Towards optimal mixed finite elements for general shell structures
Thesis (Sc.D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1999.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2005
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| Online Access: | http://hdl.handle.net/1721.1/9416 |
| _version_ | 1826202043273969664 |
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| author | Iosilevich, Alexander G |
| author2 | Klaus-Jürgen Bathe. |
| author_facet | Klaus-Jürgen Bathe. Iosilevich, Alexander G |
| author_sort | Iosilevich, Alexander G |
| collection | MIT |
| description | Thesis (Sc.D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1999. |
| first_indexed | 2024-09-23T12:01:17Z |
| format | Thesis |
| id | mit-1721.1/9416 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T12:01:17Z |
| publishDate | 2005 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/94162020-03-30T22:10:40Z Towards optimal mixed finite elements for general shell structures Iosilevich, Alexander G Klaus-Jürgen Bathe. Massachusetts Institute of Technology. Department of Mechanical Engineering Mechanical Engineering Thesis (Sc.D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1999. Includes bibliographical references (leaves 194-199). Optimal finite elements are available for many engineering applications, such as incompressible media, beam and plate bending problems. However, no existing general shell elements have been shown to satisfy the mathematical conditions of optimality in the analysis of shell structures. The objective in this thesis is to work towards optimal shell elements that possess properties of uniform convergence independent of the problem solved. We develop a thorough numerical convergence study methodology for bending dominated and membrane-dominated shells and apply it to the family of quadrilateral MITC (Mixed-Interpolated Tensorial Components) shell elements proposed by Bathe, Dvorkin and Bucalem. The study demonstrates the superior performance of these elements. We also develop a new simple and effective triangular mixed-interpolated shell element and demonstrate the element reliability. Deriving the relation between the MITC approach and the classical constrained minimization problem leads to the conclusion that the optimal shell elements must satisfy the relevant inf-sup condition in the analysis of bending-dominated shells. In practice, this condition is virtually impossible to check analytically, especially when general geometries and/or distorted meshes are considered. Using appropriate bounds, we develop a new numerical inf-sup test aimed to indicate if a particular finite element discretization satisfies this fundamental condition. While the displacement based elements, of course, fail the test, the quadrilateral and the new triangular MITC elements pass the test. by Alexander G. Iosilevich. Sc.D. 2005-08-22T18:11:59Z 2005-08-22T18:11:59Z 1999 1999 Thesis http://hdl.handle.net/1721.1/9416 43303740 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 199 leaves 10590919 bytes 10590675 bytes application/pdf application/pdf application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mechanical Engineering Iosilevich, Alexander G Towards optimal mixed finite elements for general shell structures |
| title | Towards optimal mixed finite elements for general shell structures |
| title_full | Towards optimal mixed finite elements for general shell structures |
| title_fullStr | Towards optimal mixed finite elements for general shell structures |
| title_full_unstemmed | Towards optimal mixed finite elements for general shell structures |
| title_short | Towards optimal mixed finite elements for general shell structures |
| title_sort | towards optimal mixed finite elements for general shell structures |
| topic | Mechanical Engineering |
| url | http://hdl.handle.net/1721.1/9416 |
| work_keys_str_mv | AT iosilevichalexanderg towardsoptimalmixedfiniteelementsforgeneralshellstructures |