Rigid body considerations for non?linear finite element analysis
Journal
International Journal for Numerical Methods in Engineering
Journal Volume
33
Journal Issue
8
Pages
1597-1610
Date Issued
1992
Author(s)
Abstract
Abstract The purpose of the paper is to demonstrate how the concept of rigid body motions can be employed to derive the external stiffness matrix for an initially stressed finite element. Such a matrix is as important as the elastic and geometric stiffness matrices. It can be used not only in an eigenvalue analysis for testing the zero energy modes of a finite element under initial loadings, but for calculating the element forces in a step‐by‐step non‐linear analysis. The two‐dimensional beam element presented in this paper serves as a vehicle to demonstrate the concept involved. The principle of virtual work in its updated Lagrangian form has been adopted as the method of formulation. Several examples are provided to illustrate the adequacy of the present approach.
SDGs
Type
journal article