Mechanic of Structures

Recommended Prerequisites

To attend this course, students must possess the knowledge of Elasticity and Plasticity, Strength of Materials.

Teaching Methods

Each lecture will be divided into two parts: the first part (30 min) will be taken questions on the subject that was presented in the previous class and, that students must have studied at home, then the topic that should be studied to next class is presented (1:30 hours).The first part of the pratical lessons (30 min) will be used to calrify dubouts. Thereafter one or more illustrative problems of matter will be solved and, one or more problems will be distributed to be solved at home by students.

Learning Outcomes

The course aims to present itself as a factor of unity between the learning of basic knowledge and its application in solving real problems. So, should demonstrate the need to model the reality in mathematical terms, to introduce simplifying assumptions and using alternative formulations. In the end, students should be able to: 1) Application of the energy methods to calculate displacements; 2) Solving hyperstatic systems by the method of forces; 3)  Solving Elastic instability problems – buckling; 4) Apply virtual work and variational principles for the formulation of one-dimensional structural problems; 5) Obtain analytical solutions of displacements and stresses of one-dimensional structural elements; 6) Application of the principles to develop finite elements for specific purposes and implement the finite element method for the numerical solution of one-dimensional structural problem.

Work Placement(s)

No

Syllabus

1.Formulation and solution of problems in Solid Mechanics

2. Application of the energy methods to calculate displacements: Potential energy of deformation; Castigliano theorem and its generalization; Theorem of reciprocity of works and displacements.

3. Solving hyperstatic systems using the method of forces: Definition of the hyperestaticity degree; Canonical equations; Application of symmetry properties of structures and systems of forces;

4. Elastic instability - buckling: Euler problem; Definition of critical load and its dependence on boundary conditions, Buckling design.

5. Formulation and solution of problems of bars, shafts and beams. Formulation of the problem: Differential Formulation; Weak integral formulation. Troubleshooting: Analytical methods; Numerical methods: development and application of finite elements.

6. Formulation and numerical solution of one-dimensional coupled problems. 

Head Lecturer(s)

Maria Augusta Neto

Assessment Methods

Assessment
Exam: 100.0%

Bibliography

M.A. Neto, A. Amaro, L. Roseiro, J. Cirne, R. Leal, Engineering computation of structures: the finite element method, Springer, https://www.springer.com/gp/book/9783319177090, 2015.

A. Amaro, M.A. Neto, J. Cirne, R. Resistência de Materiais – Parte II, publicações didáticas DEM/UC, 2019.

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.