[pt] O problema tratado nesta dissertação é o da modelagem da excitação, propagação e sensoriamento de ondas acústicas de alta frequência em compósitos piezoelétricos laminados. Empregou-se uma formulação de vigas baseada na teoria discreta de Reddy para compósitos laminados. Esta teoria tem como característica o emprego de funções de interpolação de ordem arbitrária para descrever a variação dos campos de deslocamento e do potencial elétrico ao longo da espessura do laminado. A utilização deste tipo de teoria possibilita a representação de campos de deslocamento que variam rapidamente ao longo da espessura, e que na faixa de altas frequências, são representativos daqueles associados com ondas guiadas em compósitos laminados. No domínio da frequência, o sistema de equações que descreve a resposta eletromecânica do laminado piezoelétrico é colocado na forma de uma equação de estado. A técnica de solução utilizada é baseada no método da imersão invariante, também conhecido como método da varredura ou método de Riccati. Para avaliar os limites da faixa de frequências onde diferentes aproximações são válidas, empregou-se uma técnica baseada na comparação entre o espectro de dispersão exato e aquele previsto pela teoria aproximada. Os resultados destas comparações, mostram que utilizando-se o número de funções de interpolação apropriado, a teoria discreta de Reddy é capaz de representar ondas de comprimento até quatro vezes menores que a espessura da viga. Na faixa de baixas frequências, os resultados são comparados com soluções numéricas fornecidas pelo método dos elementos finitos. Também são apresentados resultados que mostram a variação na resposta eletro-mecânica da viga quando descontinuidades são introduzidas nesta, bem como resultados de experimentos que envolvem a utilização de piezoelétricos como atuadores e sensores. / [en] The proposed contribution adresses the problem of modeling high- frequency excitation, propagation, and sensing, of structural waves in composites containing piezoelectric sensors and actuators. The model for the active composite beam proposed here is based on Reddy’s discrete layerwise laminate theory. The displacement and electric potential are interpolated in the through-thickness direction using piecewise linear functions. In the frequency domain, the governing equations are written in a state space form. Comparisons between approximate and exact wave dispersion spectra are performed in order to assess the efficiency of the layerwise theory in a given frequency range. It is shown that by employing the proper interpolation, Reddy s theory is able to describe the dynamic response of the composite at frequencies where the associated wavelengths are of the same order or even shorter than the thickness of the piezoelectric layers. Next, the solution for the state space equation is obtained by employing an algorithm based on a discrete version of the Riccati transformation, It is shown that the algorithm is stable over a wide range of frequencies. In the low frequency range, the analytical results are compared with finite element results. Also are shown the change in the electrical and mechanical response when discontinuites are introduced in the beam, as well as basic experiments involving piezoelectric sensors and actuators.

abstract: Laminated composite materials are used in aerospace, civil and mechanical structural systems due to their superior material properties compared to the constituent materials as well as in comparison to traditional materials such as metals. Laminate structures are composed of multiple orthotropic material layers bonded together to form a single performing part. As such, the layup design of the material largely influences the structural performance. Optimization techniques such as the Genetic Algorithm (GA), Differential Evolution (DE), the Method of Feasible Directions (MFD), and others can be used to determine the optimal laminate composite material layup. In this thesis, sizing, shape and topology design optimization of laminated composites is carried out. Sizing optimization, such as the layer thickness, topology optimization, such as the layer orientation and material and the number of layers present, and shape optimization of the overall composite part contribute to the design optimization process of laminates. An optimization host program written in C++ has been developed to implement the optimization methodology of both population based and numerical gradient based methods. The performance of the composite structural system is evaluated through explicit finite element analysis of shell elements carried out using LS-DYNA. Results from numerical examples demonstrate that optimization design processes can significantly improve composite part performance through implementation of optimum material layup and part shape. / Dissertation/Thesis / Masters Thesis Civil and Environmental Engineering 2014

