Browsing by Author "Silva, Tiago A. N."
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- Assessing static and dynamic response variability due to parametric uncertainty on fibre-reinforced compositesPublication . Carvalho, Alda; Silva, Tiago A. N.; Loja, M.A.R.Composite structures are known for their ability to be tailored according to specific operating requisites. Therefore, when modelling these types of structures or components, it is important to account for their response variability, which is mainly due to significant parametric uncertainty compared to traditional materials. The possibility of manufacturing a material according to certain needs provides greater flexibility in design but it also introduces additional sources of uncertainty. Regardless of the origin of the material and/or geometrical variabilities, they will influence the structural responses. Therefore, it is important to anticipate and quantify these uncertainties as much as possible. With the present work, we intend to assess the influence of uncertain material and geometrical parameters on the responses of composite structures. Behind this characterization, linear static and free vibration analyses are performed considering that several material properties, the thickness of each layer and the fibre orientation angles are deemed to be uncertain. In this study, multivariable linear regression models are used to model the maximum transverse deflection and fundamental frequency for a given set of plates, aiming at characterizing the contribution of each modelling parameter to the explanation of the response variability. A set of simulations and numerical results are presented and discussed.
- Assessing static and dynamic response variability due to parametric uncertainty on fibre-reinforced compositesPublication . Carvalho, Alda; Silva, Tiago A. N.; Ramos Loja, M.A.Composite structures are known for their ability to be tailored according to specific operating requisites. Therefore, when modelling these types of structures or components, it is important to account for their response variability, which is mainly due to significant parametric uncertainty compared to traditional materials. The possibility of manufacturing a material according to certain needs provides greater flexibility in design but it also introduces additional sources of uncertainty. Regardless of the origin of the material and/or geometrical variabilities, they will influence the structural responses. Therefore, it is important to anticipate and quantify these uncertainties as much as possible. With the present work, we intend to assess the influence of uncertain material and geometrical parameters on the responses of composite structures. Behind this characterization, linear static and free vibration analyses are performed considering that several material properties, the thickness of each layer and the fibre orientation angles are deemed to be uncertain. In this study, multivariable linear regression models are used to model the maximum transverse deflection and fundamental frequency for a given set of plates, aiming at characterizing the contribution of each modelling parameter to the explanation of the response variability. A set of simulations and numerical results are presented and discussed.
- Elastically restrained Bernoulli-Euler beams applied to rotary machinery modellingPublication . Silva, Tiago A. N.; Maia, Nuno M. M.Facing the lateral vibration problem of a machine rotor as a beam on elastic supports in bending, the authors deal with the free vibration of elastically restrained Bernoulli-Euler beams carrying a finite number of concentrated elements along their length. Based on Rayleigh's quotient, an iterative strategy is developed to find the approximated torsional stiffness coefficients, which allows the reconciliation between the theoretical model results and the experimental ones, obtained through impact tests. The mentioned algorithm treats the vibration of continuous beams under a determined set of boundary and continuity conditions, including different torsional stiffness coefficients and the effect of attached concentrated masses and rotational inertias, not only in the energetic terms of the Rayleigh's quotient but also on the mode shapes, considering the shape functions defined in branches. Several loading cases are examined and examples are given to illustrate the validity of the model and accuracy of the obtained natural frequencies.
- A global optimization approach based on adaptive populationsPublication . Silva, Tiago A. N.; Loja, Amélia; Carvalho, Alda; Maia, Nuno M. M.; Barbosa, JoaquimThe solution of inverse problems based on experimental data is itself an important research issue. In this context and assuming that an experimental sample is available, rather than trying to find a specific deterministic solution for the inverse problem, one aims to determine the probabilistic distribution of the modelling parameters, based on the minimization of the dissimilarity between the empirical cumulative distribution function of an experimental solution and its simulation counterpart. The present paper presents na innovative framework, where Differential Evolution is extended in order to estimate not only an optimal set of modelling parameters, but to estimate their optimal probabilistic distributions. Additionally, the Adaptive Empirical Distributions optimization scheme is here introduced. Both schemes rely on the two samples Kolmogorov-Smirnov goodness-offit test in order to evaluate the resemblance between two empirical cumulative distribution functions. A numerical example is considered in order to assess the performance of the proposed strategies and validity of their solutions.
