Book Fundamentals of Finite Element Analysis: Linear Finite Element Analysis pdf


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Book Fundamentals of Finite Element Analysis: Linear Finite Element Analysis pdf

Book Fundamentals of Finite Element Analysis: Linear Finite Element Analysis pdf

Pages 729

By Ioannis Koutromanos 

This text grew out of a set of notes, originally created for a graduate class on Finite Element (FE) analysis of structures that I teach in the Civil and Environmental Engineering
department of Virginia Tech. The book attempts to provide an understanding or the salient features of linear FE analysis, beginning with the mathematics describing an actual
physical problem and continuing with the introduction of the FE approximation and the
calculation of pertinent arrays and vectors.
The mathematical description of various physical problems in this book (primarily
elasticity and heat conduction) employs the “strong form–weak form” paradigm. Given
a physical problem, the strong form (governing differential equations and boundary conditions) is established. Then, a weak form is obtained, into which the finite element
approximation is subsequently introduced. I believe the strong form–weak form paradigm is a more efficient way of teaching the method than, for example, variational principles, because it is fairly straightforward and also more powerful from a teaching point of
view. For example, the derivation of the weak form for solid and structural mechanics
provides a formal proof of the principle of virtual work.
The book contains a total of 19 chapters and 4 appendices.
Chapter 1 constitutes an introduction, with an explanation of the necessity of numerical simulation, the essence of FE approximations and a brief presentation of the early
history of FE analysis. Chapters 2 and 3 present the conceptual steps required for setting
up and solving the FE equations of a one-dimensional physical problem. Specifically,
Chapter 2 describes the process by which we can establish the governing differential
equations and boundary conditions, which we collectively call the strong form of a
problem, and how to obtain the corresponding weak form, which is an alternative mathematical statement of the governing physics, fully equivalent to the strong form. The
weak form turns out to be more convenient for the subsequent introduction of
the FE approximation. The latter is described in Chapter 3, wherein we see how the
discretization of a domain into a finite element mesh and the stipulation of a piecewise
approximation allows us to transform the weak form to a system of linear equations.
Computational procedures accompanying finite element analysis, such as Gaussian
quadrature, are also introduced in Chapter 3.

Fundamentals of Finite Element Analysis_ Linear Finite Element Analysis

 


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