The effect of longitudinal stiffeners located on one side of a plate on the compressive buckling stress of the plate-stiffener combination
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Seide, Paul↗
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Use of the Coanda Effect for Jet Deflection and Vertical Lift with Multiple-flat-plate and Curved-plate Deflection Surfaces
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Von Glahn, Uwe H↗
Receptivity of Flat-Plate Boundary Layer in a Non-Uniform Free Stream (Vorticity Normal to the Plate)
Experimental and theoretical studies of low speed leading edge boundary layer receptivity to free-stream vorticity produced by upstream wires normal to the leading edge are discussed. Data include parametric variations in leading edge configuration and details of the incident disturbance field including single and multiple wakes. The induced disturbance amplitude increases with increases in the leading edge diameter and wake interactions. Measurements agree with the theory of M. E. Goldstein.
Kogan, M. N.↗
Neutronic Simulation of Curved Fuel Plate with Flat Plate Geometry
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73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Buckling and postbuckling behavior of square compression-loaded graphite-epoxy plates with circular cutouts
Results are presented for unidirectional (0, 10)(sub s) and (90,10)(sub s) plates, ((0/90)(sub 5)(sub s)) plates, and for aluminum plates. Results are also presented for ((+/- theta)(sub 6)(sub s)) angle-ply plates for values of theta = 30, 45, and 60 degrees. The results indicate that the change in axial stiffness of a plate at buckling is strongly dependent upon cutout size and plate orthotropy. The presence of a cutout gives rise to an internal load distribution that changes, sometimes dramatically, as a function of cutout size coupled with the plate orthotropy. In the buckled state, the role of orthotropy becomes more significant since bending in addition to membrane orthotropy is present. Most of the plates with cutouts exhibited less postbuckling stiffness than the corresponding plate without a cutout, and the postbuckling stiffness decreased with increasing cutout size. However, some of the highly orthotropic plates with cutouts exhibited more postbuckling stiffness than the corresponding plate without a cutout. These results suggest the possibility of tailoring the cutout size and the stacking sequence of a composite plate to optimize postbuckling stiffness. It was found that plates with large radius cutouts do exhibit some postbuckling strength. The results also indicate that a cutout can influence modal interaction in a plate. Specifically, results are presented that show a plate with a relatively small cutout buckling at a higher load than the corresponding plate without a cutout, due to modal interaction. Other results are presented that indicate the presence of nonlinear prebuckling deformations, due to material nonlinearity, in the angle-ply plates with theta = 45 and 60 degrees. The nonlinear prebuckling deformations are more pronounced in the plates with theta = 45 degrees and become even more pronounced as the cutout size increases. Results are also presented that show how load-path eccentricity due to improper machining of the test specimens affects the buckling behavior. Some of the plates with cutouts and eccentricity exhibited a snap-through type of buckling behavior.
Nemeth, Michael P.↗
Plate motion controls on back-arc spreading
The motions of the subducting and the overriding plates influence the spatial and temporal distribution of back-arc spreading. Cenozoic plate motions in hot spot-fixed and no-net-rotation reference frames were studied with attention to correlations between changes in motion and episodes of back-arc spreading in the western Pacific. The results suggest that major back-arc opening occurs when both the overriding plate retreats from the trench in an absolute sense and the subducting plate undergoes a significant speed-up. Neither phenomenon alone is sufficient to initiate spreading. Three major plate velocity increases can be identified in the Cenozoic: (1) the Pacific plate 5-9 Ma; (2) the Indian plate at 27 Ma; and (3) the Pacific plate at 43 Ma, due to its shift from northerly to more westerly motion. At the present time, the Indian and Philippine are the only overriding plates that are retreating from their Pacific trenches and back-arc spreading occurs only on these two retreating plates. Although the Indian plate has been retreating for at least 25 Ma, back-arc spreading began only following the Pacific plate speed-up 5-9 Ma. Earlier, during the Indian plate speed-up, no overriding plates were retreating strongly and no back-arc spreading epsiodes are preserved from this time. For the earliest Pacific plate shift at 43 Ma, the Eurasian plate was not advancing, thus creating the only favorable plate kinematic conditions in the Cenozoic for back-arc basin formation in this region. It is unclear whether extension in the Japan Sea is a result of these conditions.
