ME 567 Advanced Finite Element Analysis

This advanced course in the finite element method begins with an overview of linear finite element analyses including the direct stiffness method, the principle of minimum potential energy, and the method of weighted residuals.  The sources of nonlinearity including geometric, material, and boundary condition nonlinearities are presented in detail.  Nonlinear compatibility and constitutive relationships are introduced.  Geometric nonlinearity topics include stress and strain measures for large deformation and total and updated Lagragian descriptions.  Material nonlinearity including yield criteria, work hardening, creep, and viscoelasticity and viscoplasticity are investigated.  Contact and friction are included as boundary condition nonlinearity topics. Incremental and iterative solution procedures for nonlinear problems including full and modified Newton-Raphson methods are also introduced.  Implicit and explicit time integration procedures are presented for nonlinear dynamic analyses.  Analyses will include the use of commercially available finite element software.