O crescente aumento do uso de madeira laminada colada (MLC) em peças estruturais exige dos meios acadêmicos a pesquisa e desenvolvimento de teorias e rotinas de cálculo, que proporcionem suporte teórico para projetos estruturais que empreguem tal material. Nesta pesquisa foi desenvolvido em laboratório de modelos estruturais, um programa para o cálculo estrutural de vigas de madeira laminada colada (MLC), por meio do método dos elementos finitos para material ortotrópico e material isotrópico. Foram rompidas, em uma prensa universal, vigas de Madeira Laminada Colada (MLC), em escala natural, com e sem emendas nas lâminas, com a finalidade de comparação dos resultados assim obtidos, com os obtidos em modelos de cálculo existentes para vigas maciças de material isotrópico, como o método de cálculo da NBR 7190/97 e o método de cálculo da Teoria da Elasticidade (Timoshenko). Tais resultados também foram comparados com os resultados obtidos pelo método dos Elementos Finitos para materiais isotrópicos e ortotrópicos, acima citados. Para comparação entre as propriedades da madeira maciça e da madeira laminada colada, foram retirados corpos de prova das partes intactas das vigas sacrificadas, para realização de ensaios de cisalhamento na linha de cola e nas lâminas coladas, bem como corpos de prova para ensaios de flexão nas lâminas maciças das vigas de MLC. Para obtenção da tensão de ruptura a compressão paralela às fibras e do módulo de elasticidade, foram rompidos corpos de prova de 5cm x 5 cm x 15 cm. A comparação e análise dos resultados obtidos pelos procedimentos acima, levou à conclusão de que a madeira laminada colada (MLC), quando fabricada com cola estrutural, comporta-se como madeira maciça. Também foi possível observar que os modelos de cálculo empregando elementos finitos, ortotrópicos ou isotrópicos, reproduzem o comportamento de uma viga de madeira laminada colada. O modelo de cálculo da NBR 7190/97, pode ser empregado, mas apresenta resultados conservadores, a favor da segurança. Assim como o modelo de cálculo da Teoria da Elasticidade não deve ser empregado sem adaptação à madeira, pois apresentou resultados muito discrepantes. Os módulos de elasticidade da madeira maciça obtidos por ensaios de flexão e a partir do ensaio de compressão paralela às fibra, não representa o módulo de elasticidade representativo de uma viga de MLC. Da mesma forma a existência ou não de emendas nas lâminas, não altera os resultados. / The increasing use of glued laminated timber in structural parts requires academic research and development of theories and calculation routines that provide theoretical support for structural designs employing such material. In this research was developed in the laboratory of structural models, a program for calculating structural glued laminated timber beams by the finite element method for orthotropic material and isotropic material. Were disrupted in a press universal beam of glued laminated wood in full scale with and without splices blades, for the purpose of comparison of the results thus obtained with those obtained in calculation models exist for solid beams material isotropic, as the method of calculating the NBR 7190/97 and the calculation method of the theory of elasticity (Timoshenko). These results were also compared with results obtained by the method of finite elements for isotropic and orthotropic materials, mentioned above. To compare the properties of solid wood and glued laminated timber, specimens were removed from intact parts of the broken beams for testing shear line glue and glued the layers, as well as specimens for bending tests blades massive beam. To obtain the tensile strength parallel to the compression of the fibers and elastic modulus were broken specimens with the dimensions 5 cm x 5 cm x 15 cm. The comparison and analysis of the results obtained by the above procedure led to the conclusion that the glued laminated wood when manufactured with structural adhesive, behaves as solid wood. It was also noted that the model calculations using finite elements, both isotropic and orthotropic represent the behavior of a beam of glued laminated wood. The calculation model of the NBR 7190/97, can be employed, but has conservative results, in favor of security. As the calculation model of the theory of elasticity should not be used without adjustment to the wood, because it showed very discrepant results. The modulus of elasticity of solid wood obtained by bending tests from test and compression parallel to the fiber, it is not the representative elastic modulus of a beam of glued laminated wood. Likewise, the presence or absence of amendments in the layers, does not change the results.

