A geometrically nonlinear finite element analysis based upon a deformed beam axis definition of curvature.

摘要

Nonlinear mechanics, and specifically geometric nonlinear mechanics, is still an emerging field. The objective of the research effort reported in this document was to develop a finite element code using a refined definition of the curvature of an inplane beam.; The general nonlinear equations of equilibrium were derived for a three dimensional body using a Total Lagrangian formulation. These equations were linearized using a Newton-Raphson technique and recurrence relations were obtained. First, these relations were specialized to obtain a load-deflection path for a single degree of freedom (bar-spring) problem. The relations were then used for an inplane two dimensional beam element. Orthogonal polynomials were used to define the shape functions of the beam element. Based upon this formulation, the internal forces due to geometric nonlinearities and the stiffness matrix were obtained. Efficient and accurate solutions of the equations of equilibrium are a major concern in nonlinear analyses of solid mechanics. Therefore, considerable attention was given to the convergence and divergence criteria that was implemented in the computer code.; The code was validated by application to a series of beam and simple frame problems subjected to large displacements. The results obtained with the code developed were compared with closed form solutions when available and to responses generated using NASTRAN models. The comparisons indicated good agreement with the published data.