Dissertations / Theses on the topic 'DEFLECTOR PLATE'

Thesis (MScEng (Mechanical and Mechatronic Engineering))--University of Stellenbosch, 2009.
ENGLISH ABSTRACT: In the primary circuit components of high temperature reactors, various unwanted particles have been found. These particles include, for example, graphite and silver- 110 (110mAg). The silver-110 (110mAg) particles are radioactive, with a half-life of 253 days. The presence of radioactive particles in the primary circuit components constitutes an unwanted maintenance problem from a radiation hazard point of view. The development of a method to remove these particles from the helium stream is therefore needed. This thesis consideres two possible methods of removing silver from the helium stream, namely laser ablation of microparticles and electrostatic precipitation. These methods require the generation of silver ions or charged particles, the deflection of these particles in a helium gas stream passing through an electric field and the subsequent plate-out of these particles onto deflection electrodes. To find a suitable method of generating ions, various methods to generate the silver ions were investigated and evaluated. These methods include existing ion sources, thermionic, field and photoelectric emission and laser ablation of microparticles. No existing ion sources could be found which could be utilised in helium at high pressure. From calculations it was concluded that thermionic, field and photoelectric emission could also not be used to raise the energy of the emitted electrons sufficiently to ionize silver in a helium flight path. These methods were found not to be feasible ion sources in helium at high pressures. However, laser ablation of microparticles was found to constitute a feasible technology. Laser ablation was successfully utilised by Nichols et al. (2000) to deflect silver nanoparticles in an electric field across a two bar helium stream. An apparatus, similar to the one developed by Nichols et al. (2000), was designed and built. The apparatus included a silver insertion mechanism and tests with this apparatus were called the microparticle tests. To determine the efficacy of the silver insertion mechanism, the microparticle tests were done without the use of a laser. It was found that a laser was not necessary as microparticles collected on both the deflection electrodes. Dielectrophoresis was proposed as a possible explanation for the deflection and the plate-out of the mcroparticles. To theoretically model the deflection of the silver particles, two models were proposed, namely the deterministic and the stochastic deflection models. The latter describes the deflection of atoms, ions and polarized particles by using probability theory. From this model it was found that the Brownian motion force is far larger that the force created by the polarizibility of the atom due to an electric field. The deterministic deflection model describes the deflection of larger particles in a continuum. From this model it was found that a silver microparticle with a radius of 3 mm in a helium stream with bulk velocity of 0.0198 m/s would deflect 4.6 mm per helium flight path length of 140 mm. From these calculation it was found that the apparatus which had been built was not long enough to deflect and plate-out all the silver microparticles. The dielectrophoresis force on nanoparticles cannot be calculated, as the theory of dielectrophoresis is only valid for particles with diameter larger than 1 mm. Changes were therefore made to the apparatus to generate nanoparticles as their mobility is larger than that of microparticles. The nanoparticles were created by means of an arc discharge in helium; therefore tests with this modified apparatus were called the arc discharge test. The nanoparticles so created, deflected and deposited on both deflection electrodes. With the use of an atomic force microscope some of the particles could be classified as microparticles. According to the deterministic deflection model they should not have deflected. Combined with the fact that oxygen was in the plasma, due to the oxidation of the electrodes, a hypothesis of bipolar charging was thus proposed. The deterministic deflection model was used and supplemented with field and diffusion charging calculations, to support this hypothesis. A reasonable correlation between the theoretical model and this experimental results was obtained. Based on the arc discharge test, electrostatic precipitation was proposed as the indicated means of scrubbing silver and other particles such as graphite from a helium stream. It is recommended that a new apparatus be built and that the deterministic deflection model be used to predict the deflection of the particles. With this apparatus the uncertainties of breakdown voltage, the effect of thermionic emission and the size of the particles, all of which have been identified as being important, can then also be determined.
AFRIKAANSE OPSOMMING: In die primêre komponente van die kringloop van hoë temperatuurreaktors, was verskillende ongewenste partikels soos grafiet en silwer-110 (110mAg) teenwoordg. Silwer- 110 (110mAg) is radioaktief met ’n halfleeftyd van 253 dae. Vanuit ’n radiasie-risiko oogpunt word daar onderhoudsimplikasies geskep deur die teenwoordigheid van radioaktiewe partikels in die primêre komponente. Die ontwikkeling van ’n metode om hierdie partikels uit die heliumstroom the verwyder was dus nodig. Hierdie tesis ondersoek twee moontlike metodes van verwydering van silwer uit die heliumstroom, naamlik laser-ablasie van mikropartikels en elektrostatiese presipitasie. Hierdie metodes benodig die generasie van silwer ione of gelaaide partikels, die defleksie daarvan in ’n heliumstroom wat deur ’n elektriese veld vloei en die platering van die partikels op defleksie elektrodes. Om ’n geskikte metode the vind wat ione genereer was, verskillende metodes om die silwer ione te verkry, ondersoek en geëvalueer. Hierdie metodes sluit in bestaande ioonbronne, termioniese, veld en fotoëlektriese emissie en laser-ablasie van mikropartikels. Geen ioonbronne was gevind wat gebruik kan word in helium by hoë druk nie. Die gevolgtrekking is gemaak vanaf berekeninge dat termioniese, veld en fotoëlektriese emissie ook nie gebruik kan word om die energie van die voortgebronge elektrone genoeg te verhoog om silwer in ’n heliumstroom te ioniseer nie. Daar was gevind dat hierdie metodes nie geskik is as ioonbronne in helium by hoë druk nie. Daarenteen was laser-ablasie van mikropartikels gevind om ’n geskikte tegnologie voor te stel. Laser-ablasie van mikropartikels was suksesvol deur Nichols et al. (2000) gebruik om silwer nanopartikels te deflekteer in ’n elektriese veld oor helium van twee bar. ’n Apparaat soortgelyk aan Nichols et al. (2000) se eksperiment, was dus ontwerp en gebou. Die apparaat het ’n silwer insitmeganisme bevat en toetse met hierdie apparaat was die mikropartikel toetse genoem. Om die effektiwiteit van die insitmeganisme te bepaal, was toetse gedoen sonder opstelling van die laser. Daar was eksperimenteel gevind dat die laser nie nodig was nie, omdat mikropartikels op beide defleksie elektrodes geplateer het. Dielektroforese was voorgestel as ’n moontlike verduideliking vir deflektering en platering vir die silwer mikropartikels. Om die defleksie van silwer partikels teoreties te moduleer was twee modelle voorgestel, naamlik deterministiese en stogastiese defleksiemodelle. Laasgenoemde beskryf die defleksie van atome, ione en gepolariseerde partikels deur gebruik te maak van waarskynlikheidsteorie. Die stogastiese defleksiemodel dui aan dat die Brownian bewegingskrag veel groter is as die krag wat geskep word deur die polarisasie van ’n atoom as gevolg van ’n elektriese veld. Die deterministiese defleksiemodel beskryf die defleksie van groter partikels in ’n kontiuum. Met hierdie model was gevind dat silwer mikropartikels met ’n radius van 3 mmin ’n heliumstroom van snelheid van 0.0198 m/s, 4.6 mm sal deflekteer per 140 mm van heliumstroom lengte. Dit bewys dat die apparaat wat gebou was, se lengte onvoldoende was om al die silwer mikropartikels te deflekteer en te laat neerslaan. Die dielektroforese krag van nanopartikels kan nie uitgewerk word nie, omdat die dielektroforese model slegs geldig is vir partikels groter as 1 mm. Veranderings was dus aan die apparaat gemaak om nanopartikels te genereer omdat hul mobiliteit hoër is as die van mikropartikels. Die nanopartikels was geskep deur gebruik van ’n boogontlading in helium; daarom was toetse met hierdie gemodifiseerde apparaat die boogontladingstoets genoem. Die nanopartikels wat so geskep was, het gedeflekteer en het op beide elektrodes neergeslaan. Met die gebruik van ’n atomiese krag mikroskoop was dit gevind dat sommige van hierdie partikels mikropartikels was. Volgens die deterministiese defleksiemodel moes hul nie gedeflekteer het nie. Gekombineerd met die feit dat daar, weens oksidasie van die elektrodes, suurstof in die plasma was, was ’n hipotese van bipolêre lading voorgestel. Die deterministiese defleksiemodel is saam met die veld- en diffusielading gebruik om hierdie hipotese te staaf. ’n Redelike korrelasie tussen die teoretiese en eksperimentele data was gevind. Gebaseer op die boogontladingstoets, was elektrostatiese presipitasie voorgestel as ’n metode om silwer en ander partikels soos grafiet uit ’n heliumstroom te verwyder. Daar word voorgestel dat ’n nuwe apparaat gebou word en dat die deterministiese defleksiemodel gebruik word vir die bepaling van defleksie van die partikels. Deur die nuwe apparaat te gebruik kan die onsekerhede van deurslagspanning, effek van termioniese emissie en grootte van die partikels wat geidentifiseer is as belangrik, ook bepaal word.

