Problems with Incompressibility in Finite Element Analysis - Maitland, Kyle (2011)
Within this study, low order finite elements were applied to problems with (near) incompressible material behaviour. Solutions were obtained for creep, using transient and dynamic iterative solvers with volumetric strain enhancement algorithms, as well as a flow solution obtained using the fractional step method. To enhance creep algorithm performance, a radial return procedure was implemented. Preliminary results show that the fraction step method and dynamic iterative solver implementing dynamic relaxation provided adequate results, while other methods required improvement. Volumetric strain enhancement was insufficient to correct pressure drift when using transient analysis. The fractional step method was able to provide good results, but is sensitive to time step and initial stress field. A thorough evaluation of convergence criteria was conducted through tracking of norms and errors. The trend of norms was used to evaluate the number of iterations required to reach steady-state. The solution acquired from the method of successive approximations was improved and quality pressure plots were obtained, in contrast to the experience from the preliminary analysis. An analysis of the Barnes ice cap was conducted to verify formulation performance in the context of a real problem. Dynamic relaxation provided results closest to the measured trend and values. Master of Applied Science (MASc)