Results for “stress equilibrium” — Page 8

NASA NTRS1947

A Simplified Method of Elastic-Stability Analysis for Thin Cylindrical Shells

This paper develops a new method for determining the buckling stresses of cylindrical shells under various loading conditions. In part I, the equation for the equilibrium of cylindrical shells introduced by Donnell in NACA report no. 479 to find the critical stresses of cylinders in torsion is applied to find critical stresses for cylinders with simply supported edges under other loading conditions. In part II, a modified form of Donnell's equation for the equilibrium of thin cylindrical shells is derived which is equivalent to Donnell's equation but has certain advantages in physical interpretation and in ease of solution, particularly in the case of shells having clamped edges. The question of implicit boundary conditions is also considered.

Batdorf, S B↗

NASA NTRS1996

Element Library for Three-Dimensional Stress Analysis by the Integrated Force Method

The Integrated Force Method, a recently developed method for analyzing structures, is extended in this paper to three-dimensional structural analysis. First, a general formulation is developed to generate the stress interpolation matrix in terms of complete polynomials of the required order. The formulation is based on definitions of the stress tensor components in term of stress functions. The stress functions are written as complete polynomials and substituted into expressions for stress components. Then elimination of the dependent coefficients leaves the stress components expressed as complete polynomials whose coefficients are defined as generalized independent forces. Such derived components of the stress tensor identically satisfy homogenous Navier equations of equilibrium. The resulting element matrices are invariant with respect to coordinate transformation and are free of spurious zero-energy modes. The formulation provides a rational way to calculate the exact number of independent forces necessary to arrive at an approximation of the required order for complete polynomials. The influence of reducing the number of independent forces on the accuracy of the response is also analyzed. The stress fields derived are used to develop a comprehensive finite element library for three-dimensional structural analysis by the Integrated Force Method. Both tetrahedral- and hexahedral-shaped elements capable of modeling arbitrary geometric configurations are developed. A number of examples with known analytical solutions are solved by using the developments presented herein. The results are in good agreement with the analytical solutions. The responses obtained with the Integrated Force Method are also compared with those generated by the standard displacement method. In most cases, the performance of the Integrated Force Method is better overall.

Kaljevic, Igor↗

NASA NTRS1985

Finite elements based on consistently assumed stresses and displacements

Finite element stiffness matrices are derived using an extended Hellinger-Reissner principle in which internal displacements are added to serve as Lagrange multipliers to introduce the equilibrium constraint in each element. In a consistent formulation the assumed stresses are initially unconstrained and complete polynomials and the total displacements are also complete such that the corresponding strains are complete in the same order as the stresses. Several examples indicate that resulting properties for elements constructed by this consistent formulation are ideal and are less sensitive to distortions of element geometries. The method has been used to find the optimal stress terms for plane elements, 3-D solids, axisymmetric solids, and plate bending elements.

Pian, T. H. H.↗

NASA NTRS1974

Gravitational effects of process-induced dislocations in silicon

Matters pertaining to semiconductor device fabrication were studied in terms of the influence of gravity on the production of dislocations in silicon wafers during thermal cycling in a controlled ambient where no impurities are present and oxidation is minimal. Both n-type and p-type silicon wafers having a diameter of 1.25 in to 1.5 in, with fixed orientation and resistivity values, were used. The surface dislocation densities were measured quantitatively by the Sirtl etch technique. The results show two significant features of the plastic flow phenomenon as it is related to gravitational stress: (1) the density of dislocations generated during a given thermal cycle is directly related to the duration of the cycle; and (2) the duration of the thermal cycle required to produce a given dislocation density is inversely related to the equilibrium temperature. Analysis of the results indicates that gravitational stress is instrumental in process-induced defect generation.

Porter, W. A.↗

DOE OSTI2025

Investigation of residual stress distribution in wire-arc directed energy deposited refractory molybdenum alloy utilizing numerical thermo-mechanical analysis and neutron diffraction method

Directed energy deposition (DED), a metal additive manufacturing (AM) technique, offers higher deposition rates and energy efficiency, making it suitable for fabricating components from refractory molybdenum alloys, such as molybdenum-titanium-zirconium (TZM). However, large thermal gradients and non-equilibrium thermal cycles in DED could generate high residual stress in the component, potentially deteriorating quality and performance. Thus, this study aims to investigate residual stress generation and its distribution in wire-arc DED of TZM thin-wall, utilizing thermo-mechanical analysis and high-fidelity neutron diffraction (ND) method. Two interpass temperatures (50°C and 200°C) have been considered to investigate their impact on residual stress formation. During experiments, in-situ thermal data has been recorded using thermocouples, which have been utilized for calibrating the thermal model. Thermocouple data shows a good agreement with the simulation results, having a difference of less than 10 %. Post-deposition part deformation has been observed, which is measured using a coordinate measuring machine, showing maximum values of 0.93 mm and 0.78 mm for interpass temperatures of 50°C and 200°C, respectively. Numerical predictions of distortion deviated by less than 15% from the experimental results. ND measurement and simulation results indicate that residual stress magnitude and evolution vary across the TZM deposits, revealing microstructural anisotropy in both conditions. Notably, lower interpass temperatures resulted in higher residual stresses, confirmed by experimental and simulation data. Further, this study demonstrated that an integrated experimental and thermo-mechanical analysis can potentially reveal the temperature history, part deformation, and residual stress formation in wire-arc DED TZM alloy.

36 MATERIALS SCIENCE↗

NASA NTRS1995

Effect of mesh distortion on the accuracy of transverse shear stresses and their sensitivity coefficients in multilayered composites

A study is made of the effect of mesh distortion on the accuracy of transverse shear stresses and their first-order and second-order sensitivity coefficients in multilayered composite panels subjected to mechanical and thermal loads. The panels are discretized by using a two-field degenerate solid element, with the fundamental unknowns consisting of both displacement and strain components, and the displacement components having a linear variation throughout the thickness of the laminate. A two-step computational procedure is used for evaluating the transverse shear stresses. In the first step, the in-plane stresses in the different layers are calculated at the numerical quadrature points for each element. In the second step, the transverse shear stresses are evaluated by using piecewise integration, in the thickness direction, of the three-dimensional equilibrium equations. The same procedure is used for evaluating the sensitivity coefficients of transverse shear stresses. Numerical results are presented showing no noticeable degradation in the accuracy of the in-plane stresses and their sensitivity coefficients with mesh distortion. However, such degradation is observed for the transverse shear stresses and their sensitivity coefficients. The standard of comparison is taken to be the exact solution of the three-dimensional thermoelasticity equations of the panel.

Noor, Ahmed K.↗

NASA NTRS1965

Estimates for the derivatives of the stresses in a thin shell and interior shell equations.

Stress derivatives for perfectly elastic homogeneous and isotropic shell in equilibrium with forces acting along edges, applying theory of elliptic partial differential equations

THIN WALLED SHELL↗

NASA NTRS1984

Rational approach for assumed stress finite elements

A new method for the formulation of hybrid elements by the Hellinger-Reissner principle is established by expanding the essential terms of the assumed stresses as complete polynomials in the natural coordinates of the element. The equilibrium conditions are imposed in a variational sense through the internal displacements which are also expanded in the natural co-ordinates. The resulting element possesses all the ideal qualities, i.e. it is invariant, it is less sensitive to geometric distortion, it contains a minimum number of stress parameters and it provides accurate stress calculations. For the formulation of a 4-node plane stress element, a small perturbation method is used to determine the equilibrium constraint equations. The element has been proved to be always rank sufficient.

Pian, T. H. H.↗

DOE OSTI2026

Data for Soil Oxygen Dynamics: A Key Mediator of Tile Drainage Impacts on Coupled Hydrological, Biogeochemical, and Crop Systems