A solution procedure based on the finite strip method is presented herein, for the analysis of plate systems exhibiting geometric and material non-linearities. Special emphasis is given to the particular problem of rectangular plates with stiffeners running in a direction parallel to one side of the plate. The finite strip method is selected for the analysis as the geometry of the problem is well suited for the application of this method and also as the problem is too complicated to solve analytically. Large deflection effects are included in the present study, by taking first, order non-linearities in strain-displacement relations into account. Material non-linearities are handled by following von-Mises yield criterion and associated flow rule. A bi-linear stress-strain relationship is assumed for the plate material, if tested under uniaxial conditions. Numerical integration of virtual work equations is performed by employing Gauss quadrature. The number of integration points required in a given direction is determined either by observing the individual terms to be integrated or by previous experience. The final set of non-linear equations is solved via a Newton-Raphson iterative scheme, starting with the linear solution. Numerical investigations are carried out by applying the finite strip computer programme to analyse uniformly loaded rectangular and I beams with both simply supported and clamped ends. Displacements, stresses and moments along the beam are compared with analytical solutions in linear analyses and with finite element solutions in non-linear analyses. Investigations are also extended to determine the response of laterally loaded square plates with simply supported and clamped boundaries. Finally, a uniformly loaded stiffened panel is analysed and the results are compared with finite element results. It was revealed that a single mode in the strip direction was sufficient to yield engineering accuracy for design purposes, with most problems.
Applied Science, Faculty of
Civil Engineering, Department of
Graduate

The operating motion of a ground compactor uses high power vibrations to improve mechanical properties of a compacted ground. This motion gives a good base for the vibration analysis with an aid of Signal Processing. In this thesis, the motion of a bottom plate in a compactor is of the main interest. The thesis concerns usage of two main spectral analyzing tools, Power Spectrum estimators and Power Spectral Density estimators, presenting advantages and disadvantages in the application of a vibration analysis. Moreover, an influence of two window applications, a Flattop window, and a Hanning window, is described in relation to both analyzing approaches. The results present problems that occur when a vibration with a present modulated frequency is analyzed and how a Power Spectral Density estimator arise in a more consistent estimate over analyzed vibration spectrum. What is more, an Ordinary Deflection Shapes for a simplified bottom plate model, under different motion excitations, are presented at the end of this thesis, giving a better view of the operational motion of an analyzed system.

Various models are currently in existence for determining the deflection of lithospheric plates under an applied transverse load. The most popular models treat lithospheric plates as thin elastic or thin viscoelastic plates. The equations governing the deflection of such plates have been solved successfully in two dimensions using integral transform techniques. Three dimensional models have been solved using Fourier Series expansions assuming a sinusoidal variation for the load and deflection. In the engineering context, the finite element technique has also been employed. The current aim, however, is to develop an efficient solver for the three dimensional elastic and viscoelastic problems using finite difference techniques. A variety of loading functions may therefore be considered with minimum work involved in obtaining a solution for different forcing functions once the main program has been developed. The proposed method would therefore provide a valuable technique for assessing new models for the loading of lithospheric plates as well as a useful educational tool for use in geophysics laboratories. The multigrid method, which has proved to be a fast, efficient solver for elliptic partial differential equations, is examined as the basis for a solver of both the elastic and viscoelastic problems. The viscoelastic problem, being explicitly time-dependent, is the more challenging of the two and will receive particular attention. Multigrid proves to be a very effective method applicable to the solution of both the elastic and viscoelastic problems.
Science, Faculty of
Mathematics, Department of
Graduate

Variational methods are widely used for the solution of complex differential equations in mechanics for which exact solutions are not possible. The finite difference method, although well known as an efficient numerical method was applied in the past only for the solution of linear and nonlinear thin plates. In the present study, the suitability of the method for the solution of nonlinear deflection of thick plates is studied for the first time. While there is major differences between small deflection and large deflection plate theories, the former can be treated as a particular case of the latter, when the centre deflection of the plate is less than or equal to 0.2-0.25 of the thickness of the plate. The finite difference method as applied here is a modified finite difference approach to the ordinary finite difference method generally used for the solution of thin plate problems. In this thesis thin plates are treated as a particular case of the corresponding thick plate when the boundary conditions of the plates are taken into account. The method is first applied to investigate the deflection behaviour of square clamped and simply supported square isotropic thick plates. After the validity of the method is established, it is then extended to the solution of rectangular thick plates of various aspect ratios and thicknesses. Generally, beginning with the use of a limited number of mesh sizes for a given plate aspect ratio and boundary conditions, a general solution of the problem including the investigation of accuracy and convergence was extended to rectangular thick plates by providing more detailed functions satisfying the rectangular mesh sizes generated automatically by the programme. Whenever possible results of the present method are compared with the existing solutions in the technical literature obtained by much more laborious methods and close agreements are found. Significant amounts of results presented herein are not currently available in the technical literature for various plate aspect ratios and Poisson's ratios. The submatrices involved in the formation of the finite difference equations from the governing differential equations forming the general system are generated directly by the computer programme. The subroutine SOLINV from the second directed method as developed and illustrated in Chapter V takes care of the inversion of the general matrix. The subroutine developed by the author has been proven to be more efficient than the former methods known for the computation of linear simultaneous equations [61]. Simplicity in formulation and quick convergence are the obvious advantages of the finite difference formulation developed here for small and large deflection analysis of thick plate in comparison with other numerical methods requiring extensive computer facilities.

