Lecture notes for MECH4103: Finite Element Method, taught by Dr. Behrouz Arash, Associate Professor in Mechanical Engineering at Oslo Metropolitan University (OsloMet).
| # | Topic | File |
|---|---|---|
| 02 | Discrete Systems | lecture02_discrete_systems.pdf |
| 03 | Strong and Weak Forms: 1D Problems | lecture03_srong_weak_forms_1D.pdf |
| 04 | Approximation of Trial Solutions: 1D | lecture04_trial_solutions_1D.pdf |
| 05 | Finite Element Approximation: 1D Problems I | lecture05_fem_1D_1.pdf |
| 06 | Finite Element Approximation: 1D Problems II | lecture06_fem_1D_2.pdf |
| 07 | Convergence | lecture07_convergence.pdf |
| 08 | Isoparametric Formulation | lecture08_isoparametric_formulation.pdf |
| 09 | Divergence Theorem | lecture09_divergence_theorem.pdf |
| 10 | Strong and Weak Forms: 2D/3D Problems | lecture10_srong_weak_forms_2D_3D.pdf |
| 11 | Trial Solutions 2D/3D, Part 1 | lecture11_trial_solutions_2D_3D_1.pdf |
| 12 | Trial Solutions 2D/3D, Part 2 | lecture12_trial_solutions_2D_3D_2.pdf |
| 13 | Trial Solutions 2D/3D, Part 3 | lecture13_trial_solutions_2D_3D_3.pdf |
| 14 | FEM for 2D/3D Scalar Field Problems | lecture14_fem_2D_3D_scalar_field.pdf |
| 15 | Mesh Generation | lecture15_mesh_generation.pdf |
| 16 | FEM for Multidimensional Vector Field Problems, Part 1 | lecture16_fem_2D_3D_vector_field_1.pdf |
| 17 | FEM for Multidimensional Vector Field Problems, Part 2 | lecture17_fem_2D_3D_vector_field_2.pdf |
| 18 | Linear Dynamics | lecture18_linear_dynamics.pdf |
| 19 | Structural Elements | lecture19_structural_elements.pdf |
| 20 | Introduction to Nonlinear FEM | lecture20_nonlinear_fem_intro.pdf |
| 21 | Kinematics and Strains (Nonlinear) | lecture21_kinematics_strains.pdf |
| 22 | Weak Form Linearisation | lecture22_weak_form_linearisation.pdf |
The course progresses through four major modules:
Introduction to discrete systems, strong and weak formulations, Galerkin trial solutions, 1D finite element approximation, and convergence analysis.
Isoparametric formulation, divergence theorem, 2D/3D strong and weak forms, shape functions for triangular and quadrilateral elements, scalar field problems, and mesh generation.
FEM for elasticity and vector field problems in 2D/3D, linear dynamics (modal analysis, time integration, damping), and structural elements.
Introduction to nonlinear FEM, finite kinematics and strain measures (deformation gradient, Green–Lagrange strain), hyperelastic constitutive models, and weak form linearisation for Newton's method.
Students are expected to have background knowledge in:
- Continuum mechanics and solid mechanics
- Linear algebra and calculus
- Ordinary and partial differential equations
- Basic programming skills
- T.J.R. Hughes, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Dover, 2000.
- P. Wriggers, Nonlinear Finite Element Methods, Springer, 2008.
- O.C. Zienkiewicz & R.L. Taylor, The Finite Element Method, Butterworth-Heinemann.
| Course | MECH4103 — Finite Element Method |
| Institution | Oslo Metropolitan University (OsloMet) |
| Instructor | Dr. Behrouz Arash |
| Term | Spring 2026 |
Note: These lecture notes are for educational purposes. Please respect the intellectual property of the course instructor.