Fein, J. B.↗
Failure investigation and mitigation after experimental research reactor fuel plate deformation in an irradiation device
Experimental research reactor fuel testing is conducted in the Belgian Reactor 2 (BR2) of the Belgian Nuclear Research Centre (SCK CEN) in dedicated irradiation vehicles or rigs. One such vehicle allows flat full-size fuel plates to be irradiated by inserting them into slotted baskets that captures a narrow portion of the longitudinal edges of the plates. The motion of the fuel plates within the baskets is possible within the narrow slots and thus, the plate is considered to be unattached. The design intentionally omits fixing mechanisms of the fuel plates to the baskets to facilitate the inspection and repositioning of the plates between the irradiation cycles and the accommodation of thermal expansion of the plates in the lateral direction. However, loosely inserted fuel plates have weak structural boundary conditions allowing for larger out-of-plane deflections caused by hydrodynamic loads exerted by the flowing coolant, as compared to those of fixed plates. Unexpected large deformations of plates occurred in several irradiation cycles that further resulted in a loss of cladding integrity. These deformations could not be attributed to a single source. This triggered a series of thermal hydraulic, structural, and fluid-structure interaction analyses aiming at understanding the observed phenomenon. The analyses revealed that, for a certain combination of unfavorable manufacturing and assembly tolerances, fuel plate edges could escape out of the slots in the irradiation basket due to the hydrodynamic load. Subsequently, the plate could become wedged inside the basket coolant channel opening. This resulted in reduced coolant flow and accelerated temperature increase and thermal expansion of the plate while under irradiation. This unfavorable feedback loop could then lead to excessive plate surface temperatures, deformed plates and cladding failure, as was observed in the experiments. These analyses not only provided a probable cause of the fuel plate failures, but also resulted in a new and improved design of the irradiation basket to avoid these issues in the future. In conclusion, a series of recent successful irradiations confirm that the sources of failures were identified correctly, and the implemented mitigations were adequate.
BR2↗
Polar Plate Theory for Orthogonal Anisotropy
Laminated fiber-reinforced (or filamentary) composites are used today for their high strength-to-weight and stiffness-to-weight ratios. However, because of the anisotropic behavior of composites, determining the response on a macroscopic scale is challenging. This is particularly evident in the evaluation of the governing differential equations of a circular disk with the fibers of the lamina oriented with rectilinear orthogonality. This includes any situation involving a composite plate of circular geometry in which out-of-plane displacements due to load are desired, such as fastener pull through loading of a composite plate. Current analysis techniques use numerical methods with rectilinear coordinate systems to solve problems with circular geometry. These analyses over predict plate stiffness by 20% and underpredict failure by 70%. Consequently, there is a need to transform classical composite plate theory to a polar coordinate system. In order to better analyze structures with circular geometries the classical composite plate equations are transformed into the plate equations for a rectilinearly anisotropic composite in polar coordinates. A composite plate is typically a laminate of fibers in rectilinear directions. Subsequent to the lay-tip the necessary geometry is cut out of a rectangular plate. In a similar manner, the derivation of the plate equation starts with the fundamental definitions of strain, displacement and curvature and incorporates the material property angular dependence into the equilibrium equations for a differential polar element. In the transformed state, the stiffness coefficients are no longer constant, adding to the complexity of the governing differential equations. This paper discusses the new derivation and evaluation of the plate equations for a circular composite disk with orthogonal rectilinear anisotropy. The resultant new three partial differential equations, which describe the circular anisotropic plate, can be used to evaluate out-of-plane displacements for given load conditions in design of composite Structures. Without the formation of these unique plate equations, design of such structures is not a precise engineering accomplishment due to the lack of precise design tools. Such structures are over designed to compensate and costly tests need to be performed after production to validate safety. Though impossible to present the mathematical solution within the limits of this paper, the application of the newly derived plate equation in its orthotropic form for a balanced symmetric laminate compared favorably with test results and surpassed the results of standard numerical methods. Within the limitations of the problem foundation the predictive model provides a mechanism for establishing out-of-plane deflection levels for a circular composite plate. Future work in this area should include incorporating the circular composite plate equations in Finite Element Models. The new anisotropic polar plate equations call be utilized as a design tool so that the design more accurately meets the requirements, thus taking full advantage of the weight savings of composites. These accomplishments have not previously been presented to the engineering community nor ever proposed to the IAF. Should the proposed paper be accepted for presentation, attendance is assured.