Theoretical formulations, analytical solutions, and finite element solutions for laminated composite plate and shell structures with smart material laminae are presented in the study. A unified third-order shear deformation theory is formulated and used to study vibration/deflection suppression characteristics of plate and shell structures. The von K??rm??n type geometric nonlinearity is included in the formulation. Third-order shear deformation theory based on Donnell and Sanders nonlinear shell theories is chosen for the shell formulation. The smart material used in this study to achieve damping of transverse deflection is the Terfenol-D magnetostrictive material. A negative velocity feedback control is used to control the structural system with the constant control gain. The Navier solutions of laminated composite plates and shells of rectangular planeform are obtained for the simply supported boundary conditions using the linear theories. Displacement finite element models that account for the geometric nonlinearity and dynamic response are developed. The conforming element which has eight degrees of freedom per node is used to develop the finite element model. Newmark's time integration scheme is used to reduce the ordinary differential equations in time to algebraic equations. Newton-Raphson iteration scheme is used to solve the resulting nonlinear finite element equations. A number of parametric studies are carried out to understand the damping characteristics of laminated composites with embedded smart material layers.

The behavior of wood shear walls has been the focus of researchers and engineers for many years due to their availability in the North American construction landscape. A review of the established literature showed that most of the research have focused on the shear wall behavior as a whole with no investigation specifically targeting the individual components of its deflection. Also, little to no attention has been given to the investigation of the cumulative effects especially when the out-of-plane diaphragm stiffness is considered. The current study aims at investigating the effects of construction details variation on the behavior of the shear walls and evaluating whether the current deflection equation, as per wood design standard (CSA 2014) can adequately predict the overall wall stiffness. A total of 27 full-scale single-storey walls, with different construction details and aspect ratios, were tested under either static or monotonic (as both are the same) loading. The parameters that were varied in the testing were the stud size and spacing, nail diameter and spacing, sheathing panel type and thickness and hold-down anchoring system/type. For the two-storey walls, two different loading cases were considered, namely where the load was applied at the top or bottom storey only. The results showed that the strength and stiffness correlated almost directly to the inverse of the wall aspect ratio. There was no clear trend when considering the effect of the walls’ aspect ratios on ductility. Unexpectedly, walls with aspect ratios not permitted according to the wood design standard (4:1 and 6:1) followed similar strength and stiffness trends and had sufficient ductility ratios as those with smaller aspect ratios. This observation explains in part some of the discrepancies found between engineering calculations and behavior of actual building with light frame wood shear walls. Significant discrepancies were found when comparing the various deflection constituent with those estimated using the design expression. Adding more end studs and changing the size of the studs had no significant effect on the overall wall capacity and little effect on its stiffness. Reducing the stud spacing had, as expected, no effect on the wall capacity; however, the results showed that the bending stiffness was affected by the overall number of studs in the wall and not solely by the end studs. Shear walls sheathed with plywood panels exhibits slightly higher peak load and initial stiffness than those with OSB, which was mainly attributed to the greater panel thickness, and possibly density, of the plywood. Both sheathing types provided similar levels of ductility, as expected. Thicker sheathing increased the capacity and stiffness of the wall with no significant change observed in ductility ratio. The wall strength was significantly affected by the nail diameter and nail spacing, but no difference was observed when the nail edge/end distance was increased. The results also showed that discrete hold-down system behaved in a non-linear manner with a significantly greater initial stiffness than that assumed in design. The study also showed that having continuous hold-down connections has a positive effect on the capacity, stiffness and ductility of the wall when compared with discrete hold-downs. Having no hold-down adversely affects the wall capacity and stiffness, but did not affect the ductility of the wall. For the two-storey walls, the deflection estimated based on the cumulative effect assumption showed slight differences when compared with that observed in the experimental study. It was observed that the majority of the cumulative effect stems from the rigid body rotation due to deformation in the hold-down devices. A Computer shear wall model (through SAP2000) was developed using linear “frame” and “membrane” elements for the framing and sheathing members, respectively, whereas the sheathing to framing nails and hold-down were modeled using nonlinear springs. It was found that the model was capable of predicting the peak load, ultimate deflection and yield loads with reasonable accuracy, but overestimated the initial stiffness and ductility of the walls. In general, when the force-displacement curves were compared it was evident that the model was capable of predicting the wall behaviour with reasonable accuracy. When investigating the cumulative effects using the model, the results clearly showed that the assumption of cumulative effects due to rigid body rotation is valid for stacked shearwalls with no consideration for the floor diaphragm. The effect of the diaphragm on the behavior of the shear walls, in particular its out-of-plane rigidity was simulated by modeling the floors as beam. The out of plane stiffness of the shear walls was investigated for idealized (infinitely stiff or flexible) as well as “realistic”. The results showed reductions in the shearwall deflection in the magnitude of approximately 80% considering the out of plane rigidity of the diaphragm. It was also concluded that considering conservative estimates of out of plane stiffness might lead to a very significant reduction in deflection and that assuming the floor diaphragm to be infinitely rigid out of plan seems reasonable. For diaphragms supported on multiple panels further reduction in the deflection was observed. More work, particularly at the experimental level, is needed to verify the finding obtained in the numerical investigation related to the effect of out of plane diaphragm stiffness.

In the thesis explicit dual parabolic-elliptic models are constructed for the Konenkov flexural edge wave and the Stoneley-type flexural interfacial wave in case of thin linearly elastic plates. These waves do not appear in an explicit form in the original equations of motion within the framework of the classical Kirchhoff plate theory. The thesis is aimed to highlight the contribution of the edge and interfacial waves into the overall displacement field by deriving specialised equations oriented to aforementioned waves only. The proposed models consist of a parabolic equation governing the wave propagation along a plate edge or plate junction along with an elliptic equation over the interior describing decay in depth. In this case the parabolicity of the one-dimensional edge and interfacial equations supports flexural wave dispersion. The methodology presented in the thesis reveals a dual nature of edge and interfacial plate waves contrasting them to bulk-type wave propagating in thin elastic structures. The thesis tackles a number of important examples of the edge and interfacial wave propagation. First, it addresses the propagation of Konenkov flexural wave in an elastic isotropic plate under prescribed edge loading. For the latter, parabolic-elliptic explicit models were constructed and thoroughly investigated. A similar problem for a semi-infinite orthotropic plate resulted in a more general dual parabolic-elliptic model. Finally, an anal- ogous model was derived and analysed for two isotropic semi-infinite Kirchhoff plates under perfect contact conditions.

This thesis improves a previous kinematic analysis and develops the elastic portion of the analysis of a curved compliant beam. This analysis is used to develop a Pseudo-Rigid-Body Model for the curved compliant beam. The Pseudo-Rigid-Body Model consist of kinematic and elastic parameters which can be used to simplify the computation of the large deflections of the beam as it undergoes spherical motion. The kinematic parameters that are developed are the characteristic radius, Gamma*length, the parametric angle coefficient, c_theta, and the kinematic parametrization limit, Capital_theta_max(Gamma). The elastic parameters developed are the stiffness coefficient, K_theta, and the elastic parameterization limit, Capital_theta_max(K). Additionally, curve fit parameters are developed which enable the calculation of the stress in curved beam as it deflects.

