The foundations of beam theory
Airys stress function analysis of supported beam bending under load
STRUCTURAL BEAM↗
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The bending of flat plate structures with rectangular symmetry.
Elastic bending moments and shear forces uniformly loaded flat plate structures with rectangular symmetry, using collocation technique and complex variable methods
Gupta, K. K.↗
Correlation of Structural Analysis and Test Results for the McDonnell Douglas Stitched/RFI All-Composite Wing Stub Box
The analytical and experimental results of an all-composite wing stub box are presented in this report. The wing stub box, which is representative of an inboard portion of a commercial transport high-aspect-ratio wing, was fabricated from stitched graphite-epoxy material with a Resin Film Infusion manufacturing process. The wing stub box was designed and constructed by the McDonnell Douglas Aerospace Company as part of the NASA Advanced Composites Technology program. The test article contained metallic load-introduction structures on the inboard and outboard ends of the graphite-epoxy wing stub box. The root end of the inboard load introduction structure was attached to a vertical reaction structure, and an upward load was applied to the outermost tip of the outboard load introduction structure to induce bending of the wing stub box. A finite element model was created in which the center portion of the wing-stub-box upper cover panel was modeled with a refined mesh. The refined mesh was required to represent properly the geometrically nonlinear structural behavior of the upper cover panel and to predict accurately the strains in the stringer webs of the stiffened upper cover panel. The analytical and experimental results for deflections and strains are in good agreement.
Wang, John T.↗
Design Optimization and Residual Strength Assessment of a Cylindrical Composite Shell Structure
A summary of research conducted during the specified period is presented. The research objectives included the investigation of an efficient technique for the design optimization and residual strength assessment of a semi-monocoque cylindrical shell structure made of composite materials. The response surface methodology is used in modeling the buckling response of individual skin panels under the combined axial compression and shear loading. These models are inserted into the MSC/NASTRAN code for design optimization of the cylindrical structure under a combined bending-torsion loading condition. The comparison between the monolithic and sandwich skin design cases indicated a 35% weight saving in using sandwich skin panels. In addition, the residual strength of the optimum design was obtained by identifying the most critical region of the structure and introducing a damage in the form of skin-stringer and skin-stringer-frame detachment. The comparison between the two skin design concepts indicated that the sandwich skin design is capable of retaining a higher residual strength than its monolithic counterpart. The results of this investigation are presented and discussed in this report.
Rais-Rohani, Masoud↗
Aeroelasticity of Axially Loaded Aerodynamic Structures for Truss-Braced Wing Aircraft
This paper presents an aeroelastic finite-element formulation for axially loaded aerodynamic structures. The presence of axial loading causes the bending and torsional sitffnesses to change. For aircraft with axially loaded structures such as the truss-braced wing aircraft, the aeroelastic behaviors of such structures are nonlinear and depend on the aerodynamic loading exerted on these structures. Under axial strain, a tensile force is created which can influence the stiffness of the overall aircraft structure. This tension stiffening is a geometric nonlinear effect that needs to be captured in aeroelastic analyses to better understand the behaviors of these types of aircraft structures. A frequency analysis of a rotating blade structure is performed to demonstrate the analytical method. A flutter analysis of a truss-braced wing aircraft is performed to analyze the effect of geometric nonlinear effect of tension stiffening on the flutter speed. The results show that the geometric nonlinear tension stiffening effect can have a significant impact on the flutter speed prediction. In general, increased wing loading results in an increase in the flutter speed. The study illustrates the importance of accounting for the geometric nonlinear tension stiffening effect in analyzing the truss-braced wing aircraft.
Aeroelasticity↗
Structural and aerodynamic loads and performance measurements of an SA349/2 helicopter with an advanced geometry rotor
A flight test program was conducted to obtain data from an upgraded Gazelle helicopter with an advanced geometry, three bladed rotor. Data were acquired on upper and lower surface chordwise blade pressure, blade bending and torsion moments, and fuselage structural loads. Results are presented from 16 individual flight conditions, including level flights ranging from 10 to 77 m/sec at 50 to 3000 m altitude, turning flights up to 2.0 g, and autorotation. Rotor aerodynamic data include information from 51 pressure transducers distributed chordwise at 75, 88, and 97% radial stations. Individual tranducer pressure coefficients and airfoil section lift and pitching moment coefficients are presented, as are steady state flight condition parameters and time dependence rotor loads. All dynamic data are presented as harmonic analysis coefficients.
