Search NASA⌕ Search

SEARCH · Search NASA

Results for “PLATE THEORY”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8

Three-Dimensional Aerodynamics and Vortex-Shedding Characteristics of Wind Turbine Airfoils over 360-Degree Angles of Attack

In this work, we present the first three-dimensional (3D) computational investigation of wind turbine airfoils over 360° angles of attack to predict unsteady aerodynamic loads and vortex-shedding characteristics. To this end, static–airfoil simulations are performed for the FFA-W3 airfoil family at a Reynolds number of 107 with the Improved Delayed Detached Eddy Simulation turbulence model. Aerodynamic forces reveal that the onset of boundary-layer instabilities and flow separation does not necessarily coincide with the onset of stall. In addition, a comparison with two-dimensional simulation data and flat plate theory extension of airfoil polars, suggest that, in the deep stall regime, 3D effects remain critical for predicting both the unsteady loads and the vortex-shedding dynamics. For all airfoils, the vortex-shedding frequencies are found to be inversely proportional to the wake width. In the case of slender airfoils, the frequencies are nearly independent of the airfoil thickness, and their corresponding Strouhal number St is approximately 0.15. Based on the calculated St, the potential for shedding frequencies to coincide with the natural frequencies of the International Energy Agency 15 MW reference wind turbine blades is investigated. The analysis shows that vortex-induced vibrations occur primarily at angles of attack of around ±90° for all airfoils.

17 WIND ENERGY↗

Automated preliminary design of simplified wing structures to satisfy strength and flutter requirements

A simple structural model of an aircraft wing is used to show the effects of strength (stress) and flutter requirements on the design of minimum-weight aircraft-wing structures. The wing is idealized as an isotropic sandwich plate with a variable cover thickness distribution and a variable depth between covers. Plate theory is used for the structural analysis, and piston theory is used for the unsteady aerodynamics in the flutter analysis. Mathematical programming techniques are used to find the minimum-weight cover thickness distribution which satisfies flutter, strength, and minimum-gage constraints. The method of solution, some sample results, and the computer program used to obtain these results are presented. The results indicate that the cover thickness distribution obtained when designing for the strength requirement alone may be quite different from the cover thickness distribution obtained when designing for either the flutter requirement alone or for both the strength and flutter requirements concurrently. This conclusion emphasizes the need for designing for both flutter and strength from the outset.

Stroud, W. J.↗

Flutter analysis of swept-wing subsonic aircraft with parameter studies of composite wings

A computer program is presented for the flutter analysis, including the effects of rigid-body roll, pitch, and plunge of swept-wing subsonic aircraft with a flexible fuselage and engines mounted on flexible pylons. The program utilizes a direct flutter solution in which the flutter determinant is derived by using finite differences, and the root locus branches of the determinant are searched for the lowest flutter speed. In addition, a preprocessing subroutine is included which evaluates the variable bending and twisting stiffness properties of the wing by using a laminated, balanced ply, filamentary composite plate theory. The program has been substantiated by comparisons with existing flutter solutions. The program has been applied to parameter studies which examine the effect of filament orientation upon the flutter behavior of wings belonging to the following three classes: wings having different angles of sweep, wings having different mass ratios, and wings having variable skin thicknesses. These studies demonstrated that the program can perform a complete parameter study in one computer run. The program is designed to detect abrupt changes in the lowest flutter speed and mode shape as the parameters are varied.

Housner, J. M.↗

Application of NASTRAN to large deflection supersonic flutter of panels

Flat panel flutter at high supersonic Mach number is analyzed using NASTRAN Level 16.0 by means of modifications to the code. Two-dimensional plate theory and quasi-steady aerodynamic theory are employed. The finite element formulation and solution procedure are presented. Modifications to the NASTRAN code are discussed. Convergence characteristics of the iteration processes are also briefly discussed. Effects of aerodynamic damping, boundary support condition and applied in-plane loading are included. Comparison of nonlinear vibration and linear flutter results with analytical solutions demonstrate that excellent accuracy is obtained with NASTRAN.

Mei, C.↗

Calculation of planar-truss modal frequencies

Simplified method for calculating modal frequencies of four types of large area planar trusses (tetrahedral, pentahedral, hexahedral, and radial rib) treat trusses as equivalent circular plates thus allowing classical plate theories to be used.