The concept of using aluminum as the primary construction material for high speed ships and the hydroelastic behavior of the structure is widely gaining importance as a significant research topic in naval architecture. Aluminum is lighter than steel and hence can be predominantly used in high speed crafts which experiences significant slamming. This thesis work is focused on wedge shaped models. Free fall wedge impact is studied and a FORTRAN 90 computer program is developed to estimate the structural response of the wedge experiencing slamming by the use of matrix methods, finite element techniques and Newmark-Beta numerical time integration methods. The numerical solution is validated by comparison with the static solution. The theoretical hydrodynamic pressures which are used as input for this work was originally developed by using a flat cylinder theory [26]. The wedge drop at 0.6096 m (24 inch) drop height with an impact veloc- ity of v=3.05 m/s is based as the premise and the experimental pressure distributions measured by the pressure-transducers and the theoretical pressure predictions are used as inputs and the structural response is derived. Additionally, the response is compared for three different plate thicknesses and the results are compared against each other. The maximum deflection is comparable to the deflection evaluated from the experiment and tends to attain convergence as well. As the plate thickness reduces there tends to be a significant rise in the deflection values for the wedge plate, in the manner that when the plate thickness is halved there is a deviation of more than 75% in the deflection values as such.

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This work shows some NBR 6118:2003 prescriptions, intending to study, analyze and discuss the aspects regarding to the determination of the efforts to check the punch and the detailed framework to struggle it and the deflection (arrow), in the systems of flat plates since they had suffered significant changes. It will be done a comparative analysis of consideration of the non physical linearity presented by structural calculation program CYPECAD to that one done according to NBR 6118:2003, using a grill analogy through the GPLAN program to do that, as it will be also solved some examples to determine the strain and the framework structure to the punch as to deflection in the flat plates. At last, it will be done a study of case of a building in solid flat plates that presents deflection problems, as well as project failures in the dimension of the flat to punch, which subjects deserve a high attention and concern under the vision and sight of NBR 6118:2003. Specifically it will be dealt the following subjects: General features of the system; Methods to determine the strain and dimension to the punch; Verification of the deflection of the flat; Utilization of the programs to determine the strain and deflection; Performance and some examples and a study of the case.
Este trabalho apresenta algumas das prescrições da NBR 6118:2003, com o objetivo de estudar, analisar e discutir aspectos referentes à determinação de esforços para a verificação à punção, detalhamento da armadura para combatê-la e aos deslocamentos verticais (flecha), nos sistemas de lajes-sem-vigas maciças, uma vez que as mesmas sofreram significativas alterações. Será feita uma análise comparativa da consideração da não linearidade física apresentada pelo programa de cálculo estrutural CYPECAD com a feita de acordo com a NBR 6118:2003, utilizando para isso a analogia de grelha através do programa GPLAN, como também serão resolvidos alguns exemplos tanto para a determinação de esforços e armação de combate à punção como para dos deslocamentos verticais nas lajes-sem-vigas. Finalizando será feito um estudo de caso de um edifício em lajes-sem-vigas que apresentava problemas de deslocamentos verticais, como também falhas de projeto no dimensionamento das lajes à punção, assuntos esses merecedores de uma maior atenção, preocupação e abrangência aos olhos da NBR 6118:2003. Especificamente, serão abordados os seguintes assuntos: características gerais do sistema; métodos de determinação de esforços e dimensionamento à punção; verificação de deslocamentos verticais das lajes; utilização de programas para determinação de esforços e deslocamentos; realização de alguns exemplos e um estudo de caso.

The Vertically Oriented Interlocking Timber (VOIT) panel is a new solid wood panel similar to Interlocking Cross Laminated Timber (ICLT) and the more commonly known Cross Laminated Timber (CLT). Like ICLT, VOIT panels use timber connections instead of the adhesives or metal fasteners common to CLT. The difference of VOIT is the orientation of the layers. Where CLT and ICLT panels alternate the orientation of each layer, VOIT panels orient all the layers in the same direction. The vertically oriented layers are then attached to one another by smaller horizontal dovetail members.Two types of VOIT panels were provided to be tested for in-plane lateral loading. Type I had three rows of horizontal dovetail members connecting the layers and Type II had four rows of dovetail members as well as two diagonal members to provide stiffness. Two panels of each type were provided, measuring 8 ft. wide, 8 ft. tall, and 13.75 in. thick. Each panel was disassembled after monotonic lateral in-plane loading to determine possible failure modes. Testing results suggest the VOIT panels to be comparable in shear strength to other wood shear walls, including light frame, CLT, and ICLT walls. A two-part analytical model was created to determine the deflection of the wall when loaded as well as the shear strength of the wall. The model predicted deflection and wall strength reasonably well. Due to the small sample size, additional testing is necessary to confirm the results of the Type I and Type II VOIT panels. Additional testing with more variations of the panel and member geometries is also needed to validate the scope of the model.

В дипломній роботі досліджено підсилення пошкодженої монолітної плити перекриття композитами на основі сучасних карбонових волокон. Проведено експериментальні дослідження по визначенню деформацій монолітної залізобетонної плити, підсиленою композитними матеріалами під навантаженням граничного рівня. Виконано аналіз існуючих методів підсилення залізобетонної плити та існуючої методології їх розрахунку. Досліджено вплив навантаження граничного рівня на деформації підсиленої конструкції. Оцінено перспективи та ефективність підсилення карбоновими композитними волокнами.
Thesis is devoted to research strengthening damaged monolithic slab composites using modern carbon fiber. Experimental studies to determine the strain of monolithic concrete slab, reinforced composite materials under load limit level. Analyze existing methods of strengthening existing reinforced concrete slabs and methodology of their calculation. The investigate of the load limit on the strain enhanced design. The prospects of gain and efficiency of composite carbon fibers

In this work, long-term behaviour of FRP RC beams has been investigated both analytically and experimentally to further extend the knowledge in this particular research domain. In this respect, a new methodology to determine the long-term deflections due to creep and shrinkage is presented. Based on multiplicative coefficients, the methodology is straightforward and simple, and therefore suitable to be used in design. In addition, an experimental campaign on two series of GFRP RC beams subject to long-term loading has been performed. Different reinforcement ratios, concrete strengths and sustained load levels have been considered. For comparison purposes steel reinforcement has also been used. The experimental long-term results have been reported and discussed. Furthermore they have been compared to predictions using the most representative procedures, as well as, the proposed methodology presented in this work.
En aquest treball, es presenta una nova metodologia per a la determinació de fletxes diferides degudes als efectes de la fluència i la retracció del formigó. La metodologia presentada es basa en coeficients multiplicadors, essent així un mètode directe i simple, apte per ser utilitzar en el disseny. Addicionalment, l’estudi presenta els resultats d’una campanya experimental realitzada en dues etapes, on bigues armades amb barres de material compost han estat sotmeses a càrregues a llarg termini. S’han considerat diferents quanties de reforç, resistències de formigó i nivells de càrrega. Per tal de comparar-ne els resultats, també s’han assajat bigues armades amb barres d’acer. Els resultats experimentals han estat analitzats i comparats amb els models de predicció més significatius, així com amb la metodologia desenvolupada i presentada en aquest estudi.

Diploma thesis is focused on structural assessment and strengthening of the reinforced concrete flor slab disturbed by excessive deflection. Thesis included assesment of the existing construction and design method of strengthening of the floor structure with system using prestressing strands without bond.

This diploma thesis is dealing with frame multi-storey garage structure, mainly with its slab. According to the assignment there was made a parametrical study. It contains the comparision of three construction versions: solid slab, slab with void formers Cobiax and prestressed concrete slab. At the chosen variant the 3D mathematical model, which was created in software Scia Engineer, was specified and the construction was designed according to ultimate limit state and serviceability limit state. The outlet of this thesis is structural design and drawings with all designed items

Savonius Hydrokinetic Turbine (SHT) is a small-scale renewable energy source that is a sustainable solution for remote areas and rural electrification. The current research work establishes a numerical study on combined effect of deflector plate (no deflector, deflector at 90°, deflector at 45°), twist angle of blades (0°, 12.5°, 25°), and tip speed ratio (0.5 to 1.5) on the turbine efficiency in terms of power coefficient (Cp) using CFD simulation considering a realizable k-ε turbulence model. A total of 99 simulations were performed considering all the above different conditions. To validate the results, simulations were compared with the results of a previous study having no deflector plate. It has been identified that SHT with blade twist angle of 12.5° and deflector plate at 90° produces highest power coefficient as 0.364 at tip speed ratio of 0.9 and 0.5 m/s water velocity. Similarly, SHT having a blade twist angle of 25° with deflector plate at 90° yields the highest torque coefficient as 0.454 at a TSR of 0.5. It was observed that Cp increases by an average 15% for SHT having blade twist and deflector plate as compared to SHT without blade twist and deflector plate.

碩士
國立成功大學
機械工程學系碩博士班
97
This literary has studied static deflection of Kirchhoff plate with nonlinear elastic boundary conditions. Balance Method is the first step to modify governing equation and boundary condition into single parameter form. Then using Shifting Method solve static plate deflection problem with nonlinear boundary. We assume more than one mode into the equations, and further, discussing the numerical results with one mode assumption. In the end, these problems with nonlinear boundary condition can be solved by Shifting Method.

碩士
國立中央大學
機械工程學系
84
This paper analyzes static deflection problems of thin plates and membranes which are homogeneous and isotropic by finite element method. 16-DOF conforming rectangular elements is used for the analysis of plates. 4-DOF non-conforming rectangular elements is used for the analysis of membranes. This paper first uses single complex function to solve the homogeneous solutions of biharmonic partial differential equation and the partial differential equation for deflection of membranes, and develops the closed-form shape functions. Because the homogeneous solutions have the closed property, the analysis is suitable for the problems of arbitrary boundary conditions. For the analyses of small deflection of thin plates and nonlinear membranes, the resultant which is got from the closed- form shape functions will be compared with the resultant which is got from polynomial shape functions and the analytic solution. Classic thin-plate theorem only solve small deflection problems, so this paper for large deflection problems is based on von Karman theorem and use Lagrangian strains to consider the stretching action of middle surface of plates. For the analyses of finite element method, this paper neglect the axial deplacements, so the tangent stiffness matrices is only composed of bending stiffness matrices and initial stress matrices (or is called geometrical stiffness matrices). Hence, the nonlinear solutions can be solved by direct iteratiev method. Every iterative step must update the initial stress matrices and iterations stop until solutions converge. Because this paper neglect the axial deplacements for large deflection problems, the method is suitable for the immovable edges and symmetric loading problems.

碩士
中華大學
機械與航太工程研究所
92
Problem of large deflection of orthotropic rectangular plate in initial tension is studied. The governing equations follow von-Karman large deflection theory including the consideration of initial tension. A double fourier series method is employed and relevant orthogonality properties were utilized to simplify and to solve the nonlinear simultaneous governing equations, with the aid of a Newton’s numerical scheme. For the simplified case of an isotropic square plate without pretension, the results are comparable with these available for a circular plate in literature. Next, with a newly defined pretension, solutions for various prestressed quasi-isotropic and orthotropic square plates were sought. The results show that, substantial effect of either one of lateral load and initial tension appears only when the other is relatively lower. Regardless of the magnitudes of these two, however, the effect of orthotropy always comes into play in the responses of the plate. Besides, the edge effect can easily be found in a typical orthotropic plate near the edge of the minor direction, especially, for a strongly orthotropic plate under a serious pretension and a heavy lateral load.

碩士
元智大學
機械工程學系
94
In this investigation, the static deflection and harmonic vibration of plate induced by piezoelectric actuators under mixed boundary condition are examined. Two piezoelectric actuators are surface bonded or embedded in the plate and are symmetric with the mid-plane. Electric voltage with the same amplitude and opposite sign are applied to the two symmetric piezoelectric actuators, results to the bending effect on the plate. The bending moment is derived by using the theories of elasticity and piezoelectricity. This bending moment is then applied to the plate. Following the classical plate theory, the analytical solution of flexural displacement on a plate of mixed boundary condition to bending moment can be obtained. The analytical solution are compared with the finite element results to show the validation of present approach. The effects of size and location of actuators on the response of a plate under mixed boundary condition are presented through parametric study. The response can be static or harmonic according to the static or sinusoidal voltage applied to the actuators. The analytical model presented in this research demonstrates the capability of predicting the responses of smart structures to a command voltage applied to the piezoelectric actuators.

博士
國立成功大學
機械工程學系
89
This paper investigates the conditions that can possibly lead to nonlinear dynamic motion, chaotic motion and bifurcation behavior for large deflection plate with variable shapes and boundary condition by utilizing the criteria of fractal dimensions, maximum Lyapunov exponents, bifurcation diagrams and Melnikov method. The governing partial differential equation of the large deflection plate is derived by means of Galerkin method and estimated by numerical method. Several different features including time history, Fourier spectra, phase plate, Poincaré map and bifurcation diagrams are numerically computed. These features are used to characterize the dynamic behavior of these six variable plate subjected to various excitations of lateral loads and thermal loads. These examples include the double mode plate of large deflection, the thermo-elastic circular plate, the clamped and simply-support thermo-elastic circular plate with variable thickness, the spinning thermo-elastic annular plate and the rectangular plate of thermo-mechanical coupling. These examples numerical results indicate that large deflection motion of the plate with variable shapes and boundary conditions possess many periodic trajectory, bifurcation points, jump phenomena, harmonic motions, periodic-double phenomena and chaotic motions. The modeling results show that the proposed method can be employed to predict the nonlinear dynamics of the large deflection plate. The dynamic motions of the large deflection plate can thus be controlled and manipulated for periodic motion.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1988.
Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 136-141).

碩士
元智大學
機械工程學系
91
In this investigation, the static deflection and harmonic vibration of a simply supported plate induced by piezoelectric actuators are examined two piezoelectric actuators are surface bonded or embedded in the plate and are symmetric with the mid-plane. Electric voltage with the same amplitude and opposite sign are applied to the two symmetric piezoelectric actuators, results to the bending effect on the plate. The bending moment is derived by using the theories of elasticity and piezoelectricity. This bending moment is then applied to the plate. Following the classical plate theory, the analytical solution of flexural displacement on a simply supported plate subjected to bending moment can be obtained. The analytical solution are compared with the finite element results to show the validation of present approach. The effects of size and location of actuators on the response of a plate are presented through parametric study. The response can be static or harmonic according to the static or sinusoidal voltage applied to the actuators. Piezoelectric actuators are common used in smart structures. The analytical model presented in this research demonstrates the capability of predicting the responses of smart structures to a command voltage applied to the piezoelectric actuators.

