Average Circumferential Stress Research Articles

Pure Bending of Homogenous Isotropic Elastic Curved Beam

In this paper a detailed analysis is given for the pure bending problem of curved beams. The material of the curved beam is homogenous isotropic linearly elastic. The mantle of the curved beam is stress free and there is no body force on the curved beam. The plane of the curvature of the beam is the plane of symmetry for the whole beam. Paper gives the expressions of circumferential and radial normal stresses. A strength of material approach is used to derive the governing equations. A numerical example illustrates the application of the presented solutions.

An analytical formulation of unidirectional composite curved beam with out-of-plane fiber waviness under bending

A closed-form analytical solution is developed for analyzing laminated composite curved beam with out-of-plane fiber waviness under bending. Timoshenko beam theory was adopted in derivation where the effects of shear deformation was considered for moderately thick beam. Explicit expressions for evaluating equivalent axial and bending stiffness are formulated based upon the modified lamination theory and taking the structural deformation characteristics of narrow section beam into consideration. Stress distribution at any given location calculated by the proposed method is investigated. Significant increase of radial normal stress and shear stresses are observed when out-of-plane fiber waviness is introduced. The comparisons between present analytical results and numerical data indicate that the present methodology have ability to capture radial normal, circumferential normal, and shear stress distributions of composite curved beam with out-of-plane fiber waviness and the level of stress predicted is satisfactory with numerical results.

Data-driven analytical mechanics of aging viscoelastic shotcrete tunnel shells

Based on the principle of virtual power, equilibrium conditions are established for the forces within a cross section of a tunnel top heading driven according the New Austrian Tunneling Method (NATM). External forces, namely impost actions and ground pressure distributions following a third-order polynomial, are analytically linked with internal forces, such as axial forces and bending moments, arising as integrals over the shell thickness, of circumferential normal stresses. The latter are related, via an aging viscoelastic shotcrete material model, to circumferential normal strains, as well as to radial and circumferential displacement components. This allows for analytical transformation of displacement measurement data collected at the crown and the footings of the shell segment, into ground pressure and impost action evolutions, together with all the associated force and stress quantities. For the Sieberg tunnel, driven in Miocene clay marl, our data-driven analytical mechanics model evidences virtually uniform ground pressure distributions, leading to a first rapidly increasing, and then mildly decreasing utilization degree of the shotcrete shell.

Vessel Failure Analysis of a Boiling Water Reactor During a Severe Accident

In a postulated severe accident, the thermo-mechanical loads from the corium debris that has relocated to the lower head of the reactor pressure vessel (RPV) can pose a credible threat to the RPV’s structural integrity. In case of a vessel breach, it is vital to predict the mode and timing of the vessel failure. This affects the ex-vessel accident progression and plays a critical role in the development of mitigation strategies. We propose a methodology to assess RPV failure based on MELCOR and ANSYS Mechanical APDL simulations. A Nordic-type boiling water reactor (BWR) is considered with two severe accident scenarios: i) SBO (Station Blackout) and ii) SBO + LOCA (Loss of Coolant Accident). In addition, the approach considers the dynamic ablation of the vessel wall due to a high-temperature debris bed with the use of the element kill function in ANSYS. The results indicate that the stress failure mechanism is the major cause of the RPV failure, compared to the strain failure mechanism. Moreover, the axial normal stress and circumferential normal stress make the dominant contributions to the equivalent stress σ at the lower head of RPVs. As expected, the region with high ablation is most likely the failure location in both SBO and SBO + LOCA. In addition, comparisons of the failure mode and timing between SBO and SBO + LOCA are described in detail. A short discussion on RPV failure between ANSYS and MELCOR is also presented.

