Advanced Finite Element Methods (ASEN 6367) Course Material

Advanced Finite Element Methods (ASEN 6367) - Spring 2009 Aerospace Engineering Sciences - University of Colorado at Boulder
Note: Please do not download material until the link is marked with an asterisk ( ) Several topics after Ch 8 may be changed or reshuffled this year.. Course outline. Posted Jan 13, 2009. Syllabus. TBP HW submission guidelines. Spring 2009 roster TBP. If your name is missing or information is incorrect, please notify instructor. Part I: The Variational Principles of Mechanics Chapter 1 Index. Overview. Chapter 2 Index. Decomposition of Poisson Problems. HW#1, due Jan 22, posted. Solutions posted. Chapter 3 Index. Weak and Variational Forms of Poisson's equation. HW#2, due Jan 29, posted. Solutions posted.* Chapter 4 Index. The Bernoulli-Euler Beam. HW Solutions posted.* Chapter 5 Index. Three-Dimensional Linear Elastostatics. HW#3, due Feb 10, posted. Solutions posted.* Chapter 6 Index. The HR Variational Principle of Elastostatics. Chapter 7 Index. The Three-Field Variational Principle of Elastostatics. Not covered* . Solutions posted. Chapter 8 Index. Hybrid Variational Principles: Formulation. HW#4, due Feb 19, posted. Contains tentative announcement for first midterm exam. Solutions posted.* . Chapter 9 Index. Hybrid Variational Principles: Plane Stress Example. New Chapter. Skip for now until finished. Part II: Axisymmetric Solids Chapter 10 Index. Axisymmetric Solids (Structures of Revolution). Chapter 11 Index. Axisymmetric Solid Iso-P Elements. Rewritten chapter with refresher material. Chapter 12 Index. 4-node and 8-node iso-P Quadrilateral Ring Elements. Expanded chapter. Chapter 13 Index. A Complete Axisymmetric FEM Program. Chapter rewritten. Benchmark problems spinned off to Chapter 14. Chapter 14 Index. Axisymmetric Solid Benchmark problems. New Chapter: material spun off from Ch 13 because of length. Part III: General Solids* Chapter 15 Index. Solid Elements: Overview. Old Chapter 14, now 15. Chapter 16 Index. The Linear Tetrahedron. Old Chapter 15, renumbered as 16. Chapter 17 Index. The Quadratic Tetrahedron. Old Chapter 16, renumbered as 17. Note: old Chapter 17: A Compendium of FEM Integration Rules, moved to Appendix I. HW solutions posted* Chapter 18 Index. Hexahedral Elements. HW#6, due Mar 19, posted.* HW solutions posted Chapter 19 Index. Pyramid solid elements. Chapter 20 Index. Placeholder. Chapter 21 Index. Element Morphing. Under construction. Part IV: Advanced Element Derivation Tools* Chapter 22 Index. Element Fabrication Overview. Chapter written March 2006. HW#7, due Apr 2, posted.* Chapter 23 Index. The Patch Test. Chapter written March 2006. Part V: Thin Plates, Membranes, Templates* Chapter 24 Index. Kirchhoff Plates: Field equations. HW#8, due Apr 6, posted.* Chapter 25 Index. Kirchhoff Plates: BCs and Variational Forms. Chapter 26 Index. Thin Plate Bending: Overview. New Chapter. Chapter 27 Index. Triangular Plate Displacement Elements. No slides yet. Chapter 28 Index. Finite Element Templates for Plate Bending. Transcribed from a 2000 paper that appeared as book chapter. Chapter 29 Index. Optimal Membrane Triangles with Drilling Freedoms. Transcribed from a 2003 paper. Chapter 30 Index. A Template Tutorial. From a 2004 book chapter. Part VI: Shell Structures* Chapter 31 Index. Shell Structures: Basic Concepts. New Chapter. Not covered in class. Chapter 32 Index. A Solid Shell Element. New Chapter. Chapter 33 Index. A Triangular Thin-Shell Element. Reproduces Chapter 4 of Bjorn Haugen's thesis. Chapter 34 Index. A Quadrilateral Thin-Shell Element. Reproduces Chapter 5 of Bjorn Haugen's thesis. Chapter 35 Index. Numerical Examples of Thin Shell Analysis.. Reproduces Chapters 6-8 of Bjorn Haugen's thesis. Chapter 36 Index. A Thin Shell Triangular Element.. Support for Final projects using this element. Appendices, project and Exam Material Appendix A Index. Removed. Appendix B Index. Removed. Appendix C Index. Removed. Appendix I Index. A Compendium of FEM Integration Formulas. Appendix R Index. References. Midterm Exams. Take-home Exam 1 posted Mar 5, 2009. Solutions posted. Term Projects. Index for 2006 (previous course offering) term projects. *Term Projects. Index for 2009 (current offering) term projects.

