Introduction To Finite Element Methods (ASEN 5007) Course Material

Introduction to Finite Element Methods (ASEN 5007) Spring 2013 (CAETE only) Department of Aerospace Engineering Sciences University of Colorado at Boulder
This is the public web site for the graduate core course ASEN 5007: Introduction To Finite Element Methods (IFEM). This master level course is part of the Aerospace Systems Focus Area of the graduate curriculum in the Department of Aerospace Engineering Sciences of the University of Colorado at Boulder. Offered yearly during the Fall Semester, both on-campus and remotely through CAETE. First taught in 1987. This website dates from 1998 and is continuously being revised. Related courses may be accessed at AFEM: Advanced Finite Element Methods (ASEN 6347) Master & doctoral level AVMM: Advanced Variational Methods in Mechanics Master & doctoral level (in preparation) FSI: Fluid Structure Interaction (ASEN 5509) Doctoral level MFEMD: Matrix Finite Element Methods in Dynamics Master & senior-elective level (in preparation) MFEMS: Matrix Finite Element Methods in Statics Master & senior-elective level (in preparation) NFEM: Nonlinear Finite Element Methods (ASEN 6107) Master & doctoral level IAST: Intro to Aerospace Structures (ASEN 3112) Junior undergraduate level General Course Information. Syllabus, coursework, schedule, roster ... Part 0: Preface Preface Index. Part I: Finite Element Discretization and the Direct Stiffness Method Chapter 1 Index. Overview. Not covered Chapter 2 Index. The Direct Stiffness Method I. HW#1 posted, due 1/31/13; solutions posted Chapter 3 Index. The Direct Stiffness Method II. HW#1 solutions posted Chapter 4 Index. Analysis of Example Truss by a CAS. HW#2 posted, due 2/7/13; solutions posted Chapter 5 Index. Constructing MoM Members. HW#2 solutions posted Chapter 6 Index. Finite Element Modeling: Introduction. Chapter 7 Index. Finite Element Modeling: Mesh, Loads, BCs. HW#3 for CAETE students posted, due 2/14/13; solutions posted Chapter 8 Index. Multifreedom Constraints I. HW#4 for CAETE students posted, due 2/21/13. Solutions posted. Contains info on Midterm 1 Chapter 9 Index. Multifreedom Constraints II. HW#4 solutions posted Chapter 10 Index. Superelements and Global-Local Analysis. HW#4 solutions posted Part II: Mathematical Formulation of Finite Elements Chapter 11 Index. Variational Formulation of Bar Element. HW #5 for CAETE students, due 3/14/13; solutions posted Chapter 12 Index. Variational Formulation of Plane Beam Element. HW#5 solutions posted Chapter 13 Index. Advanced One-Dimensional Elements. Not covered Chapter 14 Index. The Plane Stress Problem. HW#6 solutions posted Chapter 15 Index. Three-Node Plane Stress Triangles. HW #6 for CAETE students, due 3/21/13 Chapter 16 Index. The Isoparametric Representation. Chapter 17 Index. Isoparametric Quadrilaterals. Combined HW #7-8 for CAETE students, due 4/4/1; solutions posted Chapter 18 Index. Shape Function Magic. HW solutions posted Chapter 19 Index. FEM Convergence Requirements. HW solutions posted Part III: Computer Implementation of Finite Elements Chapter 20 Index. Implementation of One-Dimensional Elements. HW#9 for CAETE students, due 4/18/13; solutions posted Chapter 21 Index. FEM Program for Space Trusses. HW solutions posted Chapter 22 Index. FEM Programs for Trusses and Frames. Not covered Chapter 23 Index. Implementation of iso-P Quadrilateral Elements. HW#10 for CAETE students, due 4/25/13; solutions posted Chapter 24 Index. Implementation of iso-P Triangular Elements. HW#10 solutions posted Chapter 25 Index. The Assembly Process. HW#11 for CAETE students, due 5/2/13; solutions posted Chapter 26 Index. Solving FEM Equations. Not covered Chapter 27 Index. A Complete Plane Stress FEM Program. Chapter 28 Index. Stress Recovery. Chapter 29 Index. Fitting Fields Over Triangles (in progress) Chapter 30 Index. Thermomechanical Effects. Part IV: Intro to Dynamics and Vibrations (new part, to be moved to MFEMD) Chapter 31 Index. Dynamics & Vibrations Overview. Chapter 32 Index. Lumped and Consistent Mass Matrices. Chapter 33 Index. Customized Mass Matrices. Appendices & Miscellaneous Stuff Appendix A Index. Linear Algebra: Vectors. Appendix B Index. Linear Algebra: Matrices. Appendix C Index. Continuum Mechanics Summary. Appendix D Index. Linear Algebra: Determinants, Inverses, Rank. Appendix E Index. Linear Algebra: Eigenproblems. Appendix F Index. Matrix Calculus. Appendix G Index. Graphics Utilities. Appendix H Index. History of MSA -> FEM. Appendix M Index. From IOMoDE to FOMoDE (advanced stuff). Appendix O Index. The Origins of the Finite Element Method. Appendix P Index. Partitioned Matrices and the Schur Complement. Appendix Q Index. Miscellaneous FEM Formulation Topics. Appendix R Index. References (in progress). Appendix S Index. Spatial Applications of Matrices. CAETE PPT files . Chapters 1-21, 23-28. Exam Material Exam Material Index. Take home exam posted April 30, 2013, due Tu May 7, 2013, by 6pm.

