Este trabalho apresenta uma modelagem de placas laminadas com sensores/atuadores piezoelétricos integrados e conectados a circuitos tipo shunt resistivo-indutivo (RL). O modelo faz uso de duas teorias de placa, FSDT (First-order Shear Deformatíon Theory) e TSDT (Third-order Shear Deformatíon Theory), e considera a possibilidade de inserção de pastilhas piezoelétricas trabalhando nos modos de extensão e cisalhamento. Um modelo de elementos finitos para placas laminadas piezoelétricas, em camada equivalente (Equivalent Single Layer), foi desenvolvido usando como graus de liberdade os deslocamentos mecânicos generalizados e a carga elétrica gerada nos circuitos acoplados. Após, uma implementação computacional foi realizada e validada através de comparações com resultados encontrados na literatura. Então, foram realizados estudos para configurações de placa laminada com diferentes quantidades de pastilhas piezoelétricas através de uma análise paramétrica para obtenção das posições de maior acoplamento entre pastilhas e estrutura para os primeiros modos de vibração da placa. Estes resultados possibilitaram a otimização da eficiência do acoplamento eletromecânico através da distribuição das pastilhas piezoelétricas para uma placa com maior quantidade de pastilhas bem como a comparação dos resultados obtidos entre as duas teorias utilizadas. / This work presents the modeling of laminate plates with embedded piezoelectric sensors and actuators connected to resistive-inductive (RL) shunt circuits. The model considers two plate theories, FSDT (First-order Shear Deformation Theory) and TSDT (Third-order Shear Deformation Theory) and allows embedded piezoelectric patches in extension and thickness-shear modes. A finite element model for piezoelectric laminate plates, using equivalent single layer (ESL), was developed considering the generalized mechanical displacements and the electric charges induced in the coupled electric circuits as degrees of freedom. Then, the model was implemented and validated by means of comparisons with results found in the literature. Thereafter, some laminate plate configurations with different numbers of piezoelectric patches were studied through a parametric analysis to obtain the positions that maximize the electromechanical coupling between patches and structure for the first vibration modes. These results allowed the optimization of the electromechanical coupling efficiency through piezoelectric patches distribution for a plate with a larger number of patches and the comparison between the results obtained with the two plate theories considered.

In this study, anisotropic shells of revolution subject to symmetric and unsymmetrical static loads are analysed. In derivation of governing equations to be used in the solution, first order transverse shear effects are included in the formulation. The governing equations can be listed as kinematic equations, constitutive equations, and equations of motion. The equations of motion are derived from Hamilton&rsquo / s principle, the constitutive equations are developed under the assumptions of the classical lamination theory and the kinematic equations are based on the Reissner-Naghdi linear shell theory. In the solution method, these governing equations are manipulated and written as a set called fundamental set of equations. In order to handle anisotropy and first order transverse shear deformations, the fundamental set of equations is transformed into 20 first order ordinary differential equations using finite exponential Fourier decomposition and then solved with multisegment method of integration, after reduction of the two-point boundary value problem to a series of initial value problems. The results are compared with finite element analysis results for a number of sample cases and good agreement is found. Case studies are performed for circular cylindrical shell and truncated spherical shell geometries. While reviewing the results, effects of temperature and pressure loads, both constant and variable throughout the shell, are discussed. Some drawbacks of the first order transverse shear deformation theory are exhibited.

