Finite Element Method for Shearing Deformation

Abstract

The separation of an axial displacement and a rotational angle at the center of an element makes it possible to derived a new finite element method (FEM) from the ordinary one for small strain. The new FEM is non-incrementally applicable to the analysis of geometrically complicated structures consisting of deformable and undeformable shapes such as gears under concentrated twisting moment. the two-dimensional static behaviors of a cantilever beam are investigated to verify practical applicability of the new FEM. The lumped mass matrix (LM) and the consistent mass matrix (CM) are derived, to calculate the natural frequencies of the beam by use of their matrices. The results calculated by the new FEM agree well with those of the beam theories for the static and dynamic behaviors.