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Results for “EQUATIONS - STRESSES PLATES”

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At least 199 records · Page 11

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DOE OSTI2022

Dimensionless parameters to categorize the failure modes of ductile plate perforation

In this work, two dimensionless parameters were derived organically from impact mechanics equations to remove the need for empirical constants. These two dimensionless parameters effectively collapse the ballistic performance of ductile metal plates along two distinct loci, depending on the projectile geometry and the corresponding failure mode. Projectiles that initiate ductile hole enlargement via cavity expansion fall along a linear curve, while shear-plugging failure modes tend to fall along a cubic curve. Results were demonstrated for various projectiles of different calibers impacting aluminum and Ti-6Al-4V alloys. The main advantage of the approach in this work is to drastically reduce the number of features for input into machine learning algorithms.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Dimensionless parameters to categorize the failure modes of ductile plate perforation

In this work, two dimensionless parameters were derived organically from impact mechanics equations to remove the need for empirical constants. These two dimensionless parameters effectively collapse the ballistic performance of ductile metal plates along two distinct loci, depending on the projectile geometry and the corresponding failure mode. Projectiles that initiate ductile hole enlargement via cavity expansion fall along a linear curve, while shear-plugging failure modes tend to fall along a cubic curve. Results were demonstrated for various projectiles of different calibers impacting aluminum and Ti-6Al-4V alloys, and further explored for more complex target combinations. The main advantage of the approach in this work is to drastically reduce the number of features for input into machine learning algorithms.

36 MATERIALS SCIENCE↗

NASA NTRS1983

Natural vibrations of laminated anisotropic plates using three-dimensional elasticity theory

The paper contains a description of the three-dimensional elasticity equations and the associated finite element model for natural vibrations of laminated anisotropic rectangular plates. The numerical results for natural frequencies are compared with those obtained by a shear deformable plate theory. A number of cross-ply and angle-ply rectangular plates are analyzed for natural frequencies. For relatively thick plates, the shear deformable-plate theory element predicts frequencies higher than those predicted by the three-dimensional elasticity theory element.

Reddy, J. N.↗

NASA NTRS1984

Statistical tests of additional plate boundaries from plate motion inversions

The application of the F-ratio test, a standard statistical technique, to the results of relative plate motion inversions has been investigated. The method tests whether the improvement in fit of the model to the data resulting from the addition of another plate to the model is greater than that expected purely by chance. This approach appears to be useful in determining whether additional plate boundaries are justified. Previous results have been confirmed favoring separate North American and South American plates with a boundary located beween 30 N and the equator. Using Chase's global relative motion data, it is shown that in addition to separate West African and Somalian plates, separate West Indian and Australian plates, with a best-fitting boundary between 70 E and 90 E, can be resolved. These results are generally consistent with the observation that the Indian plate's internal deformation extends somewhat westward of the Ninetyeast Ridge. The relative motion pole is similar to Minster and Jordan's and predicts the NW-SE compression observed in earthquake mechanisms near the Ninetyeast Ridge.

Stein, S.↗

NASA NTRS2008

Balanced Flow Measurement and Conditioning Technology (Balanced Orifice Plate 7,051,765 B1) for NASA Inventions and Contributions Board Invention of the Year Evaluation

This viewgraph document reviews the Balanced Flow Measurement (BFM) and Conditioning Technology, and makes the case for this as the NASA Invention of the Year. The BFM technology makes use of a thin, multi-hole orifice plate with holes sized and placed per a unique set of equations. It produces mass flow, volumetric flow,kinelic energy,or momentum BALANCE across the face of the plate. The flow is proportional.to the square root of upstream to downstream differential pressure. Multiple holes lead to smoother pressure measurement. Measures and conditions or can limit fluid flow. This innovation has many uses in and out of NASA.

Kelley, Anthony R.↗

NASA NTRS1980

Acoustic plane waves incident on an oblique clamped panel in a rectangular duct

The theory of acoustic plane waves incident on an oblique clamped panel in a rectangular duct was developed from basic theoretical concepts. The coupling theory between the elastic vibrations of the panel (plate) and the oblique incident acoustic plane wave in infinite space was considered in detail, and was used for the oblique clamped panel in the rectangular duct. The partial differential equation which governs the vibrations of the clamped panel (plate) was modified by adding to it stiffness (spring) forces and damping forces. The Transmission Loss coefficient and the Noise Reduction coefficient for oblique incidence were defined and derived in detail. The resonance frequencies excited by the free vibrations of the oblique finite clamped panel (plate) were derived and calculated in detail for the present case.

