Stress Distribution In Plane Research Articles

Stress Analysis of Vibrating Screen Side Plate based on Elastic Theory

To achieve a more precise understanding of the stress distribution state of the side plate and support beam of the shaker box, a mechanical model for plane stress distribution has been established. This model is based on the plane stress theory of elastic theory. Furthermore, using this model, we have predicted the plane stress distribution of the shaker box's side plate and support beam when subjected to excitation forces generated by both unilateral and bilateral rotor arrangement structures. The findings indicate that the mechanical model rooted in elastic mechanics accurately depicts the stress distribution within the perforated side plate structure and screen support beam. Specifically, the peak stress in the side plate of a symmetrically distributed structure is merely half of that observed in a unilateral structure. Furthermore, the cumulative effect of shear stress on both sides of the side plate serves to mitigate the overall shear stress on the plate. Additionally, the planar stress within the support beam is exclusively influenced by the excitation force exerted by the vibrating screen on a single support beam.

Source parameter inversion of the 2021 MW7.4 Maduo earthquake and stress transfer in the eastern Bayan Har block

In order to explore the constraint degree of GNSS and InSAR data on the Maduo earthquake under the layered earth model structure, and to understand the cause of the Maduo earthquake and the danger of the surrounding area, this paper uses D-InSAR technology to obtain the InSAR co-seismic deformation field of the Maduo earthquake on May 22,2021. Based on GNSS and InSAR data, the co-seismic slip model and fault plane stress distribution of the Maduo earthquake are jointly inverted. This paper calculates the Coulomb stress changes caused by 14 M ≥ 7 strong earthquakes co-seismic, post-seismic viscoelastic relaxation and inter-seismic tectonic stress loading of 19 fault segments in the Bayan Har block research area (96°E-106°E, 29°N-36°N) since 1900. The results show that: (1) The maximum Line Of Sight (LOS) deformation obtained based on the ascending and descending InSAR data was about 0.9 m. The maximum slip amount of GNSS + InSAR joint inversion is 4.87 m, which is located in the Dongcao Along Lake section (∼98.6°E). Combined with the stress drop distribution of the fault surface, it is found that the Maduo earthquake is dominated by strike-slip. (2) The historical strong earthquakes delayed the Maduo earthquake by nearly 103 years. The 1937 Huashixia earthquake, the 1947 Dari earthquake, the 1963 Dulan earthquake, and the 1973 Luhuo earthquake had the greatest stress unloading effect, which was equivalent to delaying the Maduo earthquake by 53 years, 21 years, 11 years, and 17 years, respectively. The cumulative Coulomb stress at the source location of the Maduo earthquake reached 0.0112 MPa. Most area of the fault sections such as the East Kunlun Fault, the Maduo-Gande Fault, the western and eastern sections of the Dari Fault, the western and eastern sections of the Qingshuihe Fault, the Ganzi-Yushu Fault, and the eastern section of the Kunlunshankou-Jiangcuo Fault are in the Coulomb stress loading area, which should be paid attention to.

Source Parameter Inversion and Century-Scale Stress Triggering Analysis of the 2021 Maduo MW7.4 Earthquake Using GNSS and InSAR Displacement Fields

To explore the degree of constraint by Global Navigation Satellite System (GNSS) and Interferometric Synthetic Aperture Radar (InSAR) data on the Maduo earthquake within a layered earth model structure and to gain an insight into the seismogenic mechanism and the seismic risk in the surrounding area, this study employs D-InSAR technology to acquire the InSAR co-seismic deformation field of the Maduo earthquake on 22 May 2021. Utilizing both GNSS and InSAR data, the inversions constrained by single and joint data are conducted and compared to determine the co-seismic slip model and fault plane stress distribution of the Maduo earthquake. Additionally, this paper calculates the Coulomb stress changes induced by 14 M ≥ 7 strong earthquakes, considering co-seismic effects, post-seismic viscoelastic relaxation, and inter-seismic tectonic stress loading, on 19 fault segments within the Bayan Har block research area (96°E~106°E, 29°N~36°N) since 1900. The findings are as follows: (1) The maximum line-of-sight (LOS) deformation was approximately 0.9 m. The joint inversion rupture was primarily located in the Dongcao Along Lake section (~98.6°E), aligning with previous research outcomes. (2) The cumulative Coulomb stress at the Maduo earthquake’s source location was −0.1333 MPa, while the inter-seismic stress loading amounted to 0.0745 MPa. The East Kunlun Fault, Maduo–Gande Fault, Ganzi–Yushu Fault, and Dari Fault C exhibited considerable stress loading, warranting attention due to heightened seismic risk. (3) Based on three different co-seismic slip models, the stress disturbance results caused by the Maduo earthquake to the surrounding area and fault did not differ significantly. After the earthquake, the seismogenic fault still has high seismic risk.

