An intended numerical analysis of solids and structures by spring cell substitutes in place of finite elements has occasioned considerable research on the subject. This paper aims to expose two alternative concepts evolving out of Argyris’ natural approach to the simplex triangular element. One is based on an approximation of the element flexibility and the other approximates the stiffness with coincidence at the ideal conditions of complete substitution.
Characteristic of the natural formalism is the homogeneous definition of strain and stress along the sides of the triangular element. The associated elastic compliance offers itself for the transition to the spring cell. The diagonal entities are interpreted immediately as springs along the element sides, and the off-diagonal terms account for the completeness of the substitution. In addition to the flexibility concept, the spring cell is deduced alternatively from the element’s natural stiffness. The difference in the flexibility result lies in the calculatory cross-sectional areas of the elastic bar members.
From the natural point of view, the spring cell evolves out of the continuum element to the desired degree of substitution. The simplest configuration of pin-joined bars discards all geometrical and physical cross effects. The approach is attractive because of its transparent simplicity.
The difference between the stiffness and the flexibility approach to spring cells is demonstrated for triangular elements that suit the problems lying in plane stress or plane strain. More general states of stress and strain involve spring cell counterparts of the tetrahedral finite element.
Apart from plane geometries, triangular spring cells are assembled to lattice models of space structures, such as membrane shells and similar.
The natural formalism of simplex finite elements is used for deducing spring cells in two variants and exploring their properties. This is a novel approach to spring cells and an original employment of the natural concept.
