Introduction to Approximate Solution Techniques, Numerical Modeling, and Finite Element Methods (Civil and Environmental Engineering)

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Functions as a self-study guide for engineers and as a textbook for nonengineering students and engineering students, emphasizing generic forms of differential equations, applying approximate solution techniques to examples, and progressing to specific physical problems in modular, self-contained chapters that integrate into the text or can stand alone!

This reference/text focuses on classical approximate solution techniques such as the finite difference method, the method of weighted residuals, and variation methods, culminating in an introduction to the finite element method (FEM).

Discusses the general notion of approximate solutions and associated errors!

With 1500 equations and more than 750 references, drawings, and tables, Introduction to Approximate Solution Techniques, Numerical Modeling, and Finite Element Methods:

Describes the approximate solution of ordinary and partial differential equations using the finite difference method

Covers the method of weighted residuals, including specific weighting and trial functions

Considers variational methods

Highlights all aspects associated with the formulation of finite element equations

Outlines meshing of the solution domain, nodal specifications, solution of global equations, solution refinement, and assessment of results

Containing appendices that present concise overviews of topics and serve as rudimentary tutorials for professionals and students without a background in computational mechanics, Introduction to Approximate Solution Techniques, Numerical Modeling, and Finite Element Methods is a blue-chip reference for civil, mechanical, structural, aerospace, and industrial engineers, and a practical text for upper-level undergraduate and graduate students studying approximate solution techniques and the FEM.

Introduction to Approximate Solution Techniques, Numerical Modeling, and Finite Element Methods (Civil and Environmental Engineering) Review

I used this book as textbook for an introductory course in Finite Element Method (FEM). Most of the book deals with linear FEM (Ch.6 to Ch.13). It is a well structured book written for (seniors and first year graduate) students in Civil and Mechanical Engineers. Therefore, the math style is the one typically seen in Engineering Mathematics texts. The FEM is described mostly using matrix notation (rather than index notation specific to Continuum Mechanics texts).

The book has two introductory chapters: Ch. 1 presents some of the differential equations commonly encountered in engineering; Ch. 2 describes errors appearing in obtaining numerical solutions.

Besides FEM, the book presents additional methods for solving differential equations. Namely, it presents Finite Difference Method in Ch. 3, the family of Method of Weighted Residuals (i.e. Collocation Method, Least-Squares, Bubnov-Galerkin etc.) in Ch. 4 and Variational Methods (i.e. Ritz method) in Ch. 5.

Chapters 6 to 10 explains fundamentals aspects of FEM such as: deriving FE equations from the differential equations via Galerkin and variational approaches, interpolation functions and element mappings.

Chapter 11 is dedicated to scalar field problems (e.g., heat transfer) and Chapter 12 to elasto-static problems.

The book is well documented, citing an impressive number of publications (612 references) which cover more advanced FEM topics. It contains useful information in the appendices about solvers, integration formulae, finite difference formulae etc., appendices which sometimes I use as a reference.

Although the book does not address FEM for time-dependent problems (e.g., transient heat transfer, elastodynamics) (maybe in a future edition), I consider this is good book to start learning finite element method.

Unfortunately, the book is a bit pricey.

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