Axisymmetric Analysis Research Articles

Numerical modeling of the effect of loading rate on the tensile load capacity of offshore caisson foundations

Suction caissons are skirted foundations frequently used in offshore environments supporting various structures. Among those lie the offshore wind turbines (OWT), which are currently one of the most common renewable energy systems. In this paper we study the tensile capacity of caisson foundations of OWT in dense sands, where the generation of excess pore pressure is analyzed. The tensile capacity of suction buckets under various loading rates is investigated using a series of quasi-static axisymmetric finite element analyses with coupled flow-deformation formulation. DeltaSand model is utilized for the soil, which is an elasto-plastic state-dependent model capturing the response of sands at varying relative densities. Numerical results are validated with available test data of scaled physical model experiments. Particular emphasis is placed on the interaction between suction-bucket and the soil. Parameters governing the soil-caisson interface playing a key role in the uplift response are identified. Lastly, a case study that can be observed in offshore foundations is simulated. Results show that the developed numerical model is applicable to capturing the uplift response of bucket in an ocean environment. The outcome of this study will contribute to closing the gap in the design of suction caissons of OWT in existing standards.

Altitude-compensating axisymmetric supersonic nozzle design and flow analysis

Altitude-adapted nozzles are designed to facilitate flow adaptation during rocket ascent in the atmosphere, without requiring mechanical activation. As a consequence, the performance of the nozzle is significantly improved. The aim of this study is to develop a new profile of axisymmetric supersonic nozzles adapted at altitude (Dual Bell Nozzle with Central Body), which is characterized by an E-D nozzle as a basic profile. The performances obtained for this nozzle (E-D Nozzle) are then compared to those of a Plug nozzle. The E-D nozzle shows significant performance advantages over the Plug nozzle, including a 13.02% increase in thrust, knowing that the length of the E-D nozzle is half that of the Plug nozzle under the same design conditions. Finally, viscous calculations using the k-ω SST turbulence model were conducted to compare the performance of the dual bell nozzle with central body (DBNCB) and the E-D nozzle with the same cross-sectional ratio, and to assess the impact of nozzle pressure ratio (NPR) variations on the operation mode of the DBNCB. The results obtained show that the DBNCB offers the best performance in most phases of flight.

An axisymmetric bioheat transfer analysis through a unified model

AbstractA unified model is developed for the analysis of heat transfer (radiation and non‐Fourier conduction) in an axisymmetric participating medium. The proposed model includes three different variants of hyperbolic–parabolic heat conduction models, that is, the single phase lag model, dual phase lag model, and the Fourier (no phase lag) model. The radiating‐conducting medium is radiatively absorbing, emitting, and isotropically scattering. Significance of all the above mentioned models on the heat transfer characteristics is investigated in a two‐dimensional axisymmetric geometry. The equation of transfer and the coupled non‐Fourier conduction‐radiation equation are solved via finite volume method. A fully implicit scheme is used to resolve the transient terms in the energy equation. For spatial resolution of radiation information, the STEP scheme is applied. Tri‐diagonal‐matrix‐algorithm is used to solve the resulting set of linear discrete equations. Effects of two important influencing parameters: the scattering albedo and the radiation‐ conduction parameter are studied on the temporal evolution of temperature field in the radiatively participating medium. The non‐Fourier effect of heat transport captured well with the proposed unified model. A good agreement can be found between the proposed model predictions and those available in the literature. It is also found that when the phase lag of the temperature gradient and the heat flux are the same, it reduces to conventional Fourier conduction‐radiation and the wave behavior diminishes. However, the reduction to this Fourier model fails in the presence of constant blood perfusion and metabolic heat generation.

Numerical analysis of the contribution of side resistance to caisson bearing capacity

The use of deep foundations is a common practice in geotechnical civil engineering designs, in which the bearing capacity of these foundations occurs by side resistance, tip, or through the combination of both. In the case of caisson, the bearing capacity is often obtained by considering only the resistance of the lower end due to its bell-shaped geometry, neglecting the skin friction resistance of the shaft, which may represent an oversizing in some cases. In this context, this paper analyzed the behavior of nine caisson prototypes laid at 10 m, 15 m and 20 m deep. At each depth, three types of caissons were analyzed, with and without an expanded base, and a third type with deformable material at the top of the base. The axisymmetric numerical analyses were conducted by using the finite element method considering an isotropic medium. Thus, it was found that with increasing depth, the skin frictional resistance of the surrounding soil of shaft contributes significantly to the bearing capacity of the caisson suggesting that little load would reach the base of the caisson in situations that would negligible the side resistance of the shaft in the design phase. This may be an important consideration in foundation design using caisson, as it would reduce risks to human life, as well as reduce material consumption and the generation of carbon released into the atmosphere.

