Hierarchical finite elements for stress concentration and stress singularity problems

• Main Author: Sidhu, Harvinder S., 1968-
• Other Authors: Memorial University of Newfoundland. Faculty of Engineering and Applied Science
• Format: Thesis
• Language: English
• Published: 1995
• Subjects: Finite element method; Singularities (Mathematics); Stress concentration; Newfoundland studies; University of Newfoundland
• Online Access: http://collections.mun.ca/cdm/ref/collection/theses3/id/205475

Thesis (M.Eng.)--Memorial University of Newfoundland, 1996. Engineering and Applied Science Bibliography: leaves 87-89 The p-version finite element method offers a distinct advantage of savings in computational time and effort in comparison with the conventional, h-version finite element method. The h-version uses low order elements and convergence studies are done by successive refinements of the mesh that imply analyzing the problem afresh. In contrast, the p-version uses a fixed discretization of the domain and higher order elements are successively employed during convergence studies. The computational advantage results from the use of hierarchical shape functions, coarse meshes and faster rates of convergence with decreased number of degrees of freedom. Consequently, the use of hierarchical finite elements can be especially advantageous for stress concentration and stress singularity problems that require very refined meshes in the h-version. -- The accuracy of hierarchical finite elements is demonstrated with the use of coarse meshes for beam and T-plate weld joint problems. A 2D "enriched hierarchical" finite element is developed for stress intensity factor evaluation that embodies the inverse square root stress singularity by including in its formulation the stress intensity factors as additional degrees of freedom. Stress intensity factors for cracked specimens are numerically evaluated quite accurately using very coarse meshes involving fewer degrees of freedom in comparison with conventional analyses. This concept is then extended to 3D crack problems and favourable results are obtained.