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- The extended unsymmetric frontal solution for multiple-point constraintsPublication . Areias, Pedro Miguel de Almeida; Rabczuk, Timon; Barbosa, JoaquimThe purpose of this paper is to discuss the linear solution of equality constrained problems by using the Frontal solution method without explicit assembling. Design/methodology/approach - Re-written frontal solution method with a priori pivot and front sequence. OpenMP parallelization, nearly linear (in elimination and substitution) up to 40 threads. Constraints enforced at the local assembling stage. Findings - When compared with both standard sparse solvers and classical frontal implementations, memory requirements and code size are significantly reduced. Research limitations/implications - Large, non-linear problems with constraints typically make use of the Newton method with Lagrange multipliers. In the context of the solution of problems with large number of constraints, the matrix transformation methods (MTM) are often more cost-effective. The paper presents a complete solution, with topological ordering, for this problem. Practical implications - A complete software package in Fortran 2003 is described. Examples of clique-based problems are shown with large systems solved in core. Social implications - More realistic non-linear problems can be solved with this Frontal code at the core of the Newton method. Originality/value - Use of topological ordering of constraints. A-priori pivot and front sequences. No need for symbolic assembling. Constraints treated at the core of the Frontal solver. Use of OpenMP in the main Frontal loop, now quantified. Availability of Software.
- A study on the modeling of sandwich functionally graded particulate compositesPublication . Loja, Amélia; Barbosa, Joaquim; Soares, C. M. MotaDual-phase functionally graded materials are a particular type of composite materials whose properties are tailored to vary continuously, depending on its two constituent's composition distribution, and which use is increasing on the most diverse application fields. These materials are known to provide superior thermal and mechanical performances when compared to the traditional laminated composites, exactly because of this continuous properties variation characteristic, which enables among other advantages smoother stresses distribution profile. In this paper we study the influence of different homogenization schemes, namely the schemes due to Voigt, Hashin-Shtrikman and Mod-Tanaka, which can be used to obtain bounds estimates for the material properties of particulate composite structures. To achieve this goal we also use a set of finite element models based on higher order shear deformation theories and also on first order theory. From the studies carried out, on linear static analyses and on free vibration analyses, it is shown that the bounds estimates are as important as the deformation kinematics basis assumed to analyse these types of multifunctional structures. Concerning to the homogenization schemes studied, it is shown that Mori-Tanaka and Hashin-Shtrikman estimates lead to less conservative results when compared to Voigt rule of mixtures.
- 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.
- Analysis of functionally graded sandwich plate structures with piezoelectric skins, using B-spline finite strip methodPublication . Loja, Amélia; Soares, C. M. Mota; Barbosa, JoaquimFunctionally graded materials are composite materials wherein the composition of the constituent phases can vary in a smooth continuous way with a gradation which is function of its spatial coordinates. This characteristic proves to be an important issue as it can minimize abrupt variations of the material properties which are usually responsible for localized high values of stresses, and simultaneously providing an effective thermal barrier in specific applications. In the present work, it is studied the static and free vibration behaviour of functionally graded sandwich plate type structures, using B-spline finite strip element models based on different shear deformation theories. The effective properties of functionally graded materials are estimated according to Mori-Tanaka homogenization scheme. These sandwich structures can also consider the existence of outer skins of piezoelectric materials, thus achieving them adaptive characteristics. The performance of the models, are illustrated through a set of test cases. (C) 2012 Elsevier Ltd. All rights reserved.
- Dynamic instability of variable stiffness composite platesPublication . Loja, Amélia; Barbosa, Joaquim; Mota Soares, C. M.Due to its tailorability intrinsic characteristics, composite materials are an effective option in structural design or on its reengineering, especially when the ratios stiffness and/or strength to weight are relevant. Dual-phase or multiphase fibre reinforced composites can thus be found in many engineering and science applications. However, in the majority of the cases these composites are made from unidirectional plies stacking. The possibility of building fibre reinforced composite structures, wherein these fibres follow curvilinear paths, may be an important enhancement to structural mechanical response and in particular to its dynamic stability, as variable fibre orientation is responsible for variable elastic stiffness within a generic layer. This work aims characterizing the dynamic instability response of variable stiffness composite plates, according to different material and geometrical parameters. To this purpose one considers Rayleigh-Ritz method to perform buckling, free vibrations and dynamic instability analyses, using orthogonal polynomials. The dynamic instability problem is solved considering Bolotin's method. A set of verification and illustrative case studies is considered and discussed.
- 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.
- A hybrid procedure to identify the optimal stiffness coefficients of elastically restrained beamsPublication . Silva, Tiago Alexandre Narciso da; Loja, Amélia; Maia, Nuno; Barbosa, JoaquimThe formulation of a bending vibration problem of an elastically restrained Bernoulli-Euler beam carrying a finite number of concentrated elements along its length is presented. In this study, the authors exploit the application of the differential evolution optimization technique to identify the torsional stiffness properties of the elastic supports of a Bernoulli-Euler beam. This hybrid strategy allows the determination of the natural frequencies and mode shapes of continuous beams, taking into account the effect of attached concentrated masses and rotational inertias, followed by a reconciliation step between the theoretical model results and the experimental ones. The proposed optimal identification of the elastic support parameters is computationally demanding if the exact eigenproblem solving is considered. Hence, the use of a Gaussian process regression as a meta-model is addressed. An experimental application is used in order to assess the accuracy of the estimated parameters throughout the comparison of the experimentally obtained natural frequency, from impact tests, and the correspondent computed eigenfrequency.
- 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.
- 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.
- Analysis of sandwich beam structures using kriging based higher order modelsPublication . Loja, Amélia; Barbosa, Joaquim; Mota Soares, Cristovão M.Functionally graded composite materials can provide continuously varying properties, which distribution can vary according to a specific location within the composite. More frequently, functionally graded materials consider a through thickness variation law, which can be more or less smoother, possessing however an important characteristic which is the continuous properties variation profiles, which eliminate the abrupt stresses discontinuities found on laminated composites. This study aims to analyze the transient dynamic behavior of sandwich structures, having a metallic core and functionally graded outer layers. To this purpose, the properties of the particulate composite metal-ceramic outer layers, are estimated using Mod-Tanaka scheme and the dynamic analyses considers first order and higher order shear deformation theories implemented though kriging finite element method. The transient dynamic response of these structures is carried out through Bossak-Newmark method. The illustrative cases presented in this work, consider the influence of the shape functions interpolation domain, the properties through-thickness distribution, the influence of considering different materials, aspect ratios and boundary conditions. (C) 2014 Elsevier Ltd. All rights reserved.
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