Axisymmetric thermal postbuckling of functionally graded graphene nanocomposite annular plates with various geometric imperfections

This paper presents the axisymmetric thermal postbuckling analysis of functionally graded graphene platelets-reinforced composite (FG-GPLRC) annular plates with various geometric imperfections within the framework of first-order shear deformation theory and von Kármán geometric nonlinearity. An imperfection model composed of trigonometric and hyperbolic functions is used to simulate possible imperfections with different shapes, amplitudes and locations. The 3D Halpin–Tsai model is employed to estimate the effective modulus of graphene nanocomposites. Nonlinear governing equations are derived by the variational principle and are then solved by the generalized differential quadrature method combined with the modified Newton–Raphson iteration. Parametric studies are conducted to highlight the influences of imperfection amplitude, localization degree, location and half-wave number on the thermal postbuckling behaviour of FG-GPLRC annular plates. It is found that the thermal postbuckling resistance is reduced due to the existence of geometric imperfections, and this effect become more/less significant as the imperfection amplitude/half-wave number increases.

FE Simulation of Truck Tire Manufacturing Process

Pneumatic Tires are one of the most important components in automobiles whether in aviation, 2/3/4 wheels drive or industrial applications. The tire is a complex assembly of numerous products which are assembled on a drum and then cured in a press under heat and pressure. Michelin being one of the premium tire manufacturing company, emphasize on use of latest technology at every stage of Tire manufacturing. The complex tire manufacturing process, from design conception till final assembly is currently simulated at Michelin using inhouse CAD/FEA simulation software. Use of FEA tools in manufacturing process simulation allows engineer to iterate over different mixes and evolving designs. In current scope, pre-defined FE template is developed for Michelin to simulate physical truck tire manufacturing process to allows user to perform automated FE iterations on iterative designs, materials etc improving the result output and increasing the productivity of user. Truck tire manufacturing process from green tire to cured tire is simulated as large displacement, 2d axisymmetric FE analysis with viscous or viscoelastic materials. Results of FE simulation are compared with that of Tire architect post manufacturing to marks effectiveness of FE analysis.

Stress wave propagation analysis of 2D-FGM axisymmetric finite hollow thick cylinder

In this paper, a numerical axisymmetric elastic stress wave propagation analysis of the 2D-FGM hollow thick finite cylinder has been performed. The new accurate material distribution model based on Mori-Tanaka scheme and third-order transition function for 2D-FGMs has been implemented in the graded finite element method with higher-order quadrilateral elements. A non-uniform impulsive pressure has been applied on the one-third of the top inner cylinder wall. Consequently, different wave velocities and reflections from the boundaries have been observed due to the graded distribution of material along with two directions. Moreover, the effects of two-dimensional material property distributions on the stress wave propagations and displacements through the cylindrical wall at different locations have been studied systematically. Normalized effective stresses based on von-Mises criteria has been performed in comparison with the internal impulsive pressure amplitude to provide a measure of the cylinder wall response to the mechanical impact loading, the effective stresses are nearly 2.5 times the internal pressure loading amplitude, closed to the impact location. According to the results, 2D material property gradations has effected the stresses significantly. Alternatively, desired stress values can be achieved through optimal design and appropriate choice of property distribution.

Axisymmetric bending vibration analysis of bidirectional functionally graded rotating micro-disk under thermo-mechanical loading

The free vibration behavior of a bidirectional functionally graded rotating micro-disk that is subjected to uniform transverse pressure and high-temperature thermal loading has been studied. The micro-disk is functionally graded along the radial and thickness directions. The problem is mathematically formulated using two distinct but interrelated steps within the framework of Kirchhoff plate theory and modified couple stress theory. The first step determines the time-invariant deformed configuration of the micro-disk under centrifugal, pressure, and thermal loading using minimum potential energy principle. The second step determines the free vibration behavior of the micro-disk in the neighborhood of the deformed configuration using Hamilton’s principle. The solutions of the governing equations for both these steps are obtained using the Ritz method. The mathematical model is successfully validated with various reduced problems. The numerical results for the first four axisymmetric bending vibration modes are presented to investigate the effects of wide range of parameters such as rotational speed, applied pressure, thermal loading, size-dependent thickness, volume fraction indices, and radius ratio. The mode shapes of vibration are illustrated through surface and contour plots.

