Numerical and analytical stress analysis for a FGM beam

Hassan S. Hedia; Majid A. Almas; Hassan M. Attar; Mohamed H. Hedia; Elamir S. Gadelmawla; Mona A. Soliman

doi:10.1515/mt-2024-0450

Article

Numerical and analytical stress analysis for a FGM beam

Hassan S. Hedia
Prof. Dr. Hassan S. Hedia, born in 1959, is Professor of Materials and Solid Mechanics at King Abdulaziz University, Jeddah Saudi Arabia. He received his BSc 1981 in the Mechanical Engineering Dept., Cairo University, Egypt, his MSc 1989 in Production Engineering, at Mansoura University, Egypt, and his PhD in 1996 in the Mechanical Engineering Dept., Leeds University, UK and Mansoura University, Egypt under the channel system. His field of interest is advanced materials, fracture mechanics, stress analysis optimum design, mechanics of materials and biomechanics. He has at least 85 papers and his h-index is 20.
, Majid A. Almas
Majid A. Almas, Assistant Professor, Head of the Department of Marine Engineering, 2020 – current. King Abdulaziz University. Carry out research in the Maritime field. Increase awareness in regards to the Maritime sector. Teach students in order for them to become worthy seafarers to serve our country.
, Hassan M. Attar
Hassan M. Attar a marine engineer with a PhD in marine engineering from Newcastle University, UK, snice 2021 an MSc in marine engineering, and a BSc in marine engineering. I am currently an assistant professor at King Abdul-Aziz University, Faculty of Maritime Studies Department of Marine Engineering where I teach courses in marine engineering and conduct research in the areas of renewable energy, biofuels, marine diesel engines, and the sustainability. I am passionate about my work, and I believe that renewable energy has the potential to make a significant contribution to the development of sustainable energy systems. I am committed to continuing my research and teaching activities, and to working with colleagues and industry partners to develop innovative solutions for the maritime sector.
, Mohamed H. Hedia
Mohamed H. Hedia, born in 1992, is Assistance Lecturer, Department of Structural Engineering, Mansoura University, Egypt. He is currently pursuing a Ph.D. at the University of Nebraska at Lincoln, USA. With a master’s degree in structural engineering from Mansoura University, Egypt. Mr. Hedia’s research interests encompass a range of areas within structural engineering, including the strength of materials, finite element analysis, and behavior of structural elements, bridge engineering, and material science. His expertise and passion lie in exploring these subjects to contribute to the advancement of the field.
, Elamir S. Gadelmawla and Mona A. Soliman
Dr. Mona A. Soliman born in 1974, is assistant professor of Mechanical design engineering, Delta higher institute for engineering and technology, Talkha, Egypt. She graduated B.Sc., M.Sc. & PhD from the production engineering and mechanical design department of Mansoura University at 1997, 2005, and 2015 respectively. She published many papers in different mechanical engineering fields. Her researches interested in fracture mechanics and finite element analysis such as analysis of composite material leaf spring, analysis of FGM material and its application in mechanical component, vibration analysis of car suspension system, fatigue life estimation, crack growth & arresting methods.

Published/Copyright: April 14, 2025

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From the journal Materials Testing Volume 67 Issue 6

Abstract

This study investigates the importance of material selection and the material index in FGM beam stress analysis. The stress distribution in functionally graded beams (FGMBs) using, FEA, numerical methods are investigated. Three different material distribution functions are examined, power law, modified symmetric power law, and sigmoid. The maximum equivalent and shear stresses occurs for each function and at different values of the material index (k) are considered. Overall, the study emphasizes the importance of material distribution function selection and material index values in determining the stress distribution and behavior of FGM beams. The study uses ANSYS 2020 for numerical analysis. The material properties of aluminum and alumina are used for the FGM beam. The results indicate that power law functions has a higher stress compared to modified symmetric power law. The best formula can be used in making FGM is modified symmetric power law as it produce minimum equivalent and shear stresses in comparison with the other formulas. The value of the material index (k) significantly affects the magnitude of both shear and equivalent stress for power law, modified symmetric power law only. The value of the material index (k) significantly influences the magnitude of both shear and equivalent stress.