Gates, R. M.↗

Boundary layer, skin friction, and boattail pressure measurements from the YF-12 airplane at Mach numbers up to 3

In-flight measurements of boundary layer and skin friction data were made on YF-12 airplanes for Mach numbers between 2.0 and 3.0. Boattail pressures were also obtained for Mach numbers between 0.7 and 3.0 with Reynolds numbers up to four hundred million. Boundary layer data measured along the lower fuselage centerline indicate local displacement and momentum thicknesses can be much larger than predicted. Skin friction coefficients measured at two of five lower fuselage stations were significantly less than predicted by flat plate theory. The presence of large differences between measured boattail pressure drag and values calculated by a potential flow solution indicates the presence of vortex effects on the upper boattail surface. At both subsonic and supersonic speeds, pressure drag on the longer of two boattail configurations was equal to or less than the pressure drag on the shorter configuration. At subsonic and transonic speeds, the difference in the drag coefficient was on the order of 0.0008 to 0.0010. In the supersonic cruise range, the difference in the drag coefficient was on the order of 0.002. Boattail drag coefficients are based on wing reference area.

Fisher, D. F.↗

Effects of debonds on the strength of composite plates

The effect of debonds on composite structures under compressive loads is investigated in this paper. Because of the inclusion of debonds, unsymmetric laminated rectangular plates are considered. The resulting bending-extension coupling is included and is shown to be quite significant for thin laminates typical of debonded regions. The solution technique is based on the Theorem of Minimum Potential Energy; and both simply supported and clamped boundaries are considered. The need to include transverse shear deformation in the analysis is documented. Also, the range of applicability of the reduced stiffness matrix technique for such plates is stated. The consideration of non-rectangular boundaries, as would normally occur for debonded regions, has been included through a finite element study. Using the results of this study, an effective laminated plate theory for irregularly shaped debonded regions is proposed.

Daugherty, R. L.↗

Sudden bending of a cracked laminate

The intensification of stresses near a through crack in the laminate that suddenly undergoes bending is investigated. A dynamic plate theory is developed which includes the effects of material inhomogeneity in the thickness direction and realistic crack edge stress singularity and distribution. Numerical examples indicate that (1) the crack moment intensity tends to decrease as the crack length to laminate thickness is increased, and (2) the average load intensity transmitted to a through crack can be reduced by making the inner layers to be stiffer than the outer layers.

Sih, G. C.↗

Stresses in adhesively bonded joints - A closed-form solution

The general plane strain problem of adhesively bonded structures consisting of two different, orthotropic adherends is considered, under the assumption that adherend thicknesses are constant and small in relation to the lateral dimensions of the bonded region, so that they may be treated as plates. The problem is reduced to a system of differential equations for the adhesive stresses which is solved in closed form, with a single lap joint and a stiffened plate under various loading conditions being considered as examples. It is found that the plate theory used in the analysis not only predicts the correct trend for adhesive stresses but gives surprisingly accurate results, the solution being obtained by assuming linear stress-strain relations for the adhesive.

Delale, F.↗

Simultaneous control and optimization for elastic systems

Studies are conducted to determine the dynamic response of beams and plates to loads which are extreme within a certain class of admissible loads. Two approaches to this problem are suggested. In approach one, Pontryagin's maximality principle is regarded as an additional constraint. The optimality of design is then determined by standard numerical techniques. The "adjoint variable approach' to sensitivity of structural design is applied for a given inhomogeneous term. The inhomogeneous term is an extremal element of admissible load vectors, which constitute a closed subspace of a Sobolev space. Again, the maximality principle is invoked. While only beam and plate theory problems are used as examples, generalizations are easy to perceive.

Komkov, V.↗

Residual stresses and their effects in composite laminates

Residual stresses in composite laminates are caused by the anisotropy in expansional properties of constituent unidirectional plies. The effect of these residual stresses on dimensional stability is studied through the warping of unsymmetric (0 sub 4/90 sub 4)sub T graphite/epoxy laminates while their effect on ply failure is analyzed for (0/90)sub 2s Kevlar 49/epoxy laminate. The classical laminated plate theory is used to predict the warping of small and large panels. The change of warping does not indicate a noticeable stress relaxation at 75 C while it is very sensitive to moisture content and hence to environment. A prolonged gellation at the initial cure temperature reduces residual stresses while postcure does not. The matrix/interface cracking in dry (0/90)sub 2s Kevlar 49/epoxy laminate is shown to be the result of the residual stress exceeding the transverse strength.