Axisymmetric buckling analysis of submerged hemi-elliptic toroidal shells

Toroidal shells have been widely used in various industrial applications for over a decade. Most studies on buckling behavior have focused on circular toroidal shells with uniform loads. In contrast, the existing literature on the shell buckling of a toroid with elliptical cross-sections has received limited attention. This study aims to present numerical solutions for axisymmetric buckling of hemi-elliptic toroidal shells under linearly hydrostatic pressure to append available data and results in this field. The thickness of the hemi-elliptic toroidal shells is assumed to be constant before and after the buckling state. Solution procedures for solving critical buckling loads dealt with eigenvalue problems and were formulated by an energy approach. All relevant parameters such as membrane and bending strain components and in-plane stress resultants were derived based on differential geometry. An in-house FEM program solved the weak formulation derived from a variational method. The buckling results for elliptic toroidal shells with various b/a ratios were established as the critical seawater depth and compared to the previously published results. Additionally, parametric studies on the effect of the variable b/a ratios and the major radius R of elliptic toroidal shells on the axisymmetric buckling loads and mode shapes were examined thoroughly and addressed in more detail herein.

Methodology of estimation of temperature mode in the 2xBgu type railway braking system

The article presents finite element models of the 2xBgu type tread brake for the simulation of extended repeated frictional heating carried out on a full-scale inertia dynamometer. The numerical calculations were conducted for the brake blocks made of two organic composite materials newly developed specifically for this study. The transient temperature changes obtained from the 2D axisymmetric and 3D finite element analyses and experimental data agreed well during continuous process of about 1200 s. Simulation of such a long period of braking sequence required introducing simplifications in the boundary conditions in the contact area, convection cooling, arrangement of the model (2D axisymmetric, 3D). The focus was laid on representation of variation of the coefficient of friction and the temperature dependence of the properties of the friction materials during braking. The carried out research indicates limitations in the finite element analysis and directions of necessary improvements in modelling as well as measurements with the use of embedded thermocouples.

Size effects on spheroidal voids by Finite Fracture Mechanics and application to corrosion pits

AbstractThe present work aims at investigating the failure size effect of a spheroidal void in an infinite linear elastic solid under remote tension by means of the coupled Finite Fracture Mechanics (FFM) approach. The opening stress field and the stress intensity factor (SIF) of an annular crack surrounding the cavity —necessary for the FFM implementation— are obtained numerically through parametric axisymmetric finite element analyses (FEAs): The spheroid aspect ratio is varied between 0.1 and 10 and Poisson's ratio between 0.1 and 0.5. Accordingly, semi‐analytical functions approximating the stress concentration factor and the SIF are put forward. Finally, the failure size effect on spheroidal voids is reported, and FFM predictions are compared with experimental results on the fatigue limit arising from corrosion pits, showing a fairly good agreement.

Axisymmetric Free Vibration Analysis of Functionally Graded Sandwich Annular Plates: A Quasi-3D Shear and Normal Deformable Model

This paper concentrates on axisymmetric free vibration of functionally graded (FG) sandwich annular plates obtained using a quasi-3D plate theory. Motion equations and corresponding boundary conditions are established via the mentioned plate theory which takes into consideration the non-uniform shear strains across the thickness and also stretching trough the thickness. Generalized differential quadrature method (GDQM) is applied to discrete the annular sandwich plate governing equations. The results of this study are applicable for optional thick plates since the adopted theory considers the shear and normal strains across the thickness direction. Outcoming results are verified on the basis of information accessible in the open literature. To investigate the influences of power law index of functionally graded materials (FGMs) and dimensions of the sandwich annular plate layers, parametric studies are presented. It was well demonstrated that the applied theory precisely predicts the natural frequencies of FG annular sandwich plates with arbitrary thickness.

