Static deflection analysis of functionally graded beams using various beam theories

Raghad Azeez Neamah; Ameen Ahmed Nassar; Luay S. Alansari; Emad Kadum Njim; Lazreg Hadji; Royal Madan

doi:10.53391/mmnsa.1524642

EN

Static deflection analysis of functionally graded beams using various beam theories

Abstract

In the current study, static deflection analysis of a functionally graded (FG) beam is carried out for various theories such as Euler, Timoshenko, and high-order shear deformation theory. The governing equation was solved using the minimum total potential energy principle. Further, for different types of loads, the static deflection analysis of the FG beam was performed using Navier’s solution using the Fortran programming language. Moreover, finite element analysis was also carried out using ANSYS software. In this method, each layer of the FG beam possesses different material properties as per a power law distribution. The different solution techniques are used to calculate the static deflection, and their results are compared. Effect of various parameters such as power index value, modulus ratio, aspect ratio (L/h), and type of loading on the dimensionless transverse deflection of this FG beam model. The results show that the aspect ratio has no significant effect on transverse dimensionless deflection in the case of the Euler beam theory. However, there is a noticeable effect for the Timoshenko and higher-order shear deformation theories, indicating that shear significantly impacts dimensionless transverse deflection for short beams. In addition, it is proven that the present model is reliable and can calculate the static deflection for any other required beam with different loads and dimensions.

Keywords

FG beam, Dimensionless transverse deflection, Euler beam theory

Supporting Institution

No funding was received for this research

Project Number

NA

Ethical Statement

The authors state that this research complies with ethical standards. This research does not involve either human participants or animals.

Thanks

The authors are grateful to the University of Kufa, College of Engineering/ Iraq, for providing facilities to carry out this work

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Details

Primary Language

English

Subjects

Numerical Solution of Differential and Integral Equations, Finite Element Analysis , Theoretical and Applied Mechanics in Mathematics

Journal Section

Research Article

Authors

Raghad Azeez Neamah
0000-0003-1780-5035
Iraq

Ameen Ahmed Nassar
0000-0001-7230-4394
Iraq

Luay S. Alansari
0000-0002-2989-8614
Iraq

Emad Kadum Njim
0000-0001-9694-971X
Iraq

Lazreg Hadji
0000-0002-3333-5902
Algeria

Royal Madan ^*
0000-0002-3445-9210
India

Early Pub Date

July 15, 2025

Publication Date

June 30, 2025

Submission Date

July 31, 2024

Acceptance Date

June 17, 2025

Published in Issue

Year 2025 Volume: 5 Number: 2

DOI

https://doi.org/10.53391/mmnsa.1524642

IZ

https://izlik.org/JA84SS56DJ

APA

Azeez Neamah, R., Ahmed Nassar, A., Alansari, L. S., Kadum Njim, E., Hadji, L., & Madan, R. (2025). Static deflection analysis of functionally graded beams using various beam theories. Mathematical Modelling and Numerical Simulation With Applications, 5(2), 396-420. https://doi.org/10.53391/mmnsa.1524642

AMA

1.Azeez Neamah R, Ahmed Nassar A, Alansari LS, Kadum Njim E, Hadji L, Madan R. Static deflection analysis of functionally graded beams using various beam theories. MMNSA. 2025;5(2):396-420. doi:10.53391/mmnsa.1524642

Chicago

Azeez Neamah, Raghad, Ameen Ahmed Nassar, Luay S. Alansari, Emad Kadum Njim, Lazreg Hadji, and Royal Madan. 2025. “Static Deflection Analysis of Functionally Graded Beams Using Various Beam Theories”. Mathematical Modelling and Numerical Simulation With Applications 5 (2): 396-420. https://doi.org/10.53391/mmnsa.1524642.

EndNote

Azeez Neamah R, Ahmed Nassar A, Alansari LS, Kadum Njim E, Hadji L, Madan R (June 1, 2025) Static deflection analysis of functionally graded beams using various beam theories. Mathematical Modelling and Numerical Simulation with Applications 5 2 396–420.

IEEE

[1]R. Azeez Neamah, A. Ahmed Nassar, L. S. Alansari, E. Kadum Njim, L. Hadji, and R. Madan, “Static deflection analysis of functionally graded beams using various beam theories”, MMNSA, vol. 5, no. 2, pp. 396–420, June 2025, doi: 10.53391/mmnsa.1524642.

ISNAD

Azeez Neamah, Raghad - Ahmed Nassar, Ameen - Alansari, Luay S. - Kadum Njim, Emad - Hadji, Lazreg - Madan, Royal. “Static Deflection Analysis of Functionally Graded Beams Using Various Beam Theories”. Mathematical Modelling and Numerical Simulation with Applications 5/2 (June 1, 2025): 396-420. https://doi.org/10.53391/mmnsa.1524642.

JAMA

1.Azeez Neamah R, Ahmed Nassar A, Alansari LS, Kadum Njim E, Hadji L, Madan R. Static deflection analysis of functionally graded beams using various beam theories. MMNSA. 2025;5:396–420.

MLA

Azeez Neamah, Raghad, et al. “Static Deflection Analysis of Functionally Graded Beams Using Various Beam Theories”. Mathematical Modelling and Numerical Simulation With Applications, vol. 5, no. 2, June 2025, pp. 396-20, doi:10.53391/mmnsa.1524642.

Vancouver

1.Raghad Azeez Neamah, Ameen Ahmed Nassar, Luay S. Alansari, Emad Kadum Njim, Lazreg Hadji, Royal Madan. Static deflection analysis of functionally graded beams using various beam theories. MMNSA. 2025 Jun. 1;5(2):396-420. doi:10.53391/mmnsa.1524642