Unz, H.↗

NASA NTRS1986

Radiative and free-convective heat transfer from a finite horizontal plate inside an enclosure

An experimental and analytical investigation of heat transfer from a horizontal, thin, square plate inside of an enclosure was carried out. Experimental results were obtained from both the upward-facing and the downward-facing sides of the heated plate. Starting with the integrated momentum and energy equations, approximate solutions were obtained for heat transfer in the laminar and the turbulent regime that correlate well with experimental data. Radiative heat transfer correction was given special attention. Effects of the enclosure-related recirculation of the test fluid, as well as effects of simultaneous heat transfer on both sides of the plate, caused an early transition, and indicated a high level of internal turbulence.

Hrycak, Peter↗

DOE OSTI2024

Diffusioosmotic flow reversals due to ion–ion electrostatic correlations

Existing theories of diffusioosmosis have neglected ion–ion electrostatic correlations, which are important in concentrated electrolytes. Here, we develop a mathematical model to numerically compute the diffusioosmotic mobilities of binary symmetric electrolytes across low to high concentrations in a charged parallel-plate channel. We use the modified Poisson equation to model the ion–ion electrostatic correlations and the Bikerman model to account for the finite size of ions. We report two key findings. First, ion–ion electrostatic correlations can cause a unique reversal in the direction of diffusioosmosis. Such a reversal is not captured by existing theories, occurs at ≈ 0.4 M for a monovalent electrolyte, and at a much lower concentration of ≈ 0.003 M for a divalent electrolyte in a channel with the same surface charge. This highlights that diffusioosmosis of a concentrated electrolyte can be qualitatively different from that of a dilute electrolyte, not just in its magnitude but also its direction. Second, we predict a separate diffusioosmotic flow reversal, which is not due to electrostatic correlations but the competition between the underlying chemiosmosis and electroosmosis. This reversal can be achieved by varying the magnitude of the channel surface charge without changing its sign. However, electrostatic correlations can radically change how this flow reversal depends on the channel surface charge and ion diffusivity between a concentrated and a dilute electrolyte. Furthermore, the mathematical model developed here can be used to design diffusioosmosis of dilute and concentrated electrolytes, which is central to applications such as species mixing and separation, enhanced oil recovery, and reverse electrodialysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Effects of Accident Thermal Loading on In-Plane Shear Behavior of Steel-Plate Composite Walls

Structural walls in safety-related nuclear facilities are required to be designed for seismic and accident thermal (due to postulated high-energy pipe break events) loading combination. Current U.S. and international codes provide limited guidance for analysis and design of walls for this loading combination. This paper describes the experimental results and observations from tests conducted on a laboratory-scale (1:4 to 1:5) test unit representing steel-plate composite (SC) walls subjected to combined in-plane (seismic) and accident thermal loading. The test unit was subjected to surface temperatures of up to 450°F in combination with cyclic in-plane loading. Results of similar experiments recently conducted in Japan are also summarized (with surface temperatures up to 570°F). Surface heating combined with the low thermal conductivity and high specific heat of concrete resulted in nonlinear thermal gradients through the thickness of the specimens. These nonlinear thermal gradients and the associated self- or internal restraint led to extensive concrete cracking. This concrete cracking reduced the initial and secant stiffness of the specimens. The initial stiffness of the heated specimens reduced to 30 to 40% of the initial stiffness of the control (unheated) specimen. The secant stiffness of the heated specimens reduced up to 50% of the secant stiffness of the control (unheated) specimen. However, the in-plane shear strength of the heated SC specimens was still approximately 10 to 30% greater than the nominal in-plane shear strength calculated, for the limit state of steel plate von Mises yielding, using AISC N690 equations and measured material properties. Evaluation of the experimental results and observations suggests that the in-plane shear strength of SC walls subjected to typical accident surface temperatures (up to 570°F) can be estimated conservatively using the current provisions of AISC N690. The stiffness for accident thermal loading combinations can be considered to reduce from cracked composite stiffness at ambient temperature to fully cracked—that is, steel-only stiffness as the surface temperature increases up to typical accident value.