Computer Simulation to Determine LHP of 4 Different Types of Transient Industrial Quenched Molybdenum Steel Bars

Simulation of hardness distribution in quenched specimens has been investigated using three-dimensional finite-element (FE) analyses which reduced into a 2-dimensional axisymmetric analysis based on Ansys Software capable of predicting temperature history; evolution hardness of four different types of Molybdenum steel bars during thermal processing of materials in quenching process is presented. The Jominy test results are used to estimate specimen hardness. specimen points hardness used to be determined through conversion of evaluated characteristic cooling time for phase transformation t8/5 into hardness. The lowest hardness point (LHP) of each quenched Molybdenum steel bar has been determined to be in mid its length in the center. Experimentally, it is quite impossible to determine this hardness value, and earlier approaches could only assess surface hardness. Normally, this value of hardness at the surface is greater than (LHP), that, under certain conditions might lead to component failure and deformation. The model can be employed to establish a cooling method to attain the required microstructure as well as mechanical properties, which include hardness.

전자기 유도를 활용한 전자기 댐퍼의 구조 설계에 관한 연구

In this paper, we proposed and electro-magnetic (EM) damper that can have both the simple structure of the existing mechanical damper and the active damping ability of the Magnetic-Rheological fluid damper. The proposed EM damper has a structure similar to that of a mechanical damper, and the manufacturing cost is not high because the damping force can be generated only with the permanent magnet mounted on the plunger and the damping coil mounted on the inside of the cylinder. Damping force is generated according to the amount of change in flux linkage of the damping coil when the permanent magnet mounted on the plunger vibrates up and down. Therefore, the electromagnetic field structure of the EM damper, which is advantageous to generate a damping force that suppresses external vibration, is proposed. In order to verify the reliability of the damping capacity of the EM damper, it was analyzed by finite element analysis applying an axisymmetric analysis technique, and the damping ability to suppress external vibration was verified with the induced current waveform of the damping coil and the generated damping force waveform.

Nonlinear axisymmetric buckling analysis of the FGM sandwich shallow spherical shells under thermomechanical loads

Functionally graded material (FGM) sandwich shallow spherical shells are promising composite sandwich structures for modern engineering applications. In this paper, the axisymmetric snap-through buckling of spherical shells under uniform external pressure and non-uniform temperature rise along the shell thickness was studied. Based on the classical shell theory and the Sanders nonlinear kinematics equations, we established a two-point boundary value problem (BVP) posed by the displacement-type nonlinear ordinary differential equations governing the axisymmetric buckling of the FGM sandwich shallow spherical shells and the clamped boundary conditions. Then, the solutions of the above BVP were obtained using the numerical shooting method. The influence of initial term numbers of the infinite series defining the non-uniform temperature field on the accuracy of the solution was examined. Numerical calculations showed that a considerable initial term number of the series were needed to obtain the applicable solutions for engineering. Some valuable conclusions were drawn through detailed parameter studies. As the radius of the bottom circle increases, the lower critical load of shells decreases, the jump amplitude of buckling increases, and the upper critical load remains almost unchanged. The upper and lower critical loads and the jump amplitude increase as the circle radius of the middle surface of shells decreases. When the thickness of shells increases, their upper and lower critical loads increase, whereas the jump amplitude of buckling reduces. The gradient index has a significant effect on the steady-state response of pre-buckling spherical shells but little effect on that of post-buckling spherical shells. When the temperature rises, the upper critical load and the buckling jump amplitude of shells increase, but the lower critical load decreases. When the gradient index is greater (less) than about 0.35, the upper critical load decreases significantly (increases slightly) with the increase in the relative thickness of the FGM core. The present numerical results are well consistent with the finite element results and those in the available literature.

A three-dimensional model to describe complete human corneal oxygenation during contact lens wear.

We perform a novel 3D study to quantify the corneal oxygen consumption and diffusion in each part of the cornea with different contact lens materials. The oxygen profile is calculated as a function of oxygen tension at the cornea-tear interface and the oxygen transmissibility of the lens, with values used in previous studies. We aim to determine the influence of a detailed geometry of the cornea in their modeling compared to previous low dimensional models used in the literature. To this end, a 3-D study based on an axisymmetric volume element analysis model was applied to different contact lenses currently on the market. We have obtained that the model provides a valuable tool for understanding the flux and cornea oxygen profiles through the epithelium, stroma, and endothelium. The most important results are related to the dependence of the oxygen flux through the cornea-lens system on the contact lens thickness and geometry. Both parameters play an important role in the corneal flux and oxygen tension distribution. The decline in oxygen consumption experienced by the cornea takes place just inside the epithelium, where the oxygen tension falls to between 95 and 16 mmHg under open eye conditions, and 30 to 0.3 mmHg under closed eye conditions, depending on the contact lens worn. This helps to understand the physiological response of the corneal tissue under conditions of daily and overnight contact lens wear, and the importance of detailed geometry of the cornea in the modeling of diffusion for oxygen and other species.