Bailey, Michelle D.↗
Ionospheric plasma flow about a system of electrically biased flat plates
The steady state interaction of two electrically biased parallel plates immersed in a flowing plasma characteristic of low earth orbit is studied numerically. Fluid equations are developed to describe the motion of the cold positively charged plasma ions, and are solved using finite-differences in two dimensions on a Cartesian grid. The behavior of the plasma electrons is assumed to be described by the Maxwell-Boltzmann distribution. Results are compared to an analytical and a particle simulation technique for a simplified flow geometry consisting of a single semi-infinite negatively biased plate. Comparison of the extent of the electrical disturbance into the flowing plasma and the magnitude of the current collected by the plate is very good. The interaction of two equally biased parallel plates is studied as a function of applied potential. The separation distance at which the current collected by either plate decreases by five and twenty percent is determined as a function of applied potential. The percent decreases were based on a non-interacting case. The decrease in overall current is caused by a decrease in ionic density in the region between the plates. As the separation between the plates decreases, the plates collect the ions at a faster rate than they are supplied to the middle region by the oncoming plasma flow. The docking of spacecraft in orbit is simulated by moving two plates of unequal potential toward one another in a quasi-static manner. One plate is held at a large negative potential while the other floats electrically in the resulting potential field. It is found that the floating plate does not charge continuously negative as it approaches the other more negatively biased plate. Instead, it charges more and then less negative as ionic current decreases and then increases respectively upon approach. When the two plates come into contact, it is expected that the electrically floating plate will charge rapidly negative to a potential near that of the other plate.
Herr, Joel L.↗
Anomalous Buckling Characteristics of Laminated Metal-Matrix Composite Plates with Central Square Holes
Compressive buckling analysis was performed on metal-matrix composite (MMC) plates with central square holes. The MMC plates have varying aspect ratios and hole sizes and are supported under different boundary conditions. The finite-element structural analysis method was used to study the effects of plate boundary conditions, plate aspect ratio, hole size, and the composite stacking sequence on the compressive buckling strengths of the perforated MMC plates. Studies show that by increasing the hole sizes, compressive buckling strengths of the perforated MMC plates could be considerably increased under certain boundary conditions and aspect ratios ("anomalous" buckling behavior); and that the plate buckling mode could be symmetrical or antisymmetrical, depending on the plate boundary conditions, aspect ratio, and the hole size. For same-sized plates with same-sized holes, the compressive buckling strengths of the perforated MMC plates with [90/0/0/90]2 lamination could be as much as 10 percent higher or lower than those of the [45/- 45/- 45/45]2 laminations, depending on the plate boundary conditions, plate aspect ratios, and the hole size. Clamping the plate edges induces far stronger "anomalous" buckling behavior (enhancing compressive buckling strengths at increasing hole sizes) of the perforated MMC plates than simply supporting the plate edges.
