finite elements and to assess accuracy, critical time step and stability of the newly obtained mass matrices via grid dispersion and eigenvalue analyses. Second, an efficient treatment of geometrically non-linear problems, unilateral contact, multi-point constraints and prescribed velocity boundary conditions together with the new mass matrices is developed. Third, variational selective mass scaling methods are extended to solid shell elements. So far only algebraic methods for selective mass scaling have been applied to this family of elements.

• DFG Programme: Research Grants