The stress distribution in pin-loaded orthotropic plates

The performance of mechanically fastened composite joints was studied. Specially, a single-bolt connector was modeled as a pin-loaded, infinite plate. The model that was developed used two dimensional, complex variable, elasticity techniques combined with a boundary collocation procedure to produce solutions for the problem. Through iteration, the boundary conditions were satisfied and the stresses in the plate were calculated. Several graphite epoxy laminates were studied. In addition, parameters such as the pin modulus, coefficient of friction, and pin-plate clearance were varied. Conclusions drawn from this study indicate: (1) the material properties (i.e., laminate configuration) of the plate alter the stress state and, for highly orthotropic materials, the contact stress deviates greatly from the cosinusoidal distribution often assumed; (2) friction plays a major role in the distribution of stresses in the plate; (3) reversing the load direction also greatly effects the stress distribution in the plate; (4) clearance (or interference) fits change the contact angle and thus the location of the peak hoop stress; and (5) a rigid pin appears to be a good assumption for typical material systems

Large Deformation Dynamic Bending of Composite Beams

Studies were conducted on the large deformation response of composite beams subjected to a dynamic axial load. The beams were loaded with a moderate eccentricity to promote bending. The study was primarily experimental but some finite element results were obtained. Both the deformation and the failure of the beams were of interest. The static response of the beams was also studied to determine potential differences between the static and dynamic failure. Twelve different laminate types were tested. The beams were loaded dynamically with a gravity driven impactor traveling at 19.6 ft/sec and quasi-static tests were conducted on identical beams in a displacement controlled manner. For laminates of practical interest, the failure modes under static and dynamic loadings were identical. Failure in most of the laminate types occurred in a single event involving 40% to 50% of the plies. However, failure in laminates with 30 deg or 15 deg off-axis plies occured in several events. All laminates exhibited bimodular elastic properties. Using empirically determined flexural properties, a finite element analysis was reasonably accurate in predicting the static and dynamic deformation response

A study of the response of nonlinear springs

The various phases to developing a methodology for studying the response of a spring-reinforced arch subjected to a point load are discussed. The arch is simply supported at its ends with both the spring and the point load assumed to be at midspan. The spring is present to off-set the typical snap through behavior normally associated with arches, and to provide a structure that responds with constant resistance over a finite displacement. The various phases discussed consist of the following: (1) development of the closed-form solution for the shallow arch case; (2) development of a finite difference analysis to study (shallow) arches; and (3) development of a finite element analysis for studying more general shallow and nonshallow arches. The two numerical analyses rely on a continuation scheme to move the solution past limit points, and to move onto bifurcated paths, both characteristics being common to the arch problem. An eigenvalue method is used for a continuation scheme. The finite difference analysis is based on a mixed formulation (force and displacement variables) of the governing equations. The governing equations for the mixed formulation are in first order form, making the finite difference implementation convenient. However, the mixed formulation is not well-suited for the eigenvalue continuation scheme. This provided the motivation for the displacement based finite element analysis. Both the finite difference and the finite element analyses are compared with the closed form shallow arch solution. Agreement is excellent, except for the potential problems with the finite difference analysis and the continuation scheme. Agreement between the finite element analysis and another investigator's numerical analysis for deep arches is also good

The response of cylindrical panels fabricated from symmetrically and unsymmetrically laminated composite materials

Equations are developed which govern the deflection response of long cylindrical panels subjected to a line load. The line load is directed toward the center of curvature of the panel, is located at an arbitrary point along the arc length of the panel, and is included at an arbitrary angle relative to the radial direction. Only the geometrically linear problem is considered and the spatial dependence in the problem is reduced to one independent variable, specifically, the arc length along the panel. The problem is thus solvable in closed form. Both symmetrically laminated and the less common unsymmetrically laminated simply supported panels are studied. The unsymmetrically laminated case was considered because the natural shape of an unsymmetric laminate is cylindrical. Results are presented which show the influence of the location and inclination of the line load on panel deflection. Shallow and deep panels are considered. Both the symmetric and unsymmetric panels exhibit similar behavior, the unsymmetric configurations being less stiff. Limited experimental results are presented

Thermal expansion of graphite-epoxy between 116 K and 366 K

A Priest laser interferometer was developed to measure the thermal strain of composite laminates. The salient features of this interferometer are that: (1) it operates between 116 K and 366 K; (2) it is easy to operate; (3) minimum specimen preparation is required; (4) coefficients of thermal expansion in the range of 0-5 micro epsilon/K can be measured; and (5) the resolution of thermal strain is on the order of micro epsilon. The thermal response of quasi-isotropic, T300/5208, grahite-epoxy composite material was studied with this interferometer. The study showed that: (1) for the material tested, thermal cycling effects are negligible; (2) variability of thermal response from specimen to specimen may become significant at cryogenic temperatures; and (3) the thermal response of 0.6 cm and 2.5 cm wide specimens are the same above room temperature

