Homework Exercises For Chapter 5 Asen 5007

Presentation on theme: "University of Colorado - Dept of Aerospace Engineering Sciences This is ASEN 6107: Nonlinear Finite Element Methods."— Presentation transcript:

1 University of Colorado - Dept of Aerospace Engineering Sciences This is ASEN 6107: Nonlinear Finite Element Methods

2 University of Colorado - Dept of Aerospace Engineering Sciences Course Prerequisites An advanced, graduate-elective course offered every 2 years (occasionally 3). Primarily a continuation of ASEN 5007: Introduction to Finite Element Methods (IFEM) Prerequisites: A graduate-level intro course in FEM Uses Linear Algebra & Differential Equations at a deeper level than IFEM Prior experience in solving nonlinear equations helpful but not required

3 University of Colorado - Dept of Aerospace Engineering Sciences Course Web Site Course web site: http://caswww.colorado.edu/courses.d/NFEM.d/Home.html All ready-to-post course material: syllabus, coursework info, office hrs, Notes, class slides, Homework, HW solutions, and so on, will be placed there. Material ready to download is marked by an asterisk * at link start

4 University of Colorado - Dept of Aerospace Engineering Sciences Coursework Grading Weights Weekly homework: 30% (Posted on website) Two take-home midterm exams: 20% each (Usually posted on website Tu, due Th @ class time) Final take home exam: 20% (Posted on web site on or before Fri April 27, due on last class Th May 3)

5 University of Colorado - Dept of Aerospace Engineering Sciences Course Syllabus Part 1. Overview of Nonlinear Problems Part 2. Formulation of Geometrically Nonlinear Finite Elements Part 3. Solution of Nonlinear Equations Part 4. Computer Implementation of Nonlinear Analysis (concurrent w/Parts 2-3) Part 5. Applications to Structural Stability Part 6. Nonconservative Problems

6 University of Colorado - Dept of Aerospace Engineering Sciences Homework Rules Usually assigned weekly, except for take home exam weeks and final week. Group collaboration for HW allowed. However each student must submit own HW, with names of collaborators if group work was done. If identical HWs are submitted, no credit is given. See posted HW rules for details.

Introduction to Finite Element Methods (ASEN 5007)
Fall 2017
Department of Aerospace Engineering Sciences
University of Colorado at Boulder

This is the public web site for the graduate core course ASEN 5007: IntroductionTo Finite Element Methods (IFEM). This master levelcourse 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 9/7/17. Solutions posted
Chapter 3 Index. The Direct Stiffness Method II. HW#1 solutions posted
Chapter 4 Index. Plane Truss Analysis by a CAS. HW#2 posted, due 9/14/17. 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 posted, due 9/21/17. Solutions posted
Chapter 8 Index. Multifreedom Constraints I. HW#4 posted, due 9/28/17. Has detailed info on Midterm 1. Solutions posted
Chapter 9 Index. Multifreedom Constraints II. HW#4 solutions posted
Chapter 10 Index. Superelements and Global-Local Analysis. HW#5 posted, due 10/5/17. Solutions posted

Part II: Mathematical Formulation of Finite Elements
Chapter 11 Index. Variational Formulation of Bar Element. HW#6 posted, due 10/19/17. Solutions posted
Chapter 12 Index. Variational Formulation of Plane Beam Element. HW#6 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#7 posted, due 10/26/17. Solutions posted.
Chapter 16 Index. The Isoparametric Representation. HW#7 Solutions posted
Chapter 17 Index. Isoparametric Quadrilaterals. HW#8 posted, due 11/2/17, has info on Midterm 2. Solutions posted
Chapter 18 Index. Shape Function Magic. HW#8 solutions posted
Chapter 19 Index. FEM Convergence Requirements HW#9 posted due 11/9/17; has info on Midterm 2.Solutions posted

Part III: Computer Implementation of Finite Elements
Chapter 20 Index. Implementation of One-Dimensional Elements. HW#10 posted, due 11/30/17. Solutions posted
Chapter 21 Index. FEM Program for Space Trusses. HW#10 solutions posted
Chapter 22 Index. FEM Programs for Frameworks. Not covered
Chapter 23 Index. Implementation of iso-P Quadrilateral Elements. HW#11 posted, due 12/7/17. Solutions posted
Chapter 24 Index. Implementation of iso-P Triangular Elements. HW#11 solutions posted
Chapter 25 Index. The Assembly Process. HW#12 (last HW) due 12/14/16, posted. Containsinformation on TH final exam.
Chapter 26 Index. Solving FEM Equations. Not covered
Chapter 27 Index. A Complete Plane Stress FEM Program. For demos.
Chapter 28 Index. Stress Recovery.
Chapter 29 Index. Fitting Fields Over Triangles (in progress) Not covered
Chapter 30 Index. Thermomechanical Effects. Not covered

Part IV: Intro to Dynamics and Vibrations
This Part has been moved to the MFEMD web site.

Appendices & Miscellaneous Stuff
Appendix A Index. Linear Algebra: Vectors.
Appendix B Index. Linear Algebra: Matrices.
Appendix C Index. Linear Algebra: Matrix Calculus.
Appendix E Index. Linear Algebra: Eigenproblems.
Appendix F Index. Fitting Element Fields.
Appendix G1 Index. Graphics Utilities: Contour Plotters.
Appendix G2 Index. Graphics Utilities: Shape Plotters.
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.
Appendix T Index. Three-Dimensional Continuum Mechanics.
CAETE PPT files . Chapters 1-21, 23-28.

Exam Material
Exam Material Index. Midterm exams 1 and 2,and their solutions posted. Final exam posted 12/13/17 at noon.

Last update: December 13, 2017.

This page constructed by Carlos Felippa: carlos.felippa@colorado.edu


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