Class Modeling and Analysis of Structures

In the scope of modern engineering design projects it is of utmost importance the knowledge of the strains and stress (and related) fields. In such context, mathematical models allow the description of the physical behaviour of structures. The curricular unit seeks to present the fundamentals of modelling though the Finite Element Method. Various options for the modelling of more complex structural elements, like shells and structural walls/cores are presented in detail. Various types of finite element analyses are covered (static and dynamic, linear and non-linear). 

LINEAR ELASTICITY PROBLEMS

• Governing equations of linear elasticity
• Boundary conditions

FEM PRINCIPLES. THE TRUSS ELEMENT

• Approximation functions
• Govering equation at the element level. Stiffness matrix
• Govering equation at the structural level. Resolutive system
• Local and global referentials
• Quality of the solution. Refinements “p” and “h”
• Convergence

THE BEAM ELEMENT

• Governing equations
• Approximation functions
• Stiffness matrix

THE PLANE ELASTICITY ELEMENT

• Triangular elements
• Approximation functions. Cartesian and Natural References
• Stiffness matrix
• Rectangular elements
• Approximation functions
• Stiffness matrix

THE SHELL ELEMENT

• Non-conforming rectangular element
• Approximation functions
• Stiffness matrix

STRUCTURAL MODELING

• Modeling slabs using bar shell elements
• Modeling of structural cores using bar shell elements
• Static and dynamic analyses
• Linear and non-linear analyses

The discipline combines theoretical knowledge about the Finite Element Method with the presentation of commercial computer programs for their application to practical problems.

• K.J. Bathe. Finite element procedures. Prentice-Hall, 1996.
• O.C. Zienkiewicz and R.L. Taylor and J. Z. Zhu. The finite elemento method. Volume 1: Its Basis and Fundamentals. Butterworth-Heinemann, 2005.
• J.N. Reddy. Na Introduction to the Finite Element Method. McGraw Hill, 1993.
• GHALI, A., NEVILLE, A. M. - Structural Analysis: A Unified Classical and Matrix Approach. 7th Edition. Boca Raton: CRC Press, 2017. ISBN: 9781498725064.
• NAFEMS resources: https://old.nafems.org/