Axisymmetric Stress Analysis Research Articles

Some axially symmetric contact problems

Axisymmetric stress analysis problems are considered where mixed boundary conditions apply over the interior of a cylinder. A brief indication of some generalisations is also given.

Axi-symmetric thermoelastic stress analysis of a thin circular plate due to heat generation

The aim of this work is to determine the temperature, displacement function, thermal stresses and thermal deflection of a thin circular plate defined as 0 ≤ r ≤ a, 0 ≤ z ≤ h under an unsteady temperature field due to internal heat generation within it. Initially, the plate is kept at an arbitrary temperature F(r, z). For times t > 0, heat is generated within the thin circular plate at a rate of g(r, z, t) W. m-3. The governing heat conduction equation has been solved by generalised finite Fourier transform and finite Hankel transform technique. The results are obtained in a series form in terms of Bessel's functions. The results for temperature, displacement function, thermal stresses and thermal deflection have been computed numerically and are illustrated graphically.

Axi-symmetric thermoelastic stress analysis of a thin circular plate due to heat generation

Axi-symmetric thermoelastic stress analysis of a thin circular plate due to heat generation

Methodology of impeller curved vanes modelling in 2D axisymmetric stress analysis

The purpose of this paper is to propose a more suitable methodology of impeller vanes modelling in axisymmetric 2D models which improves the results but does not increase the computational complexity of the task. For this purpose, two different approaches have been tested which led to a significant improvement in 2D axisymmetric model results. The first approach directly models the spatial curvature of the vanes using shell elements which are connected to axisymmetric disk elements using coupled degrees of freedom. The second approach modifies the commonly used methodology which simulates the vanes using plane elements under the plane stress conditions. The influence of spatial curvature of the vanes is then empirically considered by reducing the Young’s modulus of elasticity of vanes material. In addition, this approach has been extended using orthotropic material that allows material properties to be changed in certain directions. Advantages and disadvantages of these approaches are reported.

The axisymmetric stress analysis of double contact problem for functionally graded materials layer with arbitrary graded materials properties

In this paper, the axisymmetric double contact problems for a functionally graded layer indented by a rigid cylindrical indenter and a rigid spherical indenter are considered. A linear multi-layered model is applied to model the functionally graded layer whose shear modulus varies as an arbitrary function. The Hankel integral transform technique and the transfer matrix method are applied to convert the double contact problem to a system of coupled singular integral equations which are solved by the numerical method. The numerical results show that the stiffness ratio and the gradient index have great effect on the contact region and the contact pressure.

An elasticity-equilibrium-based zigzag theory for axisymmetric bending and stress analysis of the functionally graded circular sandwich plates, using a Maclaurin-type series solution

Abstract The available semi-analytical solutions for bending and stress analysis of the composite/sandwich plates have mainly been proposed for rectangular plates with specific material properties and edge conditions. In the present paper, axisymmetric bending and stress analysis of circular functionally graded sandwich plates subjected to transversely distributed loads is performed. The governing equations are derived based on an elasticity-equilibrium-based (rather than the traditional constitutive-equations-based) zigzag theory. Therefore, both ideas of using the local variations of the displacement field and satisfying a priori the continuity conditions of the transverse stresses at the layer interfaces for predicting the global and local responses of the sandwich circular plates are employed, for the first time. The resulting governing equations are then solved by a semi-analytical Maclaurin-type power-series solution. Each layer of the plate may be made of functionally graded materials. The transverse shear and normal stresses are determined based on the three-dimensional theory of elasticity. Comparisons made with results of a numerical finite element code (ABAQUS software) reveal that even for thick sandwich plates with soft cores, accuracy of results of the present formulation is comparable with that of the three-dimensional theory of elasticity.

Errata for “Axisymmetric Stress Analysis of a Thick Conical Shell with Varying Thickness under Nonuniform Internal Pressure” by H. R. Eipakchi, S. E. Khadem, and G. H. Rahimi S.

Errata for “Axisymmetric Stress Analysis of a Thick Conical Shell with Varying Thickness under Nonuniform Internal Pressure” by H. R. Eipakchi, S. E. Khadem, and G. H. Rahimi S.

