Finite Element Analysis

<p>Preface <br>Acknowledgments</p> <p><strong>1. Introduction</strong><br>1.1 Engineering Problems <br>1.2 Numerical Methods <br>1.3 A Brief History of the Finite Element Method and ANSYS <br>1.4 Basic Steps in the Finite Element Method <br>1.5 Direct Formulation <br>1.6 Minimum Total Potential Energy Formulation <br>1.7 Weighted Residual Formulations <br>1.8 Verification of Results <br>1.9 Understanding the Problem <br>Summary <br>References <br>Problems</p> <p><strong>2. Matrix Algebra</strong><br>2.1 Basic Definitions <br>2.2 Matrix Addition or Subtraction <br>2.3 Matrix Multiplication <br>2.4 Partitioning of a Matrix <br>2.5 Transpose of a Matrix <br>2.6 Determinant of a Matrix <br>2.7 Solutions of Simultaneous Linear Equations <br>2.8 Inverse of a Matrix <br>2.9 Eigenvalues and Eigenvectors <br>2.10 Using MATLAB to Manipulate Matrices <br>2.11 Using Excel to Manipulate Matrices <br>2.12 Solutions of Simultaneous Nonlinear Equations <br>Summary <br>References <br>Problems</p> <p><strong>3. Trusses</strong><br>3.1 Definition of a Truss <br>3.2 Finite Element Formulation <br>3.3 Space Trusses <br>3.4 Overview of the ANSYS Program <br>3.5 ANSYS Workbench Enviornment <br>3.6 Examples Using ANSYS <br>3.7 Verification of Results <br>Summary <br>References <br>Problems</p> <p><strong>4. Axial members, Beams, and Frames</strong><br>4.1 Members Under Axial Loading <br>4.2 Beams <br>4.3 Finite Element Formulation of Beams <br>4.4 Finite Element Formulation of Frames <br>4.5 Three- Dimensional Beam Element <br>4.6 An Example Using ANSYS <br>4.7 Verification of Results <br>Summary <br>References <br>Problems</p> <p><strong>5. One-Dimensional Elements</strong><br>5.1 Linear Elements <br>5.2 Quadratic Elements <br>5.3 Cubic Elements <br>5.4 Global, Local, and Natural Coordinates <br>5.5 Isoparametric Elements <br>5.6 Numerical Integration: Gauss-Legendre Quadrature <br>5.7 Examples of One-Dimensional Elements in ANSYS <br>Summary <br>References <br>Problems</p> <p><strong>6. Analysis of One-Dimensional Problems</strong><br>6.1 Heat Transfer Problems <br>6.2 A Fluid Mechanics Problem <br>6.3 An Example Using ANSYS <br>6.4 Verification of Results <br>6.5 Members Under Axial Loading with Temperature Change <br>Summary <br>References <br>Problems</p> <p><strong>7. Two-Dimensional Elements</strong><br>7.1 Rectangular Elements <br>7.2 Quadratic Quadrilateral Elements <br>7.3 Linear Triangular Elements <br>7.4 Quadratic Triangular Elements <br>7.5 Axisymmetric Elements <br>7.6 Isoparametric Elements <br>7.7 Two- Dimensional Integrals: Gauss-Legendre Quadrature <br>7.8 Examples of Two-Dimensional Elements in ANSYS <br>Summary <br>References <br>Problems</p> <p><strong>8. More Ansys</strong><br>8.1 ANSYS Program <br>8.2 ANSYS Database and Files <br>8.3 Creating a Finite Element Model with ANSYS: Preprocessing <br>8.4 h- Method Versus p- Method <br>8.5 Applying Boundary Conditions, Loads, and the Solution <br>8.6 Results of Your Finite Element Model: Postprocessing <br>8.7 Selection Options <br>8.8 Graphics Capabilities <br>8.9 Error-Estimation Procedures <br>8.10 ANSYS Workbench Environment <br>8.11 An Example Problem <br>Summary <br>References</p> <p><strong>9. Analysis of Two-Dimensional Heat Transfer Problems</strong><br>9.1 General Conduction Problems <br>9.2 Formulation with Rectangular Elements <br>9.3 Formulation with Triangular Elements <br>9.4 Axisymmetric Formulation of Three-Dimensional Problems <br>9.5 Unsteady Heat Transfer <br>9.6 Conduction Elements used by ANSYS <br>9.7 Examples Using ANSYS <br>9.8 Verification of Results <br>Summary <br>References <br>Problems</p> <p><strong>10. Analysis of Two-Dimensional Solid Mechanics Problems</strong><br>10.1 Torsion of Members with Arbitrary Cross-Section Shape <br>10.2 Plane-Stress Formulation <br>10.3 Isoparametric Formulation: Using a Quadrilateral Element <br>10.4 Axisymmetric Formulation <br>10.5 Basic Failure Theories <br>10.6 Examples Using ANSYS <br>10.7 Verification of Results <br>Summary <br>References <br>Problems</p> <p><strong>11. Dynamic Problems</strong><br>11.1 Review of Dynamics <br>11.2 Review of Vibration of Mechanical and Structural Systems <br>11.3 Lagrange's Equations <br>11.4 Finite Element Formulation of Axial Members <br>11.5 Finite Element Formulation of Beams and Frames <br>11.6 Examples Using ANSYS <br>Summary <br>References <br>Problems</p> <p><strong>12. Analysis of Fluid Mechanics Problems</strong><br>12.1 Direct Formulation of Flow Through Pipes <br>12.2 Ideal Fluid Flow <br>12.3 Groundwater Flow <br>12.4 Examples Using ANSYS <br>12.5 Verification of Results <br>Summary <br>References <br>Problems</p> <p><strong>13. Three-Dimensional Elements</strong><br>13.1 The Four-Node Tetrahedral Element <br>13.2 Analysis of Three-Dimensional Solid Problems Using Four-Node <br>13.3 The Eight-Node Brick Element <br>13.4 The Ten-Node Tetrahedral Element <br>13.5 The Twenty-Node Brick Element <br>13.6 Examples of Three-Dimensional Elements in ANSYS <br>13.7 Basic Solid-Modeling Ideas <br>13.8 A Thermal Example Using ANSYS <br>13.9 A Structural Example Using ANSYS <br>Summary <br>References <br>Problems <br>Tetrahedral Elements</p> <p><strong>14. Design and Material Selection</strong><br>14.1 Engineering Design Process <br>14.2 Material Selection <br>14.3 Electrical, Mechanical, and Thermophysical Properties of Materials <br>14.4 Common Solid Engineering Materials <br>14.5 Some Common Fluid Materials <br>Summary <br>References <br>Problems</p> <p><strong>15. Design Optimization</strong><br>15.1 Introduction to Design Optimization <br>15.2 The Parametric Design Language of ANSYS <br>15.3 Examples of Batch Files <br>Summary <br>References <br>Problems</p> <p>Appendix A: Mechanical Properties of Some Materials <br>Appendix B: Thermophysical Properties of Some Materials <br>Appendix C: Properties of Common Line and Area Shapes <br>Appendix D: Geometrical Properties of Structural Steel Shapes <br>Appendix E: ANSYS Workbench Environment and Examples <br>Appendix F: An introduction to MATLAB</p>