A method for detecting two‐dimensional plane stress distribution in basin‐type insulator based on critically refracted longitudinal wave

AbstractBasin‐type insulator often has small cracks due to stress concentration. The current method cannot accurately reflect the stress condition of the insulator to find the stress concentration areas. To solve these problems, a method for detecting two‐dimensional plane stress (δ1 and δ2) within different depth ranges in a basin‐type insulator is proposed based on critically refracted longitudinal (LCR) wave. First, the acoustoelastic equation characterising the relationship between the variation of LCR wave propagation time and the plane stress was derived. Next, the propagation characteristics of LCR wave in epoxy resin samples were investigated. Then, the stress distribution within different depth ranges of the insulator subjected to hydraulic load was measured using the proposed method, including direction (θ), δ1 and δ2. The results show that the magnitude of the stress alone cannot accurately characterise the stress state. Points with equal distances to the centre have similar stress magnitudes, but their directions are not the same. With increasing depth, θ remains essentially unchanged at the same location, while δ1 and δ2 decrease, and the rate of decrease varies at different locations. Comparing the measured and simulated data, the results showed that they were in good agreement, and the maximum errors of stress value and θ were 0.69 MPa and 2.97°, respectively, which confirmed the feasibility and accuracy of the stress detection in the proposed method.

Variational Stress Analysis of Laminates Containing Regions with Different Material Properties in Loading Direction

In this study, a variational stress analysis was performed on a laminate that contained regions with varying material properties in the loading direction. Investigation of material properties and damage behavior of laminates with fiber discontinuity (resin-rich region) has been the main motivation for this study. The analysis considered an arbitrary number of regions with different material properties. For simplicity, we assumed a plane stress condition or stress distribution, we assumed that the normal stress in the loading direction was constant along the direction of thickness in each ply. The admissible stress state that satisfied both equilibrium and boundary/continuity conditions was constructed with unknown functions that were determined using the principle of minimum complementary energy. The analysis was applied to laminates with single fiber discontinuity and with distributed fiber discontinuities. These results were compared using finite element analyses, which obtained good agreement. The results show the validity of this analysis, which can be used to investigate the effects of fiber discontinuity on the laminate mechanical properties and damage behavior in laminates with fiber discontinuities.

Analytical Solution for Estimating Bearing Capacity of a Closed Soil Plug: Verification Using An On-Site Static Pile Test

When the open-ended pile penetrates the soil layer, the resistance generated by the soil plug cannot be ignored. A pile with a full-size pressure sensor installed at pile tip can detect resistance more accurately than a microsensor when the pile penetrates into the soil. In this paper, the pile installed full-size pressure sensor was used for penetration test and the relationship between formation parameters and pile tip force is obtained. Using the solution of the Kelvin problem in infinite space and the plane stress distribution function, the analytical solution of the bearing capacity of the soil plug is derived under the condition that the displacements of the bottom of the pile and the soil plug are consistent. The results show that the ultimate stress of the soil plug is closely related to the pile diameter and pipe thickness. The bearing capacity of the soil plug is closely related to the properties of the soil layer. The analytical solution of the bearing capacity of the soil plug has a linear relationship with the formation parameters SPT and CPT. The analytical solution of the ultimate bearing capacity of the soil plug has been verified by field test data and has a good match with the geometric dimensions of the pile tip and the formation parameters.

Stress Distribution in Silicon Subjected to Atomic Scale Grinding with a Curved Tool Path.

Molecular dynamics (MD) simulations were applied to study the fundamental mechanism of nanoscale grinding with a modeled tool trajectory of straight lines. Nevertheless, these models ignore curvature changes of actual tool paths, which need optimization to facilitate understanding of the underlying science of the machining processes. In this work, a three-dimensional MD model considering the effect of tool paths was employed to investigate distributions of stresses including hydrostatic stress, von Mises stress, normal and shear stresses during atomic grinding. Simulation results showed that average values of the stresses are greatly influenced by the radius of the tool trajectory and the grinding depth. Besides the averaged stresses, plane stress distribution was also analyzed, which was obtained by intercepting stresses on the internal planes of the workpiece. For the case of a grinding depth of 25 Å and an arc radius 40 Å, snapshots of the stresses on the X–Y, X–Z and Y–Z planes showed internal stress concentration. The results show that phase transformation occurred from α- silicon to β- silicon in the region with hydrostatic stress over 8 GPa. Moreover, lateral snapshots of the three-dimensional stress distribution are comprehensively discussed. It can be deduced from MD simulations of stress distribution in monocrystalline silicon with the designed new model that a curved tool trajectory leads to asymmetric distribution and concentration of stress during atomic-scale grinding. The analysis of stress distribution with varying curve geometries and cutting depths can aid fundamental mechanism development in nanomanufacturing and provide theoretical support for ultraprecision grinding.

