Uncertainty assessment approach for composite structures based on global sensitivity indices

The problem of uncertainty propagation in composite laminate structures is studied. An approach based on the optimal design of composite structures to achieve a target reliability level is proposed. Using the Uniform Design Method (UDM), a set of design points is generated over a design domain centred at mean values of random variables, aimed at studying the space variability. The most critical Tsai number, the structural reliability index and the sensitivities are obtained for each UDM design point, using the maximum load obtained from optimal design search. Using the UDM design points as input/output patterns, an Artificial Neural Network (ANN) is developed based on supervised evolutionary learning. Finally, using the developed ANN a Monte Carlo simulation procedure is implemented and the variability of the structural response based on global sensitivity analysis (GSA) is studied. The GSA is based on the first order Sobol indices and relative sensitivities. An appropriate GSA algorithm aiming to obtain Sobol indices is proposed. The most important sources of uncertainty are identified.

Redes “Fiber To The Home – FTTH”. O despertar de novos serviços de telecomunicações

Se ha poucos anos nao imaginavamos as nossas vidas sem o conforto proporcionado pela iluminacao artificial, fruto do desenvolvimento e proliferacao da producao, transporte e distribuicao de energia electrica, seguramente que nos dias de hoje e indissociavel juntar a esse mesmo conforto e estilo de vida a utilizacao dos meios de telecomunicacoes actuais. Com efeito, a vulgarizacao do uso de telemoveis, a recepcao e transmissao de dados a velocidades cada vez maiores, o aparecimento de televisao de alta definicao (TVAD) em substituicao do actual formato PAL, a surgimento de ofertas de novos servicos como o Video on Demand a par da emergente televisao digital terrestre constituem, seguramente, uma nova revolucao nas infra-estruturas de telecomunicacoes domesticas e profissionais. O sector das telecomunicacoes tem sido aquele que se encontra em pleno crescimento, com os fabricantes e operadores a lancarem novos produtos e solucoes de forma continuada, bem como uma atenta e perspicaz reaccao por parte dos legisladores. Assiste-se verdadeiramente na industria das telecomunicacoes a um movimento relacionado com a convergencia para as redes IP (“Internet Protocol”, ou Protocolo de Internet).

Uncertainty analysis based on sensitivity applied to angle-ply composite structures

This article describes a finite element-based formulation for the statistical analysis of the response of stochastic structural composite systems whose material properties are described by random fields. A first-order technique is used to obtain the second-order statistics for the structural response considering means and variances of the displacement and stress fields of plate or shell composite structures. Propagation of uncertainties depends on sensitivities taken as measurement of variation effects. The adjoint variable method is used to obtain the sensitivity matrix. This method is appropriated for composite structures due to the large number of random input parameters. Dominant effects on the stochastic characteristics are studied analyzing the influence of different random parameters. In particular, a study of the anisotropy influence on uncertainties propagation of angle-ply composites is carried out based on the proposed approach.

From local to global importance measures of uncertainty propagation in composite structures

The influence of uncertainties of input parameters on output response of composite structures is investigated in this paper. In particular, the effects of deviations in mechanical properties, ply angles, ply thickness and on applied loads are studied. The uncertainty propagation and the importance measure of input parameters are analysed using three different approaches: a first-order local method, a Global Sensitivity Analysis (GSA) supported by a variance-based method and an extension of local variance to estimate the global variance over the domain of inputs. Sample results are shown for a shell composite laminated structure built with different composite systems including multi-materials. The importance measures of input parameters on structural response based on numerical results are established and discussed as a function of the anisotropy of composite materials. Needs for global variance methods are discussed by comparing the results obtained from different proposed methodologies. The objective of this paper is to contribute for the use of GSA techniques together with low expensive local importance measures.

