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- Multiscale stress analysis in CFRC using microscope image data of carbon fibresPublication . Graça, R. J. R.; Rodrigues, José Alberto; Loja, Amélia; Jorge, PedroComposite materials, are known as strong candidates to improve different kinds of structures. The micromechanical study of these materials is very important, because it may define the best composite characteristics to be used and/or predict more accurately its response. In the present work a multi-stage procedure comprising different fibre contour modelling strategies and a sequent hierarchic multiscale analysis is performed. With this study it is intended to achieve a more realistic characterization of the stresses maximum values for a set of case studies, through the use of fibre geometry data obtained from microscope images of carbon fibre laminated composites. The theoretical circular cross-section is also considered to enable a comparative study among the different situations.
- Using the finite element method to understand calculusPublication . Rodrigues, José Alberto; Loja, Amélia; Barbosa, JoaquimThis paper presents a complementary, alternative teaching and learning methodology based on the use of the finite element method to illustrate mathematical models and to explore their (numerical) solutions in the context of vector calculus properties understanding. This methodology is illustrated via a set of examples focused on specific engineering problems, but its scope can also be widened to other scientific areas. The examples presented on this paper allow concluding that this approach may be an interesting way to re-think and complement the perspective usually considered in the transmission of mathematical concepts. The use of a freeware finite element method computational package, FreeFEM++ may also be an important issue to stimulate the dissemination of this phenomena modelling and comprehension approach.
- A study on the structural behaviour of FGM plates static and free vibrations analysesPublication . Bernardo, G. M. S.; Damásio, F. R.; Silva, T. A. N.; Loja, AméliaFunctionally graded materials are characterised by a determined spatial composition variation of their phases’ constituents, which enable for a closer suitability of the material properties to the desired mechanical behaviour. Concerning to the engineered construction of these materials, they can be thought as being achieved by considering a continuous variation of their phases and thus of their properties, or by considering a discrete stacking of a sufficient number of layers, in order to ensure a less abrupt variation profile of their properties. Also, depending on the nature of the applications, it may be important to consider a sandwich configuration, where the three-layered constitution may correspond to a functional requisite. With the present work, these two situations will be studied, considering different methodologies based either on a meshless method or on different approaches based on the finite element method. A comparative study of the performance and adequacy of the developed models is carried out through a set of illustrative cases focused on the study of static and free vibrations behaviour of plate structures.
- Developments on finite element methods for medical image supported diagnosticsPublication . Almeida, Ana; Barbosa, Joaquim; Carvalho, André; Loja, Amélia; Portal, Ricardo; Rodrigues, José Alberto; Vieira, Lina OliveiraVariational image-processing models offer high-quality processing capabilities for imaging. They have been widely developed and used in the last two decades, enriching the fields of mathematics as well as information science. Mathematically, several tools are needed: energy optimization, regularization, partial differential equations, level set functions, and numerical algorithms. For this work we consider a second-order variational model for solving medical image problems. The aim is to obtain as far as possible fine features of the initial image and identify medical pathologies. The approach consists of constructing a regularized functional and to locally analyse the obtained solution. Some parameters selection is performed at the discrete level in the framework of the finite element method. We present several numerical simulations to test the efficiency of the proposed approach.
- Effect of BaTiO3/CoFe2O4 micro-topological textures on the coupled static behaviour of magneto-electro-thermo-elastic beams in different thermal environmentPublication . M, Vinyas; Kattimani, S. C.; Loja, Amélia; Mahesh, VishwasThe use of composite materials with multifunctional capabilities is an increasing requirement for structures or components where the sensory function is accompanied by the diagnosis and the actuation functions, such as autonomic, adaptive or self-sustaining systems. In this context, the present study aims to characterize the coupled response of magneto-electro-thermo-elastic (METE) beams made from Barium Titanate (BaTiO3) and Cobalt Ferric Oxide (CoFe2O4) composite having various micro-topological textures, as well as their static response when submitted to different temperature distribution profiles. To this purpose, a three-dimensional finite element accounting for the coupling between the multiple physical fields in presence, is developed and implemented. The spatial heterogeneous BaTiO3/CoFe2O4 microstructure is also assessed by considering typical Body Centered Cubic (BCC), Face Centered Cubic (FCC) and Simple Cubic (SC) spatial packing arrangements. A special attention is paid to the influence of these micro-topological structures on the pyroeffects and its contribution towards the direct and derived quantities of the METE beam. The results obtained, suggest that the composite heterogeneous microstructure have a relevant influence on the static response of the METE beam in thermal environment.
- Finite element techniques for medical image processingPublication . Almeida, A.; Barbosa, Joaquim; Carvalho, A.; Loja, Amélia; Portal, Ricardo; Rodrigues, José Alberto; Vieira, L.We consider some second-order variational model for solving medical image problems. The aim is to obtain as far as possible fine features of the initial image and identify medical pathologies. The approach consists of constructing a family of regularized functionals and to select locally and adaptively the regularization parameters. The parameters selection is performed at the discrete level in the framework of the finite element method. We present several numerical simulations to test the efficiency of the proposed approach.