Dynamical behaviour of multi-particle large-scale systems

Collective behaviours can be observed in both natural and man-made systems composed of a large number of elemental subsystems. Typically, each elemental subsystem has its own dynamics but, whenever interaction between individuals occurs, the individual behaviours tend to be relaxed, and collective behaviours emerge. In this paper, the collective behaviour of a large-scale system composed of several coupled elemental particles is analysed. The dynamics of the particles are governed by the same type of equations but having different parameter values and initial conditions. Coupling between particles is based on statistical feedback, which means that each particle is affected by the average behaviour of its neighbours. It is shown that the global system may unveil several types of collective behaviours, corresponding to partial synchronisation, characterised by the existence of several clusters of synchronised subsystems, and global synchronisation between particles, where all the elemental particles synchronise completely.

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.

Task-based occupational exposure assessment and particle number concentration: two important data resources to perform risk assessment for occupational exposure to particles

Environment monitoring has an important role in occupational exposure assessment. However, due to several factors is done with insufficient frequency and normally don´t give the necessary information to choose the most adequate safety measures to avoid or control exposure. Identifying all the tasks developed in each workplace and conducting a task-based exposure assessment help to refine the exposure characterization and reduce assessment errors. A task-based assessment can provide also a better evaluation of exposure variability, instead of assessing personal exposures using continuous 8-hour time weighted average measurements. Health effects related with exposure to particles have mainly been investigated with mass-measuring instruments or gravimetric analysis. However, more recently, there are some studies that support that size distribution and particle number concentration may have advantages over particle mass concentration for assessing the health effects of airborne particles. Several exposure assessments were performed in different occupational settings (bakery, grill house, cork industry and horse stable) and were applied these two resources: task-based exposure assessment and particle number concentration by size. The results showed interesting results: task-based approach applied permitted to identify the tasks with higher exposure to the smaller particles (0.3 μm) in the different occupational settings. The data obtained allow more concrete and effective risk assessment and the identification of priorities for safety investments.

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.

Particle swarm optimization: dynamical analysis through fractional calculus

This chapter considers the particle swarm optimization algorithm as a system, whose dynamics is studied from the point of view of fractional calculus. In this study some initial swarm particles are randomly changed, for the system stimulation, and its response is compared with a non-perturbed reference response. The perturbation effect in the PSO evolution is observed in the perspective of the fitness time behaviour of the best particle. The dynamics is represented through the median of a sample of experiments, while adopting the Fourier analysis for describing the phenomena. The influence upon the global dynamics is also analyzed. Two main issues are reported: the PSO dynamics when the system is subjected to random perturbations, and its modelling with fractional order transfer functions.

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.

Utilização de algoritmos de processamento e análise de imagem na avaliação do dano em placas compósitas

PTDC/EME–TME/66207/2006 e POSC/EEA-SRI/55386/2004