Advanced Finite Element Methods (ASEN 6367) - Spring 2017
Department of Aerospace Engineering Sciences
University of Colorado at Boulder
(Web site under revision for Spring 17 - please be patient)
This is the public web site for the graduate core course ASEN 6367: Advanced Finite Element Methods for Solids, Plates and Shells (AFEM). This master and doctoral 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 every 2-3 years during the Spring Semester. First taught in 1990. This website dates from 1998 and is continuously being revised. Related courses may be accessed at
AVVM: Advanced Variational Methods in Mechanics Master & doctoral level (in progress)
FSI: Fluid Structure Interaction (ASEN 5509) Advanced doctoral level
IFEM: Introduction to Finite Element Methods (ASEN 5007) Master 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. Outline, syllabus, coursework, schedule, roster ...
Part 0: Introduction
Chapter 1 Index. Introduction. HW#1 and solutions posted
Part 1: Variational Methods in Mechanics
Material available from Chapters of the (under development) web site: Advanced Variational Methods in Mechanics Covered AVMM chapters are directly linked below for convenience:
AVMM Ch 6 Index. Decomposition of Poisson Problems. AFEM HW#1 and solutions posted
AVMM Ch 7 Index. Weak and Variational Forms of Poisson's Equation. AFEM HW#2 posted & solutions posted
AVMM Ch 8 Index. The Bernoulli-Euler Beam. AFEM HW#2 solutions posted
AVMM Ch 10 Index Three-Dimensional Linear Elastostatics. AFEM HW#3, due 2/9/17, and solutions posted.
AVMM Ch 11 Index. The HR Variational Principle of Elastostatics. HW#3 solutions posted
AVMM Ch 12 Index. The Three-Field Mixed Principle of Elastostatics.
AVMM Ch 13 Index. Hybrid Variational Principles: Formulation. AFEM HW#4, due 2/16/17, and solutions posted
AVMM Ch 14 Index. Hybrid Variational Principles: 1D Application Examples. Renovated Feb 2017. HW#4 solutions posted
AVMM Ch 15 Index. Hybrid Variational Principles: 2D Application Examples. Under renovation.
Part 2: Axisymmetric Solids
Chapter 2 Index. Axisymmetric Solids, a.k.a. Structures of Revolution. AFEM HW#5 posted, due 2/23/17. Solutions posted
Chapter 3 Index. Axisymmetric Solid Iso-P Elements. HW#5 solutions posted
Chapter 4 Index. Iso-P Quadrilateral Ring Elements. Expanded chapter, rewritten in 2009.
Chapter 5 Index. Placeholder.
Chapter 6 Index. A Complete Axisymmetric FEM Program.
Chapter 7 Index. Axisymmetric Solid Benchmark Problems. Split from Ch 6 in 2013. HW#6, due 2/9/17, posted
Part 3: General Solids
Chapter 8 Index. Solid Elements: Overview.
Chapter 9 Index. The Linear Tetrahedron. AFEM HW#7 posted. Solutions posted
Chapter 10 Index The Quadratic Tetrahedron. AFEM HW#8 posted, due 3/23/17 Note: old Chapter: A Compendium of FEM Integration Rules, moved to Appendix I.
Chapter 11 Index. The 8-Node Hexahedron.
Chapter 12 Index. The 20-Node Hexahedron.
Chapter 13 Index. Placeholder.
Chapter 13 Index. Pyramid solid elements: a successful application of morphing.
Chapter 14 Index. Placeholder.
Part 4: Advanced Element Derivation Tools
Chapter 15 Index. The Patch Test. AFEM HW#9 posted, due 4/6/17
Chapter 16 Index. Finite Element Fabrication Overview.
Chapter 17 Index. Element Morphing. Under construction. Not covered.
Chapter 18 Index. Placeholder.
Chapter 19 Index. Placeholder.
Part 5: Thin Plates, Membranes, Templates
Chapter 20 Index. Kirchhoff Plates: Field Equations.
Chapter 21 Index. Kirchhoff Plates: BCs and Variational Forms.
Chapter 22 Index. Thin Plate Bending: Overview.
Chapter 23 Index. Triangular Plate Displacement Elements.
Chapter 24 Index. Placeholder.
Chapter 25 Index. Placeholder.
Chapter 26 Index. Finite Element Templates for Plate Bending. Transcribed from a 2000 book chapter.
Chapter 27 Index. Optimal Membrane Triangles with Drilling Freedoms. Transcribed from a 2003 paper.
Chapter 28 Index. A Template Tutorial. From a 2004 book chapter. Not covered in class.
Chapter 29 Index. Placeholder.
Chapter 30 Index. Placeholder.
Part 6: 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, Exam Material, and Project Material
Midterm Exams. Midterm Exam 1 posted 2/22/17. Solutions posted.
Appendix A Index. Removed.
Appendix B Index. Removed.
Appendix C Index. Removed.
Appendix G Index. Graphic Utilities.
Appendix I Index. A Compendium of FEM Integration Formulas.
Appendix R Index. References.
2006 Term Projects. Index for 2006 term projects.
2009 Term Projects. Index for 2009 term projects.
2011 Term Projects.
2013 Term Projects. Updated as of 5/8/13.
2017 Term Projects.
Last update: March 23, 2017.
This page constructed by Carlos Felippa: email@example.com