No description available.

Advanced composite materials have seen major market growth in recent years due to their high strength and low weight properties. These materials are often made using a process that creates a composite laminate by stacking several composite layers together. However, the design, analysis and optimization of laminate composite materials are often a labor intensive process when done manually. This thesis discusses CAD independent algorithms that are integrated into commercial CAD tools to streamline these processes. Methods have been developed to automatically create 3D ply geometry for a laminate composite lay-up, streamline the creation of a laminate composite finite element model and optimize the composite lay-up for a multi-layered laminate composite part. Integrating a CAD independent geometry kernel into the NX laminate composite design automation application significantly improves the run time of that application. In addition, the automated composite finite element tool creates laminate composite finite element models that are more detailed than those made with zone based methods. This tool will save engineers, who are making laminate composite finite element models manually, dozens of hours of work per model. The automated composite finite element tool can also be integrated into an optimization framework, used in conjunction with a method to automatically apply boundary conditions, to create an effective optimization of a laminate composite part.

Genetic algorithms are well known for being expensive optimization tools, especially if the cost for the analysis of each individual design is high. In the past few years, significant effort has been put forth in addressing the high computational cost GAs. The research conducted in the first part of this thesis continues this effort by implementing new multiple elitist and variable elitist selection schemes for the creation of successive populations in the genetic search process. The new selection schemes allow the GA to take advantage of a greater amount of important genetic information that may be contained in the parent designs, information that is not utilized when using a traditional elitist method selection scheme. By varying the amount of information that may be passed to successive generations from the parent population, the explorative and exploitative characteristics of the GA can be adjusted throughout the genetic search also. The new schemes provided slight reductions in the computational cost of the GA and produced many designs with good fitness' in the final population, while maintaining a high level of reliability. Genetic algorithms can be easily adapted to many different optimization problems also. This capability is demonstrated by modifying the basic GA, which utilizes a single chromosome string, to include a second string so that composite laminates comprised of multiple materials can be studied with greater efficiently. By using two strings, only minor adjustments to the basic GA were required. The modified GA was used to simultaneously minimize the cost and weight of a simply supported composite plate under different combinations of axial loading. Two materials were used, with one significantly stronger, but more expensive than the other. The optimization formulation was implemented by using convex combinations of cost and weight objective functions into a single value for laminate fitness, and thus required no additional modifications to the GA. To obtain a Pareto-optimal set of designs, the influence of cost and weight on the overall fitness of a laminate configuration was adjusted from one extreme to the other by adjusting the scale factors accordingly. The modified GA provided a simple yet reliable means of designing high performance composite laminates at costs lower than laminates comprised of one material. / Master of Science