Heffernan, Ruth M.↗
Conical isogrid adapter structural test results
The structural characteristics of isogrid composite structures are discussed. To demonstrate the feasibility of applying isogrid to conical structures, a full scale flanged isogrid conical adapter similar to the configuration of the D-1 Centaur equipment module was constructed. The adapter was tested to evaluate the response of the conical isogrid structure to various combinations of bending and axial compression loading. The analysis techniques for predicting conical isogrid structural capability are examined.
Dyer, J. E.↗
Crack Turning Mechanics of Composite Wing Skin Panels
The safety of future composite wing skin integral stiffener panels requires a full understanding of failure mechanisms of these damage tolerance critical structures under both in-plane and bending loads. Of primary interest is to derive mathematical models using fracture mechanics in anisotropic cracked plate structures, to assess the crack turning mechanisms, and thereby to enhance the residual strength in the integral stiffener composite structures. The use of fracture mechanics to assess the failure behavior in a cracked structure requires the identification of critical fracture parameters which govern the severity of stress and deformation field ahead of the flaw, and which can be evaluated using information obtained from the flaw tip. In the three-year grant, the crack-tip fields under plane deformation, crack-tip fields for anisotropic plates and anisotropic shells have been obtained. In addition, methods for determining the stress intensity factors, energy release rate, and the T-stresses have been proposed and verified. The research accomplishments can be summarized as follows: (1) Under plane deformation in anisotropic solids, the asymptotic crack-tip fields have been obtained using Stroh formalism; (2) The T-stress and the coefficient of the second term for sigma(sub y), g(sub 32), have been obtained using path-independent integral, the J-integral and Betti's reciprocal theorem together with auxiliary fields; (3) With experimental data performed by NASA, analyses indicated that the mode-I critical stress intensity factor K(sub Q) provides a satisfactory characterization of fracture initiation for a given laminate thickness, provided the failure is fiber-dominated and crack extends in a self-similar manner; (4) The high constraint specimens, especially for CT specimens, due to large T-stress and large magnitude of negative g(sub 32) term may be expected to inhibit the crack extension in the same plane and promote crack turning; (5) Crack turning out of crack plane in generally anisotropic solids under plane deformation has been studied; (6) The role of T-stress and the higher-order term of sigma(sub y) on the crack turning and stability of the kinked crack has been quantified; (7) Asymptotic crack-tip fields including the effect of transverse shear deformation (Reissner plate theory) in an anisotropic plate under bending, twisting moments, and transverse shear loads has been presented; (8) The expression of the path-independent J-integral in terms of the generalized stress and strain has been derived; (9) Asymptotic crack-tip fields including the effect of transverse shear deformation (Reissner shallow shell theory) in a general anisotropic shell has been developed; (10) The Stroh formalism was used to characterize the crack tip fields in shells up to the second term and the energy release rate was expressed in a very compact form.
Yuan, F. G.↗
A Non Rigid Reusable Surface Insulation Concept for the Space Shuttle Thermal Protection System
A reusable thermal protection system concept was developed for the space shuttle that utilizes a flexible, woven ceramic mat insulation beneath an aerodynamic skin and moisture barrier consisting of either a dense ceramic coating or a super alloy metallic foil. The resulting heat shield material has unique structural characteristics. The shear modulus of the woven mat is very low such that bending and membrane loads introduced into the underlying structural panel remain isolated from the surface skin.
Alexander, J. G.↗
Progressive Fracture of Fiber Composite Builtup Structures
The damage progression and fracture of builtup composite structures was evaluated by using computational simulation to examine the behavior and response of a stiffened composite (0 +/- 45/90)(sub s6) laminate panel subjected to a bending load. The damage initiation, growth, accumulation, progression, and propagation to structural collapse were simulated. An integrated computer code (CODSTRAN) was augmented for the simulation of the progressive damage and fracture of builtup composite structures under mechanical loading. Results showed that damage initiation and progression have a significant effect on the structural response. Also investigated was the influence of different types of bending load on the damage initiation, propagation, and final fracture of the builtup composite panel.
Gotsis, Pascal K.↗
Torsion and bending of prismatic rods of hollow rectangular section
The torsion and bending of hollow rectangular beams was investigated without the requirement that wall thickness be small compared with the transverse dimensions. The limits of applicability of the usual Bredt formula are indicated for the case of a square hollow tube in torsion. Formulas are given for bending stresses at different parts of the cross section of a hollow rectangular beam.
