Gain a clear understanding of the basics of the finite element method (FEM) with this simple, direct, contemporary approach in Logan's A FIRST COURSE IN THE FINITE ELEMENT METHOD, ENHANCED 6th Edition. This unique presentation is written so you can easily comprehend content without the usual prerequisites, such as structural analysis. This book is ideal, whether you are a civil or mechanical engineering student primarily interested in stress analysis and heat transfer, or you need a foundation for applying FEM as a tool in solving practical physical problems. New and expanded realworld examples and problems demonstrate FEM applications in a variety of engineering and mathematical physicsrelated fields. Each chapter uses a consistent structure with stepbystep, workedout examples, ideal for undergraduate or graduatelevel study. A new WebAssign digital platform provides additional online resources to clarify concepts and assist you in completing assignments.
1. INTRODUCTION.
Brief History. Introduction to Matrix Notation. Role of the Computer. General Steps of the Finite Element Method. Applications of the Finite Element Method. Advantages of the Finite Element Method. Computer Programs for the Finite Element Method.
2. INTRODUCTION TO THE STIFFNESS (DISPLACEMENT) METHOD.
Definition of the Stiffness Matrix. Derivation of the Stiffness Matrix for a Spring Element. Example of a Spring Assemblage. Assembling the Total Stiffness Matrix by Superposition (Direct Stiffness Method). Boundary Conditions. Potential Energy Approach to Derive Spring Element Equations.
3. DEVELOPMENT OF TRUSS EQUATIONS.
Derivation of the Stiffness Matrix for a Bar Element in Local Coordinates. Selecting Approximation Functions for Displacements. Transformation of Vectors in Two Dimensions. Global Stiffness Matrix for Bar Arbitrarily Oriented in the Plane. Computation of Stress for a Bar in the xy Plane. Solution of a Plane Truss. Transformation Matrix and Stiffness Matrix for a Bar in ThreeDimensional Space. Use of Symmetry in Structure. Inclined, or Skewed, Supports. Potential Energy Approach to Derive Bar Element Equations. Comparison of Finite Element Solution to Exact Solution for Bar. Galerkin's Residual Method and Its Use to Derive the OneDimensional Bar Element Equations. Other Residual Methods and Their Application to a OneDimensional Bar Problem. Flowchart for Solutions of ThreeDimensional Truss Problems. Computer Program Assisted StepbyStep Solution for Truss Problem.
4. DEVELOPMENT OF BEAM EQUATIONS.
Beam Stiffness. Example of Assemblage of Beam Stiffness Matrices. Examples of Beam Analysis Using the Direct Stiffness Method. Distribution Loading. Comparison of the Finite Element Solution to the Exact Solution for a Beam. Beam Element with Nodal Hinge. Potential Energy Approach to Derive Beam Element Equations. Galerkin's Method for Deriving Beam Element Equations.
5. FRAME AND GRID EQUATIONS.
TwoDimensional Arbitrarily Oriented Beam Element. Rigid Plane Frame Examples. Inclined or Skewed Supports  Frame Element. Grid Equations. Beam Element Arbitrarily Oriented in Space. Concept of Substructure Analysis.
6. DEVELOPMENT OF THE PLANE STRESS AND STRAIN STIFFNESS EQUATIONS.
Basic Concepts of Plane Stress and Plane Strain. Derivation of the ConstantStrain Triangular Element Stiffness Matrix and Equations. Treatment of Body and Surface Forces. Explicit Expression for the ConstantStrain Triangle Stiffness Matrix. Finite Element Solution of a Plane Stress Problem. Rectangular Plane Element (Bilinear Rectangle, Q4).
7. PRACTICAL CONSIDERATIONS IN MODELING: INTERPRETING RESULTS AND EXAMPLES OF PLANE STRESSSTRAIN ANALYSIS.
Finite Element Modeling. Equilibrium and Compatibility of Finite Element Results. Convergence of Solution. Interpretation of Stresses. Static Condensation. Flowchart for the Solution of Plane StressStrain Problems. Computer ProgramAssisted StepbyStep Solution, Other Models, and Results for Plane StressStrain Problems.
8. DEVELOPMENT OF THE LINEARSTRAIN TRIANGLE EQUATIONS.
Derivation of the LinearStrain Triangular Element Stiffness Matrix and Equations. Example of LST Stiffness Determination. Comparison of Elements.
9. AXISYMMETRIC ELEMENTS.
Derivation of the Stiffness Matrix. Solution of an Axisymmetric Pressure Vessel. Applications of Axisymmetric Elements.
10. ISOPARAMETRIC FORMULATION.
Isoparametric Formulation of the Bar Element Stiffness Matrix. Isoparametric Formulation of the Plane Quadrilateral Element Stiffness Matrix. NewtonCotes and Gaussian Quadrature. Evaluation of the Stiffness Matrix and Stress Matrix by Gaussian Quadrature. HigherOrder Shape Functions.
11. THREEDIMENSIONAL STRESS ANALYSIS.
ThreeDimensional Stress and Strain. Tetrahedral Element. Isoparametric Formulation and Hexahedral Element.
12. PLATE BENDING ELEMENT.
Basic Concepts of Plate Bending. Derivation of a Plate Bending Element Stiffness Matrix and Equations. Some Plate Element Numerical Comparisons. Computer Solutions for Plate Bending Problems.
13. HEAT TRANSFER AND MASS TRANSPORT.
Derivation of the Basic Differential Equation. Heat Transfer with Convection. Typical Units; Thermal Conductivities, K; and HeatTransfer Coefficients, h. OneDimensional Finite Element Formulation Using a Variational Method. TwoDimensional Finite Element Formulation. Line or Point Sources. ThreeDimensional Heat Transfer by the Finite Element Method. OneDimensional Heat Transfer with Mass Transport. Finite Element Formulation of Heat Transfer with Mass Transport by Galerkin's Method. Flowchart and Examples of a HeatTransfer Program.
14. FLUID FLOW IN POROUS MEDIA AND THROUGH HYDRAULIC NETWORKS; AND ELECTRICAL NETWORKS AND ELECTROSTATICS.
Derivation of the Basic Differential Equations. OneDimensional Finite Element Formulation. TwoDimensional Finite Element Formulation. Flowchart and Example of a FluidFlow Program. Electrical Networks. Electrostatics.
15. THERMAL STRESS.
Formulation of the Thermal Stress Problem and Examples.
16. STRUCTURAL DYNAMICS AND TIMEDEPENDENT HEAT TRANSFER
Dynamics of a SpringMass System. Direct Derivation of the Bar Element Equations. Numerical Integration in Time. Natural Frequencies of a OneDimensional Bar. TimeDependent OneDimensional Bar Analysis. Beam Element Mass Matrices and Natural Frequencies. Truss, Plane Frame, Plane Stress, Plane Strain, Axisymmetric, and Solid Element Mass Matrices. TimeDependent HeatTransfer. Computer Program Example Solutions for Structural Dynamics.
APPENDIX A: MATRIX ALGEBRA.
Definition of a Matrix. Matrix Operations. Cofactor of Adjoint Method to Determine the Inverse of a Matrix. Inverse of a Matrix by Row Reduction. Properties of Stiffness Matrices.
APPENDIX B: METHODS FOR SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS.
Introduction. General Form of the Equations. Uniqueness, Nonuniqueness, and Nonexistence of Solution. Methods for Solving Linear Algebraic Equations. BandedSymmetric Matrices, Bandwidth, Skyline, and Wavefront Methods.
APPENDIX C: EQUATIONS FOR ELASTICITY THEORY.
Introduction. Differential Equations of Equilibrium. Strain/Displacement and Compatibility Equations. StressStrain Relationships.
APPENDIX D: EQUIVALENT NODAL FORCES.
APPENDIX E: PRINCIPLE OF VIRTUAL WORK.
APPENDIX F: PROPERTIES OF STRUCTURAL STEEL AND ALUMINUM SHAPES.
ANSWERS TO SELECTED PROBLEMS.
INDEX.

