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At least 37 records · Page 2

The effect of nonsymmetric pressure stiffness on the dynamic characteristics of Solid Rocket Motors

This paper discusses the effect of pressure on the dynamics of pre-stiffened structures such as the Advanced Solid Rocket Motor (ASRM). Previous work in which the stiffness terms resulting from constant pressure were derived has been extended to enable modeling of nonconstant pressure applied over nonenclosed volumes. These conditions will result in nonsymmetric terms in the global stiffness matrix which will not cancel out. Three new pressure stiffness elements incorporating these nonsymmetric terms have been implemented as dummy elements in COSMIC NASTRAN and have been tested on various simple examples as well as an existing ASRM NASTRAN finite element model. The results indicate that for all load cases of practical interest to the ASRM program, the nonsymmetric terms have very little effect on the dynamic characteristics. In addition, the pressure stiffness elements developed in the previous work which assumed constant pressure gave virtually the same results as the new elements even for problems in which the pressures are not constant. The original elements appear to work well as long as the pressure gradient across any individual element is no larger than about 0.75 psi/inch. The new elements are therefore most useful for determining the conditions under which the original pressure stiffness elements can be used.

Christensen, Eric R.↗

Stiffness and strength tailoring in uniform space-filling truss structures

This paper presents a deterministic procedure for tailoring the continuum stiffness and strength of uniform space-filling truss structures through the appropriate selection of truss geometry and member sizes (i.e., flexural and axial stiffnesses and length). The trusses considered herein are generated by replication of a characteristic truss cell uniformly through space. The repeating cells are categorized by one of a set of possible geometric symmetry groups derived using the techniques of crystallography. The elastic symmetry associated with each geometric symmetry group is identified to aid in the selection of an appropriate truss geometry for a given application. Stiffness and strength tailoring of a given truss geometry is enabled through explicit expressions relating the continuum stiffnesses and failure stresses of the truss to the stiffnesses and failure loads of its members. These expressions are derived using an existing equivalent continuum analysis technique and a newly developed analytical failure theory for trusses. Several examples are presented to illustrate the application of these techniques, and to demonstrate the usefulness of the information gained from this analysis.

Lake, Mark S.↗

Effect of Hindlimb Unloading on Rat Soleus Fiber Force, Stiffness, and Calcium Sensitivity

The purpose of this study was to examine the time course of change in soleus muscle fiber peak force (N), tension (P(sub 0), kN/sq m), elastic modulus (E(sub 0)), and force-pCa and stiffness - pCa relationships. After 1, 2, or 3 wk of Hindlimb Unloading (HU), single fibers were isolated and placed between a motor arm and a transducer, and fiber diameter, peak absolute force, P(sub 0), E(sub 0), and force-pCa and stiffness-pca relationships were characterized. One week of HU resulted in a significant reduction in fiber diameter (68 +/- 2 vs. 57 +/- 1 micrometer), force (3.59 +/- 0.15 vs. 2.19 +/- 0.12 x 10(exp -4) N), P(sub 0) (102 +/- 4 vs. 85 +/- 2 kN/sq m), and E(sub 0) (1.96 +/- 0.12 vs. 1.37 +/- 0.13 X 10(exp 7) N/sq m) and 2 wk of HU caused a further decline in fiber diameter (45 +/- 1 micrometer), force (1.31 +/- 0.06 x 10(exp -4) N), and E(sub 0)(0.96 +/- 0.09 x 10(exp 7) N/sq m). Although the mean fiber diameter and absolute force continued to decline through 3 wk of HU, P(sub 0) recovered to values not significantly different from control. The P(sub 0)/E(sub 0) ratio was significantly increased after 1 (5.5 +/- 0.3 to 7.1 +/- 0.6), 2, and 3 wk of HU, and the 2-wk (9.5 +/- 0.4) and 3-wk (9.4 +/- 0.8) values were significantly greater than the 1-wk values. The force-pCa and stiffness-pCa curves were shifted right- ward after 1, 2, and 3 wk of HU. At 1 wk of HU, the Ca(2+) sensitivity of isometric force, assessed by Ca(2+) concentration required for half-maximal force, was increased from the control value of 1.83 +/- 0.12 to 2.30 +/- 0.10 micrometers. In conclusion, after HU, the decrease in soleus fiber P(sub 0) can be explained by a reduction in the number of myofibrillar cross bridges per cross-sectional area. Our working hypothesis is that the loss of contractile protein reduces the number of cross bridges per cross-sectional area and increases the filament lattice spacing. The increased spacing reduces cross-bridge force and stiffness, but P(sub 0)/E(sub 0) increases because of a quantitatively greater effect on stiffness.

