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Finite element analysis of electrostatic coupled systems using geometrically nonlinear mixed assumed stress finite elements
Dissertation (MEng (Mechanical))--University of Pretoria, 2007.
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| Format: | Thesis |
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University of Pretoria
2013
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| _version_ | 1867613573892538368 |
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| access_status_str | Open Access |
| author2 | Groenwold, Albert A. |
| author_browse | Groenwold, Albert A. |
| author_facet | Groenwold, Albert A. |
| collection | Thesis |
| dc_rights_str_mv | © University of Pretoria 20 |
| description | Dissertation (MEng (Mechanical))--University of Pretoria, 2007. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/24342 |
| institution | University of Pretoria (South Africa) |
| last_indexed | 2026-06-10T12:38:18.160Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2013 |
| publishDateRange | 2013 |
| publishDateSort | 2013 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/24342 Finite element analysis of electrostatic coupled systems using geometrically nonlinear mixed assumed stress finite elements Groenwold, Albert A. cheng.lai@sasol.com Kok, Schalk Lai, Zhi Cheng Coupled fields Assumed stress Geometrically nonlinear Finite element Newton’s method Mems Analytical gradient UCTD Dissertation (MEng (Mechanical))--University of Pretoria, 2007. The micro-electromechanical systems (MEMS) industry has grown incredibly fast over the past few years, due to the irresistible character and properties of MEMS. MEMS devices have been widely used in various fields such as aerospace, microelectronics, and the automobile industry. Increasing prominence is given to the development and research of MEMS; this is largely driven by the market requirements. Multi-physics coupled fields are often present in MEMS. This makes the modelling and analysis o such devices difficult and sometimes costly. The coupling between electrostatic and mechanical fields in MEMS is one of the most common and fundamental phenomena in MEMS; it is this configuration that is studied in this thesis. The following issues are addressed: 1. Due to the complexity in the structural geometry, as well as the difficulty to analyze the behaviour in the presence of coupled fields, simple analytical solutions are normally not available for MEMS. The finite element method (FEM) is therefore used to model electrostaticmechanical coupled MEMS. In this thesis, this avenue is followed. 2. In order to capture the configuration of the system accurately, with relatively little computational effort, a geometric non-linear mixed assumed stress element is developed and used in the FE analyses. It is shown that the developed geometrically non-linear mixed assumed stress element can produce an accuracy level comparable to that of the Q8 element, while the number of the degrees of freedom is that of the Q4 element. 3. Selected algorithms for solving highly non-linear coupled systems are evaluated. It is concluded that the simple, accurate and quadratic convergent Newton-Raphson algorithm remains best. To reduce the single most frustrating disadvantage of the Newton method, namely the computational cost of constructing the gradients, analytical gradients are evaluated and implemented. It is shown the CPU time is significantly reduced when the analytical gradients are used. 4. Finally, a practical engineering MEMS problem is studied. The developed geometric nonlinear mixed element is used to model the structural part of a fixed-fixed beam that experiences large axial stress due to an applied electrostatic force. The Newton method with analytical gradients is used to solve this geometrically nonlinear coupled MEMS problem. Mechanical and Aeronautical Engineering unrestricted 2013-09-06T17:16:25Z 2008-07-08 2013-09-06T17:16:25Z 2007-09-07 2007 2008-05-05 Dissertation a 2007 http://hdl.handle.net/2263/24342 http://upetd.up.ac.za/thesis/available/etd-05052008-101337/ © University of Pretoria 20 application/pdf University of Pretoria |
| spellingShingle | Coupled fields Assumed stress Geometrically nonlinear Finite element Newton’s method Mems Analytical gradient UCTD Finite element analysis of electrostatic coupled systems using geometrically nonlinear mixed assumed stress finite elements |
| title | Finite element analysis of electrostatic coupled systems using geometrically nonlinear mixed assumed stress finite elements |
| title_full | Finite element analysis of electrostatic coupled systems using geometrically nonlinear mixed assumed stress finite elements |
| title_fullStr | Finite element analysis of electrostatic coupled systems using geometrically nonlinear mixed assumed stress finite elements |
| title_full_unstemmed | Finite element analysis of electrostatic coupled systems using geometrically nonlinear mixed assumed stress finite elements |
| title_short | Finite element analysis of electrostatic coupled systems using geometrically nonlinear mixed assumed stress finite elements |
| title_sort | finite element analysis of electrostatic coupled systems using geometrically nonlinear mixed assumed stress finite elements |
| topic | Coupled fields Assumed stress Geometrically nonlinear Finite element Newton’s method Mems Analytical gradient UCTD |
| url | http://hdl.handle.net/2263/24342 http://upetd.up.ac.za/thesis/available/etd-05052008-101337/ |