Construction & Building Technology↗

NASA NTRS1968

Duality in finite element methods.

Duality between basic equations and dependent variables in problems of plate stretching and bending applied to finite element method

Elias, Z. M.↗

NASA NTRS1972

Hydrodynamic water impact

The hydrodynamic impact of a falling body upon a viscous incompressible fluid was investigated by numerically solving the equations of motion. Initially the mathematical model simulated the axisymmetric impact of a rigid right circular cylinder upon the initially quiescent free surface of a fluid. A compressible air layer exists between the falling cylinder and the liquid free surface. The mathematical model was developed by applying the Navier-Stokes equations to the incompressible air layer and the incompressible fluid. Assuming the flow to be one dimensional within the air layer, the average velocity, pressure and density distributions were calculated. The liquid free surface was allowed to deform as the air pressure acting on it increases. For the liquid the normalized equations were expressed in two-dimensional cylindrical coordinates. The governing equations for the air layer and the liquid were expressed in finite difference form and solved numerically. For the liquid a modified version of the Marker-and-Cell method was used. The mathematical model has been reexamined and a new approach has recently been initiated. Essentially this consists of examining the impact of an inclined plate onto a quiesent water surface with the equations now formulated in cartesian coordinates.

Kettleborough, C. F.↗

NASA NTRS1980

The dynamics and control of large flexible space structures. Volume 3, part B: The modelling, dynamics, and stability of large Earth pointing orbiting structures

The dynamics and stability of large orbiting flexible beams, and platforms and dish type structures oriented along the local horizontal are treated both analytically and numerically. It is assumed that such structures could be gravitationally stabilized by attaching a rigid light-weight dumbbell at the center of mass by a spring loaded hinge which also could provide viscous damping. For the beam, the small amplitude inplane pitch motion, dumbbell librational motion, and the anti-symmetric elastic modes are all coupled. The three dimensional equations of motion for a circular flat plate and shallow spherical shell in orbit with a two-degree-of freedom gimballed dumbbell are also developed and show that only those elastic modes described by a single nodal diameter line are influenced by the dumbbell motion. Stability criteria are developed for all the examples and a sensitivity study of the system response characteristics to the key system parameters is carried out.

Bainum, P. M.↗

NASA NTRS1980

On the dynamics of large orbiting flexible beams and platforms oriented along the local horizontal

The dynamics and stability of large orbiting flexible beams and platforms oriented along the local horizontal are treated both analytically and numerically. It is assumed that such structures could be gravitationally stabilized by attaching a rigid lightweight dumbbell at the center of mass by a spring loaded hinge which also could provide viscous damping. For the beam it is seen that the small amplitude inplane pitch motion, dumbbell librational motion, and the anti-symmetric elastic modes are all coupled. The three dimensional equations of motion for a circular flat plate in orbit with a two-degree-of-freedom gimballed dumbbell are also developed and show that only those elastic modes described by a single nodal diameter line are influenced by the dumbbell motion. Stability criteria are developed for both examples and a parametric study of the least damped mode characteristics together with numerically simulated transient responses are carried out.

Bainum, P. M.↗

NASA NTRS1982

Implementation of a C-1 triangular element based on the P-version of the finite element method

The implementation of a computer code CONE (for C(1) continuity) based on the p-version of the finite element method is described. A hierarchic family of triangular finite elements of degree p 5 is used. This family enforces C(1)-continuity across interelement boundaries, and the code is applicable to fourth order partial differential equations in two independent variables, in particular to the biharmonic equation. Applications to several benchmark problems in plate bending are presented. Sample results are examined and compared with theoretical predictions. In particular the analysis of the bending of a rhombic plate shows a significant improvement over othr published results.

