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- Nonlocal free vibrations of metallic FGM beamsPublication . Loja, M.A.R.; Rzeszut, Katarzyna; Barbosa, JoaquimThis work aims to analyse the free-vibration response of functionally graded, simply supported beams with different gradient directions, taking into account nonlocal effects. To this purpose, the first-order shear deformation theory and the nonlocal elasticity theory of Eringen are used, in order to assess the influence of size dependency effects on the free-vibration responses of those beams. The influence of other factors such as the aspect ratio of the beams and the evolution of the constituents’ mixture through the beam thickness and along its length is also considered. In this last case, a mixture distribution is proposed, accounting for the boundary conditions’ characteristics. The finite element model is first verified against existing alternative solutions, to assess and illustrate its performance. Based on the conclusions achieved, a set of parametric studies is then developed. The results are discussed considering the material distribution profiles, and conclusions are drawn with respect to their relative performance under the analysed conditions.
- In-plane functionally graded plates: A study on the free vibration and dynamic instability behavioursPublication . Loja, Amélia; Barbosa, JoaquimFunctionally graded materials are well-known composite materials, characterized by a continuously varying mixture of materials' phases, tailored to meet structures operating requirements while contributing to minimize abrupt stress transitions at dissimilar materials' interfaces, as occur in composite laminates. Hence, designing a functionally graded material to comply with these objectives constitutes an important modelling tool to improve structures' functionality. These graded composite materials present more commonly a mixture variation through the structures' thickness direction. However, when dealing with thin structures this solution may present evident limitations, both from the manufacturing perspective as well as from the through-thickness distribution influence on the structure response. It is therefore important to explore other spatial mixture distributions' possibilities. To this purpose, the present work considers thin graded materials' plates which constitution is defined by a set of different in-plane volume fraction distributions. The influence of these distributions on the free vibrations and dynamic instability of thin plates is assessed through a comprehensive set of parametric studies. The free vibration problem and the dynamic instability problem' solutions are respectively obtained by Rayleigh-Ritz and Bolotin's methods. As a complementary analysis contribution, image correlation studies are also developed for a set of fundamental mode shapes.
- Image driven analysis of plates coated by cold spray coating process using a layerwise approachPublication . Mota, A. F.; Loja, Amélia; Singh, Harminder; Kalsi, S. B. S.; Barbosa, JoaquimFunctionally graded materials are characterized by its continuous spatial properties' variation which provides them a better behaviour concerning strain and stress transition, hence avoiding the abrupt changes typical of composite fibre reinforced laminates. Although manufacturing systems and techniques used in the production of such materials has evolved significantly, porosities may arise as non-desirable characteristic. Other situations exist where pores are desirable as they may contribute to a specific better performance. Regardless the specific application, it is expected that mechanical properties of graded material will be affected by the existence of porosities. This work presents a study on the static and free vibrations behaviour of plates constituted by a substrate coated by the cold spray coating process. This coating presents inherent porosities which distribution matters to characterize in order to assess its influence on the plate behaviour. To this purpose, a layerwise approach considering the first order shear deformation theory was used, in order to be able to carry out a more representative study of the system substrate-coating. The results obtained show that for a small relation between the coating thickness and the plate's total thickness, the relative deviations obtained, considering the porosity-free coating plate as reference, denotes no evidence of significant influence of the number of terms on the volume fraction approximation, for the static and free vibrations results.
- Porous functionally graded plates: na assessment of the influence of shear correction factor on static behaviorPublication . Mota, Ana F.; Loja, Amélia; Barbosa, Joaquim; Rodrigues, José AlbertoThe known multifunctional characteristic of porous graded materials makes them very attractive in a number of diversified application fields, which simultaneously poses the need to deepen research efforts in this broad field. The study of functionally graded porous materials is a research topic of interest, particularly concerning the modeling of porosity distributions and th ecorresponding estimations of their material properties—in both real situations and from a material modeling perspective. This work aims to assess the influence of different porosity distribution approaches on the shear correction factor, used in the context of the first-order shear deformation theory, which in turn may introduce significant effects in a structure’s behavior. To this purpose, we evaluated porous functionally graded plates with varying composition through their thickness. The bending behavior of these plates was studied using the finite element method with two quadrilateral plate element models. Verification studies were performed to assess the representativeness of the developed and implemented models, namely, considering an alternative higher-order model also employed for this specific purpose. Comparative analyses were developed to assess how porosity distributions influence the shear correction factor, and ultimately the static behavior, of the plates.
- Mechanical behavior of a sandwich plate with aluminum foam core, using an image-based layerwise modelPublication . Mota, A. F.; Loja, Amélia; Barbosa, J.I.; Vinyas, M.Functionally graded materials are an advanced type of composite materials whose properties’ spatial evolution can be designed through the definition of the spatial distribution of the constituent phases’ mixture. This feature is particularly important if specific non-homogeneous properties’ requirements are required without introducing abrupt phases’ transitions, as happens in laminated materials. Porosities’ distributions within these materials, may constitute a design requisite for some applications, such as medical implants, but can also be highly undesirable in other cases such as for aeronautical applications. Regardless the specific situation, its characterization is of high importance to the prediction of the resulting materials’ behavior. This work is focused on the static and free vibrations’ analysis of a sandwich plate with a porous aluminum foam core and outer aluminum skins. The porosities’ distribution is modeled by different fitting functions, based on data obtained from a preliminary image processing stage of X-ray CT image of the sandwich plate’ cross-section. A layerwise approach is considered for subsequent numerical simulations’ purpose, where the sandwich skins’ kinematics are modeled using the first order shear deformation theory, while the core is modeled by a higher order shear deformation theory. Fitting functions’ influence on the plate’ behavior is also assessed.