碩士
中華大學
機械工程學系碩士班
101
Abstract The problem of large deflection of a pre-stressed simply supported un-symmetric layered circular plate due to lateral pressure is studied. Nonlinear governing equations were derived base on von-Karman plate theory for large deflection, which are further formulated in terms of lateral slope and radial force resultant via a non-dimensional and merging scheme. The reduced linear problem is considered, first, by neglecting the nonlinear terms, yielding a modified Bessel equation for the lateral slope. The linear analytical solution is obtained following the definitions of modified Bessel functions and the boundary conditions of the problem. For the nonlinear problem, on the other hand, numerical solutions are sought using a finite difference method incorporated with an iteration scheme, by taking the previously obtained linear solution as an initial gues The developed approaches were implemented mainly for 2-layered unsymmetric plate with various physical parameters including different magnitudes of pretensions, lateral pressures, and ratios in modulus and thickness between the layers. For a nearly monolithic plate, the results for a very low pretension correlate well with those obtained following CPT (classical plate theory) method and thus the present approach is checked. For typical two-layered plates, the obtained results show that, there is no edge effect like a clamped plate. In addition, although pretension may extend the range of linear behavior as in the case of a clamped plate, the allowable lateral load for linearity is comparatively lower. For a low modulus ratio between the layers of the plate with a high pretension, linear analytical solution may provide reasonable results. For the case of a high modulus ratio, however, the problem would require the presented nonlinear numerical approach to obtain more accurate results. Keywords : Initial Tension, Un-symmetric Layered Plate, Von-Karman Large Deflection, Modified Bessel Function, Finite Difference Method.

碩士
中華大學
機械工程學系碩士班
97
In this work a mathematical model of a cylindrical bending of a plate on an elastic foun- dation is presented. The possible application in MEMS pressure sensor part is discussed. The second part of this textbook is focused on selected theoretical details of precision 3D computer vision measurements and software design. A precision camera calibration procedure is described and details of the easy calibration technique are given in text. A new approach for fast normalized cross-correlation in Fourier domain is presented and a novel approach for normalized cross-correlation method for color images is shown. Clear and detailed description of a digital image correlation using the Newton-Raphson method is presented along with a detailed description of the algorithm. The experimental setup for single-camera and two-camera measurements is explained. Finally, the method and functionality of designed software are demonstrated on two experiments and results are discussed. Possible applications and perspective research are suggested in the end of this publication.

碩士
國立成功大學
機械工程學系碩博士班
100
In this paper, we have studied static deflection of circular plate (Kirchhoff plate) with nonlinear elastic boundary conditions. The paper will be exhibited completed solution to two problems. The first one will show the circular plate’s both ends with nonlinear boundary condition. The first step is to simplify governing equation and boundary condition by non-dimensional process. Then using Shifting Method solve static plate deflection problem with nonlinear boundary. And finally, we will use Maple program to plot 3D-diagram. The second one will show the circular plate’s with nonlinear elastic foundation. In the problem, we’ll use variation parameter method to solve particular solution. Finally, we even show the easy way to get the critical e value to fit the perturbation method. In the conclusion, these problems with nonlinear boundary condition can be solved by Shifting Function Method. We can get completely exact solution.

碩士
國立中興大學
機械工程研究所
82
The aim of this thesis is to employ the finite element and adjoint variable methods to study the large deflection and to do sensitivity analysis of stiffened composite laminated plates. A higher-order displacement theory in conjunction with von Karman strains are used in the derivation of the nonlinear finite element models of plate and beam. The elements being used are nine-node isoparametric quadrilateral plate element and three-node isoparametric quadratic element. Each node has seven degrees of freedom. By considering the compatibility between the displacement fields of plate and beam elements and invoking the principle of minimum total potential energy, the governing equations of stiffened plates are derived. These nolinear equations are then solved by Newton-Raphson method. For sensitivity analysis the adjoint variable method is adopted, where the strain energy is chosen as a cost function, while the fiber angles of laminae are taken as design variables. At last, detailed numetical studies are carried out for the cases of cross-and angle-ply stiffened laminated plates.

碩士
國立臺灣科技大學
營建工程系
93
The main purpose of the thesis is to analyze the mechanical problems of functionally graded materials (FGM) by the theory of elasticity. The geometric and loading conditions discussed in this thesis are the following: (1.) The plate, which is simply supported in the opposite edges of x-axis and fixed in one edge of y-axis but simply supported in the other edge of y-axis, has a moment loading in one simply supported edge of y-axis. (2.) The plate, which is simply supported in the opposite edges of x-axis and fixed in the opposite edges of y-axis, has a vertical deflection in one edge of y-axis. For the problems of FGM plates with constant Poisson’s ratio, the analytical solutions are analyzed by Fourier series expansion to determine the deflections and the stresses. The analytical solutions are compared with the numerical solutions which are obtained by MARC software of finite element method. The study is concentrated with three kinds of composites which are FGM plates, FGM coating plates, and FGM undercoating plates in which their neutral axes are different. For the case of FGM, FGM coating, and FGM undercoating plates with the same boundary conditions but different neutral axes, the deflections and stresses of them are the same. Results show that the deflections and the stresses are influenced by the stiffness coefficient C11. The deflection decreases with the increasing stiffness. For avoiding the stress discontinuity which could cause the failure of structures, the S-type of FGM is the best constitution among S-FGM, E-FGM, and P-FGM coating plates.

碩士
元智大學
機械工程學系
92
In this investigation, the static deflection and harmonic vibration of a simply supported plate induced by piezoelectric actuators are examined two piezoelectric actuators are surface bonded or embedded in the plate and are symmetric with the mid-plane. Electric voltage with the same amplitude and opposite sign are applied to the two symmetric piezoelectric actuators, results to the bending effect on the plate. The bending moment is derived by using the theories of elasticity and piezoelectricity. This bending moment is then applied to the plate. Following the classical plate theory, the analytical solution of flexural displacement on a simply supported plate subjected to bending moment can be obtained. The analytical solution are compared with the finite element results to show the validation of present approach. The effects of size and location of actuators on the response of a plate are presented through parametric study. The response can be static or harmonic according to the static or sinusoidal voltage applied to the actuators. Piezoelectric actuators are common used in smart structures. The analytical model presented in this research demonstrates the capability of predicting the responses of smart structures to a command voltage applied to the piezoelectric actuators.

碩士
中華大學
機械工程學系
104
This study proposes an approximate solution based on energy method to solve the large deflection problem of rigidly-bossed micro plate of typical semiconducting material. The purpose is to simulate the physical condition of a bossed sensing or actuating device, The approach extends classical plate theory (CLT) method for solving a flat plate to a rigid bossed plate problem, first. Then energy-minimum potential energy principle is utilized that accounts for stretching and bending strain energy including Von Karman large deflection consideration to develop the approximate solution of large deflection for a rigid bossed plate. The boundary conditions of a bossed plate are employed to solve for the unknown constants arise in the general solution for lateral deflection. Meanwhile, Matlab symbolic manipulation tool was utilized to derive the analytical formulation for the lengthy integration terms following the minimum potential energy principle. The obtained approximate solution for lateral deflection following large deflection consideration were utilized to derive the strains and stresses using strain-displacement and stress-strain relations. The developed method was implemented with bossed plate made of typical silicon-based semiconducting materials with various boss size and lateral pressure cited from literature. The objective is to explore the effects of varying boss size and lateral pressure on the obtained approximate solution considering large deflection based on energy method. For a narrow bossed plate, the obtained CLT and approximate solution for large deflection were found to correlate well with those of a flat plate. The results following various physical parameters show that the influence due to lateral pressure will become more apparent if the radial size of the rigid boss is enlarged. That is, for a wider boss, the rigidity of the annular plate is increased, yielding an apparent decrease in the related geometrical responses, and stress and strain results.