Assessment of an Assumed Strain-based Quadrilateral Membrane Element

This paper describes the development of a simple quadrilateral strain-based element for plane stress and strain problems. This element has five nodes, four located at its corners and one at the center. Each of the four corner nodes had two essential external degrees of freedom (u, v), while the center node had three degrees of freedom (u, v, ɵ); the static condensation method was used for the internal node. This element was used for both linear and dynamic analysis. Its performance was assessed using a variety of membrane and axisymmetric analysis problems. The obtained results demonstrated the good performance and accuracy of the proposed element.

Numerical Evaluation of Reinforcement Structure Against Electromagnetic and Thermal Stresses in Stacked REBCO Pancake Coils

In recent years, high field REBCO coils have been applied with great interest to NMR and accelerators due to their high thermal stability and high current density. However, deteriorations and damages of REBCO coils are occurring. During the charge and discharge of REBCO coils, screening currents are induced to circulate in the windings, resulting in a non-uniform current distribution in the wires. It has been reported that the electromagnetic force distribution in the wire becomes significantly non-uniform, resulting in degradation of REBCO coils. In this study, the effects of stress and deformation of REBCO coils were investigated through electromagnetic stress analysis using two-dimensional axisymmetric structural analyses, taking into account thermal stress during cooling, tension during winding and electromagnetic force during not only charge and but also discharge, and the suppression of stress and deformation by the currently devised YOROI—coil (Y-based oxide superconductor and reinforcing outer integrated coil) structure and over-banding was evaluated.

Evaluation of capacity of power hammer machine foundation from high strain dynamic load test: Field test and axisymmetric numerical modeling

The power hammer machines induce harmful vibrations in different parts of the foundation which may result in excessive dynamic settlement. While designing the hammer machine foundation, variety of static and repetitive impact load tests are generally conducted to ensure both the stability and serviceability of the foundation system. The static load test (SLT) is performed in the case of such foundations to obtain the ultimate capacity. However, the SLT is unable to predict the reliable response of the machine foundation. Hence, the current study is aimed to investigate the static and dynamic resistance of power hammer machine foundation by employing the high strain dynamic load test (DLT). The test procedure involves measuring the acceleration, axial force and settlement at the top of the machine foundation. Additionally, the soil resistance pertaining to damping is assumed to disappear with the zero-velocity at the first moment, which is identical to the unloading point method (UPM). Also, the field test and axisymmetric finite element analysis by considering the nonlinear soil model were performed to evaluate the stress settlement curve (SSC) from both SLT and DLT. The results reveal that the capacity of the machine foundation subjected to repetitive dynamic loads increases gradually and then tend to remain stable in case of additional impact loads. The SLTs showed 3–4 % higher static resistance than the first DLT and 8–9 % reduction in contrast to the second DLT. Moreover, the residual plastic deformation of the soil beneath the machine foundation was recorded to rapidly increase at the beginning of hammer tamping while it decreased steadily with further increasing of the hammer blows.

A numerical method based on Polonsky-Keer's conjugate gradient iterative scheme for solving axisymmetric contact of layered half-space

Axisymmetric contact analysis of layered half-space is of considerable interest in many tribological applications including protective hard coating, metal-matrix composites, etc. Polonsky-Keer's iterative scheme based on conjugate gradient method (CGM) is powerful for a general three-dimensional contact problem using rectangular meshes, but would inevitably lead to excessive computational burden and inaccurate boundary discretization for axisymmetric contact. In this paper, Polonsky-Keer's CG-based iterative scheme is adapted for axisymmetric indentation of a layered elastic half-space by taking advantage of annular ring discretization, where the elementary solutions for the surface deflection and subsurface stresses can be determined with assistance of the Hankel transforms. The present method can not only effectively circumvent the discretization error, but is also versatile and flexible to solve the contact between the layered materials and an arbitrary axisymmetric indenter. Parametric studies are provided to validate the present solutions, and the comparisons of the average relative errors for different types of elements are conducted to demonstrate the excellent convergence and accuracy of the proposed numerical scheme.