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The Ko displacement theory originally developed for shape predictions of straight beams is extended to shape predictions of curved beams. The surface strains needed for shape predictions were analytically generated from finite-element nodal stress outputs. With the aid of finite-element displacement outputs, mathematical functional forms for curvature-effect correction terms are established and incorporated into straight-beam deflection equations for shape predictions of both cantilever and two-point supported curved beams. The newly established deflection equations for cantilever curved beams could provide quite accurate shape predictions for different cantilever curved beams, including the quarter-circle cantilever beam. Furthermore, the newly formulated deflection equations for two-point supported curved beams could provide accurate shape predictions for a range of two-point supported curved beams, including the full-circular ring. Accuracy of the newly developed curved-beam deflection equations is validated through shape prediction analysis of curved beams embedded in the windward shallow spherical shell of a generic crew exploration vehicle. A single-point collocation method for optimization of shape predictions is discussed in detail

A technique for computing the bending strain resulting from the resonant modal deformation of a vibrating plate-like structure is described. Interferometric fringes obtained by time-average holography are used as the basis for generating a mathematically continuous series approximation of the structure's out-of-plane displacement. The terms of the series consist of the eigenfunctions of a simple beam having either clamped-free or free-free boundary conditions. Use is made of a linear least squares equation solver to compute the coefficients of the displacement series terms based upon the experimental holographic fringe values. The technique is programmed for use on an interactive computer terminal. The method is tested by comparing it to the results of an eigenvalue analysis of a cantilevered plate analyzed using the finite element computer program, NASTRAN. (Author)

A technique for computing the bending strain resulting from the resonant modal deformation of a vibrating plate-like structure is described. Interferometric fringes obtained by time-average holography are used as the basis for generating a mathematically continuous series approximation of the structure's out-of-plane displacement. The terms of the series consist of the eigenfunctions of a simple beam having either clamped-free or free-free boundary conditions. Use is made of a linear least squares equation solver to compute the coefficients of the displacement series terms based upon the experimental holographic fringe values. The technique is programmed for use on an interactive computer terminal. The method is tested by comparing it to the results of an eigenvalue analysis of a cantilevered plate analyzed using the finite element computer program, NASTRAN. (Author)

Displacement theories are developed for a variety of structures with the goal of providing real-time shape predictions for aerospace vehicles during flight. These theories are initially developed for a cantilever beam to predict the deformed shapes of the Helios flying wing. The main structural configuration of the Helios wing is a cantilever wing tubular spar subjected to bending, torsion, and combined bending and torsion loading. The displacement equations that are formulated are expressed in terms of strains measured at multiple sensing stations equally spaced on the surface of the wing spar. Displacement theories for other structures, such as tapered cantilever beams, two-point supported beams, wing boxes, and plates also are developed. The accuracy of the displacement theories is successfully validated by finite-element analysis and classical beam theory using input-strains generated by finite-element analysis. The displacement equations and associated strain-sensing system (such as fiber optic sensors) create a powerful means for in-flight deformation monitoring of aerospace structures. This method serves multiple purposes for structural shape sensing, loads monitoring, and structural health monitoring. Ultimately, the calculated displacement data can be visually displayed to the ground-based pilot or used as input to the control system to actively control the shape of structures during flight.

Displacement theories are developed for a variety of structures with the goal of providing real-time shape predictions for aerospace vehicles during flight. These theories are initially developed for a cantilever beam to predict the deformed shapes of the Helios flying wing. The main structural configuration of the Helios wing is a cantilever wing tubular spar subjected to bending, torsion, and combined bending and torsion loading. The displacement equations that are formulated are expressed in terms of strains measured at multiple sensing stations equally spaced on the surface of the wing spar. Displacement theories for other structures, such as tapered cantilever beams, two-point supported beams, wing boxes, and plates also are developed. The accuracy of the displacement theories is successfully validated by finite-element analysis and classical beam theory using input-strains generated by finite-element analysis. The displacement equations and associated strain-sensing system (such as fiber optic sensors) create a powerful means for in-flight deformation monitoring of aerospace structures. This method serves multiple purposes for structural shape sensing, loads monitoring, and structural health monitoring. Ultimately, the calculated displacement data can be visually displayed to the ground-based pilot or used as input to the control system to actively control the shape of structures during flight.

Capacitor field calculations for capacitive displacement measurement of open mesh structures such as radio telescopes and radar receivers

Increasing attention is being focussed on the use of symmetry-adapted functions to describe magnetic structures, structural distortions, and incommensurate crystallography. Though the calculation of such functions is well developed, significant difficulties can arise, such as the generation of too many or too few basis functions to minimally span the linear vector space. We present an elegant solution to these difficulties using the concept of basis sets, and discuss previous work in this area using this concept. Further, we highlight the significance of unitary irreducible representations in this method, and provide the first validation that the irreducible representations of the crystallographic space groups tabulated by Kovalev are unitary

