Beam and Truss Element for Non-Linear Geometric Analysis

Abstract

The present paper investigates possible improvements to the performances of beam finite element with curvature correction where large slopes as well as large displacement are involved. The displacement field of the beam element is based on simple strain functions satisfying the requirement of exact representation of curvature. The truss element is introduced with the current cross sectional and the current length instead of initial area and initial length in large displacement solution. The finite element method is used in conjunction with linearised incrementation and the Newton-Raphson iterative technique. The two basic formulations to problem involving geometric non-linear, Eulerian and Lagrangian are also discussed. The present elements offer significant advantages over existing stiffness-based elements. Consequently, fewer elements are needed to yield results of comparable accuracy. This is demonstrated with the analysis of several simple example structures by comparing the results to those of stiffness based elements and analytical solution.