Numerical prediction of delamination onset in carbon/epoxy composites drilling

Despite the fact that their physical properties make them an attractive family of materials, composites machining can cause several damage modes such as delamination, fibre pull-out, thermal degradation, and others. Minimization of axial thrust force during drilling reduces the probability of delamination onset, as it has been demonstrated by analytical models based on linear elastic fracture mechanics (LEFM). A finite element model considering solid elements of the ABAQUS® software library and interface elements including a cohesive damage model was developed in order to simulate thrust forces and delamination onset during drilling. Thrust force results for delamination onset are compared with existing analytical models.

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.

Buckling strength of adhesively-bonded single and double-strap repairs on carbon-epoxy structures

This work reports on an experimental and finite element method (FEM) parametric study of adhesively-bonded single and double-strap repairs on carbon-epoxy structures under buckling unrestrained compression. The influence of the overlap length and patch thickness was evaluated. This loading gains a particular significance from the additional characteristic mechanisms of structures under compression, such as fibres microbuckling, for buckling restrained structures, or global buckling of the assembly, if no transverse restriction exists. The FEM analysis is based on the use of cohesive elements including mixed-mode criteria to simulate a cohesive fracture of the adhesive layer. Trapezoidal laws in pure modes I and II were used to account for the ductility of most structural adhesives. These laws were estimated for the adhesive used from double cantilever beam (DCB) and end-notched flexure (ENF) tests, respectively, using an inverse technique. The pure mode III cohesive law was equalled to the pure mode II one. Compression failure in the laminates was predicted using a stress-based criterion. The accurate FEM predictions open a good prospect for the reduction of the extensive experimentation in the design of carbon-epoxy repairs. Design principles were also established for these repairs under buckling.

Strength prediction of single- and double-lap joints by standard and extended finite element modelling

The structural integrity of multi-component structures is usually determined by the strength and durability of their unions. Adhesive bonding is often chosen over welding, riveting and bolting, due to the reduction of stress concentrations, reduced weight penalty and easy manufacturing, amongst other issues. In the past decades, the Finite Element Method (FEM) has been used for the simulation and strength prediction of bonded structures, by strength of materials or fracture mechanics-based criteria. Cohesive-zone models (CZMs) have already proved to be an effective tool in modelling damage growth, surpassing a few limitations of the aforementioned techniques. Despite this fact, they still suffer from the restriction of damage growth only at predefined growth paths. The eXtended Finite Element Method (XFEM) is a recent improvement of the FEM, developed to allow the growth of discontinuities within bulk solids along an arbitrary path, by enriching degrees of freedom with special displacement functions, thus overcoming the main restriction of CZMs. These two techniques were tested to simulate adhesively bonded single- and double-lap joints. The comparative evaluation of the two methods showed their capabilities and/or limitations for this specific purpose.

Fractional electrical impedances in botanical elements

Fractional calculus (FC) is no longer considered solely from a mathematical viewpoint, and is now applied in many emerging scientific areas, such as electricity, magnetism, mechanics, fluid dynamics, and medicine. In the field of dynamical systems, significant work has been carried out proving the importance of fractional order mathematical models. This article studies the electrical impedance of vegetables and fruits from a FC perspective. From this line of thought, several experiments are developed for measuring the impedance of botanical elements. The results are analyzed using Bode and polar diagrams, which lead to electrical circuit models revealing fractional-order behaviour.

Finite Element Analysis (FEA) applied to heat transfer optimization process of pultrusion die systems

The aim of this study is to optimize the heat flow through the pultrusion die assembly system on the manufacturing process of a specific glass-fiber reinforced polymer (GFRP) pultrusion profile. The control of heat flow and its distribution through whole die assembly system is of vital importance in optimizing the actual GFRP pultrusion process. Through mathematical modeling of heating-die process, by means of Finite Element Analysis (FEA) program, an optimum heater selection, die position and temperature control was achieved. The thermal environment within the die was critically modeled relative not only to the applied heat sources, but also to the conductive and convective losses, as well as the thermal contribution arising from the exothermic reaction of resin matrix as it cures or polymerizes from the liquid to solid condition. Numerical simulation was validated with basis on thermographic measurements carried out on key points along the die during pultrusion process.