BOXES, STRUCTURAL↗
Design and evaluation of a foam-filled hat-stiffened panel concept for aircraft primary structural applications
Geodesically stiffened structures are very efficient in carrying combined bending, torsion, and pressure loading that is typical of primary aircraft structures. They are also very damage tolerant since there are multiple load paths available to redistribute loads compared to prismatically stiffened structures. Geodesically stiffened structures utilize continuous filament composite materials which make them amenable to automated manufacturing processes to reduce cost. The current practice for geodesically stiffened structures is to use a solid blade construction for the stiffener. This stiffener configuration is not an efficient concept and there is a need to identify other stiffener configurations that are more efficient but utilize the same manufacturing process as the solid blade. This paper describes a foam-filled stiffener cross section that is more efficient than a solid-blade stiffener in the load range corresponding to primary aircraft structures. A prismatic hat-stiffener panel design is then selected for structural evaluation in uni-axial compression with and without impact damage. Experimental results for both single stiffener specimens and multi-stiffener panel specimens are presented. Finite element analysis results are presented that predict the buckling and postbuckling response of the test specimens. Analytical results for both the element and panel specimens are compared with experimental results.
Ambur, Damodar R.↗
Investigation of Maximum Blade Loading Capability of Lift-Offset Rotors
Maximum blade loading capability of a coaxial, lift-offset rotor is investigated using a rotorcraft configuration designed in the context of short-haul, medium-size civil and military missions. The aircraft was sized for a 6600-lb payload and a range of 300 nm. The rotor planform and twist were optimized for hover and cruise performance. For the present rotor performance calculations, the collective pitch angle is progressively increased up to and through stall with the shaft angle set to zero. The effects of lift offset on rotor lift, power, controls, and blade airloads and structural loads are examined. The maximum lift capability of the coaxial rotor increases as lift offset increases and extends well beyond the McHugh lift boundary as the lift potential of the advancing blades are fully realized. A parametric study is conducted to examine the differences between the present coaxial rotor and the McHugh rotor in terms of maximum lift capabilities and to identify important design parameters that define the maximum lift capability of the rotor. The effects of lift offset on rotor blade airloads and structural loads are also investigated. Flap bending moment increases substantially as lift offset increases to carry the hub roll moment even at low collective values. The magnitude of flap bending moment is dictated by the lift-offset value (hub roll moment) but is less sensitive to collective and speed.
Yeo, Hyeonsoo↗
Composite Bending Box Section Modal Vibration Fault Detection
One of the primary concerns with Composite construction in critical structures such as wings and stabilizers is that hidden faults and cracks can develop operationally. In the real world, catastrophic sudden failure can result from these undetected faults in composite structures. Vibration data incorporating a broad frequency modal approach, could detect significant changes prior to failure. The purpose of this report is to investigate the usefulness of frequency mode testing before and after bending and torsion loading on a composite bending Box Test section. This test article is representative of construction techniques being developed for the recent NASA Blended Wing Body Low Speed Vehicle Project. The Box section represents the construction technique on the proposed blended wing aircraft. Modal testing using an impact hammer provides an frequency fingerprint before and after bending and torsional loading. If a significant structural discontinuity develops, the vibration response is expected to change. The limitations of the data will be evaluated for future use as a non-destructive in-situ method of assessing hidden damage in similarly constructed composite wing assemblies. Modal vibration fault detection sensitivity to band-width, location and axis will be investigated. Do the sensor accelerometers need to be near the fault and or in the same axis? The response data used in this report was recorded at 17 locations using tri-axial accelerometers. The modal tests were conducted following 5 independent loading conditions before load to failure and 2 following load to failure over a period of 6 weeks. Redundant data was used to minimize effects from uncontrolled variables which could lead to incorrect interpretations. It will be shown that vibrational modes detected failure at many locations when skin de-bonding failures occurred near the center section. Important considerations are the axis selected and frequency range.
Werlink, Rudy↗
Theory of thin-walled rods
Starting with the Love equations for bending of extensible shells, "principal stress states" are sought for a thin-walled rod of arbitrary but open cross section. Principal stress states exclude those local states arising from end conditions which damp out with distance from the ends. It is found that for rods of intermediate length, long enough to avoid local bending at a support, and short enough that elementary torsion and bending are not the most significant stress states, four principal states exist. Three of these states are associated with the planar distribution of axial stress and are equivalent to the engineering theory of extension and bending of solid sections. The fourth state resembles that which has been called in the literature "bending stress due to torsional", except that cross sections are permitted to bend and the shear along the center line of the cross section is permitted to differ from zero.
