Divisor Structure of Finite Element Eigenproblems Arising From Negative and Zero Masses

摘要

This document explains why and when the divisor structures of finite element eigenproblems is non-pathological 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. Keywords: Degree of precision; Mass matrix; Quadrature.