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At least 199 records · Page 11

The crack problem in a reinforced cylindrical shell

In this paper a partially reinforced cylinder containing an axial through crack is considered. The reinforcement is assumed to be fully bonded to the main cylinder. The composite cylinder is thus modelled by a nonhomogeneous shell having a step change in the elastic properties at the z=0 plane, z being the axial coordinate. Using a Reissner type transverse shear theory the problem is reduced to a pair of singular integral equations. In the special case of a crack tip touching the bimaterial interface it is shown that the dominant parts of the kernels of the integral equations associated with both membrane loading and bending of the shell reduce to the generalized Cauchy kernel obtained for the corresponding plane stress case. The integral equations are solved and the stress intensity factors are given for various crack and shell dimensions. A bonded fiberglass reinforcement which may serve as a crack arrestor is used as an example.

Yahsi, O. S.↗

The elastic layer with a cylindrical hole subjected to a nonuniform axisymmetric radial displacement.

A problem in the linear theory of elasticity is considered wherein a layer with a circular cylindrical hole is subjected to a nonuniform axisymmetric radial displacement. The solution utilizes Navier's equations of elasticity which are solved by means of extended Hankel transforms. A special case in which the radial displacement is a linear function of the axial coordinate is presented. Numerical results are given in graphical form for the case when hole radius and layer thickness are equal. The inversion integrals were evaluated numerically using Longman's technique for computing infinite integrals of oscillatory functions.

Grissom, D. S.↗

Resolution of Tolerance Variations

The connector/adapter assembly (CAA) is one component of a higher-level assembly. A simplified representation of the CAA is illustrated in Figure 1. The location of each CAA is required to meet a specific positional requirement. Several CAAs have been measured and found to be out of tolerance. The connector and the adapter are welded to each other such that the cylindrical axes of the two components are coaxial. The positional tolerance condition requires that all points on the outer surface of the CAA must be within a defined maximum diameter, as illustrated in Figure 1. Two different methods have been developed to measure the CAA positions from coordinate measuring machine (CMM) data. One method (RevD) extrapolates the data from two circles approximately midway from the weld region to each end. The second method (RevF) measures points that are much closer to the actual ends.

42 ENGINEERING↗

Effects of Model Uncertainties in Underground Chemical Explosions on Far-field Results

We used the CTH shock physics code to simulate the explosion of an 18-t chemical explosive at a depth of 250 m. We used the CTH in the two-dimensional axisymmetric (cylindrical) geometry (2DC) and most simulations included fully tamped explosions in wet tuff. Our study focused on parametric studies of three of the traditional strength models available in CTH, namely, geologic-yield, elastic perfectly-plastic von Mises, and Johnson-Cook strength (flow stress) models. We processed CTH results through a code that generates Reduced Displacement Potential (RDP) histories for each simulation. Since RDP is the solution of the linear wave equation in spherical coordinates, it is mainly valid at far-enough distance from the explosion the elastic radius. Among various parameters examined, we found the yield strength to have the greatest effect on the resulting RDP, where the peak RDP reduces almost linearly in log-log space as the yield strength increases. Moreover, an underground chemical explosion results in a cavity whose final diameter is inversely proportional to the material yield strength, i.e., as the material's yield strength increases the resulting final cavity radius decreases. Additionally, we found the choice of explosive material (COMP-C4 versus COMP-B) has minor effects on the peak RDP, where denser COMP-C4 shows higher peak RDP than the less dense COMP-B by a factor of ~1.1. In addition to wet tuff, we studied explosions in dry tuff, salt, and basalt, for a single strength model and yield strength value. We found wet tuff has the highest peak RDP value, followed by dry tuff, salt, and basalt. 2DC simulations of explosions in 11 m radius spherical, hemispherical, and cylindrical cavities showed the RDP signals have much lower magnitude than tamped explosions, where the cavity explosions mimicked nearly decoupled explosions.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

Investigating Lignin Aggregation and Interactions with Solvents during γ-Valerolactone (GVL) Pretreatment: A Combined Small Angle Neutron Scattering and Molecular Simulations Study

The strong tendency of lignin to aggregate in solution, coupled with limited understanding of how its molecular structure governs this behavior, hinders its effective utilization in biorefineries. Here, in this study, we investigated the solution behavior of lignin extracted from poplar using γ-valerolactone/water (GVL/H2O, 9:1 wt/wt) through combined small-angle neutron scattering (SANS) and molecular dynamics (MD) simulations. Lignin samples obtained at 100 °C (L100) and 120 °C (L120) differed in β–O–4 content, hydroxyl distribution, and S/G ratio, enabling direct assessment of how molecular composition governs solvation and aggregation. SANS showed that L120 formed rigid and elongated cylindrical aggregates at 25 °C that transitioned to more flexible spheroidal structures by 50 °C and remained stable up to 80 °C, whereas L100 adopted globular aggregates that progressively collapsed with increasing temperature. MD simulations reinforced these observations by showing that S-rich (L120-like) oligomers had larger radii of gyration, stronger solvent coordination driven by methoxy groups, and fewer lignin–lignin contacts. In contrast, G-rich (L100-like) oligomers displayed persistent aggregation and lower solubility. Collectively, these results reveal that increased aromatic methoxylation enhances lignin–solvent interactions and suppresses self-association, whereas reduced methoxylation and higher β–O–4 content promote persistent aggregation into colloid-like structures with restricted solvent penetration into the aggregate interior.

biorefinery pretreatment↗

Vibrations of blades with variable thickness and curvature by shell theory

A procedure for analyzing the vibrations of rotating turbomachinery blades has been previously developed. This procedure is based upon shallow shell theory, and utilizes the Ritz method to determine frequencies and mode shapes. However, it has been limited heretofore to blades of uniform thickness, uniform curvature, and/or twist and rectangular planform. The present work shows how the procedure may be generalized to eliminate the aforementioned restrictions. Nonrectangular planforms are dealt with by a suitable coordinate transformation. This, as well as variable thickness, curvature and twist, require using numerical integration. The procedure is demonstrated on four examples of cantilevered blades for which theoretical and experimental data have been previously published: (1) flat plate with spanwise taper, (2) flat plate with chordwise taper, (3) twisted plate with chordwise taper, and (4) cylindrical shell with chordwise taper.

Lee, J. K.↗

Compression strength of composite primary structural components

The linear elastic response is determined for an internally pressurized, long circular cylindrical shell stiffened on the inside by a regular arrangement of identical stringers and identical rings. Periodicity of this configuration permits the analysis of a portion of the shell wall centered over a generic stringer-ring joint; i.e., a unit cell model. The stiffeners are modeled as discrete beams, and the stringer is assumed to have a symmetrical cross section and the ring an asymmetrical section. Asymmetery causes out-of-plane bending and torsion of the ring. Displacements are assumed as truncated double Fourier series plus simple terms in the axial coordinate to account for the closed and pressure vessel effect (a non-periodic effect). The interacting line loads between the stiffeners and the inside shell wall are Lagrange multipliers in the formulation, and they are also assumed as truncated Fourier series. Displacement continuity constraints between the stiffeners and shell along the contact lines are satisfied point-wise. Equilibrium is imposed by the principle of virtual work. A composite material crown panel from the fuselage of a large transport aircraft is the numerical example. The distributions of the interacting line loads, and the out-of-plane bending moment and torque in the ring, are strongly dependent on modeling the deformations due to transverse shear and cross-sectional warping of the ring in torsion. This paper contains the results from the semiannual report on research on 'Pressure Pillowing of an Orthogonally Stiffened Cylindrical Shell'. The results of the new work are illustrated in the included appendix.

Johnson, Eric R.↗

The coupling effects of kinematics and flexibility on the Lagrangian dynamic formulation of open chain deformable links

A nonlinear Lagrangian formulation for the spatial kinematic and dynamic analysis of open chain deformable links consisting of cylindrical joints that connect pairs of flexible links is developed. The special cases of revolute or prismatic joint can also be obtained from the kinematic equations. The kinematic equations are described using a 4x4 matrix method. The configuration of each deformable link in the open loop kinematic chain is identified using a coupled set of relative joint variables, constant geometric parameters, and elastic coordinates. The elastic coordinates define the link deformation with respect to a selected joint coordinate system that is consistent with the kinematic constraints on the boundary of the deformable link. These coordinates can be introduced using approximation techniques such as Rayleigh-Ritz method, finite element technique or any other desired approach. The large relative motion between two neighboring links are defined by a set of joint coordinates which describes the large relative translational and rotational motion between two neighboring joint coordinate systems. The origin of these coordinate systems are rigidly attached to the neighboring links at the joint definition points along the axis of motion.

Changizi, Koorosh↗

On the question of instabilities upstream of cylindrical bodies

In an attempt to understand the unsteady vortical phenomena in perturbed stagnation regions of cylindrical bodies, a critical review of the theoretical and experimental evidence was made. Current theory is revealed to be incomplete, incorrect, or inapplicable to the phenomena observed experimentally. The formalistic approach via the principle of exchange of instabilities should most likely be replaced by a forced-disturbance approach. Also, many false conclusions were reached by ignoring that treatment of the base and perturbed flows in Hiemenz coordinate eta is asymptotic in nature. Almost surely the techniques of matched asymptotic expansions are expected to be used to capture correctly the diffusive and vorticity amplifying processes of the disturbances regarding the mean-flow boundary layer and outer potential field as eta and y/diameter approach infinity. The serious uncertainties in the experiments are discussed in detail.

Morkovin, M. V.↗

Propellant Densification Ground Testing Conducted for Launch Vehicles

The NASA Glenn Research Center at Lewis Field has taken the lead in the development of practical densified cryogenic propellants for launch vehicle applications. The technology of subcooling cryogenic propellants below their normal boiling point to produce a denser fluid is one of the key process technologies necessary to meet the challenge of single-stage-to-orbit and reusable launch vehicles. Densified propellants are critical to lowering launch costs because they enable more propellant to be packed into a given unit volume, thus improving the performance by reducing the overall size and weight of the launch vehicle. This two-pronged research and test program has evolved into (1) conducting tank loading tests using densified liquid hydrogen and (2) developing two large-scale propellant densification systems that will be performance tested next year at Glenn. The propellant-loading test program was undertaken at Glenn in coordination with Lockheed Martin Michoud Space Systems. In this testing, the liquid hydrogen recirculation and densification process was simulated, and the thermal stratification of the densified propellant was recorded throughout the tank. The test article was a flight-weight tank constructed from composite materials similar to those to be used on the X-33 launch vehicle. The tank geometry as designed by Lockheed Martin had two cylindrical lobes with a center septum. Liquid hydrogen flow rate, pressure data, and temperature data plotted over time were collected while the subscale tank was filled with 27 R (15 K) densified liquid hydrogen propellant. This testing has validated mathematical models and demonstrated the readiness of densified propellant technology for near-term use. It marks the first time that such a process has been carried out with a multiple-lobe, flight-similar tank. Glenn researchers have also been working on providing a process and critical test data for the continuous production of densified liquid hydrogen (LH2) and densified liquid oxygen (LO2). Each densification production process uses a high-efficiency, subatmospheric boiling bath heat exchanger to cool the working fluid. A near triple-point hydrogen boiling bath is used to condition and subcool hydrogen to 27 R (15 K), and a nitrogen boiling bath is used to cool the liquid oxygen to 120 R (66.7 K). Multistage centrifugal compressors operating at cryogenic inlet conditions maintain the heat exchanger bath vapor pressure below 1 atm. The LO2 propellant densification unit shown in the photograph has a 30 lb/sec capacity, whereas the LH2 unit was designed to process 8 lb/sec of propellant. Each densification unit will be transported to Glenn's South Forty area after all fabrication work is completed sometime late next year. There the LO2 and LH2 densifier performance tests will be conducted with another larger Lockheed Martin tank designated the Structural Test Article (STA). This liquid oxygen tank is a full-scale, flight-weight, prototype aluminum tank designed for the X-33. It has a capacity of 20,000 gallons of LO2. The tank loading and recirculation testing planned for next year with STA will provide the data necessary for full-scale development of propellant densification technology.

Tomsik, Thomas M.↗

Development of a CFD Code for Analysis of Fluid Dynamic Forces in Seals

The aim is to develop a 3-D computational fluid dynamics (CFD) code for the analysis of fluid flow in cylindrical seals and evaluation of the dynamic forces on the seals. This code is expected to serve as a scientific tool for detailed flow analysis as well as a check for the accuracy of the 2D industrial codes. The features necessary in the CFD code are outlined. The initial focus was to develop or modify and implement new techniques and physical models. These include collocated grid formulation, rotating coordinate frames and moving grid formulation. Other advanced numerical techniques include higher order spatial and temporal differencing and an efficient linear equation solver. These techniques were implemented in a 2D flow solver for initial testing. Several benchmark test cases were computed using the 2D code, and the results of these were compared to analytical solutions or experimental data to check the accuracy. Tests presented here include planar wedge flow, flow due to an enclosed rotor, and flow in a 2D seal with a whirling rotor. Comparisons between numerical and experimental results for an annular seal and a 7-cavity labyrinth seal are also included.

Athavale, Mahesh M.↗

Near-Net Forging Technology Demonstration Program

Significant advantages in specific mechanical properties, when compared to conventional aluminum (Al) alloys, make aluminum-lithium (Al-Li) alloys attractive candidate materials for use in cryogenic propellant tanks and dry bay structures. However, the cost of Al-Li alloys is typically five times that of 2219 aluminum. If conventional fabrication processes are employed to fabricate launch vehicle structure, the material costs will restrict their utilization. In order to fully exploit the potential cost and performance benefits of Al-Li alloys, it is necessary that near-net manufacturing methods be developed to off-set or reduce raw material costs. Near-net forging is an advanced manufacturing method that uses elevated temperature metal movement (forging) to fabricate a single piece, near-net shape, structure. This process is termed 'near-net' because only a minimal amount of post-forge machining is required. The near-net forging process was developed to reduce the material scrap rate (buy-to-fly ratio) and fabrication costs associated with conventional manufacturing methods. The goal for the near-net forging process, when mature, is to achieve an overall cost reduction of approximately 50 percent compared with conventional manufacturing options for producing structures fabricated from Al-Li alloys. This NASA Marshall Space Flight Center (MSFC) sponsored program has been a part of a unique government / industry partnership, coordinated to develop and demonstrate near-net forging technology. The objective of this program was to demonstrate scale-up of the near-net forging process. This objective was successfully achieved by fabricating four integrally stiffened, 170- inch diameter by 20-inch tall, Al-Li alloy 2195, Y-ring adapters. Initially, two 2195 Al-Li ingots were converted and back extruded to produce four cylindrical blockers. Conventional ring rolling of the blockers was performed to produce ring preforms, which were then contour ring rolled to produce 'contour preforms'. All of the contour preforms on this first-of-a-kind effort were imperfect, and the ingot used to fabricate two of the preforms was of an earlier vintage. As lessons were learned throughout the program, the tooling and procedures evolved, and hence the preform quality. Two of the best contour preforms were near- net forged to produce a process pathfinder Y-ring adapter and a 'mechanical properties pathfinder' Y-ring adapter. At this point, Lockheed Martin Astronautics elected to procure additional 2195 aluminum-lithium ingot of the latest vintage, produce two additional preforms, and substitute them for older vintage material non-perfectly filled preforms already produced on this contract. The existing preforms could have been used to fulfill the requirements of the contract.

Hall, I. Keith↗

Low-Velocity Impact Response of Sandwich Beams with Functionally Graded Core

The problem of low-speed impact of a one-dimensional sandwich panel by a rigid cylindrical projectile is considered. The core of the sandwich panel is functionally graded such that the density, and hence its stiffness, vary through the thickness. The problem is a combination of static contact problem and dynamic response of the sandwich panel obtained via a simple nonlinear spring-mass model (quasi-static approximation). The variation of core Young's modulus is represented by a polynomial in the thickness coordinate, but the Poisson's ratio is kept constant. The two-dimensional elasticity equations for the plane sandwich structure are solved using a combination of Fourier series and Galerkin method. The contact problem is solved using the assumed contact stress distribution method. For the impact problem we used a simple dynamic model based on quasi-static behavior of the panel - the sandwich beam was modeled as a combination of two springs, a linear spring to account for the global deflection and a nonlinear spring to represent the local indentation effects. Results indicate that the contact stiffness of thc beam with graded core Increases causing the contact stresses and other stress components in the vicinity of contact to increase. However, the values of maximum strains corresponding to the maximum impact load arc reduced considerably due to grading of thc core properties. For a better comparison, the thickness of the functionally graded cores was chosen such that the flexural stiffness was equal to that of a beam with homogeneous core. The results indicate that functionally graded cores can be used effectively to mitigate or completely prevent impact damage in sandwich composites.

Apetre, N. A.↗

Numerical procedure for three-dimensional hypersonic viscous flow over aerobrake configuration

A numerical method, which is simpler and more efficient than others currently in use, is proposed for the computation of the full viscous flow over an aerobrake body in hypersonic stream at high altitude. It treats the shock layer surrounding the blunt forebody and the near wake behind the base simultaneously by formulating the Navier-Stokes equations in conformal and azimuthal-angle coordinates. The computational domain is confined by the body wall, outflow surface and the shock, which is adjusted along the coordinate normal to the wall in the course of iterations. Because of the optimal grid and a well developed alternating direction implicit factorization technique for the governing equations, reasonably accurate results can be obtained with a 28 x 36 x 7 grid and 400 time-marching iterations. Excellent agreement of shock location is found between the present result and the schlieren photograph. Details of the base flow and shear layer impingement on the cylindrical aft body are presented for an adiabatic wall case.

Li, C. P.↗

Analytical and experimental study of a standing torus with normal loads

Finite element analysis is applied to study the large deflection and stress of a thin-walled pressurized torus loaded by normal contact with a plane. Experimentally determined stresses are compared to those resulting from finite element analysis at various meridional and circumferential coordinates of the torus, including the footprint area. Circumferential strains compare favorably while meridional strains are higher in the finite element analysis, probably due to slippage of the boundary at the rim. The STAGS finite element computer program was used. The purpose of the study was to evaluate the various program options for structural loading, for material modeling, for stress analysis, and for grid refinement. The experimental model, a thin-walled rubber tube mounted on a steel cylindrical rim, provided measured results to compare with various analytical trade-offs. It was found that there was almost no difference in predicted deflections or stress distributions between linear and nonlinear material description. However, the difference between linear analysis and that of geometric nonlinearities utilizing incremental loading was marked.

Mack, M. J., Jr.↗

Coupled mixed-field laminate theory and finite element for smart piezoelectric composite shell structures

Mechanics for the analysis of laminated composite shells with piezoelectric actuators and sensors are presented. A new mixed-field laminate theory for piezoelectric shells is formulated in curvilinear coordinates which combines single-layer assumptions for the displacements and a layerwise representation for the electric potential. The resultant coupled governing equations for curvilinear piezoelectric laminates are described. Structural mechanics are subsequently developed and an 8-node finite-element is formulated for the static and dynamic analysis of adaptive composite structures of general laminations containing piezoelectric layers. Evaluations of the method and comparisons with reported results are presented for laminated piezoelectric-composite plates, a closed cylindrical shell with a continuous piezoceramic layer and a laminated composite semi-circular cantilever shell with discrete cylindrical piezoelectric actuators and/or sensors.

Saravanos, Dimitris A.↗

Taylor wave solution for a general equation of state

This document describes a solution procedure for calculating the Taylor wave behind an unsupported Chapman–Jouguet (CJ) detonation in planar, cylindrical, and spherical geometries given a general equation of state. The resulting semi-analytic solution can be utilized to examine new equation of state models for detonation products and during the verification of hydrodynamic codes. The governing partial differential equations are reduced to ordinary differential equations in both characteristic and self-similar forms. The first-order systems corresponding to each geometry are amenable to solution numerically using commonly available methods. A difficulty arises at the CJ point in radial coordinates where the similarity equations become singular. Two separate strategies are proposed to integrate the first-order system. The first one uses an asymptotic approximation near the CJ point that can be used to perturb the boundary conditions. The second one applies a change of variables which removes the singularity at the expense of an additional equation to be integrated. A test problem is provided for the Davis products equation of state to illustrate the qualitative features of the Taylor wave in each geometric configuration and compared with a Lagrangian hydrodynamics research code. A Python code listing gives an implementation using the SciPy library to assists users in generating the results.

97 MATHEMATICS AND COMPUTING↗