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Abstract
We discuss numerical methods for solving initial boundary value problems in solid mechanics (static/dynamic elastic problems of solids and structures, thermal problems). Focus is on finite differences and on the finite element method, its theoretical foundation, the choices made when using it, its application for solving problems of engineering interest, and the interpretation of results.
Objective
By the end of this course, students will be able to apply the computational methods of finite differences (FDs) and finite elements (FEs) to analyze and solve mechanical and thermal engineering problems with a focus on elastic solids and structures. Specifically, students will be able to (1) solve initial boundary value problems by finite differences, (2) solve mechanical boundary value problems and initial boundary value problems by finite elements, and (3) create numerical code that implements finite difference and finite element techniques.
Content
1. Introduction, direct and indirect numerical methods. 2. Finite differences, stability analysis. 3. Variational methods. 4. Finite element method. 5. Structural elements (bars and beams). 6. 2D and 3D solid elements (isoparametric and simplicial elements), numerical quadrature. 7. Assembly, solvers, finite element technology. 8. Dynamics, vibrations. 9. Selected topics in finite element analysis.
Resources
Lecture Notes
Lecture notes will be provided. Students are encouraged to take their own notes during class.
Literature
No textbook required; relevant reference material will be suggested.