Thermo-mechanical coupling analysis of the end faces for a mechanical seal under dry friction

A three-dimensional rotating sliding contact model was developed to study transient dry friction characteristics of a mechanical seal based on a modified W-M fractal function. The mechanical action and thermal-mechanical coupling between asperities were simulated using the software ABAQUS. The effects of external load, rotating speed and roughness on contact characteristics of the friction pair (carbon graphite/tungsten carbide) were investigated. The stress on cross section of the rough entity was studied. The results show that circumferential normal stress of contact asperity changes in axial direction from compressive stress to tensile stress to compressive stress, and tensile stress may cause crack propagation in the carbon graphite ring. The roughness Ra has great influence on stress and temperature distribution of rough entity.

Non Full Contact of Highway Pressure Tunnel Lining with Single Centre Circle Considering non Continuous Interfacial Circumferential Normal Stress and Experimental Validation

Non Full Contact of Highway Pressure Tunnel Lining with Single Centre Circle Considering non Continuous Interfacial Circumferential Normal Stress and Experimental Validation

An analytical solution for static problems of curved composite beams

Abstract An analytical solution is presented for the determination of deformation of curved composite beams. Each cross-section is assumed to be symmetrical and the applied loads are acted in the plane of symmetry of curved beam. In-plane deformations are considered of composite curved beams. Assumed form of the displacement field assures the fulfillment of the classical Bernoulli-Euler beam theory. The curvature of beam is constant and the internal forces in a cross-section is replaced by an equivalent forcecouple system at the origin of the cylindrical coordinate system used. The internal forces are expressed in terms of two kinematical variables, which are the radial displacement and the rotation of the cross-sections. The determination of the analytical solutions of the considered static problems are based on the fundamental solutions. Linear combination of the fundamental solutions which are filling to the given loading and boundary conditions, gives the total solution. Closed form formulae are derived for the radial displacement, cross-sectional rotation, nomral and shear forces and bending moments. The circumferential and radial normal stresses and shear stresses are obtained by the integration of equilibrium equations. Examples illustrate the developed method.

Determination of optimal residual stress profiles for improved rolling contact fatigue resistance

A theoretical framework is developed for the evaluation of favorable residual stress profiles, suppressing fatigue damage initiation in rolling contact fatigue. Non-metallic inclusions at the microstructure of bearings are one of the most important reasons for fatigue damage initiation since they act as stress risers. In order to evaluate the stress state around such inclusions at the micro-scale, macroscopic stress histories are determined by Hertzian contact theory at different depths below the raceway for a typical roller bearing. These stress distributions are then used as far-field stresses for a micro-scale model accounting for single inclusions of different geometries and orientations. Eshelby’s method is used to relate far-field and local stresses in the vicinity of inclusions. The von Mises stress criterion is then used as a conservative estimator of crack initiation due to micro-scale plasticity. The effect of compressive residual stresses added to the axial and circumferential normal stress components at different depths is analyzed. The von Mises stress field around different inclusions at different depths is investigated in order to determine the most critical case in terms of micro-scale plastic deformation. Finally, an optimization process is carried out in order to determine the residual stresses that minimize the maximum observed von Mises stress as a function of depth.

Histology and Biaxial Mechanical Behavior of Abdominal Aortic Aneurysm Tissue Samples.

Abdominal aortic aneurysms (AAAs) represent permanent, localized dilations of the abdominal aorta that can be life-threatening if progressing to rupture. Evaluation of risk of rupture depends on understanding the mechanical behavior of patient AAA walls. In this project, a series of patient AAA wall tissue samples have been evaluated through a combined anamnestic, mechanical, and histopathologic approach. Mechanical properties of the samples have been characterized using a novel, strain-controlled, planar biaxial testing protocol emulating the in vivo deformation of the aorta. Histologically, the tissue ultrastructure was highly disrupted. All samples showed pronounced mechanical stiffening with stretch and were notably anisotropic, with greater stiffness in the circumferential than the axial direction. However, there were significant intrapatient variations in wall stiffness and stress. In biaxial tests in which the longitudinal stretch was held constant at 1.1 as the circumferential stretch was extended to 1.1, the maximum average circumferential stress was 330 ± 70 kPa, while the maximum average axial stress was 190 ± 30 kPa. A constitutive model considering the wall as anisotropic with two preferred directions fit the measured data well. No statistically significant differences in tissue mechanical properties were found based on patient gender, age, maximum bulge diameter, height, weight, body mass index, or smoking history. Although a larger patient cohort is merited to confirm these conclusions, the project provides new insight into the relationships between patient natural history, histopathology, and mechanical behavior that may be useful in the development of accurate methods for rupture risk evaluation.