Taking advantage of their inherent abrasion resistant, weather resistant, and outstanding mechanical strength, film-grade thermoplastic polyurethanes (TPU) are currently being used as paint protective films but are also being considered for paint replacement within the automotive industry. Special grades of TPU with shape memory behaviour offer an additional feature of self-healing to decorative coatings but there are concerns of shape fixity at service temperatures which are above their glass transition temperature (Tg). In this study, the shape memory behaviour of a developmental TPU film with Tg around room temperature was investigated. In order to understand the shape memory behaviour, the TPU film was laminated to a rigid polymer substrate of either polypropylene (PP) or acrylonitrile butadiene styrene (ABS). Three different acrylic based pressure sensitive adhesives were tested to bond the film to the substrate, namely a commercial high shear strength transfer tape and two solvent based adhesives of high and low shear strength that were manually cast. The influence of the adhesive was given significant attention as a variable of study in this thesis. The characterization of all the polymeric films and substrates was based on a series of thermo-mechanical tests (tensile test, stress relaxation test, DSC and DMA). The adhesives were characterized by lap-shear test, peel test, and parallel plate rheometry. The results of material characterization were used to support the analysis and interpretation of shape memory behaviour. The TPU based laminate was deformed by a matched mold thermoforming process with a pair of arched matched molds. The recovery behaviour of formed samples was quantified with a newly designed measurement method and the results were reported as recovery ratio and recovery rate. During recovery, the surrounding temperature was considered to be an important variable. The recovery behaviour of specimens was investigated in a controlled environment at setpoint temperatures of 15oC, 45oC or 65oC. No shape memory effect was found at 15oC (below TPU’s Tg), and yet both recovery ratio and recovery rate increased with temperature, from 45oC to 65oC (both above the TPU’s Tg). Since the recovery process was related to the elastic response of the hard segment phase within the TPU, the recovery stress was strongly related to strain conditions. By varying the draw depth into the mold from 6 mm, to 10 mm or 12 mm (8.86%, 15.90% or 19.88% strain, respectively), the recovery measurement results showed that the shape memory effect was weaker with lower strain as less recovery stresses were generated in the TPU film. With the draw depth of 10 mm, the highest recovery ratio and recovery rate were observed, and yet an inexplicable decrease in the recovery ratio and recovery rate occurred as the draw depth increased further from 10mm to 12mm. In regards to the influence by a substrate, TPU/PP laminate showed a more significant recovery behaviour than TPU/ABS laminates at both 45oC and 65oC. The elastic modulus of the substrate was found to have a key role on the recovery process; the recovery nature of formed laminate decreased with stiffer substrate. Three adhesives with differing rheological and adhesion properties were tested to bond the TPU film to a substrate. The formed laminates with “strongest” adhesive (transfer tape) in terms of stiffness and adhesion strength showed the highest recovery ratio/rate over laminates made with “weaker” solvent cast adhesives, at both 45oC and 65oC. A finite element analysis (FEA) was employed to simulate the stress transfer within a multilayer structure bonded by a viscoelastic adhesive layer of varying stiffness; the simulated result showed that the relatively low stiffness adhesive could reduce the stress transfer efficiency within layers of a laminate. It suggested that more recovery stresses were transferred from TPU to substrate with a stiffer adhesive layer (transfer tape) and hence increased the recovery ratio and recovery rate. Therefore, adhesive with relatively low stiffness and adhesion strength could be a better choice to reduce the recovery effect of TPU laminate after forming. However, TPU was found to slide at the unsealed edge of formed laminate when the solvent based adhesives were used; the sliding behavior reduced the recovery by releasing stored recovery stress. In the case of HS and LS adhesives at high temperature (65oC), cohesive failure was observed when the edge of specimen was sealed led to a higher bending moment thus increased the recovery ratio over 24 hours investigations. Therefore, adhesives of weaker shear strength do not necessarily overcome the nature of shape recovery by the TPU when formed part shape needs to be preserved. / Thesis / Master of Applied Science (MASc) / Nowadays, smart materials in particular shape-memory polymers have been widely used in the industrial and medical applications. Thermoplastic polyurethane (TPU) is one of the significant shape memory polymer groups. The two-phase morphology of a typical TPU gives a unique shape memory behaviour over a defined temperature range. However, this shape memory effect affects the shape fixity of formed TPU. In this study, a special-grade TPU film was laminated to a rigid polymer substrate using selected pressure sensitive adhesives (PSAs). In order to investigate the effect of adhesive layer on the shape memory behaviour of this TPU based laminate, three PSAs with varying properties were applied. The laminate was thermoformed, quenched and processed in a temperature-controlled chamber with a designed recovery measurement method. The shape memory effect was observed at temperatures above the transition temperature of TPU, and this recovery effect was enhanced at higher temperature. Furthermore, the mechanical property of the substrate material was considered as a key factor on the recovery behaviour of the laminate; the recovery of the formed laminate was restricted with a stiffer substrate. The most significant discovery from the recovery results indicated that the shape memory effect was reduced with the adhesive with relatively low adhesion strength, however, the delamination of the laminate occurs with weaker adhesives.