McDonald Kerry S.↗

A Comparison of Total and Intrinsic Muscle Stiffness Among Flexors and Extensors of the Ankle, Knee and Elbow

This study examined 3 methods that assessed muscle stiffness. Muscle stiffness has been quantified by tissue reactive force (transverse stiffness), vibration, and force (or torque) over displacement. Muscle stiffness also has two components: reflex (due to muscle sensor activity) and intrinsic (tonic firing of motor units, elastic nature of actin and myosin cross bridges, and connective tissue). This study compared three methods of measuring muscle stiffness of agonist-antagonist muscle pairs of the ankle, knee and elbow.

Lemoine, Sandra M.↗

Running in the real world: adjusting leg stiffness for different surfaces

A running animal coordinates the actions of many muscles, tendons, and ligaments in its leg so that the overall leg behaves like a single mechanical spring during ground contact. Experimental observations have revealed that an animal's leg stiffness is independent of both speed and gravity level, suggesting that it is dictated by inherent musculoskeletal properties. However, if leg stiffness was invariant, the biomechanics of running (e.g. peak ground reaction force and ground contact time) would change when an animal encountered different surfaces in the natural world. We found that human runners adjust their leg stiffness to accommodate changes in surface stiffness, allowing them to maintain similar running mechanics on different surfaces. These results provide important insight into mechanics and control of animal locomotion and suggest that incorporating an adjustable leg stiffness in the design of hopping and running robots is important if they are to match the agility and speed of animals on varied terrain.

NASA Discipline Musculoskeletal↗

Variable Stiffness Panel Structural Analyses With Material Nonlinearity and Correlation With Tests

Results from structural analyses of three tow-placed AS4/977-3 composite panels with both geometric and material nonlinearities are presented. Two of the panels have variable stiffness layups where the fiber orientation angle varies as a continuous function of location on the panel planform. One variable stiffness panel has overlapping tow bands of varying thickness, while the other has a theoretically uniform thickness. The third panel has a conventional uniform-thickness [plus or minus 45](sub 5s) layup with straight fibers, providing a baseline for comparing the performance of the variable stiffness panels. Parametric finite element analyses including nonlinear material shear are first compared with material characterization test results for two orthotropic layups. This nonlinear material model is incorporated into structural analysis models of the variable stiffness and baseline panels with applied end shortenings. Measured geometric imperfections and mechanical prestresses, generated by forcing the variable stiffness panels from their cured anticlastic shapes into their flatter test configurations, are also modeled. Results of these structural analyses are then compared to the measured panel structural response. Good correlation is observed between the analysis results and displacement test data throughout deep postbuckling up to global failure, suggesting that nonlinear material behavior is an important component of the actual panel structural response.

