Spring Cell Equivalence of Simplex Finite Elements – Exploration of an Iterative Approach

Abstract

Natural spring cell substitutes of triangular and tetrahedral finite elements at constant strain take advantage of a formalism oriented along the element sides/edges. Two different models in use account just for the diagonal entities of either the flexibility matrix of the element or of its stiffness matrix. Both are incomplete substitutes, and defective to a degree depending on the significance of the off-diagonal parts of the element matrices. The present work discusses an iterative completeness of the substitution accounting for the discarded parts by additives to the spring members of the cell. In this connection, the iteration schemes are set up for either model at the material and at the element level, and convergence criteria are defined in terms of the spectral radii of the iteration operators. The convergence regions are confined for triangular elements, and are demonstrated with reference to a case study.