Course Details

Basic principles of Continuum Mechanics. Nonlinear kinematic relations, Green-Lagrange strains. Cauchy and Piola-Kirchoff stresses. Principle of virtual work, nonlinear equilibrium equations. Total and updated incremental Lagrangian formulations.

Linearization of equilibrium equations. Incremental-iterative solution methods for the static and dynamic nonlinear equilibrium equations. Newton-Raphson type methods and path-following strategies with line search and arc length techniques for overpassing limit points. Geometrically nonlinear isoparametric finite elements of 2D and 3D elasticity problems as well as of plates and shells.

Tangent stiffness matrices. Material nonlinearity. Explicit and implicit integration of the incremental stresses. Tangent and consistent constitutive matrices. Elastoplastic stiffness matrices of isoparametric 2D and 3D continuum elements and isoparametric plates and shell structural elements. Applications of nonlinear FEA using commercial finite element codes.