Finite Element Analysis

Finite element analysis is a popular technique for studying engineering structures in detail, but it requires mathematical rigour to develop and apply. It is an extremely powerful tool for analysis, but the volume of calculations required to solve all but the most trivial of them is such that the assistance of a computer is necessary. Questions arise concerning the fundamental mathematical formulations, numerical solution techniques, and practical application of the method, and misapplication of finite element analysis programs is most likely to arise when the analyst is ignorant of engineering phenomena.

Format: Paperback / softback
Length: 154 pages
Publication date: 31 March 2021
Publisher: Taylor & Francis Ltd

Finite element analysis (FEA) has emerged as a widely employed technique for thoroughly examining engineering structures. Its applicability is particularly advantageous when the complexity of the geometry or loading conditions renders alternative methods inadequate. The fundamental premise of FEA is that a complex structure can be decomposed into a finite number of smaller elements, each exhibiting known or postulated behaviour. These elements can then be assembled to simulate the overall behaviour of the structure. While intuitively appealing, numerous crucial questions need to be addressed. To address these questions, a rigorous mathematical approach is necessary, combining intuitive engineering principles with appropriate mathematical proofs. This book aims to develop the essential concepts and methodologies from an intuitive engineering perspective, supported by mathematical proofs where required. It will become evident that FEA is a highly effective tool for analysing structures and other field problems, but the computational demands of solving complex structures often necessitate the assistance of a computer.
Numerous questions arise regarding finite element analysis. These questions pertain to the fundamental mathematical formulations, numerical solution techniques, and practical application of the method. To address these questions, the engineer/analyst must comprehend the nature and limitations of the finite element approximation and the fundamental behaviour of the structure. Misapplication of finite element analysis can lead to inaccurate results and erroneous conclusions.
Finite element analysis (FEA) is a powerful tool for studying engineering structures in detail. It is particularly useful when the complexity of the geometry or loading is such that alternative methods are inappropriate. The premise of FEA is that a complex structure can be broken down into finitely many smaller pieces (elements), each of which is known or can be postulated. These elements can then be assembled to model the behaviour of the structure.
However, there are many important questions that need to be answered regarding FEA. In order to answer them, it is necessary to apply a degree of mathematical rigour to the development of finite element techniques. The approach that will be taken in this book is to develop the fundamental ideas and methodologies based on an intuitive engineering approach, and then to support them with appropriate mathematical proofs where necessary.
It will rapidly become clear that FEA is an extremely powerful tool for the analysis of structures (and for other field problems), but that the volume of calculations required to solve all but the most trivial of them is such that the assistance of a computer is necessary.
Numerous questions arise concerning finite element analysis. Some of these questions are associated with the fundamental mathematical formulations, some with numerical solution techniques, and others with the practical application of the method. In order to answer these questions, the engineer/analyst needs to understand both the nature and limitations of the finite element approximation and the fundamental behaviour of the structure. Misapplication of finite element analysis can lead to inaccurate results and erroneous conclusions.
One of the key challenges in finite element analysis is the development of accurate and efficient numerical solution techniques. These techniques must be able to handle the complex geometry and loading conditions of engineering structures, while also being computationally efficient. There are many different numerical solution techniques available, including finite difference, finite element, and finite volume methods. Each of these techniques has its own advantages and disadvantages, and the choice of technique depends on the specific problem being studied.
Another challenge in finite element analysis is the validation of the results. It is important to ensure that the results obtained from the analysis are accurate and reliable. This can be done by comparing the results with experimental data or by performing sensitivity analysis. Sensitivity analysis involves varying the input parameters of the analysis and observing the effect on the results.
Finite element analysis has been used in a wide range of applications, including civil engineering, mechanical engineering, aerospace engineering, and environmental engineering. It has been used to design and analyze buildings, bridges, aircraft, and other structures. It has also been used to study the behaviour of materials and to predict the behaviour of natural disasters.
In conclusion, finite element analysis is a powerful tool for studying engineering structures in detail. It is particularly useful when the complexity of the geometry or loading is such that alternative methods are inappropriate. The premise of FEA is that a complex structure can be broken down into finitely many smaller pieces (elements), each of which is known or can be postulated. These elements can then be assembled to model the behaviour of the structure. However, there are many important questions that need to be answered regarding FEA, and it is necessary to apply a degree of mathematical rigour to the development of finite element techniques. By understanding the nature and limitations of the finite element approximation and the fundamental behaviour of the structure, engineers/analysts can ensure that the results obtained from the analysis are accurate and reliable.

Weight: 299g
Dimension: 234 x 156 (mm)
ISBN-13: 9780367781026