Designing a solar and wind hybrid system for small-scale irrigation: a case study for Kalangala district in Uganda

BackgroundDynamics in rainfall patterns are posing a threat to crop production in Uganda. Irrigation can be used to ensure constant production; however, the motorized powered irrigation methods are quite costly to run in addition to being environmentally unsustainable. There is thus need for alternative irrigation methods. Renewable energy sources which are readily available can be used to power irrigation systems. This study hence sought to design an appropriate wind-solar hybrid system for irrigating 1 acre of banana plantation in Kalangala district, Uganda.MethodsUsing metrological data, mean wind speed and monthly solar irradiance of global radiation horizontal for the district were analysed. A wind-solar hybrid system was optimally designed for a standalone drip irrigation system of 450 banana plants on 1-acre land with water requirement of 33.73 m3 d−1. The wind turbine was simulated to analyse for static pressure, cut plane flow behaviour, turbulence intensity and stress distribution exposed at 20 m s−1 wind speed. A cost analysis was done to estimate the total project investment, maintenance and operational cost, annual project gross income, net income stream and the annual net real rate of returns.Results and conclusionsThe simulation results showed that the system could effectively operate at speeds of 20 m s−1 without deformation. The net present value of income stream for the first 5 years at r = 5% was 12,935,468 UGX with a net real rate of return of 3.5% per year. The study will, therefore, be a useful guideline in making investment decisions in hybrids irrigation systems.

Simulation of tabular mine face advance rates using a simplified fracture zone model

This paper describes a method to determine the time-dependent stability of the fracture zone near the edges of tabular excavation layouts when different mining rates and face advance increment lengths are scheduled. Some analytic properties of the proposed time-dependent fracture zone evolution model are presented initially for a simplified mining geometry. The implementation of the model in a general tabular layout setting is described next including a novel scheme to allow for partially fractured elements. The reef plane stress distribution in the fracture zone is solved using a fast marching method that is coupled to a displacement discontinuity solution of the excavation and fracture zone deformations. The numerical scheme is illustrated by considering the extraction of a hypothetical deep-level mining layout. The sensitivity of the results to changes in the mining rate schedule and the face advance step size are discussed. Further extensions to the solution scheme are noted.

Ion Doping Effects on the Lattice Distortion and Interlayer Mismatch of Aurivillius-Type Bismuth Titanate Compounds.

Taking Bismuth Titanate (Bi4Ti3O12) as a Aurivillius-type compound with m = 3 for example, the ion (W6+/Cr3+) doping effect on the lattice distortion and interlayer mismatch of Bi4Ti3O12 structure were investigated by stress analysis, based on an elastic model. Since oxygen-octahedron rotates in the ab-plane, and inclines away from the c-axis, a lattice model for describing the status change of oxygen-octahedron was built according to the substituting mechanism of W6+/Cr3+ for Ti4+, which was used to investigate the variation of orthorhombic distortion degree (a/b) of Bi4Ti3O12 with the doping content. The analysis shows that the incorporation of W6+/Cr3+ into Bi4Ti3O12 tends to relieve the distortion of pseudo-perovskite layer, which also helps it to become more stiff. Since the bismuth-oxide layer expands while the pseudo-perovskite layer tightens, an analytic model for the plane stress distribution in the crystal lattice of Bi4Ti3O12 was developed from the constitutive relationship of alternating layer structure. The calculations reveal that the structural mismatch of Bi4Ti3O12 is constrained in the ab-plane of a unit cell, since both the interlayer mismatch degree and the total strain energy vary with the doping content in a similar trend to the lattice parameters of ab-plane.

