Computational Mechanics

Course Description: The course covers computational methods for the solution of problems in solid mechanics. The first half of the course focuses on finite element methods for linear elasticity, covering mixed, assumed strain, enhanced strain and other advanced methods addressing a number of limitations of basic methods, especially locking. The
different methods are presented with details of their numerical implementation and mathematical analysis.
Numerical techniques for the enforcement of constraints (like penalty and augmented Lagrangian methods) are also discussed in this context, considering different applications like incompressibility and contact problems. The second part of the course focuses on nonlinear problems in solid mechanics, including materially and geometrically nonlinear problems. Basic solution strategies for general nonlinear problems are covered first (like Newton-Raphson, line searches and arc length methods). Finite elements for finite deformation problems in solid mechanics are then discussed in detail.
The emphasis throughout the course is that the students program and incorporate all these different numerical methods
in an existing finite element code. Students need to have taken a basic course in finite element methods, with basic knowledge of solid mechanics (full course on nonlinear continuum mechanics not required), or consent of instructor.