Daryl L. Logan
Dr. Daryl L. Logan is professor of mechanical engineering at the University of WisconsinPlatteville. He received his Ph.D. from the University of IllinoisChicago. He has been an active member of the American Society of Mechanical Engineers (ASME), Tau Beta Pi  National Honor Society and the American Society for Engineering Education (ASEE). Dr. Logan holds a professional engineer's license in the state of Indiana.

CONTEMPORARY REALWORLD EXAMPLES AND PROBLEMS FURTHER CLARIFY CONCEPTS. Realworld examples and problems throughout this edition illustrate the latest developments and applications from the field today. These current examples and problems enhance student understanding and reinforce updated content and concepts presented in this enhanced edition.

LARGE VARIETY OF EXAMPLES DEMONSTRATE FEM APPLICATIONS IN DIVERSE DISCIPLES. Examples from other fields now illustrate how students can use the Finite Element Method (FEM) to solve problems in a variety of engineering and mathematical physics areas today.

CLEAR GRAPHICAL METHOD. Students can use this graphical method to derive the transformation matrix relating local and global displacements and forces.

CHAPTER OBJECTIVES AND ENDOFCHAPTER SUMMARY EQUATIONS INCREASE UNDERSTANDING. The chapter objectives guide student attention to key concepts, so readers know where to focus study efforts and which content is most important to retain. Key summary equations also help students efficiently review important content.

CLEAR PRESENTATION IS IDEAL FOR THOSE NEW TO THE FIELD. Written as a basic learning tool for students in civil and mechanical engineering, this text does not presume an extensive background in structural analysis. All mathematical concepts are presented in a simple and straightforward manner to maximize comprehension.

PRACTICAL, CONSISTENT STRUCTURE ENSURES STUDENT UNDERSTANDING. Topics progress from basic to advanced as each chapter follows a similar structure and format. General principles are presented for each topic, followed by traditional applications of these principles as well as computer applications, where relevant.

EXTENSIVE APPENDICES OFFER ADDITIONAL SUPPORT FOR REVIEW OR ADVANCED STUDY. Helpful appendices review basic matrix algebra that is used throughout the text as well as solutions methods for simultaneous equations, equations from elasticity theory, equivalent nodal forces, the principle of virtual work and the properties of structural steel and aluminum shapes.

STEPBYSTEP, COMPLETED EXAMPLES CLEARLY ILLUSTRATE CONCEPTS. Many workedout examples appear throughout the text to demonstrate correct methodology. These examples are solved stepbystep to show students how to apply essential concepts.

HELPFUL 16PAGE COLOR INSERT VISUALLY CLARIFIES CONCEPTS. Many of the threedimensional images in the book are carefully illustrated within this special insert to clarify principles at work and boost student comprehension.
A First Course in the Finite Element Method
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