Advanced Finite Element Methods (ASEN 6367) - Spring 2009
Aerospace Engineering Sciences - University of Colorado at Boulder

Note: Please do not download material until the link is marked with an asterisk ( ) Several topics after Ch 8 may be changed or reshuffled this year..

*Course outline. Posted Jan 13, 2009. Syllabus. TBP
*HW submission guidelines.
Spring 2009 roster TBP. If your name is missing or information is incorrect, please notify instructor.

Part I: The Variational Principles of Mechanics

*Chapter 1 Index. Overview.

*Chapter 2 Index. Decomposition of Poisson Problems. HW#1, due Jan 22, posted. Solutions posted.

*Chapter 3 Index. Weak and Variational Forms of Poisson's equation. HW#2, due Jan 29, posted. Solutions posted.

*Chapter 4 Index. The Bernoulli-Euler Beam. HW Solutions posted.

*Chapter 5 Index. Three-Dimensional Linear Elastostatics. HW#3, due Feb 10, posted. Solutions posted.

*Chapter 6 Index. The HR Variational Principle of Elastostatics.

Chapter 7 Index. The Three-Field Variational Principle of Elastostatics. Not covered . Solutions posted.

*Chapter 8 Index. Hybrid Variational Principles: Formulation. HW#4, due Feb 19, posted. Contains tentative announcement for first midterm exam. Solutions posted. .

Chapter 9 Index. Hybrid Variational Principles: Plane Stress Example. New Chapter. Skip for now until finished.

Part II: Axisymmetric Solids

*Chapter 10 Index. Axisymmetric Solids (Structures of Revolution).

*Chapter 11 Index. Axisymmetric Solid Iso-P Elements. Rewritten chapter with refresher material.

*Chapter 12 Index. 4-node and 8-node iso-P Quadrilateral Ring Elements. Expanded chapter.

*Chapter 13 Index. A Complete Axisymmetric FEM Program. Chapter rewritten. Benchmark problems spinned off to Chapter 14.

*Chapter 14 Index. Axisymmetric Solid Benchmark problems. New Chapter: material spun off from Ch 13 because of length.

Part III: General Solids

*Chapter 15 Index. Solid Elements: Overview. Old Chapter 14, now 15.

*Chapter 16 Index. The Linear Tetrahedron. Old Chapter 15, renumbered as 16.

*Chapter 17 Index. The Quadratic Tetrahedron. Old Chapter 16, renumbered as 17.
Note: old Chapter 17: A Compendium of FEM Integration Rules, moved to Appendix I. HW solutions posted

*Chapter 18 Index. Hexahedral Elements. HW#6, due Mar 19, posted. HW solutions posted

*Chapter 19 Index. Pyramid solid elements.

Chapter 20 Index. Placeholder.

Chapter 21 Index. Element Morphing. Under construction.

Part IV: Advanced Element Derivation Tools

*Chapter 22 Index. Element Fabrication Overview. Chapter written March 2006. HW#7, due Apr 2, posted.

*Chapter 23 Index. The Patch Test. Chapter written March 2006.

Part V: Thin Plates, Membranes, Templates

*Chapter 24 Index. Kirchhoff Plates: Field equations. HW#8, due Apr 6, posted.

*Chapter 25 Index. Kirchhoff Plates: BCs and Variational Forms.

*Chapter 26 Index. Thin Plate Bending: Overview. New Chapter.

*Chapter 27 Index. Triangular Plate Displacement Elements. No slides yet.

*Chapter 28 Index. Finite Element Templates for Plate Bending. Transcribed from a 2000 paper that appeared as book chapter.

*Chapter 29 Index. Optimal Membrane Triangles with Drilling Freedoms. Transcribed from a 2003 paper.

Chapter 30 Index. A Template Tutorial. From a 2004 book chapter.

Part VI: Shell Structures

Chapter 31 Index. Shell Structures: Basic Concepts. New Chapter. Not covered in class.

Chapter 32 Index. A Solid Shell Element. New Chapter.

Chapter 33 Index. A Triangular Thin-Shell Element. Reproduces Chapter 4 of Bjorn Haugen's thesis.

Chapter 34 Index. A Quadrilateral Thin-Shell Element. Reproduces Chapter 5 of Bjorn Haugen's thesis.

Chapter 35 Index. Numerical Examples of Thin Shell Analysis.. Reproduces Chapters 6-8 of Bjorn Haugen's thesis.

Chapter 36 Index. A Thin Shell Triangular Element.. Support for Final projects using this element.

Appendices, project and Exam Material

Appendix A Index. Removed.

Appendix B Index. Removed.

Appendix C Index. Removed.

Appendix I Index. A Compendium of FEM Integration Formulas.

Appendix R Index. References.

Midterm Exams. Take-home Exam 1 posted Mar 5, 2009. Solutions posted.

Term Projects. Index for 2006 (previous course offering) term projects.

*Term Projects. Index for 2009 (current offering) term projects.