Analysis of incompressible axisymmetric system using stabilized triangular meshed finite element method - Navarro, Ron Gabriel O.
Finite element procedures are important in numerical calculation of the stresses and strains attained in a system subjected to surface and body loads. Different programs are commercially available that utilize this method to more easily analyze such problems. However, the limitations arise in the capability of these programs in solving problems involving incompressible materials. Stress-oscillations and locking occur in these analyses as certain elements of matrices blow up as others disappear due to the nature of incompressible elasticity (Poisson's ratio = 0.5). This has been addressed mostly for higher-ordered meshes by the introduction of stabilizing methods that reduce the oscillations that occur. However, due to the simplicity of triangular elements, it is desirable to apply stabilizing methods to these as well. The study aimed to provide a stabilizing procedure that will greatly improve the behavior of triangular elements when used in a finite element analysis, particularly for axisymmetric systems of incompressible soil. The outcome of the study included a working program written in the Fortran language that was able to perform the algorithm. The problems were defined and the results were analyzed using Gmsh. The evaluation of the improvement caused by the stabilizing method was done by comparing the results obtained from the stabilized finite element analysis with the unstabilized finite element analysis. The study was divided into two parts. First, the displacements were compared to see if the stabilizing method caused a significant reduction in the apparent stiffening of the incompressible elements when subjected to particular meshing and boundary conditions. Second, the pressures were analyzed to determine whether there was a significant reduction of the stress oscillation that occurs in the analysis of incompressible media. The evaluations were both positive, as the stabilized finite element analysis was able to give better displacement and pressure results compared to the unstabilized finite element analysis. To verify the results of the stabilized analysis, it was compared to the results obtained from an integration of the Boussinesq's fundamental solution, and it was determined that the results were of acceptable accuracy when compared with the theoretical solution.