Uncertainty propagation in inverse reliability-based design of composite structures

An approach for the analysis of uncertainty propagation in reliability-based design optimization of composite laminate structures is presented. Using the Uniform Design Method (UDM), a set of design points is generated over a domain centered on the mean reference values of the random variables. A methodology based on inverse optimal design of composite structures to achieve a specified reliability level is proposed, and the corresponding maximum load is outlined as a function of ply angle. Using the generated UDM design points as input/output patterns, an Artificial Neural Network (ANN) is developed based on an evolutionary learning process. Then, a Monte Carlo simulation using ANN development is performed to simulate the behavior of the critical Tsai number, structural reliability index, and their relative sensitivities as a function of the ply angle of laminates. The results are generated for uniformly distributed random variables on a domain centered on mean values. The statistical analysis of the results enables the study of the variability of the reliability index and its sensitivity relative to the ply angle. Numerical examples showing the utility of the approach for robust design of angle-ply laminates are presented.

Castor fiber na gruta do Caldeirão. Existência, distribuição e extinção do castor em Portugal

Beaver only had been found in Portugal in a Chalcolithic locality, the Vila Nova de S. Pedro castrum. It has now been identified in the Upper Paleolithic (Solutrean) from Gruta do Caldeirão, near Tomar. The species has been found recently at «Gruta do Almonda»; 4 teeth were collected in bed C, older than a Solutrean sequence (see Anexo for details). The species seems to have been rare, as it was also the case with portuguese Miocene Castoridae Enroxenomys minutus and Chalicomys jaegeri. If account is taken of the presence in the Middle Ages until Castille of words meaning beaver (relared to the popular latin Fiber/Biber), it is obvious that these animais still existed then. Such nouns were largely predominant over rhe rather erudite latin (greek deríved) words as Castor,-óris and derived ones, as it could be expected. This allowed us to recognize that veiro should be the corresponding word with Fiber affinities in archaic portuguese. It was previously supposed to mean only expensive furs then imported into Portugal. Indeed it was also a zoonym. Anywày, beaver should be scarce by XIIIth century since it is not included in the quite detailed price list imposed by the «Lei da Almotaçaria» from December 26, 1253 (see Quadro II). Toponyms in veiro and derived words (fig. 2; Quadro III) (plural, feminines, diminutives, inhabited places) give a resrrictive view of rhe Middle Age distribution. Some of them are certainly older than Portugal itself (firsr half of XIlth cenrury); others existed by the XIVth century bur were probably older. Some rare toponyms seem to be derived from the erudite latin Castor,-óris. Nothing suggests that these words were still in use as zoonyms during the Middle Ages. All toponyms are located in regions near rivers and other freshwaters ecologically suitable for beavers, so we can approximately retrace its former, Middle Age disrribution in Portugal (fig. 2; Quadro III). Most of them are locared in the Center-West and Northwest of Portugal, with a suitable c1imate (rainfall in general over 800 mílimerers per year); the only sure geographical exception is Veiros, in Alto Alentejo province, in a region with comparable precipitations and less dry climate conditions than mosr of the territories South of rhe Tagus. There are less and less of these toponyms towards rhe South and the inner part of the country, and they are enrirely lacking in all drier regions from Trás-os-Montes, Beira, Alentejo beyond Tagus' basin, and in Algarve. Nothing suggests beavers lived there, No post-medieval toponym is known, nor any reference after middle XVth century. No such locality was at, or close by to, any frontier. Hence the hypothesis of veiro (et al.} as meaning but points where expensive furs (supposedly known as veiros in general but without c1early saying from what animal they were obrained from) is to be discarded. During the Middle Ages, beaver discriburion concerned all the main river basins from Minho to Tagus ones. Quite rarefied in rhe XIIIth, the beavers may have disappeared from Portugal during the XVth century. Ecological requiremenrs restricted their former distriburion. Vulnerability to natural causes (i.e., severe drought) and to human pressure may have accounted heavily for this species' extinction. Last (1446) reference for Portugal known to us suggests the species was by then almost extinct.

Damage evaluation of drilled carbon/epoxy laminates based on area assessment methods

The characteristics of carbon fibre reinforced laminates had widened their use, from aerospace to domestic appliances. A common characteristic is the need of drilling for assembly purposes. It is known that a drilling process that reduces the drill thrust force can decrease the risk of delamination. In this work, delamination assessment methods based on radiographic data are compared and correlated with mechanical test results (bearing test).