abstract: Stress-related failure such as cracking are an important photovoltaic (PV) reliability issue since it accounts for a high percentage of power losses in the midlife-failure and wear-out failure regimes. Cell cracking can only be correlated with module degradation when cracks are of detectable size and detrimental to the performance. Several techniques have been explored to access the deflection and stress status on solar cell, but they have disadvantages such as high surface sensitivity. This dissertation presents a new and non-destructive method for mapping the deflection on encapsulated solar cells using X-ray topography (XRT). This method is based on Bragg diffraction imaging, where only the areas that meet diffraction conditions will present contrast. By taking XRT images of the solar cell at various sample positions and applying an in-house developed algorithm framework, the cell‘s deflection map is obtained. Error analysis has demonstrated that the errors from the experiment and the data processing are below 4.4 and 3.3%. Von Karman plate theory has been applied to access the stress state of the solar cells. Under the assumptions that the samples experience pure bending and plain stress conditions, the principal stresses are obtained from the cell deflection data. Results from a statistical analysis using a Weibull distribution suggest that 0.1% of the data points can contribute to critical failure. Both the soldering and lamination processes put large amounts of stress on solar cells. Even though glass/glass packaging symmetry is preferred over glass/backsheet, the solar cells inside the glass/glass packaging experience significantly more stress. Through a series of in-situ four-point bending test, the assumptions behind Von Karman theory are validated for cases where the neutral plane is displaced by the tensile and compressive stresses. The deflection and stress mapping method is applied to two next generation PV concepts named Flex-circuit and PVMirror. The Flex-circuit module concept replaces traditional metal ribbons with Al foils for electrical contact and PVMirror concept utilizes a curved PV module design with a dichroic film for thermal storage and electrical output. The XRT framework proposed in this dissertation successfully characterized the impact of various novel interconnection and packaging solutions.
Dissertation/Thesis
Doctoral Dissertation Materials Science and Engineering 2019

碩士
中華大學
機械工程學系碩士班
98
Problem of nonlinear large-deflection of an elastically-bossed and clamped symmetrically layered isotropic circular plate under pretension due to uniform lateral load is studied. Based on von-Karman large deflection plate theory, the thus obtained nonlinear governing equations were formulated in a non-dimensional form in terms of lateral slope and radial force resultant. The small defection condition is considered first by neglecting the arising nonlinear terms, yielding a linear differential equation for the lateral slope. The reduced linear problem of large-deflection is solved by employing the recurrence relations between Modified Bessel functions as well as the boundary conditions at the clamped end and interface continuity condition between the central boss and the annular plate. The associated linear analytical solution was found to be expressible in terms of the first and the second kind of Modified Bessel functions, rather than just the first kind for a single–layered flat plate. A finite difference method is employed incorporating an iteration scheme in solving the nonlinear problem, by taking the obtained linear solution as the initial value. For a nearly monolithic single-layered plate with a tiny central boss under a small initial tension, the results correlate well with those available for a single-layer plate, thus the prevent approach was validated. Increasing the thickness ratio between the central boss and annular plate, the central boss will gradually illustrate a rigid behavior and has an apparent influence upon the structural responses of the entire plate. Meanwhile, the range of lateral pressure and initial tension for the existence of plate behavior will also be stretched. In other words, the onset of nonlinear behavior will be delayed to occur with increasing initial tension or lateral pressure magnitude. Moreover, the edg-zone effect of the plate tends to exasperate, as the lateral pressure and initial tension proceeds or the size and thickness of the central boss increases. On the other hand, the influence due to difference in layer moduli appears to be insignificant. The pressure sensitivity of plate increases as the central elastic boss illustrates a rigid behavior but decreases as the magnitude of initial tension is increased.

碩士
國立臺灣科技大學
營建工程技術學系
84
With the rapid development of economics, many major traffic projects are proposed in Taiwan. However, it''s not easy to get land to carry out these projects these times, therefor, they are often constructed by high-rise way, and the pile foundations are the most used in this way. In general, pile foundations are often made of cast-in-place concrete and gathered in pile groups , thus, the behaviors of such kind foundations due to lateral loads become an important study. In this study, we use Focht- koch (model to analize pile groups and take P-factor ( suggested by Reese-Wang(1989) )and Y-factor( apply Mindlin Equation (1936)) into account. According to this structure of analysis, we edit a computer program "GROUP" to analize these behaviors and hope to understand further the "Group Effects" due to these behaviors. Also in this study, we use API p-y curves in single pile, and modify them due to the in-situ cast-in-place pile load tests. After that, we apply modified API p-y curves in the analysis of pile groups. Because of none of lateral cast-in- place pile groups tests in usual soils, we take examples of such cases of Taipei and then find the factors affecting them. Accor- ding to the analysis of examples, the modified model of this study can improve the disadvantage of Focht-Koch method and the analized results of distribution of shears of pile heads are also reasonable. Besides, from the analysis of factors, pile spacing is the most important factor affecting the behaviors of lateral loaded pile groups. With the pile spacing decreasing, group effects become more and more remarkable, the rigidity of pile groups lows down, the most largest moment of each pile increases and the ranges of the distribution of shears of pile heads also increase.

碩士
元智大學
機械工程學系
96
In this investigation, the static deflection and harmonic vibration of laminated plate induced by piezoelectric actuators under mixed boundary condition are examined. Two piezoelectric actuators are surface bonded or embedded in the plate and are symmetric with the mid-plane. Electric voltages with the same amplitude and opposite sign are applied to the two symmetric piezoelectric actuators, results to the bending effect on the laminated plate. The bending moment is derived by using the theories of elasticity and piezoelectricity. This bending moment is then applied to the laminated plate. The laminated plate is simply supported along the left and right edges, and fixed along the top and bottom edges. The principle of superposition and Levy’s solution are employed to solve the static doformation and harmonic vibration of the laminated plate with mixed boundary condition.The analytical solutions are compared with the three dimentional finite element results to show the accuracy of present approach. The effects of size and location of actuators on the response of the laminated plate under mixed boundary condition are presented through parametric study. The analytical model presented in this research demonstrates the capability of predicting the responses of smart structures to a command voltage applied to the piezoelectric actuators. Keyword ：piezoelectric actuator, Levy’s solution, harmonic vibration, mixed boundary condition

碩士
中華大學
機械工程學系碩士班
99
The problem of large deflection of a pre-stressed un-symmetric layered plate with an elastic boss due to lateral pressure is studied. The governing equations were developed based on von-Karman plate theory for large deflection, which are further formulated in terms of lateral slope and radial force resultant via a non-dimensional and merging scheme. The small defection condition is considered, first, by neglecting the arising nonlinear terms, reducing to a simplified linear problem and thus a modified Bessel equation for the lateral slope. The linear analytical solution is then developed, using the definition of modified Bessel function incorporated with the clamped-end boundary condition and the continuity at the interface between the boss and the annual plate. The associated linear analytical solution was found to be expressible in terms of the first kind and second kind modified Bessel functions, rather than just the first kind for a single layered flat plate. For the nonlinear problem, on the other hand, finite difference method is employed incorporating with an interation scheme, by taking the obtained linear solution as an initial guess. The developed approach was implemented with various in-plane sizes for the boss, ratios between the center boss and annular plate, as well as ratios in layer modulus and a wide range of pretension and lateral pressure, for three different types of plates. For a nearly monolithic plate with a thin boss（Plate 1）, the linear and nonlinear solutions agree well with those of a single-layered plate available in literature. Thus, the developed approach is checked. Following the solution for various modulus rations and geometrical configurations, it is seen, increasing the thickness ratio and modulus ratio between the central boss and annular plate, the central boss will gradually illustrate a rigid behavior and the range of maximum lateral pressure for the validity of linear solution will be reduced in a low pretension condition. For a larger boss, however, the range of maximum linear loading will increase with the thickness ratio. In addition, in a relatively low pretension condition, the geometry of the bossed plate such as thickness ratio and also the boss sizes and modulus ratio may all have a significant influence on the linear and nonlinear solutions. Under a high initial tension however, the solutions will not be affected by the geometric dimension of plates. Thus, the geometric effect will be dominated by the pretension effect due to the membrane behavior in a high pretension condition.