Wang, D. W.↗

NASA NTRS1985

Quantitative non-destructive testing

The work undertaken during this period included two primary efforts. The first is a continuation of theoretical development from the previous year of models and data analyses for NDE using the Optical Thermal Infra-Red Measurement System (OPTITHIRMS) system, which involves heat injection with a laser and observation of the resulting thermal pattern with an infrared imaging system. The second is an investigation into the use of the thermoelastic effect as an effective tool for NDE. As in the past, the effort is aimed towards NDE techniques applicable to composite materials in structural applications. The theoretical development described produced several models of temperature patterns over several geometries and material types. Agreement between model data and temperature observations was obtained. A model study with one of these models investigated some fundamental difficulties with the proposed method (the primitive equation method) for obtaining diffusivity values in plates of thickness and supplied guidelines for avoiding these difficulties. A wide range of computing speeds was found among the various models, with a one-dimensional model based on Laplace's integral solution being both very fast and very accurate.

Welch, C. S.↗

NASA NTRS1986

Analysis of Delamination Growth from Matrix Cracks in Laminates Subjected to Bending Loads

A major source of delamination damage in laminated composite materials is from low-velocity impact. In thin composite laminates under point loads, matrix cracks develop first in the plies, and delaminations then grow from these cracks at the ply interfaces. The purpose of this study was to quantify the combined effects of bending and transverse shear loads on delamination initiation from matrix cracks. Graphite-epoxy laminates with 90 deg. plies on the outside were used to provide a two-dimensional simulation of the damage due to low-velocity impact. Three plate bending problems were considered: a 4-point bending, 3-point bending, and an end-clamped center-loaded plate. Under bending, a matrix crack will form on the tension side of the laminate, through the outer 90 deg. plies and parallel to the fibers. Delaminations will then grow in the interface between the cracked 90 deg. ply and the next adjacent ply. Laminate plate theory was used to derive simple equations relating the total strain energy release rate, G, associated with the delamination growth from a 90 deg. ply crack to the applied bending load and laminate stiffness properties. Three different lay-ups were tested and results compared. Test results verified that the delamination always formed at the interface between the cracked 90 deg. ply and the next adjacent ply. Calculated values for total G sub c from the analysis showed good agreement for all configurations. The analysis was able to predict the delamination onset load for the cases considered. The result indicated that the opening mode component (Mode I) for delamination growth from a matrix crack may be much larger than the component due to interlaminar shear (Mode II).

Murri, G. B.↗

NASA NTRS1987

Performance studies of the multigrid algorithms implemented on hypercube multiprocessor systems

In this paper, we analyze and compare the performance on a hypercube multiprocessor of some of the major multigrid techniques used in practice. The model problem considered here is that of solving the 2-D incompressible Navier-Stokes equations representing the flow between two parallel plates. Results obtained by implementing the different multigrid schemes on an iPSC are presented. Effects on the overall performance of various parameters of the algorithms, of the partitioning strategies employed, and of some of the characteristics of the underlying architecture are discussed.

Naik, Vijay K.↗

NASA NTRS1988

Analysis of delamination growth from matrix cracks in laminates subjected to bending loads

A major source of delamination damage in laminated composite materials is from low-velocity impact. In thin composite laminates under point loads, matrix cracks develop first in the plies, and delaminations then grow from these cracks at the ply interfaces. The purpose of this study was to quantify the combined effects of bending and transverse shear loads on delamination initiation from matrix cracks. Graphite-epoxy laminates with 90 deg plies on the outside were used to provide a two-dimensional simulation of the damage due to low-velocity impact. Three plate bending problems were considered: a 4-point bending, 3-point bending, and an end-clamped center-loaded plate. Under bending, a matrix crack will form on the tension side of the laminate, through the outer 90 deg plies and parallel to the fibers. Delaminations will then grow in the interface between the cracked 90 deg ply and the next adjacent ply. Laminate plate theory was used to derive simple equations relating the total strain energy release rate, G, associated with the delamination growth from a 90 deg ply crack to the applied bending load and laminate stiffness properties. Three different lay-ups were tested and results compared. Test results verified that the delamination always formed at the interface between the cracked 90 deg ply and the next adjacent ply. Calculated values for total G sub c from the analysis showed good agreement for all configurations. The analysis was able to predict the delamination onset load for the cases considered. The result indicated that the opening mode component (Mode I) for delamination growth from a matrix crack may be much larger than the component due to interlaminar shear (Mode II).

Murri, Gretchen Bostaph↗