http://www.unipv.it/compmech/NL20 course/program 
NONLINEAR COMPUTATIONAL SOLID & STRUCTURAL MECHANICS
Theoretical formulations, technologies and computations
May 2529, 2020


NL20 course>Program  
COURSE SCHEDULE
09.0010.00 Lecture 1
10.0010.15 Coffee break 10.1511.15 Lecture 2 11.1512.15 Lecture 3 12.1514.00 Lunch 14.0015.00 Lecture 4 15.0015.15 Coffee break 15.1516.30 Tutorial 16.3017.00 Open discussion PROGRAM
Monday
1. Variational formulation in linear solid mechanics (RLT) Strong, weak and variational forms of BVP in linear elasticity FEM technology for 1D problems 2. FEM technology in 1D problems (MB) Axisymmetric 1d elasticity EulerBernoulli and Timoshenko beam models Locking numerical evidences 3. FEM technology in solids problems (MB) Isoparametric elements and numerical integration Incompressibility / near incompressibility Hybrid and mixed FE Enhanced strain FE 4. Structural finite elements (MB) Dimensional reduction Plate and shell models Finite elements for thinwalled structures 5. Introduction to FEAP and problem solution (TUTORIAL) Tutorial on FEAP command language Tutorial on programming in FEAP environment Tuesday 6. Enhancing structural FEM performance (MB) Shell theory and finite elements Assumed strain and enhanced strain FE Reduced integration plus stabilization 7. Theoretical foundation of mixed interpolation methods (FB) Locking phenomena Infsup condition 8. Inelastic constitutive behavior at small strains (FA) Inelasticity and plasticity models Solution schemes (return map) Integration of evolution equations Operator split method and consistent tangent modulus 9. Nonlinear solid mechanics for large displacements (FA) Kinematics and strain measure at large displacement First and second PiolaKirchhoff, Kirchhoff and Cauchy stress tensors. Finite element interpolations; consistent linearization 10. Locking problems in plasticity (TUTORIAL) Development and debugging of inelastic models Choice of element type for FE analysis Tutorial on FEAP Command language Tutorial on programming usermodels in FEAP environment Wednesday 11. Advanced inelastic constitutive behavior at small strains (FA) Generalized plasticity Nonlinear kinematic hardening Shapememory alloys Extension to capture soil/concrete behaviors 12. Nonlinear constitutive models for large displacements (FA) Formulations in reference and current configurations Finite elasticity (stored energy function forms) 13. Nonlinear structural mechanics and stability analysis (MB) Nonlinear structural models Solution methods, path following techniques Identification of critical points, buckling and snapthrough phenomena Prebuckling analysis and nonlinear stability analysis 14. Nonlinear constitutive models for large displacements (FA) Plasticity at large deformations 15. Nonlinear problems (TUTORIAL) Example on instability issues using symbolic approach Finitestrain problem solution in FEAP Programming finitestrain usermodels in FEAP Thursday 16. Isogeometric modeling and analysis (AR) Introduction to splines and NURBS Basics of isogeometric analysis Simple investigations 17. Isogeometric modeling and analysis (GS) Properties of isogeometric fields Local refinement by non tensorproduct splines Incompressible materials: stability and divfree exactness ReissnerMindlin plates and KirchoffLove limit 18. Isogeometric modeling and analysis (RLT) Computational technologies Implementation details for displacement and mixed forms Examples applications for elastic and inelastic materials 19. Structural Dynamics Problems (AR) Explicit vs. implicit integration schemes Central difference, Newmark, and generalized alphamethods High order approximations in structural vibration and dynamics 20. Tutorial on isogeometric analysis (TUTORIAL) Simple inhouse Matlab codes Isogeometric problem solution in FEAP Friday 21. Contact problems (RLT) Formulation of contact problems (penalty, augmented Lagrangian) Implementation of nodal and surface methods Impact dynamics and contact 22. Particle, meshless, and collocation schemes (AR) An introduction to meshless methods Smoothed particle hydrodynamics and other approaches Some recent developments on particle methods Isogeometric collocation methods 23. Fluid Dynamics and Fluid Structure Interaction (MB) Phenomena of fluid flow, incompressible NavierStokes equations Computational modeling of fluids Basic remarks on coupled problems, phenomena of fluid structure interaction, solution algorithms for FSI problems 24. Multiscale problems (RLT) Homogenization methods Scale bridging using representative volume elements (FE2) Parallel implementation details Example applications 25. Virtual Element Methods in Structural Mechanics (FB) Poligonal and polyhedral decompositions Applications to linear elasticity, plate bending Application to composite and/or fractured materials 
NL20 Secretariat: Sonia Padovan Address: via Ferrata 3, 27100 Pavia, Italy Email: sonia.padovan@unipv.it Secretariat: +390382985463 Fax: +390382528422 