Conforming shear-locking-free four-node rectangular finite element of moderately thick plate
An outline of the modified Mindlin plate theory, which deals with bending deflection as a single variable, is presented. Shear deflection and cross-section rotation angles are functions of bending deflection. A new four-node rectangular finite element of moderately thick plate is formulated by utili...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2016-12-01
|
| Series: | Journal of the Mechanical Behavior of Materials |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/jmbm-2017-0001 |
| _version_ | 1819123877136039936 |
|---|---|
| author | Senjanović Ivo Tomić Marko Rudan Smiljko Hadžić Neven |
| author_facet | Senjanović Ivo Tomić Marko Rudan Smiljko Hadžić Neven |
| author_sort | Senjanović Ivo |
| collection | DOAJ |
| description | An outline of the modified Mindlin plate theory, which deals with bending deflection as a single variable, is presented. Shear deflection and cross-section rotation angles are functions of bending deflection. A new four-node rectangular finite element of moderately thick plate is formulated by utilizing the modified Mindlin theory. Shape functions of total (bending+shear) deflections are defined as a product of the Timshenko beam shape functions in the plate longitudinal and transversal direction. The bending and shear stiffness matrices, and translational and rotary mass matrices are specified. In this way conforming and shear-locking-free finite element is obtained. Numerical examples of plate vibration analysis, performed for various combinations of boundary conditions, show high level of accuracy and monotonic convergence of natural frequencies to analytical values. The new finite element is superior to some sophisticated finite elements incorporated in commercial software. |
| first_indexed | 2024-12-22T07:15:19Z |
| format | Article |
| id | doaj.art-6a6e11cbf4dc47fa8d6b35816d5049f0 |
| institution | Directory Open Access Journal |
| issn | 0334-8938 2191-0243 |
| language | English |
| last_indexed | 2024-12-22T07:15:19Z |
| publishDate | 2016-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Journal of the Mechanical Behavior of Materials |
| spelling | doaj.art-6a6e11cbf4dc47fa8d6b35816d5049f02022-12-21T18:34:24ZengDe GruyterJournal of the Mechanical Behavior of Materials0334-89382191-02432016-12-01255-614115210.1515/jmbm-2017-0001Conforming shear-locking-free four-node rectangular finite element of moderately thick plateSenjanović Ivo0Tomić Marko1Rudan Smiljko2Hadžić Neven3University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, Zagreb, CroatiaUniversity of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, Zagreb, CroatiaUniversity of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, Zagreb, CroatiaUniversity of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, Zagreb, CroatiaAn outline of the modified Mindlin plate theory, which deals with bending deflection as a single variable, is presented. Shear deflection and cross-section rotation angles are functions of bending deflection. A new four-node rectangular finite element of moderately thick plate is formulated by utilizing the modified Mindlin theory. Shape functions of total (bending+shear) deflections are defined as a product of the Timshenko beam shape functions in the plate longitudinal and transversal direction. The bending and shear stiffness matrices, and translational and rotary mass matrices are specified. In this way conforming and shear-locking-free finite element is obtained. Numerical examples of plate vibration analysis, performed for various combinations of boundary conditions, show high level of accuracy and monotonic convergence of natural frequencies to analytical values. The new finite element is superior to some sophisticated finite elements incorporated in commercial software.https://doi.org/10.1515/jmbm-2017-0001conformityfinite element formulationmodified mindlin plate theoryshear-locking |
| spellingShingle | Senjanović Ivo Tomić Marko Rudan Smiljko Hadžić Neven Conforming shear-locking-free four-node rectangular finite element of moderately thick plate Journal of the Mechanical Behavior of Materials conformity finite element formulation modified mindlin plate theory shear-locking |
| title | Conforming shear-locking-free four-node rectangular finite element of moderately thick plate |
| title_full | Conforming shear-locking-free four-node rectangular finite element of moderately thick plate |
| title_fullStr | Conforming shear-locking-free four-node rectangular finite element of moderately thick plate |
| title_full_unstemmed | Conforming shear-locking-free four-node rectangular finite element of moderately thick plate |
| title_short | Conforming shear-locking-free four-node rectangular finite element of moderately thick plate |
| title_sort | conforming shear locking free four node rectangular finite element of moderately thick plate |
| topic | conformity finite element formulation modified mindlin plate theory shear-locking |
| url | https://doi.org/10.1515/jmbm-2017-0001 |
| work_keys_str_mv | AT senjanovicivo conformingshearlockingfreefournoderectangularfiniteelementofmoderatelythickplate AT tomicmarko conformingshearlockingfreefournoderectangularfiniteelementofmoderatelythickplate AT rudansmiljko conformingshearlockingfreefournoderectangularfiniteelementofmoderatelythickplate AT hadzicneven conformingshearlockingfreefournoderectangularfiniteelementofmoderatelythickplate |