A study of the finite element method, with reference to the Adina finite element package

Abstract

This dissertation presents a theoretical and practical study of the finite element met hod using the ADINA finite element program. The package was applied to the analysis of three different problems, namely: A nonlinear static analysis; a free vibration analysis and a themal analysis. The first two analyses were supplemented with experimental results for the purpose of comparison whilst the last was compared with a closed form analytic solution. The first problem consisted of a materially nonlinear static analysis of a cast iron sheave wheel. The sheave was physically loaded with a rope up to failure of the rim. Strain gauges monitored strain at twenty-four locations. In order to simulate the nonlinear properties of the east iron, a Drucker Prager yield criterion was utilised and accordingly, a subroutine describing the elasto-plastic constitutive laws was interfaced with the ADINA package. Owing to self-imposed limitations on computer resources, the sheave was modelled as a two-dimensional body. The results correlated well in the linear region but deviated when plastic deformation was pronounced. It is suspected that this was due to a combination of approximations in modelling the geometry and the material. In the free vibration analysis, a simple portal frame was built in order to compare its natural mode shapes and frequencies with those obtained from a finite element simulation. This comparison proved satisfactory. The thermal analysis was executed primarily to test and gain first hand experience with the ADINAT package. A two-dimensional flat plate subjected to a sinusoidal temperature load was simulated. Although the application was simple, the accuracy of the FEM results confirmed that the package was operating correctly. In all these exercises ADINA package performed satisfactorily. Experience show that the programme was not user-friendly, however this is not considered a drawback in a research environment.