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CVEN 5511: Introduction to Finite Element Analysis
Description
Theory and application of the linear, static and dynamic, finite element method for continuum mechanics. We will work through, in detail, the formulation of finite element equations for a 1D axially-loaded bar: differential equation (strong form), integral or variational equation (weak form), discrete approximation of weak form (Galerkin form), and the finite element equations (matrix form to solve numerically). We will derive shape functions and discuss numerical integration. We will formulate and integrate numerically in time the 1D elastodynamics equations for transient analysis and discuss modal analysis. We will study also linear heat conduction and linear elastostatics for 2D and 3D boundary value problems. Proper use of finite elements and appropriate prescription of boundary conditions will be discussed. Matlab (or other "programming language") will be used to program and solve finite element equations for simple boundary value problems. You will complete assignments and a project using the finite element analysis software package Abaqus, (www.simulia.com), or a theoretical project involving formulation and coding of finite element equations. You will learn to use the Abaqus UEL (user element coded in Fortran). We have 20 Expanded Teaching Edition CAE seats (100 analysis tokens) in the Bechtel Lab, and Student Editions will be available in the book. Usage of Abaqus will be covered in separate Bechtel lab sessions (time TBD).
SAME AS CVEN 4511.
SAME AS CVEN 4511.
Outline
1. Theory and programming of FE equations (some sections referred to Hughes book).
- One-dimensional bar (Ch.1): strong form, weak form, Galerkin approximation, finite element shape functions and equations; convergence and completeness; boundary conditions; multi-element assembly; natural coordinate and spatial numerical integration; dynamics and temporal numerical integration; modal analysis
- Two-dimensional linear heat conduction (Sect. 2.1-2.6, Sect. 7.1, Sect. 8.1) and analogy to groundwater flow: strong form to finite element equations; triangular and quadrilateral elements; isoparametric elements and spatial numerical integration; multielement assembly; analysis of simple thermal problems; analogy to groundwater flow; temporal numerical integration of parabolic equations (generalized trapezoidal rule)
- Two- and three-dimensional linear elastostatics and dynamics (Sect. 2.8-2.12, Ch. 3, Sect. 4.6, Sect. 7.2, 7.3, Sect. 9.1, 9.2): general three-dimensional, plane stress, plane strain, and axisymmetric formulations; hexahedral element; temporal numerical integration of hyperbolic equations (Newmark's method); modal analysis
- Project: The project report will be due the last day of class, and you will deliver a short 10min presentation of your results. You will be required also to meet with Prof. Regueiro in order to have your project idea approved. The objective of the project is to expose you to a finite element analysis experience using a commercial program (e.g., Abaqus) that you may encounter while working at an engineering design firm, or to expose you to a research-oriented finite element programming experience. Those interested in more theoretical aspects of the FEM may choose to do a theoretical/programming project with the approval of Prof. Regueiro.
Objectives
Sufficient understanding of the theory of the finite element method and its practical application in order to use commercial finite element software knowledgably or develop your own finite element code for analyzing continuum mechanics problems.
Prerequisites
CVEN 3161 and APPM 2360, or equivalent; introductory structural mechanics and mechanics of materials, linear algebra, some basic coding experience. Matlab is useful. Review the tutorials on the CULearn webpage if you are unfamiliar with Matlab. Mathematica can also be useful and
has its own short 10 minute tutorial when opened.
Education Officer (EO)
Required
Textbooks
None required; notes provided. Books on reserve in the Engineering Library:
- Astley, Finite Elements in Solids and Structures, Chapman & Hall, 1992.
- Bathe, Finite Element Procedures, Prentice-Hall, 1995.
- Cook et al., Concepts and Applications of Finite Elements Analysis, 4th ed., John Wiley & Sons, 2001.
- Fish and Belytschko, A First Course in Finite Elements, Wiley, 2007. Book website.
- Hughes, The Finite Element Methods: Linear Static and Dynamic Finite Element Analysis, Dover, 2000.
Upcoming & Previous Offerings
Meeting Days Legend: Monday (M), Tuesday (T), Wednesday (W), Thursday (R), Friday (F), Saturday (S), Sunday (U)
Summer Terms: M = Maymester, A = 1st 5 weeks, B= 2nd 5 weeks, C = 8 weeks, D= 10 weeks
Refer to the Academic Calendar for specific dates.
| Semester | Term | Time | Days | Location | Instructor | Additional Instructors |
| Fall 2007 | 09:30 AM - 10:45 AM | TR | ECCS 1B14 | Regueiro, R |