Desenvolvimento de programa em linguagem Matlab® para cálculo pelo método de elementos finitos

Para o projeto de qualquer estrutura existente (edifícios, pontes, veículos, máquinas, etc.) é necessário conhecer as condições de carga, geometria e comportamento de todas as suas partes, assim como respeitar as normativas em vigor nos países nos quais a estrutura será aplicada. A primeira parte de qualquer projeto nesta área passa pela fase da análise estrutural, onde são calculadas todas as interações e efeitos de cargas sobre as estruturas físicas e os seus componentes de maneira a verificar a aptidão da estrutura para o seu uso. Inicialmente parte-se de uma estrutura de geometria simplificada, pondo de parte os elementos físicos irrelevantes (elementos de fixação, revestimentos, etc.) de maneira a simplificar o cálculo de estruturas complexas e, em função dos resultados obtidos da análise estrutural, melhorar a estrutura se necessário. A análise por elementos finitos é a ferramenta principal durante esta primeira fase do projeto. E atualmente, devido às exigências do mercado, é imprescindível o suporte computorizado de maneira a agilizar esta fase do projeto. Existe para esta finalidade uma vasta gama de programas que permitem realizar tarefas que passam pelo desenho de estruturas, análise estática de cargas, análise dinâmica e vibrações, visualização do comportamento físico (deformações) em tempo real, que permitem a otimização da estrutura em análise. Porém, estes programas demostram uma certa complexidade durante a introdução dos parâmetros, levando muitas vezes a resultados errados. Assim sendo, é essencial para o projetista ter uma ferramenta fiável e simples de usar que possa ser usada para fins de projeto de estruturas e otimização. Sobre esta base nasce este projeto tese onde se elaborou um programa com interface gráfica no ambiente Matlab® para a análise de estruturas por elementos finitos, com elementos do tipo Barra e Viga, quer em 2D ou 3D. Este programa permite definir a estrutura por meio de coordenadas, introdução de forma rápida e clara, propriedades mecânicas dos elementos, condições fronteira e cargas a aplicar. Como resultados devolve ao utilizador as reações, deformações e distribuição de tensões nos elementos quer em forma tabular quer em representação gráfica sobre a estrutura em análise. Existe ainda a possibilidade de importação de dados e exportação dos resultados em ficheiros XLS e XLSX, de maneira a facilitar a gestão de informação. Foram realizados diferentes testes e análises de estruturas de forma a validar os resultados do programa e a sua integridade. Os resultados foram todos satisfatórios e convergem para os resultados de outros programas, publicados em livros, e para cálculo a mão feitos pelo autor.

Discrete fractional order system vibrations

A theory of free vibrations of discrete fractional order (FO) systems with a finite number of degrees of freedom (dof) is developed. A FO system with a finite number of dof is defined by means of three matrices: mass inertia, system rigidity and FO elements. By adopting a matrix formulation, a mathematical description of FO discrete system free vibrations is determined in the form of coupled fractional order differential equations (FODE). The corresponding solutions in analytical form, for the special case of the matrix of FO properties elements, are determined and expressed as a polynomial series along time. For the eigen characteristic numbers, the system eigen main coordinates and the independent eigen FO modes are determined. A generalized function of visoelastic creep FO dissipation of energy and generalized forces of system with no ideal visoelastic creep FO dissipation of energy for generalized coordinates are formulated. Extended Lagrange FODE of second kind, for FO system dynamics, are also introduced. Two examples of FO chain systems are analyzed and the corresponding eigen characteristic numbers determined. It is shown that the oscillatory phenomena of a FO mechanical chain have analogies to electrical FO circuits. A FO electrical resistor is introduced and its constitutive voltage–current is formulated. Also a function of thermal energy FO dissipation of a FO electrical relation is discussed.

