Name: VITOR FOLADOR GONÇALVES
Type: MSc dissertation
Publication date: 28/06/2017
Advisor:
Name |
Role |
|---|---|
| WALNÓRIO GRAÇA FERREIRA | Advisor * |
Examining board:
| Name |
Role |
|---|---|
| MACKSUEL SOARES DE AZEVEDO | Internal Examiner * |
| RODRIGO SILVEIRA CAMARGO | Internal Examiner * |
| WALNÓRIO GRAÇA FERREIRA | Advisor * |
Summary: The Finite Difference Method (FDM) is a numerical method for solving differential equations in which the derivatives are approximated by using a finite difference equation. Thus, the FDM is a method based on the discretization process. However, its formulation is even simple and easier than other known numerical methods such as Finite Element Method, Boundary Element Method and Finite Volume Method. In general, the FDM approach related to engineering is superficially discussed in books
and scientific papers, being restricted to introduction chapters. Because of that, it was thought that it would be very interesting to covering in depth a variety of solution strategies of several engineering problems to be solved by the FDM. This research aims to rescue the use of the Finite Difference Method (FDM) on the Computational Engineering based on its current increase in publications of scientific research papers about this method. This research also shows the usage of the FDM in a variety of engineering problems which belongs to the numerical methods field. In addition, this work is closely related to the studies of the FDM as a mean of finding approximate solutions of differential equations that overns several engineering problems. The scope of this research ontains engineering problems such as calculation of beam deflections, columns buckling, bending of plates, thermal problems (including the case of a beam under fire which is a transient problem) and beams on elastic
foundations. All those topics are present in any type of real structures. In order to clarify and better understand the method, a summary of the theoretical background of each engineering problem is shown as well as the main FDM strategies of solution, including numerical examples using a variety of boundary conditions. And, at the end of this work, the scientific society could have available a complete bibliography all about this topic, assisting students and researchers of this field.
Keywords: Finite Difference Method. Elastic buckling. Bending of plates. Elastic foundations. Thermal problems. Fire design.