Feasibility of the extended finite element method for the simulation of composite bonded joints

Adhesive-bonding for the unions in multi-component structures is gaining momentum over welding, riveting and fastening. It is vital for the design of bonded structures the availability of accurate damage models, to minimize design costs and time to market. Cohesive Zone Models (CZM’s) have been used for fracture prediction in structures. The eXtended Finite Element Method (XFEM) is a recent improvement of the Finite Element Method (FEM) that relies on traction-separation laws similar to those of CZM’s but it allows the growth of discontinuities within bulk solids along an arbitrary path, by enriching degrees of freedom. This work proposes and validates a damage law to model crack propagation in a thin layer of a structural epoxy adhesive using the XFEM. The fracture toughness in pure mode I (GIc) and tensile cohesive strength (sn0) were defined by Double-Cantilever Beam (DCB) and bulk tensile tests, respectively, which permitted to build the damage law. The XFEM simulations of the DCB tests accurately matched the experimental load-displacement (P-d) curves, which validated the analysis procedure.

Drilling delamination outcomes on glass and sisal reinforced plastics

Nowadays, fibre reinforced plastics are used in a wide variety of applications. Apart from the most known reinforcement fibres, like glass or carbon, natural fibres can be seen as an economical alternative. However, some mistrust is yet limiting the use of such materials, being one of the main reasons the inconsistency normally found in their mechanical properties. It should be noticed that these materials are more used for their low density than for their high stiffness. In this work, two different types of reinforced plates were compared: glass reinforced epoxy plate and sisal reinforced epoxy plate. For material characterization purposes, tensile and flexural tests were carried out. Main properties of both materials, like elastic modulus, tensile strength or flexural modulus, are presented and compared with reference values. Afterwards, plates were drilled under two different feed rates: low and high, with two diverse tools: twist and brad type drill, while cutting speed was kept constant. Thrust forces during drilling were monitored. Then, delamination area around the hole was assessed by using digital images that were processed using a computational platform previously developed. Finally, drilled plates were mechanically tested for bearing and open-hole resistance. Results were compared and correlated with the measured delamination. Conclusions contribute to the understanding of natural fibres reinforced plastics as a substitute to glass fibres reinforced plastics, helping on cost reductions without compromising reliability, as well as the consequence of delamination on mechanical resistance of this type of composites.

Filament wound products made with thermoplastic matrix towpregs

Cost-effective glass-reinforced thermoplastic matri x towpregs produced by a powder coating line were used to manufacture composite pipes by fi lament winding. A conventional 6 axes filament-winding equipment was adapted for processi ng such structures. The influence of the filament winding speed and mandrel temperature on t he composite final properties was studied in the present work. An optimized processin g window was established by comparing the composite theoretical expected mechanical prope rties with the experimentally obtained ones. The final properties determined on the produc ed pipes and structures and the technological changes introduced to the conventiona l filament-winding equipment will be presented and discussed. Besides the processing des cription and conditions, it will be presented the relationship between processing condi tions and mechanical properties.

Drilling of fibre reinforced plastic laminates

The use of fibre reinforced plastics – FRP’s – in structures is under a considerable increase. Advantages of their use are related with their low weight, high strength and stiffness. The improvement of the dynamic characteristics has been profitable for aeronautics, automobile, railway, naval and sporting goods industries. Drilling is a widely used machining technique as it is needed to assemble parts in a structure. This is a unique machining process, characterized by the existence of two different mechanisms: extrusion by the drill chisel edge and cutting by the rotating cutting lips. Drilling raises particular problems that can reduce mechanical and fatigue strength of the parts. In this work, quasi-isotropic hybrid laminates with 25% of carbon fibre reinforced plies and 4 mm thickness are produced, tested and drilled. Three different drill geometries are compared. Results considered are the interlaminar fracture toughness in Mode I – GIc –, thrust force during drilling and delamination extent after drilling. A bearing test is performed to evaluate tool influence on the load carrying capacity of the plate. Results consider the influence of drill geometry on delamination. A correlation linking plate damage to bearing test results is presented.

