Efficient Finite Element Approach to Four-Variable Power-Law Functionally Graded Plates
Abstract
:1. Introduction
2. Problem Description and Modeling
2.1. Modeling of Plates
2.2. Kinematic Field
3. Investigation of Numerical Problems
4. Conclusions
- A generalized power law variation led to different combinations of FGM constituents by means of appropriate choices of the material gradient parameters.
- Different FGM models incorporating various boundary conditions demonstrated marked bending responses for n > 5. Further, an asymptotic response was ensured when n reached a value greater than 50.
- It was witnessed that symmetric plates exhibited lower material gradient values, which, in turn, did not play a primary role in dictating the deflection parameter when the aspect ratio was varied.
- Linear axial stress variations in the x direction were noticed for isotropic and graded plates, and the trend was not obvious when n assumed the numerical value of 10. Also, the neutral plane shifted toward the bottom segment of the plate when n approached 10 and remained unchanged.
- A marked response was seen in the isotropic and graded FGM plates in the case of axial stress variations in the y direction, and this response was considerable in the bottom segment.
- The graded plate illustrated a noticeable response on par with that of the isotropic plates. The magnitudes of the tensile and compressive stresses were identical for the isotropic case, which was not true in the case of the graded plate.
- In all the cases, symmetric profiles were a better choice than other profiles for minimizing the deflection of the plate.
- As the mesh underwent refinement, the stress values tended to be elevated at the reentrant corners, which was a common observation.
- Based on the achieved results, the generalized power law containing four parameters provides structural designers with a flexible approach for multiple requirements.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Type | Parameter | Profile | Distribution |
---|---|---|---|
FGM 1 | a = 1, b = c = 0 | Classical | Metal and ceramic at the top and bottom, respectively |
FGM 2 | a = 1, b = 1, c = 2 | Symmetric | Ceramic at the top and bottom |
FGM 3 | a = 1, b = 1, c = 4 | Asymmetric | Ceramic at the top and bottom |
FGM 4 | a = 1, b = 0.5, c = 2 | Asymmetric | Ceramic at the bottom/top and a combination of metal and ceramic at the top/bottom |
FGM 5 | a = 0.8, b = 0.2, c = 3 | Asymmetric | Ceramic at the bottom/top and a combination of metal and ceramic at the top/bottom |
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Mohammed Nabi Anwarbasha, G.T.; Chakrabarti, A.; Bahrami, A.; Venkatesan, V.; Vikram, A.S.V.; Subramanian, J.; Mahesh, V. Efficient Finite Element Approach to Four-Variable Power-Law Functionally Graded Plates. Buildings 2023, 13, 2577. https://doi.org/10.3390/buildings13102577
Mohammed Nabi Anwarbasha GT, Chakrabarti A, Bahrami A, Venkatesan V, Vikram ASV, Subramanian J, Mahesh V. Efficient Finite Element Approach to Four-Variable Power-Law Functionally Graded Plates. Buildings. 2023; 13(10):2577. https://doi.org/10.3390/buildings13102577
Chicago/Turabian StyleMohammed Nabi Anwarbasha, Gulshan Taj, Anupam Chakrabarti, Alireza Bahrami, Vasugi Venkatesan, Abdhullapuram Sachidhanandam Vijay Vikram, Jeyabharathi Subramanian, and Vutukuru Mahesh. 2023. "Efficient Finite Element Approach to Four-Variable Power-Law Functionally Graded Plates" Buildings 13, no. 10: 2577. https://doi.org/10.3390/buildings13102577