UE Numerical methods for nonlinear mechanics

Description

From physics to numerical models: continuum mechanics problems, variational formulations, Rayleigh Ritz methods, Finite element one dimensional example
Introduction to solid mechanics problems : elastostatics virtual work theorem : finite element discretization, the example of simple finite elements (constant strain triangle), Comments about Stiffness matrices
Variational formulation of an initial boundary value problem: change of configuration, introduction to different stress and deformation tensors, the so called small strain approximation
Time discretization and incremental problem: Newton method, residual computations, auxiliary linear system computations, boundary condition issues
Space discretization : finite element method, projection on to a finite dimensional space, isoparametric finite element numerical integration Gauss method
Constitutive equations integrations : consistent tangent stiffness matrix: numerical approach, Hardening plasticity, integration algorithms, consistent tangent stiffness matrix : analytical approach, Locking ant related topics
Miscellaneous : coupling problems, the rate problem and uniqueness issues

Semester 9