LOADS AND STRESSES, STRUCTURAL - TENSION↗
Simulation of Lift plus Cruise Vehicle Models to Define a Full-Scale Crash Test Campaign
A series of dynamic simulations were completed on the National Aeronautics and Space Administration(NASA) Lift plus Cruise (LPC) concept electric Vertical Take-off and Landing (eVTOL) vehicle in preparation for an anticipated future full-scale crash-test campaign. The crash test campaign is envisioned as a data gathering exercise with an intent generating full-scale test data to inform eVTOL crashworthiness regulations, evaluate the use of energy absorbing concepts within vehicle design, and validate finite element modeling techniques used in crashworthiness predictions. This report discusses the two main objectives for the simulation efforts: the development of a structural cabin section, and a series of analyses utilized to determine the sensitivities of impact variables. A structural cabin section was created based from previous research efforts involving the LPC vehicle utilized for occupant response. To refine for the structural modifications, the wing and tail sections of the vehicle were removed. The tail was replaced with a representative mass at the aft of the fuselage. The overhead wing was replaced with a beam structure sized to approximate the bending response of the wing under crash loading conditions. The beam structure was fixed to the fuselage similar to the original Wingbox design in order to properly capture effects of this overhead mass on survivable volume within the vehicle. The fidelity of the fuselage frame structure within the FEM was increased to quantify the effect of frame sizing on structural response. From this an eVTOL test article design was developed, which satisfied basic crashworthiness requirements, was reconfigurable to assess the effect of various design avenues on structural response and optimized to improve manufacturability. The impact variable sensitivity results primarily show the orientation of the impact vector played a major role in types of injuries sustained, along with their severity. The vehicle was largely insensitive to small variations in pitch attitude but highly sensitive to both impact surface at certain angles and landing gear location.
eVTOL↗
Comparison of Rotor Structural Loads Calculated using Comprehensive Analysis
Blade flap and chord bending and torsion moments are investigated for six rotors operating at transition and high speed: H-34 in flight and wind tunnel, SA 330 (research Puma), SA 349/2, UH-60A full-scale, and BO- 105 model (HART-I). The measured data from flight and wind tunnel tests are compared with calculations obtained using the comprehensive analysis CAMRAD II. The calculations were made using two free wake models: rolled-up and multiple-trailer with consolidation models. At transition speed, there is fair to good agreement for the flap and chord bending moments between the test data and analysis for the H-34, research Puma, and SA 349/2. Torsion moment correlation, in general, is fair to good for all the rotors investigated. Better flap bending and torsion moment correlation is obtained for the UH-60A and BO-105 rotors by using the multiple-trailer with consolidation wake model. In the high speed condition, the analysis shows generally better correlation in magnitude than in phase for the flap bending and torsion moments. However, a significant underprediction of chord bending moment is observed for the research Puma and UH-60A. The poor chord bending moment correlation appears to be caused by the airloads model, not the structural dynamics.
Johnson, Wayne↗
Optimization of composite box-beam structures including effects of subcomponent interactions
Minimum mass designs are obtained for a simple box beam structure subject to bending, torque and combined bending/torque load cases. These designs are obtained subject to point strain and linear buckling constraints. The present work differs from previous efforts in that special attention is payed to including the effects of subcomponent panel interaction in the optimal design process. Two different approaches are used to impose the buckling constraints. When the global approach is used, buckling constraints are imposed on the global structure via a linear eigenvalue analysis. This approach allows the subcomponent panels to interact in a realistic manner. The results obtained using this approach are compared to results obtained using a traditional, less expensive approach, called the local approach. When the local approach is used, in-plane loads are extracted from the global model and used to impose buckling constraints on each subcomponent panel individually. In the global cases, it is found that there can be significant interaction between skin, spar, and rib design variables. This coupling is weak or nonexistent in the local designs. It is determined that weight savings of up to 7% may be obtained by using the global approach instead of the local approach to design these structures. Several of the designs obtained using the linear buckling analysis are subjected to a geometrically nonlinear analysis. For the designs which were subjected to bending loads, the innermost rib panel begins to collapse at less than half the intended design load and in a mode different from that predicted by linear analysis. The discrepancy between the predicted linear and nonlinear responses is attributed to the effects of the nonlinear rib crushing load, and the parameter which controls this rib collapse failure mode is shown to be the rib thickness. The rib collapse failure mode may be avoided by increasing the rib thickness above the value obtained from the (linear analysis based) optimizer. It is concluded that it would be necessary to include geometric nonlinearities in the design optimization process if the true optimum in this case were to be found.
Ragon, Scott A.↗