This is an introductory course for graduate students . The course is tailored to introduce students to the finite element method with applications to mechanics. The course covers the following topics:
- Introduction to the finite element method in 1D: strong form, weak form, minimum potential energy theorem, Rayleigh-Ritz method, Galerkin method, isoparametric mapping, finite element shape functions, element stiffness matrix and force vector, numerical integration.
- The finite element method in heat transfer: heat conduction, strong form, weak form, numerical integration, finite element solution.
- The finite element method in linear elastostatics: linear elasticity, strong form, weak formulations: Galerkin method, minimum potential energy method virtual work method, numerical integration, incompressible linear elasticity, mixed formulations, finite element solution.
- The finite element method in fluid mechanics: Navier-Stokes equations, constitutive model for Newtonian fluids, Stokes flow, boundary conditions for fluids, incompressibility condition, penalty function, finite element solution.
- The finite element method in structural mechanics: Strong form and weak form for the Euler-Bernoulli beam, strong and weak form for the Mindlin-Reissner plate, finite element solution .
- Introduction to nonlinear finite elements with applications to nonlinear elasticity: numerical solution of nonlinear problems, Newton’s method, Lagrangian strong and weak formulation for nonlinear elasticity, linearizations, finite element solution.
Although implementation of methods that are taught in this course are available in commercial simulation packages, students are expected to implement their own codes. Commercial codes are not allowed in this course.