Numerical Analysis

Lecture Schedule

1. Physical nonlinearity - rate independent plasticity - 3D formulation

2. Physical nonlinearity - rate dependent plasticity - 3D formulation

3. Physical nonlinearity - rate dependent plasticity with thermal softening - 3D formulation

4. Physical nonlinearity - scalar damage model - 3D formulation

5. Physical nonlinearity - hyperelastic materials

6. Introduction to linear thermomechanics

7.-8. Introduction to non-linear thermomechanics

9.-10. Review of finite elements for thermomechanical analyses

11.-12.Modeling of Interaction of Solids

13-14. Overview of the most important computer methods in civil engineering

15. Summary of lectures

Plan of exercises and laboratories

1. Dynamic calculation of cantilever loaded with concentrated force at the end: statics, the problem of natural vibrations, linear dynamics: in time and frequency domain, nonlinear dynamics. Comparison and interpretation of results. (Abaqus)

2. Dynamic calculations with the assumption of an explicit method of time integration of the interaction of the projectile and two bars. Analysis of wave phenomena in the mechanical system. Comparison with analytical solutions (Abaqus, Scilab)

3. Numerical analysis of the HMH plasticity surface in a plane state of stress for different stress ratios Sigma 11 and Sigma 22 for a given material with elastic-plastic properties. Comparison of simulation results with an analytical solution (Scilab, Abaqus)

4. Analysis of a tensile sample with a elastic-plastic material. Comparison of results: stresses, global and local strains with input data. Analysis of results and their interpretation (Abaqus)

5. Analysis of a tensile sample with a hyperelastic material (curve from task 4) - load and relieve. Analysis of results and their interpretation (Abaqus)

6. Calculations of stresses and deformations of steel frame during fire: sequential and coupled analysis (thermal-displacement). Analysis of finite elements used, material properties dependent on temperature (elastic-plastic model), thermal and mechanical loads (Abaqus)

7. Individual project carried out in pairs on the analyzed issues and its presentation before the whole group. (Abaqus)

Literature

1. O.A. Bauchau, J.I. Craig, Structural Analysis, With Applications to Aerospace Structures, Springer, 2009

2. T. Belytschko, W. Kam Liu, B. Moran, Nonlinear finite elements for continua and structures, Wiley, 2000

3. René de Borst, Mike A. Crisfield, Joris J. C. Remmers, Clemens V. Verhoosel, Non-Linear Finite Element Analysis of Solids and Structures, Second Edition, Wiley, 2012

4. G.A. Holzapfel, Nonlinear solid mechanics – A continuum approach for engineering, Willey 2000

5. P. Haupt, Continuum Mechanics and Theory of Materials, Springer, 2000

6. J.N.Reddy, Energy principles and variational methods in applied mechanics, Willey 1984

7. J.N.Reddy, An introduction to the Finite Element Method, McGraw-Hill, 2006

8. J.C. Simo, T.J.R. Hughes, Computational inelasticity, Springer, 1997

9. EA de Souza Neto, D Peric, DRJ Owen, Computational methods for plasticity – theory and applications, Wiley, 2008

10. P. Wriggers, Nonlinear Finite Element Methods, Springer, 2008

11. O.C. Zienkiewicz, R.L. Taylor, The Finite Element Method, V1-3, 2000