Three-Dimensional Free Vibration Analyses of Preloaded Cracked Plates of Functionally Graded Materials via the MLS-Ritz Method
In this study, the moving least squares (MLS)-Ritz method, which involves combining the Ritz method with admissible functions established using the MLS approach, was used to predict the vibration frequencies of cracked functionally graded material (FGM) plates under static loading on the basis of th...
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MDPI AG
2021-12-01
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| Online Access: | https://www.mdpi.com/1996-1944/14/24/7712 |
| _version_ | 1797502709848342528 |
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| author | Chiung-Shiann Huang Hao-Ting Lee Pin-Yu Li Ming-Ju Chang |
| author_facet | Chiung-Shiann Huang Hao-Ting Lee Pin-Yu Li Ming-Ju Chang |
| author_sort | Chiung-Shiann Huang |
| collection | DOAJ |
| description | In this study, the moving least squares (MLS)-Ritz method, which involves combining the Ritz method with admissible functions established using the MLS approach, was used to predict the vibration frequencies of cracked functionally graded material (FGM) plates under static loading on the basis of the three-dimensional elasticity theory. Sets of crack functions are proposed to enrich a set of polynomial functions for constructing admissible functions that represent displacement and slope discontinuities across a crack and appropriate stress singularity behaviors near a crack front. These crack functions enhance the Ritz method in terms of its ability to identify a crack in a plate. Convergence studies of frequencies and comparisons with published results were conducted to demonstrate the correctness and accuracy of the proposed solutions. The proposed approach was also employed for accurately determining the frequencies of cantilevered and simply supported side-cracked rectangular FGM plates and cantilevered internally cracked skewed rhombic FGM plates under uniaxial normal traction. Moreover, the effects of the volume fractions of the FGM constituents, crack configurations, and traction magnitudes on the vibration frequencies of cracked FGM plates were investigated. |
| first_indexed | 2024-03-10T03:39:58Z |
| format | Article |
| id | doaj.art-51d61b3b20784597919e971f62101e6d |
| institution | Directory Open Access Journal |
| issn | 1996-1944 |
| language | English |
| last_indexed | 2024-03-10T03:39:58Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Materials |
| spelling | doaj.art-51d61b3b20784597919e971f62101e6d2023-11-23T09:21:58ZengMDPI AGMaterials1996-19442021-12-011424771210.3390/ma14247712Three-Dimensional Free Vibration Analyses of Preloaded Cracked Plates of Functionally Graded Materials via the MLS-Ritz MethodChiung-Shiann Huang0Hao-Ting Lee1Pin-Yu Li2Ming-Ju Chang3Department of Civil Engineering, National Yang Ming Chiao Tung University, 1001 Ta-Hsueh Rd., Hsinchu 30010, TaiwanDepartment of Civil Engineering, National Yang Ming Chiao Tung University, 1001 Ta-Hsueh Rd., Hsinchu 30010, TaiwanDepartment of Civil Engineering, National Yang Ming Chiao Tung University, 1001 Ta-Hsueh Rd., Hsinchu 30010, TaiwanIntelligent Autonomous Guided Vehicle RD Center, Coretronic Corp., Hsinchu 30010, TaiwanIn this study, the moving least squares (MLS)-Ritz method, which involves combining the Ritz method with admissible functions established using the MLS approach, was used to predict the vibration frequencies of cracked functionally graded material (FGM) plates under static loading on the basis of the three-dimensional elasticity theory. Sets of crack functions are proposed to enrich a set of polynomial functions for constructing admissible functions that represent displacement and slope discontinuities across a crack and appropriate stress singularity behaviors near a crack front. These crack functions enhance the Ritz method in terms of its ability to identify a crack in a plate. Convergence studies of frequencies and comparisons with published results were conducted to demonstrate the correctness and accuracy of the proposed solutions. The proposed approach was also employed for accurately determining the frequencies of cantilevered and simply supported side-cracked rectangular FGM plates and cantilevered internally cracked skewed rhombic FGM plates under uniaxial normal traction. Moreover, the effects of the volume fractions of the FGM constituents, crack configurations, and traction magnitudes on the vibration frequencies of cracked FGM plates were investigated.https://www.mdpi.com/1996-1944/14/24/7712vibrationsMLS-Ritz methodenriched basis functionscracked FGM platesthree-dimensional elasticity |
| spellingShingle | Chiung-Shiann Huang Hao-Ting Lee Pin-Yu Li Ming-Ju Chang Three-Dimensional Free Vibration Analyses of Preloaded Cracked Plates of Functionally Graded Materials via the MLS-Ritz Method Materials vibrations MLS-Ritz method enriched basis functions cracked FGM plates three-dimensional elasticity |
| title | Three-Dimensional Free Vibration Analyses of Preloaded Cracked Plates of Functionally Graded Materials via the MLS-Ritz Method |
| title_full | Three-Dimensional Free Vibration Analyses of Preloaded Cracked Plates of Functionally Graded Materials via the MLS-Ritz Method |
| title_fullStr | Three-Dimensional Free Vibration Analyses of Preloaded Cracked Plates of Functionally Graded Materials via the MLS-Ritz Method |
| title_full_unstemmed | Three-Dimensional Free Vibration Analyses of Preloaded Cracked Plates of Functionally Graded Materials via the MLS-Ritz Method |
| title_short | Three-Dimensional Free Vibration Analyses of Preloaded Cracked Plates of Functionally Graded Materials via the MLS-Ritz Method |
| title_sort | three dimensional free vibration analyses of preloaded cracked plates of functionally graded materials via the mls ritz method |
| topic | vibrations MLS-Ritz method enriched basis functions cracked FGM plates three-dimensional elasticity |
| url | https://www.mdpi.com/1996-1944/14/24/7712 |
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