Tópicos Avançados em Mecânica Estrutural


The aim of the course is to enable students to learn subjects that are not part of other course subjects, but which can be considered important in the area of Structural Mechanics. This is the case of the mechanical behavior of composite materials consisting of a fiber-reinforced matrix, arranged in several layers to form a laminate, which are increasingly used to build mechanical engineering structures. It is also the case of the subject of structural optimization, which is taught in this course rather than in the Computational Methods in Mechanical Engineering course, which is, since 2017/2018, exclusively associated with the teaching of the finite element method.


General characterization





Responsible teacher

António Paulo Vale Urgueira, João Mário Burguete Botelho Cardoso


Weekly - 4

Total - 56

Teaching language



To enroll in this course it is strongly recommended that the students had done successfully the previous classes on Solid Mechanics I/II and Mechanical Vibrations.


Mechanics of Composite Materials, Robert M. Jones, Taylor & Francis, London, 1999.

Introduction to Optimum Design, Fourth Edition, Jasbir S. Arora, Science Direct, 2016

Teaching method

Theoretical lectures and laboratory sessions.

Evaluation method

The continuous evaluation finishes at the last day of classes in the semester and it consists of two projects and two mini-tests:

1st Project ( TR1 ) – Group work involving the determination of macroscopic properties of a composite through the analysis of an RVE.

2nd Project ( TR2 ) –Group work on structural modeling, analysis and optimization.

Test ( T ) – Individual and covering first part (Composites) and second part of the contents of the classes (Optimization).

All the projects and tests are mandatory and the attendance to the classes strongly sugested. The projects require the preparation of reports and must have a minimum grade of 10 points. To be approved in the discipline, the student must have positive weighted average for the four classifications, computed by the following formula,

0,35 x TR1 + 0,35 x TR2 + 0,3 x T >= 10

In the case of failure in the continuous evaluation it is possible to perform an Exam (E) that should be graded higher than 9,5 val. The final note is computed by the following formula,

0,35 x TR1 + 0,35 x TR2 + 0,3 x E >= 10

Subject matter

Introduction to composite materials made of fiber reinforced resins. Macromechanical behavior of a blade. Stress-strain relationships for anisotropic materials. Micromechanical behavior of a blade. Laminate behavior. Failure modes and failure criteria. Numerical models of composites: micro, meso and macro scale. Optimization of structures made of composite materials.

Formulation of structural optimization problems. Optimization of dimensions, shape and topology. Constrained and not constrained optimization. The Lagrange Multiplier Concept. Linear and nonlinear optimization. Optimality conditions (KKT). Continuous and discrete optimization. Gradient based algorithms and evolutionary algorithms. Solution of size structural optimization problems using OCTAVE and ANSYS.


Programs where the course is taught: