A numerical procedure for calculating stress and deformation near a slit in a three-dimensional elastic-plastic solid
Deformation and stress calculation programs for three dimensional elastic plastic solids with slits
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Deformation and stress calculation programs for three dimensional elastic plastic solids with slits
Web stresses and flange stresses were measured in three built-up beams: one of constant depth with flanges of constant cross-section, one linearly tapered in depth with flanges of constant cross section, and one linearly tapered in depth with tapered flanges. The measured stresses were compared with the calculated stresses obtained by the methods outlined in order to determine the degree of accuracy that may be expected from the stress analysis formulas. These comparisons indicated that the average measured stresses for all points in the central section of the beams did not exceed the average calculated stresses by more than 5 percent. It also indicated that the difference between average measured flange stresses and average calculated flange stresses on the net area and a fully effective web did not exceed 6.1 percent.
Stress calculator permits speedy conversion of strain data directly into maximum and minimum stresses and also determines stress direction. The calculator has a movable slide with logarithmic and linear scales, and an information and grid board. Its size is flexible for easy manipulation.
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Atomic stresses were calculated for carbon nanotubes under strain conditions. Graphitic tubules with radii ranging from approximately 2 to 11 Angstroms and two different tubule structures with varying atomic orientations were included in the calculations. Elongations and contractions were applied in the axial direction and atomic stress values were calculated for infinitely long tubules. The calculations were carried out using Brenner's function which was developed for carbon species. Results indicate that the stress is tensile in the radial direction while it is compressive in the tangential direction. Variations in stress values in the direction of the cylindrical aids were investigated as a function of applied strain. Furthermore, using the stress-strain curve (calculated based on atomic considerations), the values of Young's modulus and Poisson's ratio for nanotubules were also estimated.
Calculations were carried out to evaluate stresses for atoms located in the top several layers of (100)-(1x1), (100)-(2x1) and (111)-(1x1) surfaces of diamond. Only equilibrated surfaces were taken into consideration in this investigation. Stress values in the direction perpendicular to the exposed surface vanish. In lateral directions, however, stresses have non-vanishing values, in general. For the (100) surfaces calculated stress values are anisotropic. While the (2 x 1) reconstructed surface is under compression in both directions, calculations for the unreconstructed (1 x 1) plane, produced a compressive stress in one direction and a slight tension in the other. On the (111) surface, isotropic and relatively low compressive stress values were found. Present calculations indicate that atoms located only in a few top layers have lateral excess stresses which vanish very quickly for the atoms of interior layers as departing from the exposed surface.
While the contour method for residual stress assessment has developed rapidly, no published study documents its interlaboratory reproducibility. Objective: Here we report an initial reproducibility experiment focused on contour method data analysis and residual stress calculation. The experiment uses surface topography data from a physical process simulation of elastic-plastic beam bending. The simulation provides surface topography, for input to the contour method data analysis, as well as a known residual stress field with 130 MPa peak magnitude. Additionally, to increase realism, noise and specific artifacts are added to the topography data. A group of participants received the topography data (without the known residual stress), independently analyzed the data, and submitted results as a two-dimensional residual stress field. Analysis of submissions provides a group average residual stress field and the spatial distribution of reproducibility standard deviation. The group average residual stress agrees with the known stress in magnitude and spatial trend. The reproducibility standard deviation ranges from 2 to 54 MPa over the measurement plane, with an average of 5.4 MPa. Reproducibility standard deviation is smaller in the cross-section interior (≤ 5 MPa), modest near local extrema in the stress field (5 to 10 MPa), and larger near the cross-section boundaries (10 to 30 MPa). Overall, the largest values of reproducibility standard deviation (up to 54 MPa) occur in limited areas where artifacts had been added to the topography data; while some participants identified and removed these artifacts, some did not, leading to systematic differences that elevated the standard deviation.
Reynolds stress calculations of homogeneous turbulent shear flow are conducted with a second-order closure model modified to account for non-equilibrium vortex stretching in the dissipation rate transport equation, as recently proposed by Bernard and Speziale. As with the earlier reported k-epsilon model calculations incorporating this vortex stretching effect, a production-equals-dissipation equilibrium is obtained with bounded turbulent kinetic energy and dissipation. However, this equilibrium is not achieved until the dimensionless time greater than 60, an elapsed time that is at least twice as large as any of those considered in previous numerical and physical experiments on homogeneous shear flow. Direct quantitative comparisons between the model predictions and the results of experiments are quite favorable. In particular, it is shown that the inclusion of this non-equilibrium vortex stretching effect has the capability of explaining the significant range of production to dissipation ratios observed in experiments.
Reynolds stress calculations of homogeneous turbulent shear flow are conducted with a second-order closure model modified to account for nonequilibrium vortex stretching in the dissipation rate transport equation as recently proposed by Bernard and Speziale (1992). As with the earlier reported K-epsilon model calculations incorporating this vortex stretching effect, a production-equals-dissipation equilibrium is obtained with bounded turbulent kinetic energy and dissipation. However, this equilibrium is now not achieved until the dimensionless time St greater than 60 - an elapsed time that is at least twice as large as any of those considered in previous numerical and physical experiments on homogeneous shear flow. Direct quantitative comparisons between the model predictions and the results of experiments are quite favorable. In particular, it is shown that the inclusion of this nonequilibrium vortex stretching effect has the capability of explaining the significant range of production to dissipation ratios observed in experiments.
The mean stress, as a fundamental statistical property of a group of stress data, is essential for stress variability characterisation. However, currently in rock mechanics, the mean stress is customarily and erroneously calculated by separately averaging the principal stress magnitudes and orientations. In order to draw the attention of our community to the appropriate approach for stress variability characterisation, here we compare the customary scalar/vector mean with that obtained by the mathematically rigorous tensorial approach—the Euclidean mean. Calculation of mean stress using both a small group of actual in situ stress measurement results and a large group of simulated stress data (obtained using the combined finite– discrete element method, FEMDEM) demonstrates that the two approaches yield different results. Further investigation of these results shows that the scalar/vector approach may yield non-unique and non-orthogonal mean principal stresses, and these may deviate significantly from those of the Euclidean mean. Our calculations and comparisons reveal that the scalar/ vector approach is deficient because it processes the principal stress magnitudes and orientations separately as independent quantities and ignores the connection between them. Conversely, the tensorial approach appropriately averages the tensors that simultaneously carry not only the information of stress magnitudes and orientations, but also the inherent relations between them. Therefore, arbitrarily using scalar/vector mean stress of in situ stress measurements as input in further rock engineering analyses may yield significantly erroneous results. Finally, we advise that stress data should be statistically processed in a tensorial manner using tensors referred to a common Cartesian coordinate system.