Wu, K. Chauncey↗

A Treatise on Equivalent-Plate Stiffnesses for Stiffened Laminated-Composite Plates and Plate-Like Lattices

A survey of studies conducted since 1914 on the use of equivalent-plate stiffnesses in modeling the overall, stiffness-critical response of stiffened plates and shells is presented. Two detailed, comprehensive derivations of first-approximation equivalent-plate stiffnesses are also presented that are based on the Reissner-Mindlin-type, first-order transverse-shear deformation theory for anisotropic plates. Equivalent-plate stiffness expressions, and a corresponding symbolic manipulation computer program, are also presented for several different stiffener configurations. These expressions are very general and exhibit the full range of anisotropies permitted by the Reissner-Mindlin-type, first-order transverse-shear deformation theory for anisotropic plates. The expressions presented in the present study were also compared with available, previously published results. For the most part, the previously published results are for special cases of the general expressions presented herein and are almost in complete agreement. Analysis is also presented that extends the use of the equivalent-plate stiffness expressions to sandwich plates.

Nemeth, Michael P.↗

Sources of Uncertainty in Ultrasonic Phase-Based Assessment of Interfacial Stiffness in Adhesive Joints

Quantitative nondestructive evaluation (NDE) of adhesive joint strength is critical for certifying fastener-free bonded aerospace structures. Unfortunately, available adhesive NDE approaches are only suitable for detecting gross defects and delamination and cannot reliably detect variations in strength in intact bonds. Intact (i.e., nominally defect free) bonds are challenging to inspect because they, by definition, contain no macroscopic defects that would produce a strong NDE signature. Even in the absence of obvious defects, however, bond strength can vary substantially due to factors such as contamination, variations in the adhesive cure processes, and environmental exposure. For ultrasonic bond inspections, the effect of interactions from an imperfect adhesive interface are subtle and may include changes in the frequency content or phase of the ultrasonic signal. The bond condition can be deduced from these subtle changes in the acoustic response using an accompanying physics-based model of adhesive joint interaction. For example, researchers have used the spring network adhesion model of Baik and Thompson [1] to determine the interfacial stiffness of the joint from its ultrasonic response (e.g., [2]). This interfacial stiffness metric describes the bonds resistance to separation between the adhesive and adherent and has shown a strong correlation with joint strength. In this study, interfacial stiffness is assessed using the ultrasonic phase change associated with bond interaction in varying bond conditions. The phase change is measured precisely using a phase-locked-loop instrument over a swept range of frequencies. The phase transition at resonance, where the bond thickness is half the acoustic wavelength, produces a unique signature with which to fit a physics-based model. Interfacial stiffness is determined by minimizing the difference between the theoretical and experimental phase response. Experimental results are presented for glass specimens bonded with aerospace adhesives and a sensitivity analysis is performed to examine the effects of parameters that may be uncertain in the industrial inspection environment – namely bond thickness, adhesive and adherent properties, and porosity. The results are a first step toward an uncertainty quantified version of the measurement technique, show correlation between interfacial stiffness and bond strength, and are another key step toward maturing this approach for use in complex materials and joint geometries. [1] Baik, J.M. and Thompson, R.B., 1984. “Ultrasonic scattering from imperfect interfaces: a quasi-static model”. Journal of Nondestructive Evaluation, 4. [2] Haldren, H.A., Perey, D.F., Yost, W.T., Cramer, K.E., and Gupta, M.C., 2019. “Swept-frequency ultrasonic phase evaluation of adhesive bonding in tri-layer structures”. Journal of the Acoustical Society of America, 145.

Matt Webster↗

Synthesis of stiffness and mass matrices from experimental vibration modes.

With highly complex structures, it is sometimes desirable to derive a dynamic model of the system from experimental vibration data. This paper presents algorithms for synthesizing the mass and stiffness matrices from experimentally derived modal data in a way which preserves the physical significance of the individual mass and stiffness elements. The synthesizing procedures allow for the incorporation of other mass and stiffness data, whether empirical or based on the analyst's insight. The mass and stiffness matrices are derived for a cantilever beam example and are compared with those obtained using earlier techniques.