A fast procedure of stress state evaluation in magnetically anisotropic steels with the help of a probe with adjustable magnetizing field direction

The paper presents a novel approach to the stress state evaluation issue. It deals with a strongly (magnetically) anisotropic materials for which a direct interpretation of the Barkhausen effect (BE) intensity would lead to erroneous results. In such a case one has to take into account both the measured BE intensity and the orientation of the magnetisation direction relative to the magnetic easy axis. For the in plane stress distribution evaluation one has to perform at least three measurements in the non-collinear directions. The application of an apparatus with automatically changing magnetizing field direction allows to obtain the angular distribution of the BE intensity in about 30 s (with the angular step of 10°). Thanks to the dedicated post-processing software the procedure of the measurement data processing, resulting in the full information on the stress distribution (main stress components and their orientation in all the investigated points) is almost instantaneous. Apart from the measurement results the stress determination procedure requires two additional pieces of information. The first one is the calibration data obtained for at least two applied strain directions (along easy and hard magnetisation axes)— the data for the intermediate orientations are usually interpolated. The second one is the ‘reference level’ of the BE intensity angular distribution. In the case of welded plates it is obtained by averaging the results obtained at the analysed points before welding. The way of results presentation proposed in that paper is very illustrative and shows an interesting feature of the stress distribution in welded plates—namely the appearance of a ‘vortex’ structure of main stress.

Stress Concentration Near an Elliptic Hole or a Parabolic Notch in a Quasiorthotropic Plane

We consider the problem of stress distribution in an infinite quasiorthotropic plane containing an elliptic hole whose contour is free of external forces and a homogeneous stressed state is imposed at infinity. The solution of the problem is obtained with the help of the boundary transition from the known analytic solution for an elliptic hole in an orthotropic plane in the case where the roots of the characteristic equation approach each other. In the boundary case where the major semiaxis of the ellipse tends to infinity, these results yield the stress distribution in a plane weakened by a parabolic notch for two main types of deformation (symmetric tension and transverse shear).

Characterization of Lattice Plane Bending and Stress Distribution in Physical Vapor Transport-Grown 4H-SiC Crystals

Basal plane bending and stress distribution in physical vapor transport-grown n-type 4H-SiC crystals were investigated. High resolution X-ray diffraction measurements were performed on commercially available 3-inch-diameter 4H-SiC substrates and along the growth front surface of as-grown 1-inch-diameter 4H-SiC boules. The measurements revealed that structural parameters such as the c-lattice constant, basal plane tilting, and FWHM showed characteristic variations across the substrates and as-gown boules, indicating that the crystals had a non-uniform distribution of dislocations comprising domain structures. Residual stress measured by micro Raman spectroscopy showed a similar behavior, which was an oscillatory spatial variation. On the basis of these results, defect structures in the crystals are elucidated.

Micro-Raman spectroscopic analysis of single crystal silicon microstructures for surface stress mapping

In this paper, an experimental analysis using a micro-Raman spectroscope for surface stress distribution in single crystal silicon (SCS) microstructures is described. Specially developed tensile test equipment applies a uniaxial tensile stress on SCS specimens with a 270 nm-high, 4 µm2 convex structures in the gauge section. Raman spectra around the convex region are measured using an ultraviolet laser with an excitation line of 363.8 nm. The shape of the Raman spectrum on the flat surface is symmetrical, whereas that around the edge of the convex is asymmetrical due to the multi-stress condition. Two-curve fitting is adopted for the asymmetric spectrum obtained at the edge, and the stress distribution estimated by the two peak positions is much closer to finite element analysis (FEA) results than that obtained by the one peak position. In partial least squares (PLS) analysis that is performed at the edge of the convex section only, explanatory variables are Raman spectral parameters, such as peak position, peak intensity, and full width at half maximum, and the response variable is the FEA stress distribution. The plane stress distributions derived from PLS analyses on each component are in good agreement with that from FEA. The combination of micro-Raman spectroscopy and tensile testing enables us to directly determine the stress components as well as stress magnitudes on SCS microstructures.

Oblique and Herringbone Buckling Analysis of Steel Strip by Spline FEM

The tilted waves in steel strip during rolling and leveling of sheet metal can be classified into two different types of buckling, oblique and herringbone buckling, respectively. Numerical considerations of oblique and herringbone buckling phenomena are dealt with by the spline finite element method (FEM). It is pointed out that the shear stress due to residual strains caused by the rolling process or applied non-uniform loading is the main reason of oblique and herringbone buckle. According to the analysis of stress distribution in plane, the appropriate initial strain patterns are adopted and the corresponding buckling modes are calculated by the spline FEM. The developed numerical model provides an estimation of buckling critical load and wave configuration.

