Variationally consistent mass scaling for explicit time-integration schemes of lower- and higher-order finite element methods

TL;DR

This paper introduces a variationally consistent mass scaling technique for finite element methods that increases the critical time-step size in explicit time-integration without compromising accuracy.

Contribution

The authors develop a new mass-scaling method adding a symmetric positive-definite term, ensuring stability and efficiency for both linear and nonlinear finite element analyses.

Findings

No adverse effects on spatial accuracy for linear problems.

Significant increase in critical time-step size for nonlinear problems.

Effective across multiple dimensions and element types.

Abstract

In this paper, we propose a variationally consistent technique for decreasing the maximum eigenfrequencies of structural dynamics related finite element formulations. Our approach is based on adding a symmetric positive-definite term to the mass matrix that follows from the integral of the traction jump across element boundaries. The added term is weighted by a small factor, for which we derive a suitable, and simple, element-local parameter choice. For linear problems, we show that our mass-scaling method produces no adverse effects in terms of spatial accuracy and orders of convergence. We illustrate these properties in one, two and three spatial dimension, for quadrilateral elements and triangular elements, and for up to fourth order polynomials basis functions. To extend the method to non-linear problems, we introduce a linear approximation and show that a sizeable increase in critical time-step size can be achieved while only causing minor (even beneficial) influences on the dynamic response.