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 23 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 & seniorelective level (in preparation) MFEMS: Matrix Finite Element Methods in Statics Master & seniorelective 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 BernoulliEuler Beam. AFEM HW#2 solutions posted AVMM Ch 10 Index ThreeDimensional 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 ThreeField 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 IsoP Elements. HW#5 solutions posted Chapter 4 Index. IsoP 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 8Node Hexahedron. Chapter 12 Index. The 20Node 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 ThinShell Element. Reproduces Chapter 4 of Bjorn Haugen's thesis. Chapter 34 Index. A Quadrilateral ThinShell Element. Reproduces Chapter 5 of Bjorn Haugen's thesis. Chapter 35 Index. Numerical Examples of Thin Shell Analysis.. Reproduces Chapters 68 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: carlos.felippa@colorado.edu