Bi-ventricular finite element model of right ventricle overload in the healthy rat heart.

The recognition of RV overpressure is critical to human life, as this may signify morbidity and mortality. Right ventricle (RV) dysfunction is understood to have an impact on the performance of the left ventricle (LV), but the mechanisms remain poorly understood. It is understood that ventricular compliance has the ability to affect cardiac performance. In this study, a bi-ventricular model of the rat heart was used in preference to other, single-ventricle models. Finite element analysis (FEA) of the bi-ventricular model provides important information on the function of the healthy heart. The passive myocardium was modelled as a nearly incompressible, hyperelastic, transversely isotropic material using finite element (FE) methods. Bi-ventricular geometries of healthy rat hearts reconstructed from magnetic resonance images were imported in Abaqus©. In simulating the normal passive filling of the rat heart, pressures of 4.8kPa and 0.0098kPa were applied to the inner walls of the LV and RV respectively. In addition, to simulate the overpressure of the RV, pressures of 2.4kPa and 4.8kPa were applied to the endocardial walls of the LV and RV respectively. As boundary conditions, the circumferential and longitudinal displacements at the base were set to zero. The radial displacements at the base were left free. The results show that the average circumferential stress at the mid-wall in the overloaded model increased from 2.8kPa to 18.2kPa. The average longitudinal stress increased from 1.5kPa to 9.7kPa. Additionally, in the radial direction, the average stress increased from 0.1kPa to 0.6kPa in the mid-wall. The average circumferential strain was found to be 0.138 and 0.100 on the endocardium of the over pressured and healthy model respectively. The average circumferential stress at the epicardium, mid-wall and endocardium in the case of a normal heart is 10 times lower than in the overloaded heart model. The finite analysis method is able to provide insights into the behaviour of the over pressured model (myocardium). In the overloaded model the high stresses and strains were observed on the septal wall. The bi-ventricular model was shown to provide useful information relating to the over pressured ventricle. The possible heart dysfunction may be attributable to high stress and strain in the over pressured heart.

Greenstick fracture in composite pultruded rods

Abstract The paper analyses the greenstick fracture mode on anisotropic beams subjected to flexural loading. This fracture mode can be seen in plant branches, young mammal bones or reinforced plastic rods. Two analytical models have been studied: a straight beam model and a uniform curved beam model. Circumferential normal stress distribution has been determined considering the classical beam theory, and radial and shear stresses have been predicted by using the Airy's stress function. Experimental work has been implemented on initially straight pultruded rods with longitudinally oriented fibres. Three and four-point bending tests adopting several span-to-diameter ratios have been performed. Experimental conditions that promote a greenstick fracture mode in composite pultruded rods have been considered.

Reliability-Based Design Optimization Method of Turbine Disk with Transformed Deterministic Constraints

AbstractTo improve the computational efficiency of the reliability-based design optimization (RBDO) of a complex structure with nonlinear and implicit limit-state function, the single-loop-single-vector (SLSV)-limit-state factor (LSF) (SLSV-LSF) method was developed by fully considering the advantages of the SLSV approach and the LSF method to transform uncertain constraints into deterministic constraints. The mathematical models of SLSV and LSF were established and the basic RBDO process of the SLSV-LSF method is presented. The shape optimization of an aeroengine turbine disk was completed based on the proposed method. From the reliability sensitivity analysis of the turbine disk, it is revealed that an uncertain constraint of average circumferential stress can be transformed into a deterministic constraint and material density can be regarded as a deterministic variable. Through the min-mass shape design of the turbine disk based on different approaches, it is demonstrated that the developed method main...

Contact problem for regular hexagon weakened with full-strength hole

A problem of the plane elasticity theory is addressed for a doubly connected body with an external boundary of the regular hexagon shape and with a 6-fold symmetric hole at the center. It is assumed that all the six sides of the hexagon are subjected to uniform normal displacements via smooth rigid stamps, while the uniformly distributed normal stress is applied to the internal hole boundary. Using the methods of complex analysis, the analytical image of Kolosov-Muskhelishvili’s complex potentials and the shape of the hole contour are determined from the condition that the circumferential normal stress is constant along the hole contour. Numerical results are given and shown in relevant graphs.

A New Observation on the Stress Distribution in the Coronary Artery Wall

The stress distribution in the vessel wall has an important bearing on vascular function in health and disease. We studied the relationship between the transmural stress distribution and the opening angle (OA) to determine the stress gradient. The simulation of wall stress was based on transmural measurements of strain and material properties of coronary arteries in reference to the zero-stress state. A one-layer model with material constants of the intact vessel was used to calculate the circumferential stress distribution. A sensitivity analysis using both one- and two-layer models (intima-media and adventitia layers) was carried out to study the effect of the OA on the circumferential stress distribution and average circumferential stress. A larger OA always shifts the circumferential stress from the intima-media to the adventitia layer. We report a new observation that the circumferential stress at the adventitia may exceed that at the intima at physiological loading due to the larger OA in the porcine coronary artery. This has important implications for growth and remodeling, where an increase in opening angle may shift excessive stress from the inner layer to the outer layer.

Numerical simulations of 3D tool geometry effects on deposition residual stresses in diamond coated cutting tools

Deposition residual stresses in diamond-coated cutting tools significantly impact the coating adhesion and machining performance. In this study, Computer-Aided Design (CAD) software was used to create the solid model of coated tools, and further exported to Finite Element Analysis (FEA) software for 3D simulations of residual stresses generated. Design of experiments approach was employed to systematically investigate the tool geometry effects. Major results are summarised as follows. • the cutting edge radius is the most significant factor • for a 5 µm edge radius, the radial and circumferential normal stresses (�1 r and �1 �� ) are about 1.5 GPa in tension and 3.7 GPa in compression, respectively.

Coronary Artery Circumferential Stress: Departure from Laplace Expectations with Aging

Normal, youthful arteries generally maintain constant radius/wall thickness ratios, with the relationship being described by the Laplace Law. Whether this relationship is maintained during aging is unclear. This study first examines the Laplace relationships in postmortem coronary arteries using a novel method to correct measurements for postmortem artifacts, uses data from the literature to provide preliminary validation, and then describes histology associated with low circumferential stress. Measurements of radius and wall thickness, taken at sites free from atheromas, were used with national population estimates of age-, gender-, and race-specific blood pressure data to calculate average circumferential stress within demographic groups. The estimated circumferential stress at ages 55-74 years was about half that at ages 18-24 years because of a disproportionate increase of wall thickness relative to artery radius at older ages, violating the expected relationships described by the Laplace Law. Arteries with low circumferential stress (estimated at sites distant from atherosclerosis) had more necrotic atheromas than arteries with high stress. At sites with low stress and intimal thickening, smooth muscle cells (SMCs) were spread apart, thereby diminishing their density within both the intima and media. Thus, older arteries displayed both low circumferential stress and abundant matrix of low cellularity microscopically. Such changes might alter SMC-matrix interactions.

Remodeling of conduit arteries in hypertension and flow-overload obeys a minimum energy principle

Arterial remodeling is an important process in physiology and pathophysiology. Based on an energy minimization method, Murray's law predicts the optimal inner radius. Application of Darcy's law in the wall results in an optimal outer radius. The average wall stress is computed by the Laplace's law. Using these formulas, a large porcine coronary artery in hypertension is studied. The results reveal how wall thickness and average circumferential stress change after increasing blood pressure and volume flow rate. The theoretical predictions are in good qualitative agreement with experimental observations. The advantage and limitation of the current approach are discussed.