Este trabalho apresenta uma modelagem de placas laminadas com sensores/atuadores piezoelétricos integrados e conectados a circuitos tipo shunt resistivo-indutivo (RL). O modelo faz uso de duas teorias de placa, FSDT (First-order Shear Deformatíon Theory) e TSDT (Third-order Shear Deformatíon Theory), e considera a possibilidade de inserção de pastilhas piezoelétricas trabalhando nos modos de extensão e cisalhamento. Um modelo de elementos finitos para placas laminadas piezoelétricas, em camada equivalente (Equivalent Single Layer), foi desenvolvido usando como graus de liberdade os deslocamentos mecânicos generalizados e a carga elétrica gerada nos circuitos acoplados. Após, uma implementação computacional foi realizada e validada através de comparações com resultados encontrados na literatura. Então, foram realizados estudos para configurações de placa laminada com diferentes quantidades de pastilhas piezoelétricas através de uma análise paramétrica para obtenção das posições de maior acoplamento entre pastilhas e estrutura para os primeiros modos de vibração da placa. Estes resultados possibilitaram a otimização da eficiência do acoplamento eletromecânico através da distribuição das pastilhas piezoelétricas para uma placa com maior quantidade de pastilhas bem como a comparação dos resultados obtidos entre as duas teorias utilizadas. / This work presents the modeling of laminate plates with embedded piezoelectric sensors and actuators connected to resistive-inductive (RL) shunt circuits. The model considers two plate theories, FSDT (First-order Shear Deformation Theory) and TSDT (Third-order Shear Deformation Theory) and allows embedded piezoelectric patches in extension and thickness-shear modes. A finite element model for piezoelectric laminate plates, using equivalent single layer (ESL), was developed considering the generalized mechanical displacements and the electric charges induced in the coupled electric circuits as degrees of freedom. Then, the model was implemented and validated by means of comparisons with results found in the literature. Thereafter, some laminate plate configurations with different numbers of piezoelectric patches were studied through a parametric analysis to obtain the positions that maximize the electromechanical coupling between patches and structure for the first vibration modes. These results allowed the optimization of the electromechanical coupling efficiency through piezoelectric patches distribution for a plate with a larger number of patches and the comparison between the results obtained with the two plate theories considered.

This Master‘s thesis is focused on theoretical study of twinning in magnetic shape memory alloys based on Ni2MnGa using ab initio calculations of electronic structure within the projector augmented wave method. In particular, the effect of increasing concentration of manganese at the expense of gallium was studied on total energy and stress profiles along different deformation paths in the (10-1)[101] shear system of non-modulated martensite. Further, this work deals with the effect of the concentration of manganese on the energy of planar fault caused by presence of partial dislocation due to motion of twin boundary. The results show that the shear modulus in studied shear system increases with the increasing concentration of manganese as well as energy barrier and deformation characteristics along shear deformation paths increases, which makes the shear more difficult in Mn-rich alloys. Increasing concentration of manganese also leads to rising the planar fault energy. All these effects can be responsible for lower mobility of twin boundaries in alloys with higher concentration of manganese.

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In high rise towers, reinforced concrete elevator shafts with coupling beams are extensively used as a principal structural element to resist lateral loads. The lateral load resistance of the tower is dominantly dependent on the stiffness of the load-bearing walls, and coupling beams connecting them. In an interest to study the reduction in the stiffness of high rise tower due to cracking in the coupling beams, variability in the reinforcement content, concrete grade and the effect of joint flexibility at the beam-wall intersection, this master thesis presents the analytical and finite element approaches to determine the equivalent height of the concrete coupling beams and the overall global stability of the high-rise tower. A comprehensive parametric study on 240 combinations of reinforced concrete coupling beams and 48 models of the global tower has been carried out to backtrack the effective stiffness of the RC coupling beams from the load-deflection curve. As a result, the stiffness and the equivalent height of coupling beams are computed and plotted as a function of the concretegrade, reinforcement content and aspect ratio. Additionally, the tip deflections of the towers for both the cracked & reinforced and un-reinforced & un-cracked models are also plotted as functions of the concrete grade, reinforcement content and aspect ratio.The obtained results show that the stiffness ratio and the ratio of the equivalent height to the normal height increase with the increase in the longitudinal reinforcement ratio and aspectratio but decrease with an increase in the concrete grade for both analytical and finite element methods. The tip deflection of tower is not significantly affected by an increase in the reinforcement content of slender coupling