Introduction to Finite Elements in Engineering
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Introduction to Finite Elements in Engineering

Introduction to Finite Elements in Engineering 3rd Edition by Tirupathi R. Chandroplatla and Ashok D. Belegundu | PDF Free Download.

Introduction to Finite Elements Contents


Preface to Finite Elements in Engineering PDF

The first edition of this book appeared over 10 years ago and the second edition fol• lowed a few years later. We received positive feedback from professors who taught from the book and from students and practicing engineers who used the book.

We also benefited from the feedback received from the students in our courses for the past 20 years. We have incorporated several suggestions in this edition. The underlying philosophy of the book is to provide a clear presentation of theory, modeling, and implementation into computer programs.

The pedagogy of earlier editions has been retained in this edition. New material has been introduced in several chapters. Worked examples and exercise problems have been added to supplement the learning process. Exercise problems stress both fundamental understanding and practical considerations.

Theory and computer programs have been added to cover acoustics. axisymmetric quadrilateral elements, conjugate gradient approach, and eigenvalue evaluation. Three additional programs have now been introduced in this edition.

All the programs have been developed to work in the Windows environment. The programs have a common structure that should enable the users to follow the development easily.

The programs have been provided in Visual Basic, Microsoft Excel/Visual Basic, MATLAB, together with those provided earlier in QBASIC, FORTRAN and C. The Solutions Manual has also been updated.

Chapter 1 gives a brief historical background and develops fundamental concepts. Equations of equilibrium, stress-strain relations, strain-displacement relations, and the principles of potential energy are reviewed. The concept of Galerkin's method is introduced. Properties of matrices and determinants are reviewed in Chapter 2.

The Gaussian elimination method is presented, and its relationship to the solution of symmetric banded matrix equations and the skyline solution is discussed. Cholesky decomposition and conjugate gradient methods are discussed. Chapter 3 develops the key concepts of finite element formulation by considering one-dimensional problems.

The steps include the development of shape functions, derivation of element stiffness, the foundation of global stiffness, treatment of boundary conditions, solution of equations, and stress calculations. Both the potential energy approach and Galerkin's formulations are presented.

Consideration of temperature effects is included. Finite element fonnulation for plane and three-dimensional trusses is developed in Chapter 4. The assembly of global stiffness in banded and skyline fonns is explained. Computer programs for both banded and skyline soluti?ns are given...

Chapter 5 introduces the finite element fonnulatIon for two-dimensional plane stress and plane strain problems using constant strain triangle (CST) ele~ents. Probl~m modeling and treatment of boundary conditions are presented ~n detail.

Fonnul.atton for orthotropic materials is provided. Chapter 6 treats the modeling aspects ofaxlsymmetric solids subjected to axisymmetric loading. Formulation using triangular elements is presented. Several real-world problems are included in this chapter.

Chapter 7 introduces the concepts of isoparametric quadrilateral and higher order elements and numerical integration using Gaussian quadrature. Fonnulation for axisymmetric quadrilateral element and implementation of conjugate gradient method for quadrilateral element are given. Beams and application of Hermite shape functions are presented in Chapter 8.

The chapter covers two-dimensional and three-dimensional frames. Chapter 9 presents three-dimensional stress analysis. Tetrahedral and hexahedral elements are presented. The frontal method and its implementation aspects are discussed. Scalar field problems are treated in detail in Chapter 10.

While Galerkin as well as energy approaches have been used in every chapter, with equal importance, only Galerkin's approach is used in this chapter. This approach directly applies to the given differential equation without the need of identifying an equivalent functional to minimize.

Galerkin fonnulation for steady-state heat transfer, torsion, potential flow, seepage flow, electric and magnetic fields, fluid flow in ducts, and acoustics are presented.

Chapter 11 introduces dynamic considerations. Element mass matrices are given. Techniques for evaluation of eigenvalues (natural frequencies) and eigenvectors (mode shapes) of the generalized eigenvalue problem are discussed. Methods of inverse iteration, Jacobi, tridiagonalization and implicit shift approaches are presented.

Preprocessing and postprocessing concepts are developed in Chapter 12. Theory and implementation aspects of two-dimensional mesh generation, least-squares approach to obtain nodal stresses from element values for triangles and quadrilaterals, and contour plotting are presented.

At the undergraduate level some topics may be dropped or delivered in a different order without breaking the continuity of presentation. We encourage the introduction of the Chapter 12 programs at the end of Chapter 5. This helps the students to prepare the data in an efficient manner.

" We thank Nels Ma.dsen,.Auburn University; Arif Masud, University of Illinois, Chl~ago; Robert L Rankm,Anzona State University; John S. Strenkowsi, NC State Uni~ v.erslty; and Hormoz Zareh. ~ortland State University, who reviewed our second edi~ hon an? gave ~any constructive suggestions that helped us improve the book.

Tlfupathl Chandrupatla expresses his gratitude to 1. Tinsley Oden, whose teaching and encourag(:n~ent have been a source of inspiration to him throughout his career.

He a.lso expresses h.IS thanks to many students at Rowan University and Kettering University who took hIs courses. He expresses his thanks to his colleague Paris vonLockette. who gave valuable feedback after teaching a Course from the second edition.

We thank our production editor Fran Daniele for her meticulous approach in the final production of the book. Ashok Belegundu thanks his students at Penn State for their feedback on the course material and programs.

He expresses his gratitude to Richard C. Benson, chairman of mechanical and nuclear engineering, for his encouragement and appreciation.

He also expresses his thanks to Professor Victor W. Sparrow in the acoustics department and to Dongjai Lee, doctoral student, for discussions and help with some of the material in the book. His late father's encouragement with the first two editions of this book are an ever present inspiration.

We thank our acquisitions editor at Prentice Hall, Laura Fischer, who has made this a pleasant project for us.

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