Approximate solutions for bending of beams and buckling of columns made of functionally graded materials
Other Title(s)
حلول التقريبية لانحناء الجيزان و انبعاج الأعمدة المصنوعة من مواد متدرجة وظيفيا
Dissertant
Thesis advisor
University
Isra University
Faculty
Faculty of Engineering
Department
Engineering Project Management
University Country
Jordan
Degree
Master
Degree Date
2022
English Abstract
In this research approximate solutions are developed to solve Functionally Graded Material (FGM) beam and column problems.
FGM is considered in the transversal direction of both beams and columns using different functions; power function, exponential function, and sigmoidal function.
Also, different power values are used to consider different material concentrations in the transversal direction of beams and columns.
Approximate solutions are first developed for FGM beams using iterative techniques based on averaging the elasticity modulus in beam’s tension and compression zones to determine different structural outputs like deflection, slope, shear and moment diagrams.
Then outputs are compared to classical Euler bending theory to validate the adopted approximate method used in the solution.
In addition to beam bending problems, approximate solutions for FGM column buckling problems are also developed.
The methods adopted in solution are Rayleigh’s Quotient, Timoshenko’s Quotient, and Rayleigh-Ritz method.
These methods are compared to the analytical classical Euler buckling solution.
MATLAB program is adopted to solve both problems since it is simple and precise.
The main results of this study shed the light on the importance of approximate solutions in solving FGM bending and buckling problems.
For bending problems, the approximate method suggested resulted in trivial error (~0%) when compared to analytical solution.
As for buckling problems, Rayleigh-Ritz method showed to be the most accurate one in calculating critical buckling load with error less than 0.75%, while Rayleigh method led to significant errors (~22%).
At the end of this work, some recommendations were presented for future research work on FG structural members.
Main Subjects
No. of Pages
72
Table of Contents
Table of contents.
Abstract.
Abstract in Arabic.
Chapter One : Introduction.
Chapter Two : Literature review.
Chapter Three : Research methodology.
Chapter Four : Results and discussion.
Chapter Five : Conclusions and recommendations.
References.
American Psychological Association (APA)
al-Taani, Musab Hasan Ahmad. (2022). Approximate solutions for bending of beams and buckling of columns made of functionally graded materials. (Master's theses Theses and Dissertations Master). Isra University, Jordan
https://search.emarefa.net/detail/BIM-1429117
Modern Language Association (MLA)
al-Taani, Musab Hasan Ahmad. Approximate solutions for bending of beams and buckling of columns made of functionally graded materials. (Master's theses Theses and Dissertations Master). Isra University. (2022).
https://search.emarefa.net/detail/BIM-1429117
American Medical Association (AMA)
al-Taani, Musab Hasan Ahmad. (2022). Approximate solutions for bending of beams and buckling of columns made of functionally graded materials. (Master's theses Theses and Dissertations Master). Isra University, Jordan
https://search.emarefa.net/detail/BIM-1429117
Language
English
Data Type
Arab Theses
Record ID
BIM-1429117
