Numerical methods and techniques for solving initial boundary value problems in solid mechanics (heat conduction, static and dynamic mechanics problems of solids and structures). Finite difference methods, indirect and direct techniques, variational calculus, finite element (FE) method, FE analysis in small strains for applications in structural mechanics and solid mechanics.
To understand the concepts and application of numerical techniques for the solution of initial boundary value problems in solid and structural mechanics, particularly including the finite element method for static and dynamic problems.
1. Introduction, dimensionless forms, direct and indirect numerical methods. 2. Finite differences, stability analysis. 3. Methods of weighted residuals. 4. Variational calculus, variational methods. 5. Finite element method. 6. Structural elements (bars and beams). 7. 2D and 3D elements (isoparametric and simplicial elements), numerical quadrature. 8. Assembly, solvers, finite element technology. 9. Dynamics, transient analysis, vibrations. 10. Selected topics in finite element analysis.
Lecture notes will be provided for reference. Students are encouraged to take their own notes during class.
No textbook required; relevant reference material will be suggested.