Divisor structure of finite element eigenproblems arising from negative and zero masses
type: Item
instance of: scholarly article
title: Divisor structure of finite element eigenproblems arising from negative and zero masses
zbMATH Open document ID: 0618.73086
DOI: 10.1016/0045-7825(88)90007-2
author: David S. Malkus
author: Xianjun Qiu
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1988-01-01T00:00:00Z
review text: This note explains why and when the divisor structure of finite element eigenproblems is nonpathological even when negative and/or zero masses result from lumping schemes. The only case of concern is when the stiffness matrix is singular due to rigid-body modes, as happens, for example, with single elements. It is found that there are no pathologies if the lumping scheme adequately reproduces the kinetic energy of rigid- body motion.
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 4003671
zbMATH Keywords: divisor structure
zbMATH Keywords: finite element eigenproblems
zbMATH Keywords: non-pathological
zbMATH Keywords: zero masses
zbMATH Keywords: lumping
zbMATH Keywords: stiffness matrix
zbMATH Keywords: singular
zbMATH Keywords: right-body modes
zbMATH Keywords: kinetic energy
zbMATH Keywords: optimal nodal quadrature rule
zbMATH Keywords: higher-order elements
zbMATH Keywords: negative masses
MaRDI profile type: Publication
full work available at URL: 0045-7825(88)90007-2
OpenAlex ID: W1996452881
cites work: Zero and negative masses in finite element vibration and transient analysis
cites work: Eigenproblems associated with the discrete LBB condition for incompressible finite elements
description: scientific article; zbMATH DE number 4003671