beams and vice versa for both the analytical and the finite element method. Independently of the slenderness of the composing coupling beams, the stiffness increases significantly with an increase in the concrete grade. These results show a good picture on how to choose the equivalent height in the model with no reinforcement. So, the developed diagram will be a more practical method for the designer of awhole building at the early stage design. Thick coupling beams need to be reinforced to reach the gross section’s stiffness while slender sections will have a higher stiffness with reinforcement. This would help the designer to find a more rational model without reinforcement. Using Hans Petersson’s analytical method, regarding the joint flexibility at the beam wall intersection, to exploit the full capacity of a concrete coupling beam section, the stiffness should be reduced. For global models, independently of the slenderness of the composing coupling beams, the stiffness increases significantly with an increase in the concrete grade. / I höghus används hisschakt av armerad betong tillsammans med kopplingsbalkar i stor utsträckning som främsta konstruktionselement för att motstå horisontella laster. Tornets horisontella bärförmåga är beroende av analytiska studier och studier med finita element metoden styvheten hos de bärande väggarna, och kopplingsbalkarna som förbinder dem. För att studera minskningen av styvheten i höghustorn på grund av sprickbildning i kopplingsbalkar, variationen i armeringsmängden, betongkvaliteten och effekten av ledflexibilitet vid balk-vägg-knutpunkten, presenterar detta examensarbete kopplingsbalkarnas effektiva styvhet och höghusets globala stabilitet. En omfattande parametrisk studie på 240 olika kombinationer av armerade kopplingsbalkar och 32 modeller av ett höghus har genomförts för att härleda den effektiva styvheten i de armerade kopplingsbalkarna från last-deformationskurvan. Som ett resultat beräknas styvheten och den ekvivalenta höjden av kopplingsbalkarna och plottas som funktion av betongkvaliteten och armeringsmängden. Dessutom modelleras höghuset för både spruckna & armerade kopplingsbalkar samt oarmerade & ospruckna kopplingsbalkar för att erhålla utböjningen av höghusets topp. Resultatet plottas som funktion av betongkvaliteten och armeringsmängden. De erhållna resultaten visar att styvhetsförhållandet och förhållandet mellan ekvivalent höjd till normal höjd ökar med mer längsgående armering och tvärsnittsförhållandet men minskar med en ökning av betongkvaliteten för både den analytiska och finita elementmetoden. Utböjningen av höghusets topp påverkas inte nämnbart av en ökning av armeringsmängden i de slanka kopplingsbalkarna och vice versa för både den analytiska och finita elementmetoden. Oberoende av slankheten av kopplingsbalkarna ökar styvheten betydligt med en ökning av betongkvaliteten. Dessa resultat visar en bra bild på hur man väljer ekvivalent höjd i modellen utan armering. Därmed kommer det framtagna diagrammet vara en mer praktisk metod för att i ett tidigt skede konstruera en hel byggnad. Tjocka kopplingsbalkar måste armeras för att nå tvärsnittets styvhet medan smala tvärsnitt kommer att ha en högre styvhet med armering. Detta skulle hjälpa konstruktören att hitta en mer rationell modell utan armering. Med hjälp av Hans Peterssons analytiska metod, angående ledflexibiliteten vid balk-väggknutpunkten, bör styvheten minskas för att utnyttja den fulla kapaciteten hos en betongkopplingsbalk. För globala modeller, oberoende av de slanka kopplingsbalkarna, ökar styvheten betydligt med en ökning av betongkvaliteten.

In composite beam design, headed stud shear connectors are commonly used to transfer longitudinal shear forces across the steel¿concrete interface. Present knowledge of the load¿slip behavior and the shear capacity of the shear stud in composite beam are limited to data obtained from the experimental push-off tests. For this purpose, an effective numerical model using the finite element method to simulate the push-off test was proposed. The model has been validated against test results and compared with data given in the current Code of Practices, i.e., BS5950, EC4, and AISC. Parametric studies using this model were preformed to investigate variations in concrete strength and shear stud diameter. The finite element model provided a better understanding to the different modes of failure observed during experimental testing and hence shear capacity of headed shear studs in solid concrete slabs

The Route 601 Bridge spans 39 ft over Dickey Creek in Sugar Grove, VA and represents the first use of Strongwell's 36 in. double web beam (DWB) as the main load carrying members for a traffic bridge. The bridge was designed for AASHTO HS20-44 and AASHTO alternate military loading with a targeted deflection limit of L/800. For the preliminary design, conservative properties for the 36 in. DWB were assumed based on experience at Virginia Tech with Strongwell's 8 in. DWB used in the Tom's Creek Bridge. An elastic modulus (E) of 6,000 ksi and a shear stiffness (kGA) of 20,000 ksi-in2 were assumed and used with Timoshenko shear deformable beam theory to characterize the beams and determine the deflections. This thesis details the experimental work conducted in conjunction with the design of the Route 601 Bridge, which had two goals. First, a deck-to-girder connection was tested to determine if a bolted connection could develop composite action between the girder and the deck. This connection was shown to provide a significant amount of composite action when used with the 8 in. DWB and a composite deck, but little or no composite action when used with the 36 in. DWB and a glue-laminated timber deck. Second, eleven 36 in. DWB's were tested to determine their stiffness properties (EI and kGA) to insure that these properties were above the values assumed in the preliminary design, and all the beams had stiffness properties that were close to or above the assumed values. The eleven beams were also proof tested to a moment equivalent to five times the service load moment to insure the safety of the Route 601 Bridge, and one beam was tested to failure to determine the failure mode and residual stiffness of the 36 in. DWB. Finally, based on these results eight beams were chosen for the Route 601 Bridge. / Master of Science