碩士
中華大學
機械工程學系碩士班
99
Abstract Problem of nonlinear large-deflection of a clamped and pre-stressed unsymmetrically layered circular plate including piezoelectric effect due to uniform lateral load is studied. Based on von-Karman large deflection plate theory including the consideration of piezoelectric effect, the thus obtained nonlinear governing equations were formulated in a non-dimensional form in terms of lateral slope and radial force resultant. The small defection condition is considered first, by neglecting the arising nonlinear terms, to study a simplified linear problem. The associated analytical solutions expressible via (Modified)Bessel functions for the lateral slope is obtained. For the nonlinear problem, on the other hand, a finite difference method is employed incorporating with an iteration scheme to seek for the numerical solution, by taking the previously obtained linear solution as an initial guess. For a layered plate with nearly the same moduli under a slight voltage, the results correlate well with those available for a single-layer plate with pure mechanical load. Thus, the presented approach is checked. The developed methods are implemented with different unsymmetrically layered circular plates including a piezoelectric layer. The obtained results show that linear solution seems to have a reasonable accuracy in a low applied voltage and low pre-tension condition. On the other hand, the nonlinear approach appears to be required, for the case of high applied voltage, unless the pre-tension is relatively large. The structural responses reveal significant piezoelectric and modulus-ratio effects for in a comparatively lower loading (lateral pressure, pre-tension) condition. The extent of their influences will reduce gradually, however, as the mechanical load proceeds. In addition, lateral load tends to interact and compete with the effect of pretension, if both of them are applied at the same time. Moreover, the pressure sensitivity of the plate will be lowered with the increase of pre-tension (i.e., the residual stress), causing an adverse effect to the unsymmetrically layered plate.

碩士
中華大學
機械工程學系碩士班
103
Problem of nonlinear large-deflection of a clamped and symmetrically layered circular piezoelectric plate with an elastic boss under pre-tension due to uniform lateral load is studied. Von-Karman plate theory for large deflection is employed and extended to a symmetrically layered plate including a piezoelectric layer with an elastic boss, to derive the nonlinear governing equation for large deflection. The small deflection condition is considered first to study a simplified linear problem. The associated analytical solution is developed following recurrence relations of special functions. For the nonlinear problem, on the other hand, numerical solution is sought using a finite difference method incorporated with an iteration scheme, by talking the simplified linear solution as the initial guess. The developed approach implemented with layered plates made of typical silicon-based semi-conducting materials. In order to verify the proposed method, however, a nearly monolithic plate with a shallow and narrow boss under a very low applied voltage will be consider, first. The results will be checked against those available in literature. In addition, the numerical examples also include the cases of different thickness ratios between center boss and annular plate, various radial sizes of the elastic boss, different applied voltage across the piezoelectric layer and a wide range of lateral loads and pre-tensions. The objective is to explore all kinds of geometric responses including the center deflection and curvature, lateral deflection, slope and curvature as well as the transition behavior of the bossed piezoelectric plates and the mechanical sensitivity (dimensionless maximum radial stress). The influence of a variety of physical parameters such as the size of the elastic boss (including the thickness ratio and the radial size), the applied voltage, lateral loads and pre-tension will be intensively investigated for a thorough parametric study. For a nearly monolithic plate with a shallow and narrow boss under a low applied voltage, the results correlate well with those available for a single-layer plate with pure mechanical load in literature. Thus, the presented approach is checked. In addition, the numerical results show that piezoelectric effect may arise at a low mechanical loading condition and becomes more apparent when the center boss is widened and the applied voltage is increased. It will gradually diminish when the mechanical load is raised, however. Under a low initial tension condition, specifically the influence of piezoelectric effect will be lowered when a narrow elastic boss is considered. Yet, for a center boss with about half of the radial span, the most severe piezoelectric effect is observed. Furthermore, thickening the piezoelectric layer and thus the relative thickness of the center boss will moderate the influence of the piezoelectric effect but induces a more serious interface effect between the center boss and the annular plate.

碩士
元智大學
機械工程學系
96
In this investigation, the normal force and bending moment induced by the surface bonded or embedded piezoelectric actuators on the beam and plate are derived basing on the Euler beam theory. The effects of material property and thickness on the stress distribution are examined through a parametric study. The flexural deflection of a simply supported plate subjected to the bending moment is derived basing on the plate theory. The deflection is validated with the 3-D finite element results. Several examples are presented to demonstrate the capability of using the piezoelectric actuators to control the deformed shape of the plate.

碩士
中華大學
機械工程學系
107
Problem of nonlinear large-deflection of a simply supported and symmetrically layered circular piezoelectric plate with an elastic boss under pre-tension due to uniform lateral load is studied. Von-Karman plate theory for large deflection is employed and extended to a symmetrically layered plate including a piezoelectric layer with an elastic boss, to derive the nonlinear governing equation for large deflection. The small deflection condition is considered first to study a simplified linear problem. The associated analytical solution is developed following recurrence relations of special functions, and the limited cases of pure membrane and pure plate are studied. For the nonlinear problem, on the other hand, numerical solution is sought using a finite difference method incorporated with an iteration scheme, by taking the simplified linear solution as the initial guess. The developed approach is implemented with typical silicon-based semi-conducting materials. To verify the proposed method, however, a nearly monolithic plate with a shallow and wide boss under a very low applied voltage will be considered, first. The results are checked against those available in literature. In addition, the numerical examples also include the cases of different thickness ratios between center boss and annular plate, various radial sizes of the elastic boss, different applied voltages across the piezoelectric layer and a wide range of lateral loads and pre-tensions. The objective is to explore all kinds of geometric responses including the center deflection and curvature, lateral deflection, slope and the mechanical sensitivity (dimensionless maximum radial stress) and curvature as well as the transition behavior of the bossed piezoelectric plates. The influence of a variety of physical parameters such as the size of the elastic boss (including the thickness ratio and the radial size), the applied voltage, lateral loads and pre-tension will be intensively investigated for a thorough parametric study. For a nearly monolithic plate with a shallow and wide boss under a low applied voltage, the results correlate well with those available for a single-layer plate with pure mechanical load in literature. Thus, the presented approach is checked. In addition, the numerical results show that piezoelectric effect may arise at a low mechanical loading condition and becomes more apparent when the center boss is widened and the applied voltage is increased. It will gradually diminish when the mechanical load is raised, however. Under a low initial tension condition, specifically, the influence of piezoelectric effect will be more apparent when a shallow but wide elastic boss is considered. Yet, thickening the center boss will moderate the influence of the piezoelectric effect but induces a more serious interface effect between the center boss and the annular plate.