The WHOLESCALE acronym stands for Water & Hole Observations Leverage Effective Stress Calculations and Lessen Expenses. The goal of the WHOLESCALE project is to simulate the spatial distribution and temporal evolution of stress in the geothermal system at San Emidio in Nevada, United States. To reach this goal, the WHOLESCALE team has developed a methodology to incorporate and interpret data from four methods of measurement into a multi-physics model that couples thermal, hydrological, and mechanical (T H-M) processes. The WHOLESCALE team has applied this methodology at the San Emidio geothermal field, located ~100 km north of Reno, Nevada in the northwestern Basin and Range province. The WHOLESCALE team includes 30 individuals working at two universities, two national laboratories, and one industry partner. Two master-degree students and five post-doctoral researchers have gained professional experience and earned partial financial support via the WHOLESCALE project. The WHOLESCALE team has taken advantage of the perturbations created by changes in pumping operations during planned shutdowns in 2016, 2021, and 2022 to infer temporal changes in the state of stress in the geothermal system at San Emidio, Nevada, U.S. The WHOLESCALE results support the working hypothesis that increasing pore-fluid pressure reduces the effective normal stress acting across fault zones. During normal operations, pumping in deep production wells decreases fluid pressures and thus increases the effective normal stresses on faults, reducing microseismicity. During planned shutdowns, the cessation of production increases pore-fluid pressure and reduces effective normal stress. The WHOLESCALE products generated during the 4-year period between 2020 and 2024 include: three articles published in the open-access, peer-reviewed scientific literature, two master’s theses, 20 presentations or papers at scientific conferences, and 17 data sets available on public repositories. The WHOLESCALE project has been completed in two phases that included three performance periods separated by two Go/No-go Stage Gate Reviews. Tasks were classified by data type (i.e., Geologic Structure, Borehole, Geodesy, Hydrology, Seismology, and Modeling). The first phase of the project started July 31, 2020 and included ongoing project coordination (Task 1), a project kickoff (Task 2), analysis of existing data (Task 3), development of the initial stress model & deployment design (Task 4), and Go/No-go Decision Point #1 (Task 5). Phase II began with implementing the 2022 deployment (Task 6), followed by Go/No-go Decision Point #2 (Task 7) The remainder of Phase II consisted of analyzing data collected during deployment (Task 8), calibration of the stress model on all observations (Task 9), and the Final Review (August 23, 2024) & Reporting (Task 10).
Three dimensional elastic plastic solid, calculating stress and deformation with finite difference procedure
A procedure for generating accurate thermal stresses with coarse finite element grids (Ojalvo's method) is described. The procedure is based on the observation that for linear thermoelastic problems, the thermal stresses may be envisioned as being composed of two contributions; the first due to the strains in the structure which depend on the integral of the temperature distribution over the finite element and the second due to the local variation of the temperature in the element. The first contribution can be accurately predicted with a coarse finite-element mesh. The resulting strain distribution can then be combined via the constitutive relations with detailed temperatures from a separate thermal analysis. The result is accurate thermal stresses from coarse finite element structural models even where the temperature distributions have sharp variations. The range of applicability of the method for various classes of thermostructural problems such as in-plane or bending type problems and the effect of the nature of the temperature distribution and edge constraints are addressed. Ojalvo's method is used in conjunction with the SPAR finite element program. Results are obtained for rods, membranes, a box beam and a stiffened panel.
Iterative solution for calculating deformation and stress concentration near slits in elastic-plastic solids
The paper describes nethods of computing the stresses in disks of a given profile as well as methods of choosing the disk profiles for a given stress distribution for turhines, turbo blowers, and so forth. A new method of in tegrating the differential equations of Stodola leads to a simplification of the computation for disks of hyperbolic profile.
A three-dimensional virtual crack-closure technique is presented which calculates the strain energy release rates and the stress intensity factors using only nodal forces and displacements from a standard finite element analysis. The technique is an extension of the Rybicki-Kanninen (1977) method, and it assumes that any continuous function can be approximated by a finite number of straight line segments. Results obtained by the method for surface cracked plates with and without notches agree favorably with previous results.
Geometrically exact finite element for thin shells of revolution, using approximation to predict boundary layer stress distribution during vibration
Future launch vehicles will require the incorporation large composite parts that will make up primary and secondary components of the vehicle. NASA has explored the feasibility of manufacturing these large components using Out-of-Autoclave impregnated carbon fiber composite systems through many composites development projects. Most recently, the Composites for Exploration Project has been looking at the development of a 10 meter diameter fairing structure, similar in size to what will be required for a heavy launch vehicle. The development of new material systems requires the investigation of the material properties and the stress in the parts. Residual stress is an important factor to incorporate when modeling the stresses that a part is undergoing. Testing was performed to verify the stress free temperature with two-ply asymmetric panels. A comparison was done between three newly developed out of autoclave IM7 /Bismalieimide (BMI) systems. This paper presents the testing results and the analysis performed to determine the residual stress of the materials.