Keywords: functionally graded materials (FGM); equivalent stress; shear stress; power law function; FEM

Corresponding author: Hassan S. Hedia, Faculty of Maritime Studies, Marine Engineering Dept., King Abdulaziz University, Jeddah, Saudi Arabia, E-mail: hassanhedia87@yahoo.com

Funding source: This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah

Award Identifier / Grant number: grant no. (G-102-980-1446). The authors, therefore

About the authors

Hassan S. Hedia

Prof. Dr. Hassan S. Hedia, born in 1959, is Professor of Materials and Solid Mechanics at King Abdulaziz University, Jeddah Saudi Arabia. He received his BSc 1981 in the Mechanical Engineering Dept., Cairo University, Egypt, his MSc 1989 in Production Engineering, at Mansoura University, Egypt, and his PhD in 1996 in the Mechanical Engineering Dept., Leeds University, UK and Mansoura University, Egypt under the channel system. His field of interest is advanced materials, fracture mechanics, stress analysis optimum design, mechanics of materials and biomechanics. He has at least 85 papers and his h-index is 20.

Majid A. Almas

Majid A. Almas, Assistant Professor, Head of the Department of Marine Engineering, 2020 – current. King Abdulaziz University. Carry out research in the Maritime field. Increase awareness in regards to the Maritime sector. Teach students in order for them to become worthy seafarers to serve our country.

Hassan M. Attar

Hassan M. Attar a marine engineer with a PhD in marine engineering from Newcastle University, UK, snice 2021 an MSc in marine engineering, and a BSc in marine engineering. I am currently an assistant professor at King Abdul-Aziz University, Faculty of Maritime Studies Department of Marine Engineering where I teach courses in marine engineering and conduct research in the areas of renewable energy, biofuels, marine diesel engines, and the sustainability. I am passionate about my work, and I believe that renewable energy has the potential to make a significant contribution to the development of sustainable energy systems. I am committed to continuing my research and teaching activities, and to working with colleagues and industry partners to develop innovative solutions for the maritime sector.

Mohamed H. Hedia

Mohamed H. Hedia, born in 1992, is Assistance Lecturer, Department of Structural Engineering, Mansoura University, Egypt. He is currently pursuing a Ph.D. at the University of Nebraska at Lincoln, USA. With a master’s degree in structural engineering from Mansoura University, Egypt. Mr. Hedia’s research interests encompass a range of areas within structural engineering, including the strength of materials, finite element analysis, and behavior of structural elements, bridge engineering, and material science. His expertise and passion lie in exploring these subjects to contribute to the advancement of the field.

Mona A. Soliman

Dr. Mona A. Soliman born in 1974, is assistant professor of Mechanical design engineering, Delta higher institute for engineering and technology, Talkha, Egypt. She graduated B.Sc., M.Sc. & PhD from the production engineering and mechanical design department of Mansoura University at 1997, 2005, and 2015 respectively. She published many papers in different mechanical engineering fields. Her researches interested in fracture mechanics and finite element analysis such as analysis of composite material leaf spring, analysis of FGM material and its application in mechanical component, vibration analysis of car suspension system, fatigue life estimation, crack growth & arresting methods.

Acknowledgments

This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant no. (G-100-980-1446). The authors, therefore, gratefully acknowledge the DSR’s technical and financial support.

Research ethics: The study was conducted in accordance with the Declaration of Helsinki (as revised in 2013).
Informed consent: Informed consent was obtained from all individuals included in this study, or their legal guardians or wards.
Author contributions: “The authors have accepted responsibility for the entire content of this manuscript and approved its submission.”
Use of Large Language Models, AI and Machine Learning Tools: None declared.
Conflict of interests: “The authors state no conflict of interest.”
Research funding: This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant no. (G-100-980-1446). The authors, therefore, gratefully acknowledge the DSR’s technical and financial support.
Data availability: “Not applicable.”

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Published Online: 2025-04-14

Published in Print: 2025-06-26

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Articles in the same Issue

https://doi.org/10.1515/mt-2024-0450

Keywords for this article

functionally graded materials (FGM); equivalent stress; shear stress; power law function; FEM