Hahn, H. T.↗

Wave propagation in a graphite/epoxy laminate

Harmonic wave and wave front propagations in a graphite/epoxy laminate are investigated using a plate theory that includes transverse shear deformation. Transient waves produced by impact of a steel ball are studied experimentally and by using finite elements. The statically measured law of contact between the steel ball and the laminate is used in the finite element program to compute the dynamic contact force. It is found that use of this contact law in conjunction with the finite element modeling of the laminate yields excellent agreement with the experimental results.

Sun, C. T.↗

Interaction of part-through cracks in a flat plate

The accuracy of the line spring model is determined. The effect of interaction between two and three cracks is investigated, and extensive numerical results which may be useful in applications are provided. Line spring model with Reissner's plate theory is formulated to be used for any number and configurations of cracks provided that there is symmetry. This model is used to find stress intensity factors for elliptic internal cracks, elliptic edge cracks and two opposite elliptic edge cracks. Despite the simplicity of the line spring model, the results are found to be close.

Aksel, B.↗

Residual thermal and moisture influences on the strain energy release rate analysis of edge delamination

A laminated plate theory analysis is developed to calculate the strain energy release rate associated with edge delamination growth in a composite laminate. The analysis includes the contribution of residual thermal and moisture stresses to the strain energy released. The strain energy release rate, G, increased when residual thermal effects were combined with applied mechanical strains, but then decreased when increasing moisture content was included. A quasi-three-dimensional finite element analysis indicated identical trends and demonstrated these same trends for the individual strain energy release rate components, G sub I and G sub II, associated with interlaminar tension and shear. An experimental study indicated that for T300/5208 graphite-epoxy composites, the inclusion of residual thermal and moisture stresses did not significantly alter the calculation of interlaminar fracture toughness from strain energy release rate analysis of edge delamination data taken at room temperature, ambient conditions.

Obrien, T. K.↗

Viscoelastic behavior and life-time predictions

Fiber reinforced plastics were considered for many structural applications in automotive, aerospace and other industries. A major concern was and remains the failure modes associated with the polymer matrix which serves to bind the fibers together and transfer the load through connections, from fiber to fiber and ply to ply. An accelerated characterization procedure for prediction of delayed failures was developed. This method utilizes time-temperature-stress-moisture superposition principles in conjunction with laminated plate theory. Because failures are inherently nonlinear, the testing and analytic modeling for both moduli and strength is based upon nonlinear viscoelastic concepts.

Dillard, D. A.↗

Analysis of Delamination Growth from Matrix Cracks in Laminates Subjected to Bending Loads

A major source of delamination damage in laminated composite materials is from low-velocity impact. In thin composite laminates under point loads, matrix cracks develop first in the plies, and delaminations then grow from these cracks at the ply interfaces. The purpose of this study was to quantify the combined effects of bending and transverse shear loads on delamination initiation from matrix cracks. Graphite-epoxy laminates with 90 deg. plies on the outside were used to provide a two-dimensional simulation of the damage due to low-velocity impact. Three plate bending problems were considered: a 4-point bending, 3-point bending, and an end-clamped center-loaded plate. Under bending, a matrix crack will form on the tension side of the laminate, through the outer 90 deg. plies and parallel to the fibers. Delaminations will then grow in the interface between the cracked 90 deg. ply and the next adjacent ply. Laminate plate theory was used to derive simple equations relating the total strain energy release rate, G, associated with the delamination growth from a 90 deg. ply crack to the applied bending load and laminate stiffness properties. Three different lay-ups were tested and results compared. Test results verified that the delamination always formed at the interface between the cracked 90 deg. ply and the next adjacent ply. Calculated values for total G sub c from the analysis showed good agreement for all configurations. The analysis was able to predict the delamination onset load for the cases considered. The result indicated that the opening mode component (Mode I) for delamination growth from a matrix crack may be much larger than the component due to interlaminar shear (Mode II).

Murri, G. B.↗