Computational Mechanics

Lecture Schedule (Control questions):

1. Mathematical modelling in Civil Engineering

2. Fundamentals of continuum mechanics for Civil Engineering

3. Introduction to advanced Finite Element Method (FEM) with applications in Civil Engineering

4. Introduction to FEM - cont.

5. Modeling of building constructions as three-dimensional bodies (constructions of an arbitrary shape)

6. Modeling of building constructions as two-dimensional bodies (walls, retaining walls, dams)

7. Modeling of plate structures

8. Advanced linear/nonlinear statics of building constructions (introduction - 1D formulation)

9. Advanced nonlinear statics of building constructions (FEM) (3D formulation)

10. Advanced nonlinear statics of building constructions (FEM) (linear buckling analysis, load/displacement control and Riks methods)

11. Dynamics of building constructions - linear analysis (natural frequencies extraction, steady-state analysis - harmonic excitation)

12. Dynamics of building constructions - linear / non-linear analysis (modal superposition, implicit/explicit integration, arbitrary excitation)

13. Dynamics of building constructions - non-linear analysis (implicit/explicit integration, , arbitrary excitation)

14. Dynamics of building constructions - non-linear analysis - cont.

15. Summary

Laboratory Schedule:

1. Ex. 1 - Introduction to Abaqus – cantilever beam (Getting Started with Abaqus: Interactive Edition Appendix B).

2. Ex. 2 - Introduction to Abaqus - hinge model (Getting Started with Abaqus: Interactive Edition: Appendix C).

3. Ex. 2 - cont.

4. Ex. 2 - cont.

5. Ex. 3 - Linear statics – comparative analysis of the influence of the finite element mesh density and element type (type of shape functions, integration, etc.) / comparative analysis of the continual and structural (plate, beam) models - linear elastic isotropic material. (Exercise: PDF; Example report: PDF)

6. Ex. 3 - cont.

7. Ex. 3 - cont.

8. Ex. 4 - Non-linear statics - understanding the incremental process. (Exercise: PDF; Example report: PDF)

9. Ex. 4 - cont.

10. Ex. 5 - Linear / non-linear statics - orthotropic elastic material vs. isotropic elastic material / elasto-plastic material vs. elastic material. (Exercise: PDF; Example report: PDF)

11. Ex. 5 - cont.

12. Ex. 6 – Linear dynamics - eigenproblem / forced vibrations. (Exercise: PDF; Example report: PDF)

13. Ex. 6 - cont.

14. Consultation and realisation of individual tasks.

15. Consultation and realisation of individual tasks – Assessment.

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