Advances in the design and manufacturing technologies have greatly enhanced the utility of fiber reinforced composite materials in aircraft, helicopter and space- craft structural components. The special characteristics of composites such as high strength and stiffness, light-weight corrosion resistance make them suitable sub- stitute for metals/metallic alloys. However, composites are very sensitive to the anomalies induced during their fabrication and service life. Also, they are suscepti- ble to the impact and high frequency loading conditions because the epoxy matrix is at-least an order of magnitude weaker than the embedded reinforced carbon fibers. On the other hand, the carbon based matrix posses high electrical conductivity which is often undesirable. Subsequently, the metal matrix produces high brittleness. Var- ious forms of damage in composite laminates can be identified as indentation, fiber breakage, matrix cracking, fiber-matrix debonding and interply disbonding (delam- ination). Among all the damage modes mentioned above, delamination has been found to be serious for all cases of loading. They are caused by excessive interlaminar shear and normal stresses. The interlaminar stresses that arise in the case of composite materials due to the mismatch in the elastic constants across the plies. Delamination in composites reduce it’s tensile and compressive strengths by consid- erable margins. Hence the knowledge of these stresses is the most important aspect to be looked into. Basic theories like the Euler-Bernoulli’s theory and Timoshenko beam theory are based on many assumptions which poses limitation to determine these stresses accurately. Hence the determination of these interlaminar stresses accurately requires higher order theories to be considered. Most of the conventional methods of determination of the stresses are through the solutions, involving the trigonometric series, which are available only to small and simple problems. The most common method of solution is by Finite Element (FE) Method. There are only few elements existing in the literature and very few in the commercially available finite element software to determine the interlaminar stresses accurately in the composite laminates. Accuracy of finite element solution depends on the choice of functions to be used as interpolating polynomials for the field variable. In-appropriate choice will manifest in the form of delayed convergence. This delayed convergence and accuracy in predicting these stresses necessiates a formulation of elements with a completely new concept. The delayed convergence is sometimes attributed to the shear locking phenomena, which exist in most finite element formulation based on shear deformation theories. The present work aims in developing finite elements based on higher order theories, that alleviates the slow convergence and achieves the solutions at a faster rate without compromising on the accuracy. The accuracy primarily depends on the theory used to model the problem. Thus the basic theories (such as Elementary Beam theory and Timoshenko Beam theory) does not suffice the condition to accuratley determine the interlaminar stresses through the thickness, which is the primary cause for delamination in composites. Two different elements developed on the principle of super-convergence has been presented in this work. These elements are subjected to several numerical experiments and their performance is assessed by comparing the solutions with those available in literature. Spacecraft and aircraft structures are light in weight and are also lightly damped because of low internal damping of the material of construction. This increased exibility may allow large amplitude vibration, which might cause structural instability. In addition, they are susceptible to impact loads of very short duration, which excites many structural modes. Hence, structural dynamics and wave propagation study becomes a necessity. The wave based techniques have found appreciation in many real world problems such as in Structural Health Monitoring (SHM). Wave propagation problems are characterized by high frequency loads, that sets up stress waves to propagate through the medium. At high frequency, the wave lengths are small and from the finite element point of view, the element sizes should be of the same order as the wave lengths to prevent free edges of the element to act as a free boundary and start reflecting the stress waves. Also longer element size makes the mass distribution approximate. Hence for wave propagation problems, very large finite element mesh is an absolute necessity. However, the finite element problems size can be drastically reduced if we characterize