Computational Methods in Mechanical Engineering


The course of Computational Methods in Mechanical Engineering aims to provide the student with a theoretical background and programming skills at the level of numerical simulation by finite elements of static and dynamic mechanical systems. This is an important tool in the practice of mechanical engineering because basically the modern structural analysis in an academic, business or industrial environment is computer assisted (CAE, Computer Aided Engineering). For this reason, the course puts students in contact, on the one hand, with a commercial finite element reference software (ANSYS). On the other hand, the entire programming part is carried out in an OCTAVE environment so that the student develops their own code generation capabilities tailored to the needs of problems that may arise in engineering practice.

General characterization





Responsible teacher

Pedro Samuel Gonçalves Coelho


Weekly - 4

Total - 56

Teaching language





An Introduction to the Finite Element Method

J.N. Reddy


Problemas de Elementos Finitos em MATLAB

A.J.M. Ferreira

Fundação Calouste Gulbenkian

Método dos Elementos Finitos - Técnica de Simulação Numérica em Engenharia

Teixeira-Dias, Pinho-da-Cruz, Fontes Valente e Alves de Sousa


Teaching method

Theoretical Lectures and laboratory sessions are included. At the lectures notes at the blackboard are given as well as powerpoint slideshows. A the Lab sessions the students interact with PC machines using the installed software (OCTAVE and ANSYS).

Evaluation method

The continuous evaluation comprises two projects and one test.

1st Project ( TR1 ) – Individual work.

2nd Project ( TR2 ) – Team work.

Test ( T ) – Individual written test.

Frequency - requires the submission of the two previous projects: TR1 and TR2.

The projects require the elaboration of reports. To be approved in the discipline, the student must get frequency and the following weighted average must be positive:

0,4 x TR1 + 0,3 x TR2 + 0,3 x T >= 9,5val

In the case of unsuccess in the previous evaluation it is mandatory that student gets frequency to have access to the Exam (E) and the following weighted average must be positive: 

0,4 x TR1 + 0,3 x TR2 + 0,3 x E >= 9,5val

The student is not allowed to repeat the projects during the Exam period. The minimum for the Exam is 9,5val. The projects here correspond to the previous mandatory projects developed during the semester. 

Subject matter

Review of linear algebra and, in particular, index notation in vectorial/matrix calculus. Introduction to the Finite Element Method. Bar and beam finite elements. Assembly. Coordinate transformation. Static, dynamic, buckling and harmonic analysis. Programming of finite element code in OCTAVE using, as an example, applications in frame structures. Use of the finite element commercial program ANSYS and introduction to its programming language, APDL. Comparison of results obtained between OCTAVE and ANSYS. Plane elasticity problems solution through finite elements. Plate, Shell and Solid elements. Isoparametric elements. Numerical integration rules. Mesh quality, meshing and Remeshing. Plasticity analysis. Transient analysis. Structural applications in two and three dimensions using ANSYS.


Programs where the course is taught: