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NASA NTRS1975

A computerized symbolic integration technique for development of triangular and quadrilateral composite shallow-shell finite elements

Computerized symbolic integration was used in conjunction with group-theoretic techniques to obtain analytic expressions for the stiffness, geometric stiffness, consistent mass, and consistent load matrices of composite shallow shell structural elements. The elements are shear flexible and have variable curvature. A stiffness (displacement) formulation was used with the fundamental unknowns consisting of both the displacement and rotation components of the reference surface of the shell. The triangular elements have six and ten nodes; the quadrilateral elements have four and eight nodes and can have internal degrees of freedom associated with displacement modes which vanish along the edges of the element (bubble modes). The stiffness, geometric stiffness, consistent mass, and consistent load coefficients are expressed as linear combinations of integrals (over the element domain) whose integrands are products of shape functions and their derivatives. The evaluation of the elemental matrices is divided into two separate problems - determination of the coefficients in the linear combination and evaluation of the integrals. The integrals are performed symbolically by using the symbolic-and-algebraic-manipulation language MACSYMA. The efficiency of using symbolic integration in the element development is demonstrated by comparing the number of floating-point arithmetic operations required in this approach with those required by a commonly used numerical quadrature technique.

Anderson, C. M.↗

NASA NTRS1976

Testing of molded high temperature plastic actuator road seals for use in advanced aircraft hydraulic systems

Molded high temperature plastic first and second stage rod seal elements were evaluated in seal assemblies to determine performance characteristics. These characteristics were compared with the performance of machined seal elements. The 6.35 cm second stage Chevron seal assembly was tested using molded Chevrons fabricated from five molding materials. Impulse screening tests conducted over a range of 311 K to 478 K revealed thermal setting deficiencies in the aromatic polyimide molding materials. Seal elements fabricated from aromatic copolyester materials structurally failed during impulse cycle calibration. Endurance testing of 3.85 million cycles at 450 K using MIL-H-83283 fluid showed poorer seal performance with the unfilled aromatic polyimide material than had been attained with seals machined from Vespel SP-21 material. The 6.35 cm first stage step-cut compression loaded seal ring fabricated from copolyester injection molding material failed structurally during impulse cycle calibration. Molding of complex shape rod seals was shown to be a potentially controllable technique, but additional molding material property testing is recommended.

Waterman, A. W.↗

NASA NTRS1985

Water impact testing of a filament wound case

A lightweight Filament Wound Case (FWC) Solid Rocket Booster (SRB) is being developed by NASA to increase the payload capability of the space shuttle. As with the steel boosters, the current plan is to recover the FWC SRB's after they impact the ocean at 65 to 85 ft/sec. As the boosters enter the ocean (nozzle first) the water moves away from the vehicle creating a cavity, which then collapses on the vehicle, and results in a significant loading event. To understand this loading event, tests were conducted on a quarter scale FWC model to measure cavity collapse pressure distributions, deflected shape and the effects of end conditions and pressure scaling.

Schmidt, A. A.↗

NASA NTRS1987

Shape optimization of damping layers

Shape optimization of unconstrained and constrained damping layers is completed. The specific problem analyzed is a cantilever beam loaded at its tip by a harmonic force. Finite element modeling and mathematical programming techniques are used to obtain the solution. Performance measures are taken to be reduction of maximum diplacement and increase in fatigue lifetime. Results include the improvement, over the uniform treatment case, of these measures when the profile of the damping layer is optimized.

Lin, T.-C.↗

NASA NTRS1990

Inducing optimally directed non-routine designs

Non-routine designs are characterized by the creation of new variables and thus an expansion of the design space. These differ from routine designs in that the latter are restricted to a fixed set of variables and thus a pre-defined design space. In previous papers, the 1stPRINCE non-routine design methodology that expands the design space in such a way that optimal trends dictate the direction and form of this expansion is described. How inductive techniques can determine these optimal trends are examined. The induction techniques in 1stPRINCE utilize constraint information from monotonicity analysis to determine how to mutate the design space. The process observes the constraint information of mutated designs and induces trends from those constraints. Application of 1stPRINCE to a beam under flexural load leads to an optimally directed tapered beam. An interesting application of 1stPRINCE to determine the optimally directed shape of a spinning square block such that resistance to spinning is minimized leads to the discovery of a circular wheel.

Cagan, Jonathan↗

NASA NTRS2005

Structural Anomaly Detection Using Fiber Optic Sensors and Inverse Finite Element Method

NASA Langley Research Center is investigating a variety of techniques for mitigating aircraft accidents due to structural component failure. One technique under consideration combines distributed fiber optic strain sensing with an inverse finite element method for detecting and characterizing structural anomalies anomalies that may provide early indication of airframe structure degradation. The technique identifies structural anomalies that result in observable changes in localized strain but do not impact the overall surface shape. Surface shape information is provided by an Inverse Finite Element Method that computes full-field displacements and internal loads using strain data from in-situ fiberoptic sensors. This paper describes a prototype of such a system and reports results from a series of laboratory tests conducted on a test coupon subjected to increasing levels of damage.

