A theoretical analysis of mass scaling techniques

TL;DR

This paper provides a rigorous theoretical foundation for mass scaling techniques in finite element structural dynamics, connecting them to linear algebra to explain their effectiveness and limitations.

Contribution

It offers the first comprehensive theoretical analysis of mass scaling methods, deriving eigenvalue bounds and condition number estimates linked to established linear algebra results.

Findings

Eigenvalue bounds for mass scaling techniques

Condition number estimates related to mass scaling

Theoretical explanation of numerical observations in mass scaling

Abstract

Mass scaling is widely used in finite element models of structural dynamics for increasing the critical time step of explicit time integration methods. While the field has been flourishing over the years, it still lacks a strong theoretical basis and mostly relies on numerical experiments as the only means of assessment. This contribution thoroughly reviews existing methods and connects them to established linear algebra results to derive rigorous eigenvalue bounds and condition number estimates. Our results cover some of the most successful mass scaling techniques, unraveling for the first time well-known numerical observations.