Strength prediction of adhesively-bonded scarf repairs in composite structures under bending

This work reports on the experimental and numerical study of the bending behaviour of two-dimensional adhesively-bonded scarf repairs of carbon-epoxy laminates, bonded with the ductile adhesive Araldite 2015®. Scarf angles varying from 2 to 45º were tested. The experimental work performed was used to validate a numerical Finite Element analysis using ABAQUS® and a methodology developed by the authors to predict the strength of bonded assemblies. This methodology consists on replacing the adhesive layer by cohesive elements, including mixed-mode criteria to deal with the mixed-mode behaviour usually observed in structures. Trapezoidal laws in pure modes I and II were used to account for the ductility of the adhesive used. The cohesive laws in pure modes I and II were determined with Double Cantilever Beam and End-Notched Flexure tests, respectively, using an inverse method. Since in the experiments interlaminar and transverse intralaminar failures of the carbon-epoxy components also occurred in some regions, cohesive laws to simulate these failure modes were also obtained experimentally with a similar procedure. A good correlation with the experiments was found on the elastic stiffness, maximum load and failure mode of the repairs, showing that this methodology simulates accurately the mechanical behaviour of bonded assemblies.

Experimental and numerical evaluation of composite repairs on wood beams damaged by cross-graining

An experimental and Finite Element study was performed on the bending behaviour of wood beams of the Pinus Pinaster species repaired with adhesively-bonded carbon–epoxy patches, after sustaining damage by cross-grain failure. This damage is characterized by crack growth at a small angle to the beams longitudinal axis, due to misalignment between the wood fibres and the beam axis. Cross-grain failure can occur in large-scale in a wood member when trees that have grown spirally or with a pronounced taper are cut for lumber. Three patch lengths were tested. The simulations include the possibility of cohesive fracture of the adhesive layer, failure within the wood beam in two propagation planes and patch interlaminar failure, by the use of cohesive zone modelling. The respective cohesive properties were estimated either by an inverse method or from the literature. The comparison with the tests allowed the validation of the proposed methodology, opening a good perspective for the reduction of costs in the design stages of these repairs due to extensive experimentation.

Benchmark exact solutions for the static analysis of multi-layered piezoelectric composite using PVDF

The three-dimensional (3D) exact solutions developed in the early 1970s by Pagano for simply supported multilayered orthotropic composite plates and later in the 1990s extended to piezoelectric plates by Heyliger have been extremely useful in the assessment and development of advanced laminated plate theories and related finite element models. In fact, the well-known test cases provided by Pagano and by Heyliger in those earlier works are still used today as benchmark solutions. However, the limited number of test cases whose 3D exact solutions have been published has somewhat restricted the assessment of recent advanced models to the same few test cases. This work aims to provide additional test cases to serve as benchmark exact solutions for the static analysis of multilayered piezoelectric composite plates. The method introduced by Heyliger to derive the 3D exact solutions has been successfully implemented using symbolic computing and a number of new test cases are here presented thoroughly. Specifically, two multilayered plates using PVDF piezoelectric material are selected as test cases under two different loading conditions and considering three plate aspect ratios for thick, moderately thick and thin plate, in a total of 12 distinct test cases. (C) 2013 Elsevier Ltd. All rights reserved.

Design of a laminated composite multi-cel structure subjected to torsion

Laminate composite multi-cell structures have to support both axial and shear stresses when sustaining variable twist. Thus the properties and design of the laminate may not be the most adequate at all cross-sections to support the torsion imposed on the cells. In this work, the effect of some material and geometric parameters on the optimal mechanical behaviour of a multi-cell composite laminate structure is studied when torsion is present. A particle swarm optimization technique is used to maximize the multi-cell structure torsion constant that can be used to obtain the angle of twist of the composite laminate profile.