IUSS - Course "Nonlinear computational solid & structural mechanics"

"NONLINEAR COMPUTATIONAL SOLID & STRUCTURAL MECHANICS Theoretical formulation, FEM technology and computations"

Pavia dal 14 al 18 Maggio.

NL07 Course – May 14-18 2007

Dove:

IMATI-CNR - Via Ferrata 1, Pavia Italy

Course Program

May, Sunday 13

15:00 – 19:00 Participants registration

May, Monday 14

08:00 – 09:30 Participants registration

Morning session

09:30 – 09:50 Opening remarks
09:50 – 11:10 Lecture & Discussion
11:10 – 11:30 Coffee break
11:30 – 12:50 Lecture & Discussion
13:00 – 14:30 Lunch

Afternoon session

14:30 – 15:50 Lecture & Discussion
15:50 – 16:10 Coffee break
16:10 – 17:30 Lecture & Discussion

May, Tuesday 15 – Thursday 17

Morning session

08:30 – 09:50 Lecture & Discussion
09:50 – 11:10 Lecture & Discussion
11:10 – 11:30 Coffee break
11:30 – 12:50 Lecture & Discussion
13:00 – 14:30 Lunch

Afternoon session

14:30 – 15:50 Lecture & Discussion
15:50 – 16:10 Coffee break
16:10 – 17:30 Lecture & Discussion

May, Friday 18

Morning session

08:30 – 09:50 Lecture & Discussion
09:50 – 11:10 Lecture & Discussion
11:10 – 11:30 Coffee break
11:30 – 12:50 Lecture & Discussion

Detailed Course Program

Monday, 14 May 2007

1. Variational formulations in nonlinear solid mechanics (AI)

• Strong, weak and variational forms of 1D BVP in linear and
  nonlinear elasticity
• Basic solution methods: Gauss elimination and Newton
  iterations
• FEM technology in 1D problems: truss-bar element

2. Numerical implementation in FEM code FEAP (RLT)

• FEM technology in 1D structural problems: Euler-Bernoulli and
  Timoshenko beam models
• Macro command programming language
• Programming in FEAP environment

3. FEM technology for 2D/3D BVP in elasticity (AI)

• 2D/3D models: thermal and mechanics problems
• Isoparametric elements and numerical integration
• Non-conventional interpolations and solid elements with drilling
  degrees of freedom

4. Enhancing FEM performance – element technology (RLT/FA)

• Structural models: plates and shells
• Hybrid and mixed models
• Enhanced strain models

Tuesday, 15 May 2007

5. Theoretical foundation of mixed interpolation methods (FB)

• Locking phenomena
• Inf-sup condition
• Stabilization techniques

6. Inelastic constitutive behavior at small strains (AI)

• Thermomechanics with internal variables
• Refined constitutive models of plasticity, damage and coupled
  damage-plasticity
• Solution of weak form with internal variables

7. Implementation and performance of nonlinear constitutive
models in FEM framework (RLT)

• Integration of evolution equations
• Operator split method and consistent tangent modulus
• Locking problems in plasticity
• Choice of element type

8. Solution techniques and element performance for non-linear
problems (RLT)

• Nonlinear problem solution techniques
• Explicit vs. implicit integration schemes
• Generalized a-scheme and schemes for stiff equations
• Solution techniques with computer code FEAP

9. Advanced costitutive models (FA)

• Refined constitutive models of plasticity
• Inelastic models for solid phase transitions

Wednesday, 16 May 2007

10. Discontinuous Galerkin methods (FB)

• Introduction to DG methods
• DG methods for nearly incompressible materials
• DG methods for Reissner-Mindlin plates

11. Nonlinear solid mechanics problems at large displacements
(AI)

• Kinematics and strain measure at large displacement
• Piola-Kirchhoff first and second stress tensors
• Finite element interpolations; Consistent linearization

12. Nonlinear constitutive models for large displacements (AI)

• Nonlinear elasticity and poly-convexity conditions
• Constitutive law at large deformations: plasticity
• Lagrangian and Eulerian formulations

13. Contact problems (RLT)

• Formulation of contact problems (penalty, augmented
  Lagrangian)
• Implementation of mortar method and stress computation
• Impact dynamics and contact

14. Solution techniques for non-linear transient problems (RLT)

• Nonlinear heat transfer, nonlinear dynamics
• Explicit vs. implicit integration schemes
• Generalized a-scheme and schemes for stiff equations

Thursday, 17 May 2007

15. Nonlinear structural mechanics / I (AI)

• Computational aspects of large 3D rotations
• Geometrically exact beam model of Reissner and Simo
• Locking problems for structures

16. Nonlinear structural mechanics / II (AI)

• Geometrically exact shell models with or without drilling
  rotations
• Locking problems in shells
• Dynamics and time-integration schemes for shells

17. Flexible multibody system dynamics (RLT)

• Formulation of multibody systems: holonomic and nonholonomic
  constraints
• Modeling of flexible multibody systems and cost reduction: rigid
  component approximation

18. Instability of structures and systems (AI)

• Geometric instability: (buckling) vs. material instability
  (localization)
• Solution of problems in presence of critical points
• Dynamic instability problems

19. Advanced aspects of multi-physics problems (AI)

• Modeling of nonlinear multi-physics problems
• Thermomechanical coupling: isothermal and adiabatic operator
  split

Friday, 18 May 2007

20. Mathematical considerations on advanced FE techniques (FB)

• Contact problems
• Post-processing and solution recovery

21. Advanced aspects of multi-scale problems (AI)

• Multi-scale models of inelastic behavior
• Microstructure representation
• Heterogeneities of real materials and probability approach

22. Solution methods for coupled and interaction problems (RLT)

• Experience with large-scale nonlinear problems
• Software architecture and code coupling
• Remarks on computer code development

Document - PDF file, 779Kb

Download Flyer

NL07_flyer.pdf

More information

Organizing Committee

Prof. Ferdinando Auricchio (auricchio AT unipv DOT it)
Dr. Edoardo Artioli (artioli AT imati DOT cnr DOT it)
Dr. Alessandro Reali (alessandro DOT reali AT unipv DOT it)

Secretariat

NL07 Secretariat c/o IMATI - CNR
Via Ferrata,1 - 27100 Pavia, Italy
Tel.: +39.0382.548229
Fax.: +39.0382.548300
E-mail: NL07 AT imati DOT cnr DOT it
Web: www.imati.cnr.it/nl07/