Stiffness vs flexibility based triangular spring cell – analysis of performance

Abstract

Purpose The purpose of the present study is to explore the incomplete substitution of the simplex triangular finite element by either of two models: one evolving out as part of the element flexibility, and the other as part of the element stiffness. Design/methodology/approach The elastic energy stored in each of the units under stress or strain decides on stiffer and weaker responses. The pertaining Rayleigh quotient in terms of the flexibility matrices allows bounding the distance of the spring cell models to the finite element in dependence of the triangle configuration. Findings Despite a superiority of the flexibility cell concept observed in computations, the study reveals constellations of shape and stressing of the triangle that favour the stiffness concept. The latter is seen to behave stiffer than its flexibility counterpart and produces results more distant to the finite element in most cases. Research limitations/implications The difference between the stiffness and the flexibility approach to spring cells is investigated for triangular elements in dependence of the geometrical configuration under specific conditions of stressing. This suffices to refute an exclusive superiority of the flexibility concept although largely true. Practical implications The results of the investigation appear useful in deciding between the spring cell models depending on the case of a spring lattice application. Originality/value The flexibility approach to the spring cell is not widely known yet. This cell model deserves a study on performance and comparison to the different, more common stiffness cell model.