the stiffness of the structure accurately. This can accelerate the convergence of the dynamic solution significantly. This can be acheived by the super-convergent formulation. Numerical results are presented to illustrate the efficiency of the new approach in both the cases of dynamic studies viz., the free vibration study and the wave propagation study. The thesis is organised into five chapters. A brief organization of the thesis is presented below, Chapter-1 gives the introduction on composite material and its constitutive law. The details of shear locking phenomena and the interlaminar stress distribution across the thickness is brought out and the present methods to avoid shear locking has been presented. Chapter-2 presents the different displacement based higher order shear deformation theories existing in the literature their advantages and limitations. Chapter-3 presents the formulation of a super-convergent finite element formulation, where the effect of lateral contraction is neglected. For this element static and free vibration studies are performed and the results are validated with the solution available in the open literature. Chapter-4 presents yet another super-convergent finite element formulation, wherein the higher order effects due to lateral contraction is included in the model. In addition to static and free vibration studies, wave propagation problems are solved to demonstrate its effectiveness. In all numerical examples, the super-convergent property is emphasized. Chapter-5 gives a brief summary of the total research work performed and presents further scope of research based on the current research.

The aim of this work is to develop and validate a continuum model for the simulation of the thermomechanical response of a shape memory polymer (SMP). Rather than integral type viscoelastic model, the approach here is based on the idea of two inter-penetrating networks, one which is permanent and the other which is transient together with rate equations for the time evolution of the transient network. We find that the activation stress for network breakage and formation of the material controls the gross features of the response of the model, and exhibits a "thermal Bauschinger effect". The model developed here is similar to a thermoviscoelastic model, and is developed with an eye towards ease of numerical solutions to boundary value problems. The primary hypothesis of this model is that the hysteresis of temperature dependent activation-stress plays a lead role in controlling its main response features. Validation of this hypothesis is carried out for the uniaxial response from the experimental data available in the literature for two different SMP samples: shape memory polyurethane and Veriflex, to show the control of the evolution of the temperature sensitive activation stress on the response. We extend the validated 1D model to a three dimensional small strain continuum SMP model and carry out a systematic parameter optimization method for the identification of the activation stress coefficients, with different weights given to different features of the response to match the parameters with experimental data. A comprehensive parametric study is carried out, that varies each of the model material and loading parameters, and observes their effect on design-relevant response characteristics of the model undergoing a thermomechanical cycle. We develop "response charts" for the response characteristics: shape fixity, shape recovery and maximum stress rise during cooling, to give the designer an idea of how the simultaneous variation of two of the most influential material parameters changes a specific response parameter. To exemplify the efficacy of the model in practical applications, a thermoviscoelastic extension of a beam theory model will be developed. This SMP beam theory will account for activation stress governed inelastic response of a SMP beam. An example of a three point bend test is simulated using the beam theory model. The numerical solution is implemented by using an operator split technique that utilizes an elastic predictor and dissipative corrector. This algorithm is validated by using a three-point bending experiment for three different material cases: elastic, plastic and thermoplastic response. Time step convergence and mesh density convergence studies are carried out for the thermoviscoelastic FEM model. We implement and study this model for a SMP beam undergoing three-point bending strain recovery, stress recovery and cyclic thermomechanical loading. Finally we develop a thermodynamically consistent finite continuum model to simulate the thermomechanical response of SMPs. The SMP is modeled as an isotropic viscoplastic material where thermal changes govern the evolution of the activation stress of the material. The response of the SMP in a thermomechanical cycle is modeled as a combination of a rubbery and a glassy element in series. Using these assumptions, we propose a specific form for the Helmholtz potential and the rate of dissipation. We use the technique of upper triangular decomposition for developing the constitutive equations of the finite strain SMP model. The resulting model is implemented in an ODE solver in MATLAB, and solved for a simple shear problem. We study the response of the SMP model for shear deformation as well as cyclic shear deformation at different initial temperatures. Finally, we implement the thermomechanical cycle under shear deformations and study the behavior of the model.