An experimental study of the effects of environmental temperature and humidity conditions on long-term creep displacement data of high strength Kevlar and VectranTM woven fabric webbings under constant load for inflatable structures is presented. The restraint layer of an inflatable structure for long-duration space exploration missions is designed to bear load and consists of an assembly of high strength webbings. Long-term creep displacement data of webbings can be utilized by designers to validate service life parameters of restraint layers of inflatable structures. Five groups of high-strength webbings were researched over a two year period. Each group had a unique webbing length, load rating, applied load, and test period. The five groups consisted of 1.) 6K Vectran webbings loaded to 49% ultimate tensile strength (UTS), 2.) 6K Vectran webbings loaded to 55% UTS, 3.) 12.5K Vectran webbings loaded to 22% UTS, 4.) 6K Kevlar webbings loaded to 40% and 43% UTS, and 5.) 6K Kevlar webbings loaded to 48% UTS. Results show that all webbing groups exhibit the initial two stages of three of a typical creep curve of an elastic material. Results also show that webbings exhibit unique local wave patterns over the duration of the test period. Data indicate that the local pattern is primarily generated by daily variations in relative humidity values within the test facility. Data indicate that after a three to six month period, where webbings reach a steady-state creep condition, an annual sinusoidal displacement pattern is exhibited, primarily due to variations in annual mean temperature values. Data indicates that variations in daily temperature values and annual mean humidity values have limited secondary effects on creep displacement behavior. Results show that webbings in groups 2 and 5 do not exhibit well defined annual displacement patterns because the magnitude of the applied loads cause large deformations, and data indicate that material yielding within a webbing tends to neutralize the annual sinusoidal displacement pattern. Study indicates that applied load, environmental effects, mechanical strength, coefficient of thermal expansion, and hygroscopic properties of webbings are fundamental requirements for quantifying accurate creep displacements and behaviors over multiple year time periods. Results from a study of the environmental effects on long-term creep displacement data of Kevlar and Vectran woven webbings are presented to increase the knowledge base of webbing materials and to enhance designs of inflatable space structures for long-duration space missions.

No abstract available

Inflatable modules for space applications offer weight and launch volume savings relative to current metallic modules. Limited data exist on the creep behavior of the restraint layer of inflatable modules. Long-term displacement and strain data of two high strength woven fabric webbings, Kevlar and Vectran, under constant load is presented. The creep behavior of webbings is required by designers to help determine service life parameters of inflatable modules. Four groups of different webbings with different loads were defined for this study. Group 1 consisted of 4K Kevlar webbings loaded to 33% ultimate tensile strength and 6K Vectran webbings loaded to 27% ultimate tensile strength, group 2 consisted of 6K Kevlar webbings loaded to 40% and 43% ultimate tensile strength, and 6K Vectran webbings loaded to 50% ultimate tensile strength, group 3 consisted of 6K Kevlar webbings loaded to 52% ultimate tensile strength and 6K Vectran webbings loaded to 60% ultimate tensile strength, and group 4 consisted of 12.5K Kevlar webbings loaded to 22% ultimate tensile strength, and 12.5K Vectran webbings loaded to 22% ultimate tensile strength. The uniquely designed test facility, hardware, displacement measuring devices, and test data are presented. Test data indicate that immediately after loading all webbings stretch an inch or more, however as time increases displacement values significantly decrease to fall within a range of several hundredth of an inch over the remainder of test period. Webbings in group 1 exhibit near constant displacements and strains over a 17-month period. Data acquisition was suspended after the 17th month, however webbings continue to sustain load without any local webbing damage as of the 21st month of testing. Webbings in group 2 exhibit a combination of initial constant displacement and subsequent increases in displacement rates over a 16-month period. Webbings in group 3 exhibit steady increases in displacement rates leading to webbing failure over a 3-month period. Five of six webbings experienced local damage and subsequent failure in group 3. Data from group 4 indicates increasing webbing displacements over a 7-month period. All webbings in groups 1, 2, and 4 remain suspended without any local damage as of the writing of this paper. Variations in facility temperatures over test period seem to have had limited effect on long-term webbing displacement data.

Quantitative information on the response of soil in natural deposits to lateral loadings was obtained by the performance of field tests in conjunction with theoretical studies and in-situ and laboratory determinations. The field tests utilized a segmental pile, a lateral plate loading device, rigid poles subjected to lateral loads, and full-scale laterally loaded piles. Results of the final series of field tests and analytical studies in the program are presented in this report, along with the design recommendations formulated on the basis of the research. Procedures were developed for the prediction of nonlinear lateral soil pressure-displacement relationships applicable to undisturbed deposits of both cohesive and noncohesive soils using easily measured conventional engineering properties of the soil. These procedures were utilized in the development of design procedures for laterally loaded piles in nonhomogeneous layered soil system. An iterative solution of the laterally loaded pile problem utilizing a digital computer was developed, and a similar iterative solution for hand computations in a tabular form was evolved for use in cases where a computer cannot be used.