Ko, William L.↗
Frequencies and Flutter Speed Estimation for Damaged Aircraft Wing Using Scaled Equivalent Plate Analysis
Equivalent plate analysis is often used to replace the computationally expensive finite element analysis in initial design stages or in conceptual design of aircraft wing structures. The equivalent plate model can also be used to design a wind tunnel model to match the stiffness characteristics of the wing box of a full-scale aircraft wing model while satisfying strength-based requirements An equivalent plate analysis technique is presented to predict the static and dynamic response of an aircraft wing with or without damage. First, a geometric scale factor and a dynamic pressure scale factor are defined to relate the stiffness, load and deformation of the equivalent plate to the aircraft wing. A procedure using an optimization technique is presented to create scaled equivalent plate models from the full scale aircraft wing using geometric and dynamic pressure scale factors. The scaled models are constructed by matching the stiffness of the scaled equivalent plate with the scaled aircraft wing stiffness. It is demonstrated that the scaled equivalent plate model can be used to predict the deformation of the aircraft wing accurately. Once the full equivalent plate geometry is obtained, any other scaled equivalent plate geometry can be obtained using the geometric scale factor. Next, an average frequency scale factor is defined as the average ratio of the frequencies of the aircraft wing to the frequencies of the full-scaled equivalent plate. The average frequency scale factor combined with the geometric scale factor is used to predict the frequency response of the aircraft wing from the scaled equivalent plate analysis. A procedure is outlined to estimate the frequency response and the flutter speed of an aircraft wing from the equivalent plate analysis using the frequency scale factor and geometric scale factor. The equivalent plate analysis is demonstrated using an aircraft wing without damage and another with damage. Both of the problems show that the scaled equivalent plate analysis can be successfully used to predict the frequencies and flutter speed of a typical aircraft wing.
Krishnamurthy, Thiagarajan↗
Dynamics of the abrupt change in Pacific Plate motion around 50 million years ago
Changes in Pacific Plate motion combined near equally with hotspot drift to generate the prominent bend in the Hawaiian-Emperor seamount chain some 50 million years ago, according to kinematic plate reconstruction and global dynamic models. A drastic change in plate tectonics and mantle convection occurred around 50 Ma as exemplified by the prominent Hawaiian-Emperor Bend. Both an abrupt Pacific Plate motion change and a change in mantle plume dynamics have been proposed to account for the Hawaiian-Emperor Bend, but debates surround the relative contribution of the two mechanisms. Here we build kinematic plate reconstructions and high-resolution global dynamic models to quantify the amount of Pacific Plate motion change. We find Izanagi Plate subduction, followed by demise of the Izanagi-Pacific Ridge and Izu-Bonin-Mariana subduction initiation alone, is incapable of causing a sudden change in plate motion, challenging the conventional hypothesis on the mechanisms of Pacific Plate motion change. Instead, Palaeocene slab pull from Kronotsky intraoceanic subduction in the northern Pacific exerts a northward pull on the Pacific Plate, while its Eocene demise leads to a sudden 30-35 degrees change in plate motion, accounting for about half of the Hawaiian-Emperor Bend. We suggest the Pacific Plate motion change and hotspot drift due to plume dynamics could have contributed nearly equally to the formation of the Hawaiian-Emperor Bend. Such a scenario is consistent with available constraints from global plate circuits, palaeomagnetic data and geodynamic models.
Hu, Jiashun↗
Buckling and postbuckling behavior of square compression-loaded graphite-epoxy plates with circular cutouts
An experimental study of the postbuckling behavior of square compression-loaded graphite-epoxy plates and isotropic plates with a central circular cutout is presented. Results are presented for unidirectional (0 sub 10)s and (90 sub 10)s plates, (0/90 sub 5)s plates, and for aluminum plates. Results are also presented for (+ or - O sub 6)s angle-ply plates for values of O = 30, 46, and 60 degrees. The experimental results indicate that the change in axial stiffness of a plate at buckling is strongly dependent upon cutout size and plate orthotropy. The presence of a cutout gives rise to an internal load distribution that changes, sometimes dramtically, as a function of cutout size coupled with the plate orthotropy. In the buckled state, the role of orthotropy becomes more significant since bending in addition to membrane orthotropy is present. Most of the plates with cutouts exhibited less postbuckling stiffness than the corresponding plate without a cutout, and the postbuckling stiffness decreased with increasing cutout size. However, some of the highly orthotropic plates with cutouts exhibited more postbuckling stiffness than the corresponding plate without a cutout.