Tile drainage removes excess water and is an essential, widely adopted management practice to enhance crop productivity in the US Midwest and throughout the world. Tile drainage has been shown to significantly change hydrological and biogeochemical cycles by lowering the water table and reducing the residence time of soil water, although examining the complex interactions and feedbacks in an integrated hydrology–biogeochemistry–crop system remains elusive. Oxygen dynamics are critical to unraveling these interactions and have been ignored or oversimplified in existing models. Understanding these impacts is essential, particularly so because tile drainage has been highlighted as an adaptation under projected wetter springs and drier summers in the changing climate in the US Midwest. We used the ecosys model that uniquely incorporates first-principle soil oxygen dynamics and crop oxygen uptake mechanisms to quantify the impacts of tile drainage on hydrological and biogeochemical cycles and crop growth in corn–soybean rotation fields. The model was validated with data from a multi-treatment, multi-year experiment in Washington, IA. The relative root mean square error (rRMSE) for the corn and soybean yield in validation is 5.66 % and 12.57 %, respectively. The Pearson coefficient (r) of the monthly tile flow during the growing season is 0.78. Plant oxygen stress turns out as an emergent property of the equilibrium between the soil oxygen supply and biological demand. The impact of tile drainage on the system is achieved through a series of coupled feedback mechanisms. The model results show that tile drainage reduces the soil water content and enhances soil oxygenation. It additionally increases the subsurface discharge and elevates inorganic nitrogen leaching, with seasonal variations influenced by climate and crop phenology. The improved aerobic condition alleviates crop oxygen stress during wet springs, thereby promoting crop root growth during the early growth stage. The development of greater root density, in turn, mitigates water stress during dry summers, leading to an overall increase in the crop yield by ∼6 %. These functions indicate the potential of tile drainage in bolstering crop resilience to climate change and the use of this modeling tool for large-scale assessments of tile drainage. The model reveals the underlying causal mechanisms that drive the agroecosystem response to drainage on the coupled hydrology, biogeochemistry, and crop system dynamics.

Modeling↗

DOE OSTI2025

Soil oxygen dynamics: a key mediator of tile drainage impacts on coupled hydrological, biogeochemical, and crop systems

Tile drainage removes excess water and is an essential, widely adopted management practice to enhance crop productivity in the US Midwest and throughout the world. Tile drainage has been shown to significantly change hydrological and biogeochemical cycles by lowering the water table and reducing the residence time of soil water, although examining the complex interactions and feedbacks in an integrated hydrology–biogeochemistry–crop system remains elusive. Oxygen dynamics are critical to unraveling these interactions and have been ignored or oversimplified in existing models. Understanding these impacts is essential, particularly so because tile drainage has been highlighted as an adaptation under projected wetter springs and drier summers in the changing climate in the US Midwest. We used the ecosys model that uniquely incorporates first-principle soil oxygen dynamics and crop oxygen uptake mechanisms to quantify the impacts of tile drainage on hydrological and biogeochemical cycles and crop growth in corn–soybean rotation fields. The model was validated with data from a multi-treatment, multi-year experiment in Washington, IA. The relative root mean square error (rRMSE) for the corn and soybean yield in validation is 5.66 % and 12.57 %, respectively. The Pearson coefficient (r) of the monthly tile flow during the growing season is 0.78. Plant oxygen stress turns out as an emergent property of the equilibrium between the soil oxygen supply and biological demand. The impact of tile drainage on the system is achieved through a series of coupled feedback mechanisms. The model results show that tile drainage reduces the soil water content and enhances soil oxygenation. It additionally increases the subsurface discharge and elevates inorganic nitrogen leaching, with seasonal variations influenced by climate and crop phenology. The improved aerobic condition alleviates crop oxygen stress during wet springs, thereby promoting crop root growth during the early growth stage. The development of greater root density, in turn, mitigates water stress during dry summers, leading to an overall increase in the crop yield by ∼6 %. These functions indicate the potential of tile drainage in bolstering crop resilience to climate change and the use of this modeling tool for large-scale assessments of tile drainage. The model reveals the underlying causal mechanisms that drive the agroecosystem response to drainage on the coupled hydrology, biogeochemistry, and crop system dynamics.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2020

Fluctuation dynamo in a weakly collisional plasma

The turbulent amplification of cosmic magnetic fields depends upon the material properties of the host plasma. In many hot, dilute astrophysical systems, such as the intracluster medium (ICM) of galaxy clusters, the rarity of particle–particle collisions allows departures from local thermodynamic equilibrium. These departures – pressure anisotropies – exert anisotropic viscous stresses on the plasma motions that inhibit their ability to stretch magnetic-field lines. We present an extensive numerical study of the fluctuation dynamo in a weakly collisional plasma using magnetohydrodynamic (MHD) equations endowed with a field-parallel viscous (Braginskii) stress. When the stress is limited to values consistent with a pressure anisotropy regulated by firehose and mirror instabilities, the Braginskii-MHD dynamo largely resembles its MHD counterpart, particularly when the magnetic field is dynamically weak. If instead the parallel viscous stress is left unabated – a situation relevant to recent kinetic simulations of the fluctuation dynamo and, we argue, to the early stages of the dynamo in a magnetized ICM – the dynamo changes its character, amplifying the magnetic field while exhibiting many characteristics reminiscent of the saturated state of the large-Prandtl-number ( ${Pm}\gtrsim {1}$ ) MHD dynamo. We construct an analytic model for the Braginskii-MHD dynamo in this regime, which successfully matches simulated dynamo growth rates and magnetic-energy spectra. A prediction of this model, confirmed by our numerical simulations, is that a Braginskii-MHD plasma without pressure-anisotropy limiters will not support a dynamo if the ratio of perpendicular and parallel viscosities is too small. This ratio reflects the relative allowed rates of field-line stretching and mixing, the latter of which promotes resistive dissipation of the magnetic field. Finally, in all cases that do exhibit a viable dynamo, the generated magnetic field is organized into folds that persist into the saturated state and bias the chaotic flow to acquire a scale-dependent spectral anisotropy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Phosphoproteome Response to Dithiothreitol Reveals Unique Versus Shared Features of Saccharomyces cerevisiae Stress Responses

To cope with sudden changes in the external environment, the budding yeast Saccharomyces cerevisiae orchestrates a multifaceted response that spans many levels of physiology. Several studies have interrogated the transcriptome response to endoplasmic reticulum (ER) stress and the role of regulators such as the Ire1 kinase and Hac1 transcription factors. However, less is known about responses to ER stress at other levels of physiology. Here, we used quantitative phosphoproteomics and computational network inference to uncover the yeast phosphoproteome response to the reducing agent dithiothreitol (DTT) and the upstream signaling network that controls it. We profiled wild-type cells and mutants lacking IRE1 or MAPK kinases MKK1 and MKK2, before and at various times after DTT treatment. In addition to revealing downstream targets of these kinases, our inference approach predicted new regulators in the DTT response, including cell-cycle regulator Cdc28 and osmotic-response kinase Rck2, which we validated computationally. Our results also revealed similarities and surprising differences in responses to different stress conditions, especially in the response of protein kinase A targets. Furthermore, these results have implications for the breadth of signaling programs that can give rise to common stress response signatures.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS1986

On the modeling of low-Reynolds-number turbulence

A full Reynolds-stress closure that is capable of describing the flow all the way to the wall was formulated for turbulent flow through circular pipe. Since viscosity does not appear explicitly in the pressure redistribution terms, conventional high-number models for these terms are found to be applicable. However, the models for turbulent diffusion and viscous dissipation have to be modified to account for viscous diffusion near a wall. Two redistribution and two diffusion models are investigated for their effects on the model calculations. Wall correction to pressure redistribution modeling is also examined. Diffusion effects on calculated turbulent properties are further investigated by simplifying the transport equations to algebraic equations for Reynolds stress. Two approximations are explored. These are the equilibrium and nonequilibrium turbulence assumptions. Finally, the two-equation closure is also used to calculate the flow in question and the results compared with all the other model calculations. Fully developed pipe flows at two moderate Reynolds numbers are used to validate these model calculations.

So, R. M. C.↗

NASA NTRS1992

Determining the nuclear equation of state from neutron-star masses and radii

A method is developed for determining the nuclear equation of state directly from a knowledge of the masses and radii of neutron stars. This analysis assumes only that equilibrium neutron-star matter has the stress-energy tensor of an isotropic fluid with a barotropic equation of state, and that general relativity describes a neutron star's internal gravitational field. We present numerical examples which illustrate how well this method will determine the equation of state when the appropriate observational data become available.

