http://www.unipv.it/compmech/NL20 course/program

  Istituto Universitario di Studi Superiori di PaviaUniversità degli studi di PaviaIstituto di Matematica Applicata e Tecnologie InformaticheEccomas
NONLINEAR COMPUTATIONAL SOLID & STRUCTURAL MECHANICS
Theoretical formulations, technologies and computations
May 25-29, 2020
NL20 course>Program

COURSE SCHEDULE

09.00-10.00 Lecture 1
10.00-10.15 Coffee break
10.15-11.15 Lecture 2
11.15-12.15 Lecture 3
12.15-14.00 Lunch
14.00-15.00 Lecture 4
15.00-15.15 Coffee break
15.15-16.30 Tutorial
16.30-17.00 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 1-d elasticity
Euler-Bernoulli 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 thin-walled 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
Inf-sup 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 Piola-Kirchhoff, 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 user-models in FEAP environment

Wednesday
11. Advanced inelastic constitutive behavior at small strains (FA)
Generalized plasticity
Nonlinear kinematic hardening
Shape-memory 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 snap-through 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
Finite-strain problem solution in FEAP
Programming finite-strain user-models 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 tensor-product splines
Incompressible materials: stability and div-free exactness
Reissner-Mindlin plates and Kirchoff-Love 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 alpha-methods
High order approximations in structural vibration and dynamics
20. Tutorial on isogeometric analysis (TUTORIAL)
Simple in-house 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 Navier-Stokes equations
Computational modeling of fluids
Basic remarks on coupled problems, phenomena of fluid structure interaction, solution algorithms for FSI problems
24. Multi-scale 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
E-mail: sonia.padovan@unipv.it
Secretariat: +39-0382-985463
Fax: +39-0382-528422