Nemeth, Michael P.↗
The buckling response of symmetrically laminated composite plates having a trapezoidal planform area
The focus of this work is the buckling response of symmetrically laminated composite plates having a planform area in the shape of an isosceles trapezoid. The loading is assumed to be inplane and applied perpendicular to the parallel ends of the plate. The tapered edges of the plate are assumed to have simply supported boundary conditions, while the parallel ends are assumed to have either simply supported or clamped boundary conditions. A semi-analytic closed-form solution based on energy principles and the Trefftz stability criterion is derived and solutions are obtained using the Rayleigh-Ritz method. Intrinsic in this solution is a simplified prebuckling analysis which approximates the inplane force resultant distributions by the forms Nx=P/W(x) and Ny=Nxy=0, where P is the applied load and W(x) is the plate width which, for the trapezoidal planform, varies linearly with the lengthwise coordinate x. The out-of-plane displacement is approximated by a double trigonometric series. This analysis is posed in terms of four nondimensional parameters representing orthotropic and anisotropic material properties, and two nondimensional parameters representing geometric properties. For comparison purposes, a number of specific plate geometry, ply orientation, and stacking sequence combinations are investigated using the general purpose finite element code ABAQUS. Comparison of buckling coefficients calculated using the semi-analytical model and the finite element model show agreement within 5 percent, in general, and within 15 percent for the worst cases. In order to verify both the finite element and semi-analytical analyses, buckling loads are measured for graphite/epoxy plates having a wide range of plate geometries and stacking sequences. Test fixtures, instrumentation system, and experimental technique are described. Experimental results for the buckling load, the buckled mode shape, and the prebuckling plate stiffness are presented and show good agreement with the analytical results regarding the buckling load and the prebuckling plate stiffness. However, the experimental results show that for some cases the analysis underpredicts the number of halfwaves in the buckled mode shape. In the context of the definitions of taper ratio and aspect ratio used in this study, it is concluded that the buckling load always increases as taper ratio increases for a given aspect ratio for plates having simply supported boundary conditions on the parallel ends. There are combinations of plate geometry and ply stackling sequences, however, that reverse this trend for plates having clamped boundary conditions on the parallel ends such that an increase in the taper ratio causes a decrease in the buckling load. The clamped boundary conditions on the parallel ends of the plate are shown to increase the buckling load compared to simply supported boundary conditions. Also, anisotropy (the D16 and D26 terms) is shown to decrease the buckling load and skew the buckled mode shape for both the simply supported and clamped boundary conditions.
Radloff, H. D., II↗
Effect of Curvature on the Impact Damage Characteristics and Residual Strength of Composite Plates
The results of a study of the response and failure characteristics of thin, cylindrically curved, composite plates subjected to low-speed impact damage are presented. The results indicate that the plate radius and the plate thickness are important structural parameters that influence the nonlinear response of a plate for a given amount of impact energy. Analytical and experimental contact-force results are compared for several plates and the results correlate well. The impact-energy levels required to cause damage initiation and barely visible impact damage are a function of the plate radius for a given plate thickness. The impact-energy levels required to initiate impact damage for plates with a certain range of radii are greater than plates with other radii. The contact-force results corresponding to these impact-energy levels follow a similar trend. Residual strength results for plates with barely visible impact damage suggest that the compression-after-impact residual strength is also a function of plate radius. The residual strength of impact-damaged flat plates appears to be lower than the residual strength of the corresponding cylindrically curved plates.
Ambur, Damodar R.↗
Analysis of Heat Transfer and Pressure Drop for a Gas Flowing Through a set of Multiple Parallel Flat Plates at High Temperatures
Equations were derived representing heat transfer and pressure drop for a gas flowing in the passages of a heater composed of a series of parallel flat plates. The plates generated heat which was transferred to the flowing gas by convection. The relatively high temperature level of this system necessitated the consideration of heat transfer between the plates by radiation. The equations were solved on an IBM 704 computer, and results were obtained for hydrogen as the working fluid for a series of cases with a gas inlet temperature of 200 R, an exit temperature of 5000 0 R, and exit Mach numbers ranging from 0.2 to O.8. The length of the heater composed of the plates ranged from 2 to 4 feet, and the spacing between the plates was varied from 0.003 to 0.01 foot. Most of the results were for a five- plate heater, but results are also given for nine plates to show the effect of increasing the number of plates. The heat generation was assumed to be identical for each plate but was varied along the length of the plates. The axial variation of power used to obtain the results presented is the so-called "2/3-cosine variation." The boundaries surrounding the set of plates, and parallel to it, were assumed adiabatic, so that all the power generated in the plates went into heating the gas. The results are presented in plots of maximum plate and maximum adiabatic wall temperatures as functions of parameters proportional to f(L/D), for the case of both laminar and turbulent flow. Here f is the Fanning friction factor and (L/D) is the length to equivalent diameter ratio of the passages in the heater. The pressure drop through the heater is presented as a function of these same parameters, the exit Mach number, and the pressure at the exit of the heater.