Measurement of static and dynamic mechanical behavior of micro and nano-scale thin metal films: using micro-cantilever beam deflection

We present the results of a novel micro-beam deflection test used to investigate the static and dynamic mechanical behavior of submicron-thick metal films. The method demonstrated in this study allows researchers to observe the motion of micro and nano-scale thin films responding to electrostatic loads, by means of laser reflection measurements at frequency rates of up to 500 Hz. Researchers fabricated a supporting frame and a novel triangular shaped “paddle” beam designed to provide uniform plane stress distribution while undergoing deflection. A simple geometric calculation, based on cantilever deflection, enabled the degree of strain to be determined, which in turn provided the Young’s modus for aluminum film of a given thickness. We also studied the dynamic behavior using the dynamic frequency response of the beam, generated by electrostatic forces under various loads and vacuum pressure conditions. Our results showed that air damping has a significant influence on the free damping behavior of specimens, and only a minor influence on damping frequency. We determined the loss angle and frequency using sweep frequency and free damping methods, which were very consistent with paddle resonant frequencies. The loss angle obtained from a simple silicon micro-beam was 2.001 × 10−4°using the free damping method and 2.23 × 10−4°using the sweep frequency method. The dynamic response loss mechanism measured in this experiment provides incentive for the further study of grain boundary motion and dislocation motion in thin films.

Laser ultrasonic diagnostics of residual stress

Ultrasonic NDE is one of the most promising methods for non-destructive diagnostics of residual stresses. However the relative change of sound velocity, which is directly proportional to applied stress, is extremely small. An initial stress of 100 MPa produces the result of δV/V∼10 −4. Therefore measurements must be performed with high precision. The required accuracy can be achieved with laser-exited ultrasonic transients. Radiation from a Nd-YAG laser (pulse duration 7 ns, pulse energy 100 μJ) was absorbed by the surface of the sample. The exited ultrasonic transients resembled the form of laser pulses. A specially designed optoacoustic transducer was used both for the excitation and detecting of the ultrasonic pulses. The wide frequency band of the piezodetector made it possible to achieve the time-of-flight measurements with an accuracy of about 0.5 ns. This technique was used for measuring of plane residual stress in welds and for in-depth testing of subsurface residual stresses in metals. Plane stress distribution for welded metallic plates of different thicknesses (2–8 mm) and the subsurface stress distribution for titanium and nickel alloys were obtained. The results of conventional testing are in good agreement with the laser ultrasonic method.

Advanced x-ray stress analysis method for a single crystal using different diffraction plane families

Generalized formula of the x-ray stress analysis for a single crystal with unknown stress-free lattice parameter was proposed. This method enables us to evaluate the plane stress states with any combination of diffraction planes. We can choose and combine the appropriate x-ray sources and diffraction plane families, depending on the sample orientation and the apparatus, whenever diffraction condition is satisfied. The analysis of plane stress distributions in an iron single crystal was demonstrated combining with the diffraction data for Fe{211} and Fe{310} plane families.

Dynamical stability of finite anisotropic panels with elliptical cutouts and cracks

An approximate analysis for dynamical stability of anisotropic finite panels with centrally located elliptical cutouts is presented. The analysis is divided into two parts: a plane stress analysis and a stability analysis. The plane stress distribution is determined by using Lekhnitskii’s complex variable equations of plane elastostatics combined with a Laurent series approximation constructed by the conformal mapping and a boundary collocation method. Its solutions satisfy the conditions along the interior boundary and at a discrete number of points along the exterior panel ones. The stability analysis is conducted by using the differential equations which result from the Hamilton’s principle and the classical plate theory. The relation of vibration frequency, load parameter and stability of panels is investigated by solving the fundamental equations using separation of variables, so as to obtain the critical loads. Finally, comparisons with documented experimental results and finite element analysis are made. Results of a parameter study are presented.

On the use of finite element programs in structural evaluation and development of design charts

In many phases of structural design and analytical evaluation, the solution of stress and strain distribution in an elastic continuum is required. Special cases of such problems may range from two-dimensional plane stress or plain strain distribution, plate bending to analysis of fully three-dimensional solids. The finite element programs are often used to predict the critical regions for stress analysis and design. Stresses are generally of greater practical importance than displacements for structural design and evaluation. Most of the finite element computer programs calculate element stresses at the centroids, integration points, or nodes of elements. In this paper, examples of bridge deck analysis are used to illustrate the stress interpretation using the finite element programs. It is demonstrated that the stresses at nodes calculated by some finite element programs violate the equilibrium conditions and do not converge to the correct answers. These calculated stresses at nodes are usually too low and lead to unsafe designs and evaluations. Key words: finite element method, finite element programs, structural analysis, least square smoothing, stress interpolation.