Solid Mechanics

Recommended Prerequisites

To attend this course, students must possess the knowledge of Elasticity and Plasticity, Material Resistance I-II.

Teaching Methods

In the lecture the topics are presented and explained. The topics presented should be studied at home.

In the practical classes some problems should be solved by students and some others must be solved at home as homework.

This methodology intended to promote the self-study of students as well as their ability to work in groups.

Learning Outcomes

The course should demonstrate the need to model the reality in mathematical terms, to introduce simplifying assumptions and use alternative formulations. It must highlight the importance of using models in the formulation of real problems and allowing their resolution, even if these problems are not the real problem, they provide the Engineer with sufficient information to take decisions. In the end, students should be able to: Apply for work and variational principles for the formulation of one-dimensional structural problems; Obtain analytical solutions of displacements and stresses of one-dimensional structural elements; Apply the Rayleigh-Ritz and Galerkin approximation methods to evaluate the displacements and stresses; Explain the principles, develop finite elements for specific purposes and implement the finite element method for the numerical solution of one-dimensional structural problems; Apply the finite element method in solving numerical problems of reticular structures.

Work Placement(s)

No

Syllabus

1. Formulation and solution of problems in Solid Mechanics
2. Formulation of a 3D elasticity problem
a. Differential formulation;
b. Strong and weak formulation;
c. Weak formulation based on physical principles;
d. Equivalence of different formulations
3. Troubleshooting
a. Analytical methods;
b. Approximation methods;
c. Numerical methods.
4. Formulation and solution of problems of bars, shafts and beams
a. Formulation of the problem:
  i. Differential Formulation;
 ii. Weak integral formulation.
b. Troubleshooting:
  i. Analytical methods;
 ii. Approximation methods;
iii. Numerical methods: development and application of finite elements
5. Formulation and numerical solution of one-dimensional coupled proble
a. Development and application of the element bar-shaft;
b. Development and application of bar-beam (beam 2D);
c. Development and application of bar- shaft-beam (beam 3D);
d. Numerical problems of reticulated structures

Head Lecturer(s)

Ana Paula Bettencourt Martins Amaro

Assessment Methods

Assessment
The assessment includes two mini – tests (10% each); Final project/Work (20%) and Frequency/ exam final (60%). For the resource and special feature the mini-tests and the final work may not be considered.: 100.0%

Bibliography

R.P. Leal, Mecânica de Sólidos (Apontamentos da disciplina), DEM, 2005/6 (Texto Principal).

I.H. Shames e C.L. Dym, Energy and finite element methods in structural mechanics, McGraw Hill, 1985.

J.N. Reddy, An introduction to the finite element method, McGraw Hill, 1986.

L.J. Segerlind, Applied finite element analysis, John Wiley and Sons, 1984.

E. Oñate, Cálculo de estruturas por el método de elementos finitos. Análisis estático lineal, CIMNI, 1992.