Finite element analysis (FEA) is a computerized method for predicting how a component/assembly will react to environmental factors such as forces, heat, and vibration. Though it is called “analysis,” in the product design cycle, it is used as a virtual prototyping tool to predict what is going to happen when the product is used. Finite element analysis, as related to the mechanics of solids, is the solution of a finite set of algebraic matrix equations that approximate the relationships between load and deflection in static analysis and velocity, acceleration, and time in dynamic analysis. The word “finite” in “finite element analysis” indicates that there are a finite number of elements in a model, such as a piston. This book gives an overview of the physical and mathematical background required to understand the FEA implementation. The procedures for FEA modelling are discussed in this book for a few of classic problems such as modal analysis. It is compiled in such a manner, that it will provide in-depth knowledge about the theory and practice of finite element analysis. It deals with finite element formulation, differential equation, beam finite elements and frames finite element. It also focuses on isoparametric finite elements, galerkin approximation and partial differentiation equations. This book presents the complex subject of finite element in the most comprehensible and easy to understand language. Different approaches, evaluations and methodologies have been included in it. It will serve as a valuable source of reference for those interested in this subject.

Preface

1. Introduction 

2. Finite Element Formulation Starting from Governing Differential

Equation 

3. Finite Element Formulation based on Stationarity of a Functional

Approach 

4. Mathematical Background

5. Beam Finite Elements 

6. Frames Finite Element 

7. Two Dimensional Finite Elements 

8. One Dimensional Finite Elements 

9. Variational Principles, Galerkin Approximation and Partial

Differentiation Equations 

10. Isoparametric Finite Elements and Dynamic Analysis

Index

Elizabet Amato is a Research Associate at College of Engineering, Irkutsk. She pursued her Ph.D. in Mechanical Engineering from University of Science, Madrid. Her research primarily focuses on the modelling and simulation, analytical simulation of structural components and systems under extreme events. She has authored several articles and research papers on finite element analysis, element formulations, constitutive models and modelling schemes. Amato is also an active member of several scientific and technical societies.