Construction of Customized Mass-Stiffness Pairs Using Templates

Abstract

This paper is a tutorial exposition of the template approach to the construction of customized mass-stiffness pairs for selected applications in structural dynamics. The exposition focuses on adjusting the mass matrix while a separately provided stiffness matrix is kept fixed. Two well known kinetic-energy discretization methods described in finite-element method (FEM) textbooks since the mid-1960s lead to diagonally lumped and consistent mass matrices, respectively. These two models are sufficient to cover many engineering applications. Occasionally, however, they fall short. The gap can be filled with a more general approach that relies on the use of templates. These are algebraic forms that carry free parameters. This approach is discussed in this paper using one-dimensional structural elements as examples. Templates have the virtue of producing a set of mass matrices that satisfy certain a priori constraint conditions such as symmetry, nonnegativity, invariance, and momentum conservation. In particula...