Quach, Cuong C.↗

NASA NTRS1947

Scale effect and optimum relations for sea surface planning

From the general dimensional and mechanical similarity theory it follows that a condition of steady motion of a given shape\bottom with constant speed on the surface of water is determined by four nondimensional parameters. By considering the various systems of independent parameters which are applied in theory and practice and special tests, there is determined their mutual relations and their suitability as planning characteristics. In studying the scale effect on the basis of the Prnndtl formula for the friction coefficient for a turbulent condition the order of magnitude is given of the error in applying the model data to full scale in the case of a single-step bottom For a bottom of complicated shape it is shown how from the test data of the hydrodynamic characteristics for one speed with various loads, or one load with various speeds, there may be obtained by simple computation with good approximation the hydrodynamic characteristics for a different speed or for a different load. (These considerations may be of use in solving certain problems on the stability of planning.) This permits extrapolating the curve of resistance against speed for large speeds inaccessible in the tank tests or for other loads which were not tested. The data obtained by computation are in good agreement with the test results. Problems regarding the optimum trim angle or the optimum width in the case of planning of a flat plate are considered from the point of view of the minimum resistance for a given load on the water and planning speeds. Formulas and graphs are given for the optimum value of the planning coefficient and the corresponding values of the trim angle and width of the flat plate.

Sedov, L.↗

NASA NTRS2014

Supersonic Wing Optimization Using SpaRibs

This research investigates the advantages of using curvilinear spars and ribs, termed SpaRibs, to design a supersonic aircraft wing-box in comparison to the use of classic design concepts that employ straight spars and ribs. The objective is to achieve a more efficient load-bearing mechanism and to passively control the deformation of the structure under the flight loads. Moreover, the use of SpaRibs broadens the design space and allows for natural frequencies and natural mode shape tailoring. The SpaRibs concept is implemented in a new optimization MATLAB-based framework referred to as EBF3SSWingOpt. This optimization scheme performs both the sizing and the shaping of the internal structural elements, connecting the optimizer with the analysis software. The shape of the SpaRibs is parametrically defined using the so called Linked Shape method. Each set of SpaRibs is placed in a one by one square domain of the natural space. The set of curves is subsequently transformed in the physical space for creating the wing structure geometry layout. The shape of each curve of each set is unique; however, mathematical relations link the curvature in an effort to reduce the number of design variables. The internal structure of a High Speed Commercial Transport aircraft concept developed by Boeing is optimized subjected to stress, subsonic flutter and supersonic flutter constraints. The results show that the use of the SpaRibs allows for the reduction of the aircraft's primary structure weight without violating the constraints. A weight reduction of about 15 percent is observed.

Locatelli, David↗

NASA NTRS1993

Recent refinements and increased capabilities in balloon vertical performance analysis

The NASA Thermal Trajectory analysis model for predicting the vertical performance of balloons is described in terms of two critical refinements and recent results. The model employs heat-balance equations and a vertical equation of motion, and revised methods are employed to predict maximum balloon volume, balloon shape, and the continuous computation of gas loss. Also incorporated are modeling techniques for assessing the solar radiation input that can affect the load tapes, and autoballast control algorithms are employed. The model permits the evaluation of the presence of cap layers as well as the effects of small leaks and programmed venting. The revised model is shown to give good predictions of balloon performance during flight in terms of altitude changes, descent rates, gas-mass flow, and leak potential. The model is found to be more versatile due to autoballasting and leak analysis, and good prediction are possible for the float phase and descent of current balloon shapes.

Conrad, G. R.↗

NASA NTRS2009

Further Development of Ko Displacement Theory for Deformed Shape Predictions of Nonuniform Aerospace Structures

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.

Ko, William L.↗

NASA NTRS1996

Constitutive Models for Shape Memory Alloy Polycrystals

Shape memory alloys (SMA) exhibiting the superelastic or one-way effects can produce large recoverable strains upon application of a stress. In single crystals this stress and resulting strain are very orientation dependent. We show experimental stress/strain curves for a Ni-Al single crystal for various loading orientations. Also shown are model predictions; the open and closed circles indicate recoverable strains obtained at various stages in the transformation process. Because of the strong orientation dependence of shape memory properties, crystallographic texture can be expected to play an important role in the mechanical behavior of polycrystalline SMA. It is desirable to formulate a constitutive model to better understand and exploit the unique properties of SMA.

Comstock, R. J., Jr.↗

NASA NTRS1983

Non-Newtonian Fluid Model Incorporated into Elastohydrodynamic Lubrication of Rectangular Contacts

A procedure is outlined for the numerical solution of the complete elastohydrodynamic lubrication of rectangular contacts incorporating a non-Newtonian fluid model. The approach uses a Newtonian model as long as the shear stress is less than a limiting shear stress. If the shear stress exceeds the limiting value, the shear stress is set equal to the limiting value. The numerical solution requires the coupled solution of the pressure, film shape, and fluid rheology equations from the inlet to the outlet. Isothermal and no-side-leakage assumptions were imposed in the analysis. The influence of dimensionless speed, load, materials, and sliding velocity and limiting-shear-strength proportionality constant on dimensionless minimum film thickness was investigated. Fourteen cases were used in obtaining the minimum-film-thickness equation for an elastohydrodynamically lubricated rectangular contact incorporating a non-Newtonian fluid model. Computer plots are also presented that indicate in detail pressure distribution, film shape, shear stress at the surfaces, and flow throughout the conjunction.