Lindblom, Lee↗

NASA NTRS1994

Transverse shear stresses and their sensitivity coefficients in multilayered composite panels

A computational procedure is presented for the accurate determination of transverse shear stresses and their sensitivity coefficients in flat multilayered composite panels subjected to mechanical and thermal loads. The sensitivity coefficients measure the sensitivity of the transverse shear stresses to variations in the different lamination and material parameters of the panel. The panel is discretized by using either a three-field mixed finite element model based on a two-dimensional first- order shear deformation plate theory or a two-field degenerate solid element with each of the displacement components having a linear variation throughout the thickness of the laminate. The evaluation of transverse shear stresses can be conveniently divided into two phases. The first phase consists of using a superconvergent recovery technique for evaluating the in-plane stresses in the different layers. In the second phase, the transverse shear stresses are evaluated by using piecewise integration, in the thickness direction, of the three-dimensional equilibrium equations. The same procedure is used for evaluating the sensitivity coefficients of the transverse shear stresses. The effectiveness of the computational procedure is demonstrated by means of numerical examples of multilayered cross-ply panels subjected to transverse loading, uniform temperature change, and uniform temperature gradient through the thickness of the panel. In each case the standard of the comparison is taken to be the exact solution of the three dimensional thermoelasticity equations of the panel.

Noor, Ahmed K.↗

NASA NTRS2004

Toward Effective Shell Modeling of Wrinkled Thin-Film Membranes Exhibiting Stress Concentrations

Geometrically nonlinear shell finite element analysis has recently been applied to solar-sail membrane problems in order to model the out-of-plane deformations due to structural wrinkling. Whereas certain problems lend themselves to achieving converged nonlinear solutions that compare favorably with experimental observations, solutions to tensioned membranes exhibiting high stress concentrations have been difficult to obtain even with the best nonlinear finite element codes and advanced shell element technology. In this paper, two numerical studies are presented that pave the way to improving the modeling of this class of nonlinear problems. The studies address the issues of mesh refinement and stress-concentration alleviation, and the effects of these modeling strategies on the ability to attain converged nonlinear deformations due to wrinkling. The numerical studies demonstrate that excessive mesh refinement in the regions of stress concentration may be disadvantageous to achieving wrinkled equilibrium states, causing the nonlinear solution to lock in the membrane response mode, while totally discarding the very low-energy bending response that is necessary to cause wrinkling deformation patterns. An element-level, strain-energy density criterion is suggested for facilitating automated, adaptive mesh refinements specifically aimed at the modeling of thin-film membranes undergoing wrinkling deformations.

Tessler, Alexander↗

NASA NTRS2006

Geometrically Nonlinear Shell Analysis of Wrinkled Thin-Film Membranes with Stress Concentrations

Geometrically nonlinear shell finite element analysis has recently been applied to solar-sail membrane problems in order to model the out-of-plane deformations due to structural wrinkling. Whereas certain problems lend themselves to achieving converged nonlinear solutions that compare favorably with experimental observations, solutions to tensioned membranes exhibiting high stress concentrations have been difficult to obtain even with the best nonlinear finite element codes and advanced shell element technology. In this paper, two numerical studies are presented that pave the way to improving the modeling of this class of nonlinear problems. The studies address the issues of mesh refinement and stress-concentration alleviation, and the effects of these modeling strategies on the ability to attain converged nonlinear deformations due to wrinkling. The numerical studies demonstrate that excessive mesh refinement in the regions of stress concentration may be disadvantageous to achieving wrinkled equilibrium states, causing the nonlinear solution to lock in the membrane response mode, while totally discarding the very low-energy bending response that is necessary to cause wrinkling deformation patterns.

Tessler, Alexander↗

NASA NTRS1988

Sublaminate- or ply-level analysis of composites and strain energy release rates of end-notch and mixed-mode fracture specimens

The sublaminate or ply-level analysis of composite structures is presently undertaken by a computational procedure yielding the stresses in regions affected by delaminations, transverse cracks, and discontinuities that are related to material properties, geometries, and loads. Attention is given to layers or groups of layers that are immediately affected by flaws; these are analyzed as if they were homogeneous bodies in equilibrium, in isolation from the rest of the laminate. Computed stresses agree with those from a three-dimensional FEM analysis.

Valisetty, Rao R.↗