Advances in Moire interferometry for thermal response of composites

An experimental technique for the precise measurement of the thermal response of both sides of a laminated composite coupon specimen uses Moire interferometry with fringe multiplication which yields a sensitivity of 833 nm (32.8 micro in.) per fringe. The reference gratings used are virtual gratings and are formed by partially mirrorized glass prisms in close proximity to the specimen. Results are compared with both results obtained from tests which used Moire interferometry on one side of composite laminates, and with those predicted by classical lamination theory. The technique is shown to be capable of producing the sensitivity and accuracy necessary to measure a wide range of thermal responses and to detect small side to side variations in the measured response. Tests were conducted on four laminate configurations of T300/5208 graphite epoxy over a temperature range of 297 K (75 F) to 422 K (300 F). The technique presented allows for the generation of reference gratings for temperature regimes well outside that used in these tests

Development of a Priest interferometer for measurement of the thermal expansion of a graphite epoxy in the temperature range 116-366 K

The thermal expansion behavior of graphite epoxy laminates between 116 and 366 degrees Kelvin was investigated using as implementation of the Priest interferometer concept. The design, construction and use of the interferometer along with the experimental results it was used to generate are described. The experimental program consisted of 25 tests on 25.4 mm and 6.35 mm wide, 8 ply pi/4 quasi-isotropic T300-5208 graphite/epoxy specimens and 3 tests on a 25.4 mm wide unidirectional specimen. Experimental results are presented for all tests along with a discussion of the interferometer's limitations and some possible improvements in its design

An over-land aerosol optical depth data set for data assimilation by filtering, correction, and aggregation of MODIS Collection 5 optical depth retrievals

MODIS Collection 5 retrieved aerosol optical depth (AOD) over land (MOD04/MYD04) was evaluated using 4 years of matching AERONET observations, to assess its suitability for aerosol data assimilation in numerical weather prediction models. Examination of errors revealed important sources of variation in random errors (e.g., atmospheric path length, scattering angle "hot spot"), and systematic biases (e.g., snow and cloud contamination, surface albedo bias). A set of quality assurance (QA) filters was developed to avoid conditions with potential for significant AOD error. An empirical correction for surface boundary condition using the MODIS 16-day albedo product captured 25% of the variability in the site mean bias at low AOD. A correction for regional microphysical bias using the AERONET fine/coarse partitioning information increased the global correlation between MODIS and AERONET from <i>r</i><sup>2</sup> = 0.62–0.65 to <i>r</i><sup>2</sup> = 0.71–0.73. Application of these filters and corrections improved the global fraction of MODIS AOD within (0.05 ± 20%) of AERONET to 77%, up from 67% using only built-in MODIS QA. The compliant fraction in individual regions was improved by as much as 20% (South America). An aggregated Level 3 product for use in a data assimilation system is described, along with a prognostic error model to estimate uncertainties on a per-observation basis. The new filtered and corrected Level 3 product has improved performance over built-in MODIS QA with less than a 15% reduction in overall data available for data assimilation

Large Deformation Dynamic Bending of Composite Beams

Studies were conducted on the large deformation response of composite beams subjected to a dynamic axial load. The beams were loaded with a moderate eccentricity to promote bending. The study was primarily experimental but some finite element results were obtained. Both the deformation and the failure of the beams were of interest. The static response of the beams was also studied to determine potential differences between the static and dynamic failure. Twelve different laminate types were tested. The beams tested were 23 in. by 2 in. and generally 30 plies thick. The beams were loaded dynamically with a gravity-driven impactor traveling at 19.6 ft/sec and quasi-static tests were conducted on identical beams in a displacement controlled manner. For laminates of practical interest, the failure modes under static and dynamic loadings were identical. Failure in most of the laminate types occurred in a single event involving 40% to 50% of the plies. However, failure in laminates with 300 or 150 off-axis plies occurred in several events. All laminates exhibited bimodular elastic properties. The compressive flexural moduli in some laminates was measured to be 1/2 the tensile flexural modulus. No simple relationship could be found among the measured ultimate failure strains of the different laminate types. Using empirically determined flexural properties, a finite element analysis was reasonably accurate in predicting the static and dynamic deformation response