Zero and Negative Masses in Finite Element Vibration and Transient Analysis.
Abstract
Mass matrix lumping by quadrature is considered. Accuracy requirements seem to dictate the use of zero negative masses for multi-dimensional higher-order elements. It is shown that the zero and/or negative masses do not destroy the essential algebraic properties of the discrete eigen problems, in spite of the negative or infinite eigenvalues which may result. Explicit transient methods require positive definite lumping which, for some elements, may only be achieved by sacrificing accuracy to avoid the negative or zero masses that would render the lumping indefinite. An implicit-explicit time integration method based on quadratic triangles with optimal lumping is devised, analysed, and tested. It treats the nodes with nonzero masses explicitly and the nodes with zero masses implicitly. Analysis and numerical tests show that this formulation is optimally accurate and less costly than a similar method with nonzero masses, based on optimally lumped biquadratic rectangles. The method is also found to be substantially more accurate than the fully explicit method based on lumping the triangular elements in an ad-hoc fashion to retain non-zero masses. Keywords: Mass matrix; Numerical quadrature; Stability; Vibration modes. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1986
- Accession Number
- ADA167489
Entities
People
- David S. Malkus
- Michael E. Plesha
Organizations
- University of Wisconsin–Madison