<p> Mixed transitional finite elements, which enable the simultaneous use of the three-node triangular mixed and eight-node isoparametric displacement finite elements, are developed to reduce the amount of computer storage required in the mixed finite element method. Numerical testing of the simultaneous use of the above mixed, mixed transitional and displacement finite elements are also carried out to investigate numerical instability, orientation problems and convergence in the energy sense. The examples of a plane stress cantilever subjected to parabolically varying end shear and a plane strain, square plate with a circular hole in the middle are analyzed and the results obtained are found to be in very good agreement with those reported in the literature.</p> <p> The three-element scheme above is then applied to problems in linear elastic fracture mechanics. The energy release rate approach using the direct derivative method is incorporated to compute the Mode I stress intensity factor KI. Two plane stress isotropic rectangular plates with symmetric edge cracks and a central crack, respectively, and a plane stress orthotropic square plate with a central crack are analyzed. The stress intensity factors obtained are in excellent agreement with the available numerical results, and with significant reduction in computer storage requirements compared to that of the mixed finite element method alone.</p> <p> Mixed mode linear elastic fracture problems are also considered. In this case, Ishikawa's scheme of decomposing the near crack tip stress and displacement fields is used along with the direct derivative method to compute the mixed mode stress intensity factors KI and KII. The stress intensity factors KI and KII obtained for a deep cantilever with an edge crack subjected to end shear are within 0.62 and 3.74 percent of the numerical results reported in the literature. The prediction of the branching angles for crack extensions are examined and the criterion of maximum energy release rate is used along with Ishikawa's scheme to calculate the angles of crack branching for a plane stress square plate with an oblique crack, subject to uniaxial tension. Good agreement with the results using the maximum stress criterion is observed.</p> / Thesis / Master of Engineering (MEngr)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/18525 |
| Date | 06 1900 |
| Creators | Leung, P. T. Patrick |
| Contributors | Mirza, Farooque A., Civil Engineering and Engineering Mechanics |
| Source Sets | McMaster University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis |
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