The benefit from an adequate finite element simulation of the cold hole expansion process

The article presents outcomes from finite element and X-ray diffraction analyses of the cold hole expansion process fulfilled by means of solid mandrel gradually passing through the hole. Regardless of the manner of accomplishing – split sleeve; split mandrel; with a mating tapered split sleeve; spherical mandrelling – an axial gradient of the residual stresses is obtained due to the interaction between the layers caused by an axial force flow which passes through the mandrel, the workpiece and the support to forma closed circuit. To predict the fatigue life it is necessary to know the residual stresses on the entrance and the exit faces immediately to the hole periphery which are considered to be potential crack initiation sites. It has been proved that there are two key moments in the building of an adequate finite element model. The first is modeling of a realistic contact mandrel-workpiece with or without mediator and workpiece-support. The second is a suitable constitutive model of the workpiece material. Six hardening models of low-carbon steel obtained on the basis of a symmetric strain-controlled experiment and half-cycle test data from unidirectional tension experiment have been used consecutively in the finite element model of the process. On the basis of a comparison with experimental results obtained by means of an X-ray diffraction technique it has been established that the nonlinear kinematic hardening model obtained by a strain-controlled cyclic test to achieve a stabilized cycle secures finite element results close to the experimental ones. The chosen finite element model has been compared with simplified ones following the residual circumferential normal stress criterion and its advantages have been proved.

Interactions Inside a Coupled Oscillation System of Bubble-Viscous Liquid-Vessel and the Induced Stresses and Strains Within the Vessel Wall

ABSTRACTThe evolution of a bubble confined inside a nonlinear micro vessel fully filled with a viscous liquid, subjected to a shock lithotripsy wave (SWL), is analyzed with a previously established asymmetrical model on bubble oscillation. Both the normal and shear stress components within the vessel wall are calculated. It is observed that although the shear stress induced by viscosity is far less than the normal stresses, hypertension patients are still at more risk than normal people in SWL because of the high blood pre-pressure and stiff vessel wall accompanying their high blood viscosity. Hence, safety of hypertensive patients with high blood viscosity must be taken into careful consideration in SWL. More detailed numerical results show that the increase of circumferential normal stress and strain in SWL is significantly larger than that of other stresses and strains. Large circumferential normal stress and strain are responsible for excessive dilation of vessel wall during asymmetrical oscillation of constrained bubbles, which implies that the vessel wall will rupture mainly in the form of a cleft along the vessel axial direction.

Surrounding tissues affect the passive mechanics of the vessel wall: theory and experiment

The stress and strain in the vessel wall are important determinants of vascular physiology and pathophysiology. Vessels are constrained radially by the surrounding tissue. The hypothesis in this work is that the surrounding tissue takes up a considerable portion of the intravascular pressure and significantly reduces the wall strain and stress. Ten swine of either sex were used to test this hypothesis. An impedance catheter was inserted into the carotid or femoral artery, and after mechanical preconditioning pressure-cross-sectional area relations were obtained with the surrounding tissue intact and dissected away (untethered), respectively. The radial constraint of the surrounding tissue was quantified as an effective perivascular pressure on the outer surface of the vessel, which was estimated as 50% or more of the intravascular pressure. For carotid arteries at pressure of 100 mmHg, the circumferential wall stretch ratio in the intact state was approximately 20% lower than in the untethered state and the average circumferential stress was reduced by approximately 70%. For femoral arteries, the reductions were approximately 15% and 70%, respectively. These experimental data support the proposed hypothesis and suggest that in vitro and in vivo measurements of the mechanical properties of vessels must be interpreted with consideration of the constraint of the surrounding tissue.