Academics / Courses / Course DescriptionsCIV_ENV 327: Finite Element Methods in Mechanics
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Prerequisites
Basic computer programming (in Python)Description
Course Level: Undergraduate / Graduate
Tools & Software: Python (NumPy, scikit-learn), Abaqus, Jupyter Notebooks
Course Description: This course provides a practical introduction to the Finite Element Method (FEM), with an emphasis on hands-on implementation using Python. It covers the basic theoretical concepts necessary to understand and apply FEM, without going into extensive mathematical detail. Students will learn how to build FEM solvers with minimal external dependencies and how to use a general-purpose framework (Abaqus). The course focuses on solving elliptic partial differential equations, with applications in heat conduction, linear elasticity, and potential flow, covering a broad range of topics relevant to students of civil and mechanical engineering.
Instructor:
Dr. Bahador Bahmani
Catalysis Building, Room 321
Email bahador.bahmani@northwestern.edu
Grading:
Homework 40%, Exams 60% (Midterm 20%, Final Exam 20%, Final Project 20%), Class participation/engagement bonus (+15%)
| Topics | Sessions | Problems |
|---|---|---|
| Introduction and review basic numerical methods (differentiation and integration), matrix operations, calculus of variations, etc. | 3 | HW 1 (written + programming) |
| Strong and weak forms, boundary conditions, Rayleigh–Ritz, weighted residuals, and Galerkin methods. | 3 | HW 2 & 3 (written) |
| One-dimensional FEM for scalar fields | 3 | HW 4 & 5 (written + programming) |
| Two-dimensional FEM for scalar fields (heat conduction) | 4 | HW 6 (written + programming) |
| Two-dimensional FEM for vector fields (planar elasticity) | 4 | HW 7 (written + programming) |
| Advanced topics: locking, reduced integration, machine learning techniques, etc. | 4 | — |
Textbooks:
- (Highly Recommended) J. Fish and T. Belytschko. A first course in finite elements. Wiley & Sons Ltd., West Sussex, UK, 2007.
- (Recommended) J.R. Hughes, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Dover Publications, Inc., Mineola, NY, 2000.
- Zienkiewicz, Olgierd Cecil, and Robert Leroy Taylor. The finite element method for solid and structural mechanics. Elsevier, 2005.
Other References:
- Liu’s FEM lecture notes (previous years)
- Liu, Wing Kam, Shaofan Li, and Harold S. Park. "Eighty years of the finite element method: Birth, evolution, and future." Archives of Computational Methods in Engineering 29.6 (2022): 4431-4453.