Selective mass scaling for explicit finite element analyses

Abstract

SUMMARYDue to their inherent lack of convergence problems explicit finite element techniques are widely used for analysing non-linear mechanical processes. In many such processes the energy content in the high frequency domain is small. By focusing an artificial mass scaling on this domain, the critical time step may be increased substantially without significantly affecting the low frequency behaviour. This is what we refer to as selective mass scaling. Two methods for selective mass scaling are introduced in this work. The proposed methods are based on non-diagonal mass matrices that scale down the eigenfrequencies of the system. The applicability of the methods is illustrated in two example models where the critical time step is increased by up to 30 times its original size.

Applications of Variationally Consistent Selective Mass Scaling in Explicit Dynamics

“…The eigenvalue benchmark showed better preservation of the lowest eigenfrequencies with the proposed method in comparison to algebraic mass scaling [10]. More accurate results with the proposed method are obtained for the transient benchmark.…”

“…Selective mass scaling was proposed by group of Lars Olovsson [8,10] and it aimed increasing of stable time-step for explicit integration of solid-based shells and eight-node hexahedral elements. In combination with an iterative solver for acceleration (see [9]) it proved to be efficient for some applications such as deep drawing of metal sheets and drop tests [3], dynamics of solid-shell modeled structures [4].…”

“…The original idea of paper [10] relies on following algebraic construction of scaled mass matrix of individual element m •…”

“…Initially it was proposed to include only translational rigid body modes [10]. Later implementation also included rigid body rotation [3].…”

8-Node solid-shell elements selective mass scaling for explicit dynamic analysis of layered thin-walled structures

“…The basic idea is to modify the solid-shell element mass matrix, artificially scaling down the highest structural eigenfrequencies, without significantly altering the lowest ones. A mass scaling rigorously satisfying this requirement can be obtained by summing to the mass matrix the stiffness matrix multiplied by a scaling parameter (Macek and Aubert (1995), Olovsson et al (2005)). This solution does not alter the lowest eigenfrequencies, but it is computationally burdensome, since the diagonal structure of the mass matrix is lost.…”