An Explicit Fem Formulation of the 2-D Triangular Element for Finite Strains

Abstract

Not by means of mathematical expansions, but on the basis of a physical decomposition of its total freedom into the parameters of position as a rigid and those of deformation, an explicit discretization is developed for the 2-D triangular element with large displacements. While the material is assumed elastic even for finite strains, any geometrically nonlinear effects are taken into account, systematically and rigorously.

An Explicit Geometrically-Nonlinear Discretization of the 3-D Tetrahedral Element

“…We here develop them under the geometrical decompositions. First, by the use of (6), we re-decompose the independent displacements into the {x, y, z}directions o{x}(e)=[T({x})](e)o{x}(e) By employing me = 2e, rc= 2ec, y= 2eas the alternative shear components, we define deformation of (e) by ice)={eu, e, ecc, tnc, rcs, ran} (16) This deformation is in a one-to-one correspondence to shape g().…”