Jacobson, B. O.↗

NASA NTRS1984

Non-Newtonian fluid model incorporated into elastohydrodynamic lubrication of rectangular contacts

Jacobson, B. O.↗

NASA NTRS2015

Wing Shape Sensing from Measured Strain

A new two-step theory is investigated for predicting the deflection and slope of an entire structure using strain measurements at discrete locations. In the first step, a measured strain is fitted using a piecewise least-squares curve fitting method together with the cubic spline technique. These fitted strains are integrated twice to obtain deflection data along the fibers. In the second step, computed deflection along the fibers are combined with a finite element model of the structure in order to interpolate and extrapolate the deflection and slope of the entire structure through the use of the System Equivalent Reduction and Expansion Process. The theory is first validated on a computational model, a cantilevered rectangular plate wing. The theory is then applied to test data from a cantilevered swept-plate wing model. Computed results are compared with finite element results, results using another strainbased method, and photogrammetry data. For the computational model under an aeroelastic load, maximum deflection errors in the fore and aft, lateral, and vertical directions are -3.2%, 0.28%, and 0.09%, respectively; and maximum slope errors in roll and pitch directions are 0.28% and -3.2%, respectively. For the experimental model, deflection results at the tip are shown to be accurate to within 3.8% of the photogrammetry data and are accurate to within 2.2% in most cases. In general, excellent matching between target and computed values are accomplished in this study. Future refinement of this theory will allow it to monitor the deflection and health of an entire aircraft in real time, allowing for aerodynamic load computation, active flexible motion control, and active induced drag reduction.

shape sensing↗

NASA NTRS1977

Finite element stress analysis of the human left ventricle whose irregular shape is developed from single plane cineangiocardiogram

The three-dimensional left ventricular chamber geometrical model is developed from single plane cineangiocardiogram. This left ventricular model is loaded by an internal pressure monitored by cardiac catheterization. The resulting stresses in the left ventricular model chamber's wall are determined by computerized finite element procedure. For the discretization of this left ventricular model structure, a 20-node, isoparametric finite element is employed. The analysis and formulation of the computerised procedure is presented in the paper, along with the detailed algorithms and computer programs. The procedure is applied to determine the stresses in a left ventricle at an instant, during systole. Next, a portion (represented by a finite element) of this left ventricular chamber is simulated as being infarcted by making its active-state modulus value equal to its passive-state value; the neighbouring elements are shown to relieve the 'infarcted' element of stress by themselves taking on more stress.

Ghista, D. N.↗

NASA NTRS1987

Measurements of Flow Rate and Trajectory of Aircraft Tire-Generated Water Spray

An experimental investigation was conducted at the NASA Langley Research Center to measure the flow rate and trajectory of water spray generated by an aircraft tire operating on a flooded runway. Tests were conducted in the Hydrodynamics Research Facility and made use of a partial airframe and a nose tire from a general aviation aircraft. Nose tires from a commercial transport aircraft were also used. The effects of forward speed, tire load, and water depth on water spray patterns were evaluated by measuring the amount and location of water captured by an array of tubes mounted behind the test tire. Water ejected from the side of the tire footprint had the most significant potential for ingestion into engine inlets. A lateral wake created on the water surface by the rolling tire can dominate the shape of the spray pattern as the distance aft of the tire is increased. Forward speed increased flow rates and moved the spray pattern inboard. Increased tire load caused the spray to become less dense. Near the tire, increased water depths caused flow rates to increase. Tests using a fuselage and partial wing along with the nose gear showed that for certain configurations, wing aerodynamics can cause a concentration of spray above the wing.

Daugherty, Robert H.↗

NASA NTRS1988

Shaping Plastic Covers Quickly And Cheaply

Fixture enables thermal forming of custom-contoured plastic covers in half hour. In assembled cover-forming fixture, spring-loaded plate presses plastic sheet toward baseplate. Finished covers stacked at left side of table.

Gurman, I.↗

NASA NTRS1983

Effect of crack curvature on stress intensity factors for ASTM standard compact tension specimens

The stress intensity factors (SIF) are calculated using the method of lines for the compact tension specimen in tensile and shear loading for curved crack fronts. For the purely elastic case, it was found that as the crack front curvature increases, the SIF value at the center of the specimen decreases while increasing at the surface. For the higher values of crack front curvatures, the maximum value of the SIF occurs at an interior point located adjacent to the surface. A thickness average SIF was computed for parabolically applied shear loading. These results were used to assess the requirements of ASTM standards E399-71 and E399-81 on the shape of crack fronts. The SIF is assumed to reflect the average stress environment near the crack edge.

Alam, J.↗