Eigenvalues and Stable Time Steps for the Uniform Strain Hexahedron and Quadrilateral

Abstract

Simple formulas for bounding the maximum eigenvalues or computing them exactly are obtained for the uniform strain eight-node hexahedron and the four-node quadrilateral. The development is based on a novel technique that reduces the size of the eigenproblem to where it can be managed analytically. These formulas are useful for explicit time integration applications since they provide conserative estimates of stable time steps. The eigenvalue analysis is limited to linear, isotropic materials but the results are also useful in nonlinear problems since the linerized material properties may be used.