The steady state displacements of a rotating advanced turboprop are computed using the geometrically nonlinear capabilities of COSMIC NASTRAN Rigid Format 4 and MSC NASTRAN Solution 64. A description of the modified Newton-Raphson algorithm used by Solution 64 and the iterative scheme used by Rigid Format 4 is provided. A representative advanced turboprop, SR3, was used for the study. Displacements for SR3 are computed for rotational speeds up to 10,000 rpm. The results show Solution 64 to be superior for computating displacements of flexible rotating structures. This is attributed to its ability to update the displacement dependent centrifugal force during the solution process.

Large deformation displacement transfer functions were formulated for deformed shape predictions of highly flexible slender structures like aircraft wings. In the formulation, the embedded beam (depth wise cross section of structure along the surface strain sensing line) was first evenly discretized into multiple small domains, with surface strain sensing stations located at the domain junctures. Thus, the surface strain (bending strains) variation within each domain could be expressed with linear of nonlinear function. Such piecewise approach enabled piecewise integrations of the embedded beam curvature equations [classical (Eulerian), physical (Lagrangian), and shifted curvature equations] to yield closed form slope and deflection equations in recursive forms.

The Ko displacement theory previously formulated for deformed shape predictions of nonuniform beam structures is further developed mathematically. The further-developed displacement equations are expressed explicitly in terms of geometrical parameters of the beam and bending strains at equally spaced strain-sensing stations along the multiplexed fiber-optic sensor line installed on the bottom surface of the beam. The bending strain data can then be input into the displacement equations for calculations of local slopes, deflections, and cross-sectional twist angles for generating the overall deformed shapes of the nonuniform beam. The further-developed displacement theory can also be applied to the deformed shape predictions of nonuniform two-point supported beams, nonuniform panels, nonuniform aircraft wings and fuselages, and so forth. The high degree of accuracy of the further-developed displacement theory for nonuniform beams is validated by finite-element analysis of various nonuniform beam structures. Such structures include tapered tubular beams, depth-tapered unswept and swept wing boxes, width-tapered wing boxes, and double-tapered wing boxes, all under combined bending and torsional loads. The Ko displacement theory, combined with the fiber-optic strain-sensing system, provide a powerful tool for in-flight deformed shape monitoring of unmanned aerospace vehicles by ground-based pilots to maintain safe flights.

The Ko displacement theory previously formulated for deformed shape predictions of nonuniform beam structures is further developed mathematically. The further-developed displacement equations are expressed explicitly in terms of geometrical parameters of the beam and bending strains at equally spaced strain-sensing stations along the multiplexed fiber-optic sensor line installed on the bottom surface of the beam. The bending strain data can then be input into the displacement equations for calculations of local slopes, deflections, and cross-sectional twist angles for generating the overall deformed shapes of the nonuniform beam. The further-developed displacement theory can also be applied to the deformed shape predictions of nonuniform two-point supported beams, nonuniform panels, nonuniform aircraft wings and fuselages, and so forth. The high degree of accuracy of the further-developed displacement theory for nonuniform beams is validated by finite-element analysis of various nonuniform beam structures. Such structures include tapered tubular beams, depth-tapered unswept and swept wing boxes, width-tapered wing boxes, and double-tapered wing boxes, all under combined bending and torsional loads. The Ko displacement theory, combined with the fiber-optic strain-sensing system, provide a powerful tool for in-flight deformed shape monitoring of unmanned aerospace vehicles by ground-based pilots to maintain safe flights.

The Ko displacement theory previously formulated for deformed shape predictions of nonuniform beam structures is further developed mathematically. The further-developed displacement equations are expressed explicitly in terms of geometrical parameters of the beam and bending strains at equally spaced strain-sensing stations along the multiplexed fiber-optic sensor line installed on the bottom surface of the beam. The bending strain data can then be input into the displacement equations for calculations of local slopes, deflections, and cross-sectional twist angles for generating the overall deformed shapes of the nonuniform beam. The further-developed displacement theory can also be applied to the deformed shape predictions of nonuniform two-point supported beams, nonuniform panels, nonuniform aircraft wings and fuselages, and so forth. The high degree of accuracy of the further-developed displacement theory for nonuniform beams is validated by finite-element analysis of various nonuniform beam structures. Such structures include tapered tubular beams, depth-tapered unswept and swept wing boxes, width-tapered wing boxes, and double-tapered wing boxes, all under combined bending and torsional loads. The Ko displacement theory, combined with the fiber-optic strain-sensing system, provide a powerful tool for in-flight deformed shape monitoring of unmanned aerospace vehicles by ground-based pilots to maintain safe flights.

A study of the matrix displacement method for modeling the vibrations of structures is presented in this report. The model can analyze both the free and forced vibrations of a structure. Static loading on a structure is treated as a special case of the forced vibration analysis. A brief review of the Finite Element Method and its present use is first given. This is followed by a discussion of the methodology of the matrix displacement approach and a description of the specific model used. Examples of the use of the model to analyze the frequencies and mode shapes of the free and forced response of a beam structure and the static deflections of a beam structure are shown and compared with the closed form solutions. Finally, ways of extending the model to a more complicated structure, a turbine blade, are discussed. Conclusions are then drawn.