A Strong Form Meshless Method for the Solution of FGM Plates
Laminated composite structures suffer from failure because of concentrations of gradient fields on interfaces due to discontinuity of material properties. The rapid development of material science enables designers to replace classical laminated plate elements in aerospace structures with more advan...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-08-01
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| Series: | Aerospace |
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| Online Access: | https://www.mdpi.com/2226-4310/9/8/425 |
| _version_ | 1797411846413615104 |
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| author | Ladislav Sator Vladimir Sladek Jan Sladek |
| author_facet | Ladislav Sator Vladimir Sladek Jan Sladek |
| author_sort | Ladislav Sator |
| collection | DOAJ |
| description | Laminated composite structures suffer from failure because of concentrations of gradient fields on interfaces due to discontinuity of material properties. The rapid development of material science enables designers to replace classical laminated plate elements in aerospace structures with more advanced ones made of functionally graded materials (FGM), which are microscopic composite materials with continuous variation of material coefficients according to the contents of their micro-constituents. Utilization of FGM eliminates the inconvenience of laminated structures but gives rise to substantial changes in structural design This paper deals with the presentation of a strong formulation meshless method for the solution of FGM composite plates. Recall that the fourth-order derivatives of deflections are involved in the governing equations for plate structures. However, the high-order derivatives of field variables in partial differential equations (PDE) lead to increasing inaccuracy of approximations. For that reason, the decomposition of the high-order governing equations into the second-order PDE is proposed. For the spatial approximation of field variables, the meshless moving least square (MLS) approximation technique is employed. The reliability (numerical stability, convergence, and accuracy) as well as computational efficiency of the developed method is illustrated by several numerical investigations of the response of FGM plates with the transversal gradation of material coefficients under stationary and/or transient mechanical and thermal loadings. |
| first_indexed | 2024-03-09T04:52:12Z |
| format | Article |
| id | doaj.art-a3a09c72693746e18f8cff5e3901ece3 |
| institution | Directory Open Access Journal |
| issn | 2226-4310 |
| language | English |
| last_indexed | 2024-03-09T04:52:12Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Aerospace |
| spelling | doaj.art-a3a09c72693746e18f8cff5e3901ece32023-12-03T13:09:39ZengMDPI AGAerospace2226-43102022-08-019842510.3390/aerospace9080425A Strong Form Meshless Method for the Solution of FGM PlatesLadislav Sator0Vladimir Sladek1Jan Sladek2Institute of Construction and Architecture, Slovak Academy of Sciences, Dubravska cesta 9, 845 03 Bratislava, SlovakiaInstitute of Construction and Architecture, Slovak Academy of Sciences, Dubravska cesta 9, 845 03 Bratislava, SlovakiaInstitute of Construction and Architecture, Slovak Academy of Sciences, Dubravska cesta 9, 845 03 Bratislava, SlovakiaLaminated composite structures suffer from failure because of concentrations of gradient fields on interfaces due to discontinuity of material properties. The rapid development of material science enables designers to replace classical laminated plate elements in aerospace structures with more advanced ones made of functionally graded materials (FGM), which are microscopic composite materials with continuous variation of material coefficients according to the contents of their micro-constituents. Utilization of FGM eliminates the inconvenience of laminated structures but gives rise to substantial changes in structural design This paper deals with the presentation of a strong formulation meshless method for the solution of FGM composite plates. Recall that the fourth-order derivatives of deflections are involved in the governing equations for plate structures. However, the high-order derivatives of field variables in partial differential equations (PDE) lead to increasing inaccuracy of approximations. For that reason, the decomposition of the high-order governing equations into the second-order PDE is proposed. For the spatial approximation of field variables, the meshless moving least square (MLS) approximation technique is employed. The reliability (numerical stability, convergence, and accuracy) as well as computational efficiency of the developed method is illustrated by several numerical investigations of the response of FGM plates with the transversal gradation of material coefficients under stationary and/or transient mechanical and thermal loadings.https://www.mdpi.com/2226-4310/9/8/425strong formFGM platesmeshless methodmoving least square approximationstatic and transient loadelasticity |
| spellingShingle | Ladislav Sator Vladimir Sladek Jan Sladek A Strong Form Meshless Method for the Solution of FGM Plates Aerospace strong form FGM plates meshless method moving least square approximation static and transient load elasticity |
| title | A Strong Form Meshless Method for the Solution of FGM Plates |
| title_full | A Strong Form Meshless Method for the Solution of FGM Plates |
| title_fullStr | A Strong Form Meshless Method for the Solution of FGM Plates |
| title_full_unstemmed | A Strong Form Meshless Method for the Solution of FGM Plates |
| title_short | A Strong Form Meshless Method for the Solution of FGM Plates |
| title_sort | strong form meshless method for the solution of fgm plates |
| topic | strong form FGM plates meshless method moving least square approximation static and transient load elasticity |
| url | https://www.mdpi.com/2226-4310/9/8/425 |
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