No description available.

The development, design, and modeling of a rapid continuous processing scheme is developed to economically manufacture conductive polymer composite bipolar plates for fuel cells. Bipolar plates are required to possess several important properties for fuel cell operation, with the most sought after being electrical conductivity and mechanical strength. The polymer composite material generated at Virginia Tech is based on material generated by a wet-lay process and uses polyethylene terepthalate (PET) or polyphenylene sulfide (PPS) as the binder, although PPS is mainly used. In order to reach sufficient conductivity for use in generating bipolar plates, the polymer is doped with high levels of conductive graphite particles in the range of 70-80 wt%. The polymer system is reinforced with 6-9 wt% glass or carbon fibers. When compression molded into a solid, flat preform, the wet-lay material exhibits excellent bulk (in-plane) conductivity (> 250 S/cm). The material also exhibits tensile and flexural strengths of 57.5 and 95.8 MPa, respectively, higher than other polymer composite material being considered for bipolar plate production. However, formability and through-plane conductivity needs improvement. The laminate bipolar plates developed at Virginia Tech are made using wet-lay material in the core and a thermoplastic/graphite mixture on the surfaces. The wet-lay material provides mechanical integrity, while a powder form of PVDF or PPS and graphite mixture added to the surfaces to improve through-plane conductivity and formability. The manufacturing scheme for the production of laminate bipolar plates is based on the pre-consolidation of the wet-lay material, which establishes a solid, flat surface for the continuous addition of laminate powder. Because the laminate powder only requires heating, radiation heating is used in the process design to pre-heat the preform prior to compression molding. The heated preform passes underneath a press, where forming of channels takes place along with cooling of the bipolar plate. It is estimated that the entire process can take one minute to produce a bipolar plate. The cost of manufacturing a bipolar plate is estimated to be $8/kW, below the goal of $10/kW. The annual production is determined to be 250,000, with over 500,000 possible depending on certain design factors. / Ph. D.

Composite laminates are increasingly being used as primary load bearing members in<br />structures.  However, because of the directional dependence of the properties of<br />composite materials, additional failure modes appear that are absent in<br />homogeneous, isotropic materials.  Therefore, a stress analysis of a composite<br />laminate is not complete without an accurate representation of the transverse<br />(out-of-plane) stresses.<br /><br />Stress recovery is a common method to estimate the transverse stresses from a<br />plate or shell analysis.  This dissertation extends stress recovery to problems<br />in which geometric nonlinearities, in the sense of von K\\\'rm\\\'{a}n,  are<br />important.  The current work presents a less complex formulation for the stress<br />recovery procedure for plate geometries, compared with other implementations,<br />and results in a post-processing procedure which can be applied to data from<br />any plate analyses; analytical or numerical methods, resulting in continuous or<br />discretized data.<br /><br />Recovered transverse stress results are presented for a variety of<br />geometrically nonlinear example problems: a semi-infinite plate subjected to<br />quasi-static transverse and shear loading, and a finite plate subjected to both<br />quasi-static and dynamic transverse loading.  For all cases, the corresponding<br />results from a fully three-dimensional stress analysis are shown alongside the<br />distributions from the stress recovery procedure.  Good agreement is observed<br />between the stresses obtained from each method for the cases considered.<br />Discussion is included regarding the applicability and accuracy of the<br />technique to varying plate geometries and varying degrees of nonlinearity, as<br />well as the viability of the procedure in replacing a three-dimensional<br />analysis in regard to the time required to obtain a solution.<br /><br />The proposed geometrically nonlinear stress recovery procedure results in<br />estimations for transverse stresses which show good correlation to the<br />three-dimensional finite element solutions.  The procedure is accurate for<br />quasi-static and dynamic loading cases and proves to be a viable replacement<br />for more computationally expensive analyses. / Ph. D.