Ross, R. G., Jr.↗

Wing/store flutter with nonlinear pylon stiffness

Recent wind tunnel tests and analytical studies show that a store mounted on a pylon with soft pitch stiffness provides substantial increase in flutter speed of fighter aircraft and reduces dependency of flutter on mass and inertia of the store. This concept, termed the decoupler pylon, utilizes a low frequency control system to maintain pitch alignment of the store during maneuvers and changing flight conditions. Under rapidly changing transient loads, however, the alignment control system may allow the store to momentarily bottom against a relatively stiff backup structure in which case the pylon stiffness acts as a hardening nonlinear spring. Such structural nonlinearities are known to affect not only the flutter speed but also the basic behavior of the instability. The influence of pylon stiffness nonlinearities or the flutter characteristics of wing mounted external stores is examined.

Desmarais, R. N.↗

Wing/store flutter with nonlinear pylon stiffness

Recent wind tunnel tests and analytical studies show that a store mounted on a pylon with 'soft' pitch stiffness provides substantial increase in flutter speed of fighter aircraft and reduces dependency of flutter on mass and inertia of the store. This concept, termed the decoupler pylon, utilizes a low-frequency control system to maintain pitch alignment of the store during maneuvers and changing flight conditions. Under rapidly changing transient loads, however, the alignment control system may allow the store to momentarily bottom against a relatively stiff backup structure in which case the pylon stiffness acts as a hardening nonlinear spring. Such structural nonlinearities are known to affect not only the flutter speed but also the basic behavior of the instability. This paper examines the influence of pylon stiffness nonlinearities on the flutter characteristics of wing-mounted external stores.

Desmarais, R. N.↗

Determination of ball bearing dynamic stiffness

The dynamic radial stiffness characteristics of rolling element bearings are currently determined by analytical methods that have not been experimentally verified. These bearing data are vital to rotating machinery design integrity because accurate critical speeds and rotor stability predictions are highly dependent on the bearing stiffness. A tester was designed capable of controlling the bearing axial preload, speed, and rotor unbalance. The rotor and support structures were constructed to permit critical speeds that are predominantly determined by a 57 mm test bearing. A curve of calculated critical speed versus stiffness was used to determine the actual bearing stiffness from the empirical data. The results of extensive testing are used to verify analytical predictions, increase confidence in existing bearing computer programs, and to serve as a data base for efforts to correct these programs.

Beatty, R. F.↗

Bending Stiffness of Multiwall Sandwich

An analytical and experimental study was carried out to understand the extensional and flexural behavior of multiwall sandwich, a metallic insulation composed of alternate layers of flat and dimpled foil. The multiwall sandwich was structurally analyzed by using several simplifying assumptions combined with a finite element analysis. The simplifying assumptions made in this analysis were evaluated by bending and tensile tests. Test results validate the assumption that flat sheets in compression do not significantly contribute to the flexural stiffness of multiwall sandwich for the multiwall geometry tested. However, calculations show that thicker flat sheets may contribute significantly to bending stiffness and cannot be ignored. Results of this analytical approach compare well with test data; both show that the extensional stiffness of the dimpled sheet in he 0 deg direction is about 30 percent of that for a flat sheet, and that in the 45 deg direction, it is about 10 percent. The analytical and experimental multiwall bending stiffness showed good agreement for the particular geometry tested.

Blosser, M. L.↗

Stiffness Properties for Dynamic Modeling of Composite Graphite-Epoxy Cylindrical Orthotropic Shells

Traditional composite lamination theory was used to predict composite graphite-epoxy laminate stiffnesses for comparison to quasi-experimental stiffnesses developed from cylindrical bottle pressure testing. Stiffness sensitivities were examined for variations in constituent materials and geometric properties. The material component interactions examined were the fiber longitudinal and transverse Young's modulus, the fiber shear modulus and primary Poisson's ratio, the resin Young's modulus, shear modulus, and Poisson's ratio. The geometric variation of the helical winding angle was also examined. Two computer programs were written to generate the data used to demonstrate the stiffness variations.