Introduction to Finite Element Methods (ASEN 5007)
Spring 2013 (CAETE only)
Department of Aerospace Engineering Sciences
University of Colorado at Boulder

This is the public web site for the graduate core course ASEN 5007: Introduction To Finite Element Methods (IFEM). This master level course is part of the Aerospace Systems Focus Area of the graduate curriculum in the Department of Aerospace Engineering Sciences of the University of Colorado at Boulder. Offered yearly during the Fall Semester, both on-campus and remotely through CAETE. First taught in 1987. This website dates from 1998 and is continuously being revised. Related courses may be accessed at
AFEM: Advanced Finite Element Methods (ASEN 6347) Master & doctoral level
AVMM: Advanced Variational Methods in Mechanics Master & doctoral level (in preparation)
FSI: Fluid Structure Interaction (ASEN 5509) Doctoral level
MFEMD: Matrix Finite Element Methods in Dynamics Master & senior-elective level (in preparation)
MFEMS: Matrix Finite Element Methods in Statics Master & senior-elective level (in preparation)
NFEM: Nonlinear Finite Element Methods (ASEN 6107) Master & doctoral level
IAST: Intro to Aerospace Structures (ASEN 3112) Junior undergraduate level

General Course Information. Syllabus, coursework, schedule, roster ...

Part 0: Preface
Preface Index.

Part I: Finite Element Discretization and the Direct Stiffness Method
Chapter 1 Index. Overview. Not covered
Chapter 2 Index. The Direct Stiffness Method I. HW#1 posted, due 1/31/13; solutions posted
Chapter 3 Index. The Direct Stiffness Method II. HW#1 solutions posted
Chapter 4 Index. Analysis of Example Truss by a CAS. HW#2 posted, due 2/7/13; solutions posted
Chapter 5 Index. Constructing MoM Members. HW#2 solutions posted
Chapter 6 Index. Finite Element Modeling: Introduction.
Chapter 7 Index. Finite Element Modeling: Mesh, Loads, BCs. HW#3 for CAETE students posted, due 2/14/13; solutions posted
Chapter 8 Index. Multifreedom Constraints I. HW#4 for CAETE students posted, due 2/21/13. Solutions posted. Contains info on Midterm 1
Chapter 9 Index. Multifreedom Constraints II. HW#4 solutions posted
Chapter 10 Index. Superelements and Global-Local Analysis. HW#4 solutions posted

Part II: Mathematical Formulation of Finite Elements
Chapter 11 Index. Variational Formulation of Bar Element. HW #5 for CAETE students, due 3/14/13; solutions posted
Chapter 12 Index. Variational Formulation of Plane Beam Element. HW#5 solutions posted
Chapter 13 Index. Advanced One-Dimensional Elements. Not covered
Chapter 14 Index. The Plane Stress Problem. HW#6 solutions posted
Chapter 15 Index. Three-Node Plane Stress Triangles. HW #6 for CAETE students, due 3/21/13
Chapter 16 Index. The Isoparametric Representation.
Chapter 17 Index. Isoparametric Quadrilaterals. Combined HW #7-8 for CAETE students, due 4/4/1; solutions posted
Chapter 18 Index. Shape Function Magic. HW solutions posted
Chapter 19 Index. FEM Convergence Requirements. HW solutions posted

Part III: Computer Implementation of Finite Elements
Chapter 20 Index. Implementation of One-Dimensional Elements. HW#9 for CAETE students, due 4/18/13; solutions posted
Chapter 21 Index. FEM Program for Space Trusses. HW solutions posted
Chapter 22 Index. FEM Programs for Trusses and Frames. Not covered
Chapter 23 Index. Implementation of iso-P Quadrilateral Elements. HW#10 for CAETE students, due 4/25/13; solutions posted
Chapter 24 Index. Implementation of iso-P Triangular Elements. HW#10 solutions posted
Chapter 25 Index. The Assembly Process. HW#11 for CAETE students, due 5/2/13; solutions posted
Chapter 26 Index. Solving FEM Equations. Not covered
Chapter 27 Index. A Complete Plane Stress FEM Program.
Chapter 28 Index. Stress Recovery.
Chapter 29 Index. Fitting Fields Over Triangles (in progress)
Chapter 30 Index. Thermomechanical Effects.

Part IV: Intro to Dynamics and Vibrations (new part, to be moved to MFEMD)
Chapter 31 Index. Dynamics & Vibrations Overview.
Chapter 32 Index. Lumped and Consistent Mass Matrices.
Chapter 33 Index. Customized Mass Matrices.

Appendices & Miscellaneous Stuff
Appendix A Index. Linear Algebra: Vectors.
Appendix B Index. Linear Algebra: Matrices.
Appendix C Index. Continuum Mechanics Summary.
Appendix D Index. Linear Algebra: Determinants, Inverses, Rank.
Appendix E Index. Linear Algebra: Eigenproblems.
Appendix F Index. Matrix Calculus.
Appendix G Index. Graphics Utilities.
Appendix H Index. History of MSA -> FEM.
Appendix M Index. From IOMoDE to FOMoDE (advanced stuff).
Appendix O Index. The Origins of the Finite Element Method.
Appendix P Index. Partitioned Matrices and the Schur Complement.
Appendix Q Index. Miscellaneous FEM Formulation Topics.
Appendix R Index. References (in progress).
Appendix S Index. Spatial Applications of Matrices.
CAETE PPT files . Chapters 1-21, 23-28.

Exam Material
Exam Material Index. Take home exam posted April 30, 2013, due Tu May 7, 2013, by 6pm.