MAE5007 Advanced Computational Solid Mechanics

Instructor

• Dr. Ju Liu, Assistant Professor of MAE Department
• Office: Room 1004 North Engineering Building
• Contact by email

Teaching Assistants

TBA

Goals

This course aims to provide students with an in-depth understanding of the finite element method, with a focus on nonlinear and inelastic problems. The theoretical foundation and implementation of the finite element method will be covered, with applications primarily in the static and dynamic analysis of solids and structures.

Prerequisites

Calculus, Linear algebra, and MATLAB programming are required. It is preferable to have some basic knowledge of the finite element method and elasticity.

Grading policy

• Homework assignment: 40%
• Mid-term exam: 25%
• Final presentation & report: 32% [list of journal articles]
• Class participation: 3%

Schedule

• Lecture 01 - Heat equation: Strong- and weak-form problems. [notes]
• Lecture 02 - Heat equation: Galerkin formulation. [notes]
• Lecture 03 - Heat equation: Local assembly procedure. [notes]
• Lecture 04 - Heat equation: Formulation of the nonlinear problem I. [notes]
• Lecture 05 - Solution algorithm for nonlinear problems: Newton-type methods. [notes]
• Lecture 06 - Solution algorithm for nonlinear problems: Line-search and BFGS. [notes]
• Lecture 07 - Heat equation: Formulation of the nonlinear problem II. [notes]
• Lecture 08 - Small-strain nonlinear elastostatics. [notes]
• Lecture 09 - Finite-strain elasticity: Kinematics. [notes]
• Lecture 10 - Finite-strain elasticity: Balance equations and linearization. [notes]
• Lecture 11 - Finite-strain elasticity: Constitutive theory. [notes]
• Lecture 12 - Finite-strain elasticity: Dynamics. [notes]

Assignments

• Assignment 1 - Due Mar. 4 2024.
• Assignment 2 - Due Mar. 25 2024.
• Assignment 3 - Due Apr. 15 2024.
• Assignment 4 - Due May 13 2024.
• Assignment 5 - Due Jun. 10 2024.

References

• The Finite Element Method: linear static and dynamic finite element analysis, T.J.R. Hughes, Dover 2000. [JD]
• Computational Inelasticity, J.C. Simo and T.J.R. Hughes, Springer 2000. [JD]
• Nonlinear Finite Elements for Continua and Structures, W.K. Liu, B. Moran, T. Belytschko, and K. Elkhodary, Wiley, 2014. [JD]
• Computational methods for plasticity: theory and applications, E.A. de Souza Neto, D. Peric and D.R.J. Owen, John Wiley & Sons, 2008. [JD]
• Nonlinear solid mechanics: a continuum approach for engineering, G.A. Holzapfel, John Wiley & Sons, 2000. [JD]
• Methods of applied mathematics, T. Arbogast and J.L. Bona. [Link]