Einstein, Thomas H.↗
Finite Element and Plate Theory Modeling of Acoustic Emission Waveforms
A comparison was made between two approaches to predict acoustic emission waveforms in thin plates. A normal mode solution method for Mindlin plate theory was used to predict the response of the flexural plate mode to a point source, step-function load, applied on the plate surface. The second approach used a dynamic finite element method to model the problem using equations of motion based on exact linear elasticity. Calculations were made using properties for both isotropic (aluminum) and anisotropic (unidirectional graphite/epoxy composite) materials. For simulations of anisotropic plates, propagation along multiple directions was evaluated. In general, agreement between the two theoretical approaches was good. Discrepancies in the waveforms at longer times were caused by differences in reflections from the lateral plate boundaries. These differences resulted from the fact that the two methods used different boundary conditions. At shorter times in the signals, before reflections, the slight discrepancies in the waveforms were attributed to limitations of Mindlin plate theory, which is an approximate plate theory. The advantages of the finite element method are that it used the exact linear elasticity solutions, and that it can be used to model real source conditions and complicated, finite specimen geometries as well as thick plates. These advantages come at a cost of increased computational difficulty, requiring lengthy calculations on workstations or supercomputers. The Mindlin plate theory solutions, meanwhile, can be quickly generated on personal computers. Specimens with finite geometry can also be modeled. However, only limited simple geometries such as circular or rectangular plates can easily be accommodated with the normal mode solution technique. Likewise, very limited source configurations can be modeled and plate theory is applicable only to thin plates.
Prosser, W. H.↗
Interfacial Analysis of Blister Formation in U-10Mo Mini-Plates
A thorough investigation of potential failure mechanisms builds confidence in the performance of monolithic U-10wt%Mo (U-10Mo) fuel plates. The lowenriched uranium (LEU) fuel system is currently undergoing qualification as a high U-density fuel that can be used to convert United States high-performance research reactors from high-enriched uranium (HEU) operation. This will require establishing fuel operational limits such that fission products and a coolable geometry are retained, even during off-normal reactor operation conditions [1]. Such off-normal conditions can subject the fuel plates to temperatures where the internal pressure of precipitated fission gasses result in a permanent deformed, raised area of the cladding, referred to as a blister. These blisters can reduce the local coolability of a fuel plate and can even close coolant channels of a fuel assembly, so blistered plates are considered failed regardless of whether the fuel is truly breached. Historically, a marginto- failure is established through out-of-pile blister threshold testing of irradiated fuel plates. This is accomplished by incrementally heating irradiated fuel plates until blisters are observed. This reveals the temperature threshold that would have resulted in a blister if a plate experienced them at those irradiation conditions [2]. While the blister testing itself reveals the temperatures at which the cladding mechanical integrity was exceeded, a more thorough investigation of the interface evolution in proximity to formed blisters may reveal mechanisms as to the blister formation and retention of fission gases. Previous studies have explored potential underlying mechanisms in historical plates that may have been close to blistering [3]; however, this work is the first exploration of blister tested irradiated plates, fabricated by a commercial vendor—another requirement for qualification of the fuel system [1]. The Mini-plate 1 (MP-1) experiment was the first in a series of irradiation and post-irradiation examination (PIE) campaigns to qualify the U-10Mo monolithic fuel system. It consisted of commercially fabricated 25.4×101.5 mm Al-clad mini-plates with a monolithic U-10Mo foil coated in a Zr diffusion barrier. The primary MP-1 PIE campaign was previously completed. Among the suit of examinations was a blister testing campaign, where plates were incrementally annealed in 25°C increments until blisters were observed or a maximum temperature of 550°C was reached [4]. The previously blistered plates from this campaign were revisited in this work.
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