Tolbert, R. N.↗

Use of optimum stiffness tailoring to improve the compressive strength of composite plates with holes

A structural optimization procedure is used to tailor the cross-sectional stiffness distribution of compression-loaded composite plates with holes. Minimum mass designs are obtained for plates with cross sections consisting of two different balanced symmetric laminates with 0 deg, + or - 45 deg and 90 deg plies. The plate interior region contains the hole and is designed from a softer material system with a higher failure strain than the plate exterior region. All-graphite-epoxy plates and hybrid graphite/glass-epoxy plates were studied. Other designs with different percentages of 0 deg and + or 45 deg plies in the exterior laminate are compared with the optimum designs. Designs with uniform cross-sectional stiffnesses also are compared with the tailored cross-sectional stiffness designs. Specimens of each design were tested to verify the analytical predictions. The results show that cross-sectional stiffness tailoring can increase the compressive strength and decrease the mass of compression-loaded laminated plates with holes.

Haftka, R. T.↗

The effects of thermal cycling on matrix cracking and stiffness changes in composite tubes

The study investigated the accumulation of transverse matrix cracks and the resultant loss of torsional, extensional, and bending stiffnesses in 8 layer 0.5 in. diameter crossply tubes subjected to thermal cycling. The tubes were graphite-epoxy and the temperature range during cycling was -250 to 200 F. The effect of fiber and matrix properties was investigated through the use of T300 and P75S fibers and 934 and CE339 resins. The study considered 0, 10, 50, 100, 300, and 500 thermal cycles. Photomicrographs, X-rays, and edge replication were used to evaluate cracking. Special loading fixtures were used to measure stiffness changes. An important finding was that for the tubes studied, even with extensive cracking, the bending and extensional stiffnesses were not affected. The torsional stiffness, however, was strongly affected.

Cohen, D.↗

Semi-implicit and fully implicit shock-capturing methods for hyperbolic conservation laws with stiff source terms

Some numerical aspects of finite-difference algorithms for nonlinear multidimensional hyperbolic conservation laws with stiff nonhomogenous (source) terms are discussed. If the stiffness is entirely dominated by the source term, a semi-implicit shock-capturing method is proposed provided that the Jacobian of the soruce terms possesses certain properties. The proposed semi-implicit method can be viewed as a variant of the Bussing and Murman point-implicit scheme with a more appropriate numerical dissipation for the computation of strong shock waves. However, if the stiffness is not solely dominated by the source terms, a fully implicit method would be a better choice. The situation is complicated by problems that are higher than one dimension, and the presence of stiff source terms further complicates the solution procedures for alternating direction implicit (ADI) methods. Several alternatives are discussed. The primary motivation for constructing these schemes was to address thermally and chemically nonequilibrium flows in the hypersonic regime. Due to the unique structure of the eigenvalues and eigenvectors for fluid flows of this type, the computation can be simplified, thus providing a more efficient solution procedure than one might have anticipated.

Yee, H. C.↗

Semi-implicit and fully implicit shock-capturing methods for hyperbolic conservation laws with stiff source terms

Some numerical aspects of finite-difference algorithms for nonlinear multidimensional hyperbolic conservation laws with stiff nonhomogeneous (source) terms are discussed. If the stiffness is entirely dominated by the source term, a semi-implicit shock-capturing method is proposed provided that the Jacobian of the source terms possesses certain properties. The proposed semi-implicit method can be viewed as a variant of the Bussing and Murman point-implicit scheme with a more appropriate numerical dissipation for the computation of strong shock waves. However, if the stiffness is not solely dominated by the source terms, a fully implicit method would be a better choice. The situation is complicated by problems that are higher than one dimension, and the presence of stiff source terms further complicates the solution procedures for alternating direction implicit (ADI) methods. Several alternatives are discussed. The primary motivation for constructing these schemes was to address thermally and chemically nonequilibrium flows in the hypersonic regime. Due to the unique structure of the eigenvalues and eigenvectors for fluid flows of this type, the computation can be simplified, thus providing a more efficient solution procedure than one might have anticipated.

Yee, H. C.↗