Fate Hazardous elements in soils surrounding a coal-fired power plant complex

Proceedings of the 13th International UFZ-Deltares Conference on Sustainable Use and Management of Soil, Sediment and Water Resources - 9–12 June 2015 • Copenhagen, Denmark

Trace Elements in Ambient Air at Porto Metropolitan Area—Checking for Compliance with New European Union (Eu) Air Quality Standards

Because of the scientific evidence showing that arsenic (As), cadmium (Cd), and nickel (Ni) are human genotoxic carcinogens, the European Union (EU) recently set target values for metal concentration in ambient air (As: 6 ng/m3, Cd: 5 ng/m3, Ni: 20 ng/m3). The aim of our study was to determine the concentration levels of these trace elements in Porto Metropolitan Area (PMA) in order to assess whether compliance was occurring with these new EU air quality standards. Fine (PM2.5) and inhalable (PM10) air particles were collected from October 2011 to July 2012 at two different (urban and suburban) locations in PMA. Samples were analyzed for trace elements content by inductively coupled plasma–mass spectrometry (ICP-MS). The study focused on determination of differences in trace elements concentration between the two sites, and between PM2.5 and PM10, in order to gather information regarding emission sources. Except for chromium (Cr), the concentration of all trace elements was higher at the urban site. However, results for As, Cd, Ni, and lead (Pb) were well below the EU limit/target values (As: 1.49 ± 0.71 ng/m3; Cd: 1.67 ± 0.92 ng/m3; Ni: 3.43 ± 3.23 ng/m3; Pb: 17.1 ± 10.1 ng/m3) in the worst-case scenario. Arsenic, Cd, Ni, Pb, antimony (Sb), selenium (Se), vanadium (V), and zinc (Zn) were predominantly associated to PM2.5, indicating that anthropogenic sources such as industry and road traffic are the main source of these elements. High enrichment factors (EF > 100) were obtained for As, Cd, Pb, Sb, Se, and Zn, further confirming their anthropogenic origin.

Aplicação do modelo escoras e tirantes a vigas parede de acordo com o Eurocódigo 2:2010

O Modelo Escoras e Tirantes surgiu no início do Século XX quando Ritter e Mörsch estabeleceram a analogia entre uma treliça clássica e uma viga de betão armado. Desde então pesquisadores têm estudado esse modelo como método de dimensionamento. A partir dos anos 90 várias normas apresentaram a utilização do modelo escoras e tirantes como relevante no dimensionamento de elementos de betão armado. Os critérios de segurança do Modelo Escoras e Tirantes são neste trabalho explicados de acordo com o Eurocódigo 2:2010, e comparadas com as normas NBR 6118:2014 e ACI 318:2011. É unanime dizer que a utilização do método torna-se mais vantajosa para regiões de descontinuidade. Em todos os elementos de betão armado, o Método Escoras e Tirantes são representações dos campos de tensão idealizados por elementos comprimidos e tracionados. Para a definição destes elementos é proposto o processo de “caminho de carga” em que conhecidas as tensões elásticas e suas direções principais utilizando o Método dos Elementos Finitos o modelo das escoras e tirantes é de fácil concepção. É também possível a definição deste a partir de modelos padrão já concebidos para determinados tipos de elementos estruturais de betão armado. Para o elemento descontinuo viga-parede estudado foram apresentados cinco modelos de cálculo até otimizar a solução validando as tensões com o Método dos Elementos Finitos. Em todos os modelos foram analisadas a definição do Modelo Escoras e Tirantes, a resistência das escoras, dos tirantes e dos nós até chegar à solução construtiva da viga-parede. Concluiu-se que a definição do modelo é a chave do dimensionamento.