Master's Dissertation
DOI
10.11606/D.18.2018.tde-05032018-091807
Document
Author
Full name
Lucas Pinheiro Buffon
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2018
Supervisor
Committee
Leonel, Edson Denner (President)
Lima Junior, Eduardo Toledo de
Nogueira, Caio Gorla
Title in Portuguese
Formulações do método dos elementos de contorno para a análise mecânica de domínios planos não-homogêneos enrijecidos
Keywords in Portuguese
Acoplamento MEC/MEC 1D
Acoplamento MEC/MEF
MEC
MEC 1D
Meios enrijecidos
Modelagem de enrijecedores
Abstract in Portuguese
Title in English
Boundary Element Method formulations for non-homogeneous reinforced plane domains mechanical analysis
Keywords in English
BEM
BEM/BEM 1D coupling
BEM/FEM coupling
Reinforced media
Stiffners modelling
Abstract in English
The reinforced materials are commonly encountered in engineering applications, as in the construction of airplanes, vehicles, ships and general manufactures. In Civil Engineering, the reinforced concrete and the reinforced soil are examples of reinforced materials. The solution of this kind of problem can be found by the use of numerical methods as the Finite Element Method (FEM) and the Boundary Element Method (BEM). Particularly, the BEM use in cases with high stress gradients, such as in fracture mechanics problems, is very advantageous. The BEM models infinite domains in a natural way, being largely used in analysis as soil-structure interaction and tunnel modelling. However, as in the BEM only the boundary is discretized, became necessary the use of a numerical coupling to consider the mechanical effect of the stiffeners. For the coupling many numerical methods can be used, in this study it was realized with the FEM and with the BEM in its unidimensional way (BEM 1D). In this context, the coupling BEM/BEM 1D stands out for its advantages, like the compatibility between the methods and the reduction of approximations. Therefore, the main objective of this study is the development and the comparison of numerical solutions for reinforced media problems, considering the framework of the bidimensional BEM problems. The coupling was implemented considering the stiffeners as truss elements, initially it was implemented in the most usual way, by modelling the stiffeners through the FEM. In the following, a new coupling formulation was proposed, in which the stiffeners are modelled through the BEM 1D method. The BEM 1D implementation was validated by comparing the results with analytical and numerical solutions, the last one obtained with the software FTOOL. Both coupling strategies were compared with the solution obtained by the software ANSYS. Four examples were evaluated, with two isotropic and two anisotropic domains. Different boundary conditions, supports and materials were applied, as many discretization and the approximation degree of the stiffeners were tested. The effects of changing the approximation degree in both coupling strategies keeping the degrees of freedom constant were analysed. The results obtained with the implemented algorithms were mechanically coherent, and they were similar to ANSYS results. For all examples, there is no significant computational costs differences between the two coupling strategies. However, the coupling with the BEM 1D leaded to more stable results and better approximations. It was observed that the MEF results were instable for many results, mainly in the quadratic approximations. When the approximation degree rises, the methods tend to converge to equivalent results, becoming very close in fourth degree approximation. Lastly, it was observed stress concentration in the stiffeners ends. In these regions, the discretization and the approximation degree have large influence to the numerical response.