- A model updating technique based on FRFs for damped structuresPublication . Silva, Tiago A. N.; Maia, N. M. M.; Barbosa, JoaquimModel updating methods often neglect that in fact all physical structures are damped. Such simplification relies on the structural modelling approach, although it compromises the accuracy of the predictions of the structural dynamic behaviour. In the present work, the authors address the problem of finite element (FE) model updating based on measured frequency response functions (FRFs), considering damping. The proposed procedure is based upon the complex experimental data, which contains information related to the damped FE model parameters and presents the advantage of requiring no prior knowledge about the damping matrix structure or its content, only demanding the definition of the damping type. Numerical simulations are performed in order to establish the applicability of the proposed damped FE model updating technique and its results are discussed in terms of the correlation between the simulated experimental complex FRFs and the ones obtained from the updated FE model.
- On the characterization of parametric uncertainty on FGM platesPublication . Damásio, Fábio R.; Silva, Tiago A. N.; Carvalho, Alda; Loja, AméliaComposite materials with their intrinsic tailor-made capabilities can be strong candidates to improve the mechanical performance of structures, either by partially or totally replacing other traditional materials. These easily tailored features can be thought not only in terms of the more often used fibre reinforced laminated composites but also in the context of particulate composites. In general, the mechanical performance of composite structures can be, intentionally or not, influenced through the manipulation of geometric properties, the selection of material’s phases and its disposition in the composite, as well as, the spatial distribution of reinforcement agents, such as fibres or particles. The uncertainty associated to all these diferente aspects can be considered as the main source of variability to the mechanical behaviour of a given structure. It is therefore important to characterize the relations between the geometric and material parameters and a set of some relevant structural responses. The quantification of uncertainty is often related to the experimental behaviour of a given structure, although it can also be assessed within the design perspective, where it is useful to understand and identify the parameters with a greater influence on the uncertainty associated to the model simulations. In the present work, one considers functionally graded plates, where different material and geometric characteristics are assumed to be uncertain. The mechanical behaviour of such plates is modelled using Lagrange- and Kriging-based finite element models, developed according to the assumptions of the first order shear deformation theory. A set of numerical results is presented and discussed in order to identify the most significant modelling parameters for the description of the output variability, in this case the maximum deflection.
- Selection of modelling parameters for stochastic model updatingPublication . Silva, Tiago A. N.; Mottershead, John E.In structural dynamics, the adjustment of a set of modelling parameters based on the minimization of the discrepancy between experimental and model responses is known as model updating. In the context of stochastic model updating, the selection of a set of updating parameters from the modelling ones is very important, both in terms of computational efficiency and of the accuracy of the solution of this stochastic inverse problem. One can find in the literature several approaches to model updating. A simple expression was developed for covariance matrix correction in stochastic model updating and by its use one may observe the relevance of choosing the correct set of updating parameters. One may conclude that if the updating parameters are correctly chosen, then the covariance matrix of the outputs is correctly reconstructed, but when the updating parameters are wrongly chosen is found that the responses covariance matrix is generally not reconstructed accurately, although the reconstructing of the responses mean values is accurate. Hence, the selection of updating parameters is developed by assessing the contribution of each candidate parameter to the responses covariance matrix, thereby enabling the selection of updating parameters to ensure that both the responses mean values and covariance matrix are reconstructed by the updated model. It is shown that the scaled output covariance matrix may be decomposed to allow the contributions of each candidate parameter to be assessed. Numerical examples are given to illustrate this theory.
- Thermal Residual Stresses in Functionally Graded Structures: a Didactic Case StudyPublication . Silva, Tiago A. N.; Loja, AméliaManufacturing processes which involve plastic deformations or abrupt temperature gradients often leads thermal residual stresses to arise on materials. This fact can thus result in stress states that remain within a structural member in the absence of external loads, being desirable to obtain, as long as possible, a minimum level of residual stresses as well as smoother stresses transitions in the materials interfaces. Dual-phase functionally graded materials can be used with the purpose to mitigate stress concentrations by gradually varying the microstructure and/or composition of materials in a gradient structure. The current work presents part of a remote educational platform developed to promote and motivate mechanical engineering students to gain a broader insight of a common drawback in mechanical design. Here MATLAB and LabVIEW are used to set up an integrated tool fir engineering education and research, by taking as demonstration the problem of thermal residual stresses in functionally graded structures. The educational platform empowers students to understand the influence, on thermal residual stresses, of different design parameters. This pilot project is entering on its implementation phase, wherein students are required to explore the multiple potentialities of this platform to support their learning process.