Axisymmetric Stress Analysis of a Thick Conical Shell with Varying Thickness under Nonuniform Internal Pressure

A mathematical approach based on the perturbation theory has been used for axisymmetric stress analysis of a thick conical shell with varying thickness under nonuniform internal pressure. The equilibrium equations have been derived using the energy principle and considering the second-order shear deformation theory (SSDT), which includes shear deformation effects. This system of ordinary differential equations with variable coefficients has been solved analytically using the matched asymptotic expansion method of the perturbation theory. A comparison of the results with the finite-element method and the first-order shear deformation theory shows that the SSDT can predict the displacements and stresses of the shell for a wide range of thicknesses as well with less calculations than other analytical methods such as the Frobenius series method.

An axisymmetric stress analysis in a single fibre composite of finite length under a thermal expansion mismatch

In this paper, an exact solution is derived for the characterization of thermal stresses in a single-fibre composite of finite length. All the required boundary and interfacial conditions of the thermo-elastic problem are thus satisfied exactly. The proposed method involves a particular solution that is added to a three-dimensional (3D) complementary displacement field which satisfies automatically the Navier's equations. Based on experimental data provided by fibre Bragg grating sensors, an axisymmetric analysis is used then to determine the residual stress field inside the composite due to matrix shrinkage. The numerical results clearly indicate that all stress components vary significantly near the ends. An abrupt change of the shear stresses is thus predicted close to the edges. The results of the model are also found to be in good agreement with those obtained from finite element simulations. A comparison of the proposed approach with three other published theoretical models is also presented.

On the stress analysis of a wound coil with application to electromagnet manufacture

This paper presents an axisymmetric stress analysis of electromagnet manufacture. The processes covered are coil winding, mandrel removal, and heating or cooling. The effects of variable winding tension, mandrel elasticity, and coil-mandrel anisotropy are analysed. Distributions of radial and tangential stress are presented for a wide range of example geometries and conditions, and the use of the techniques to optimize residual stress fields at the conceptual design stage is discussed. The analysis has clear application to other winding processes such as coiling of sheet and manufacture of composite tubes. Comparisons are made between the current analysis and previous analyses of these other processes which have appeared in the literature.

ICS-09: Axisymmetric Stress Analysis and Strength of Bonded Shrink-fitted Joints of Solid Shafts subjected to Torsional Loads(ICS-II: INTERFACES AND CONTACT SURFACE MECHANICS)

ICS-09: Axisymmetric Stress Analysis and Strength of Bonded Shrink-fitted Joints of Solid Shafts subjected to Torsional Loads(ICS-II: INTERFACES AND CONTACT SURFACE MECHANICS)

Three-Dimensional Axisymmetric Stress Analysis of Superconducting Magnets Using Green’s Function Solution

A closed-form Green’s function solution for the axisymmetric stresses in an elastic coil of superconducting magnets is presented, which provides the components of stress throughout the coil and includes the shear stress in addition to the normal stresses. The Green’s function method permits the development of a solution irrespective of the type of magnetic body forces within the coil. Green’s functions are derived by using finite Hankel transforms appropriate for a cylindrical coil.

Axisymmetric Stress Analysis and Strength of Bonded Shrink-Fitted Joints of Solid Shaft Subjected to Torsional Loads.

Recently, joints that combine a shrink fit with anaerobic adhesives have been used in order to increase joint strength. In this study we deal with the stress analysis and strength evaluation of bonded shrink fitted joints subjected to torsional loads. The stress distributions in the adhesive layer of bonded shrink fitted joints are analyzed by using the axisymmetric theory of elasticity when an external torsion is applied to the upper end of the shaft. The effects of the outer diameter and the stiffness of rings on the interface stress distributions are analyzed by the numerical calculations. Using the interface stress distributions, the joint strength was predicted. In addition, the value of the joint strength was obtained experimentally. It is seen that a rupture in the adhesive is initiated from the upper edge of the interfaces when a torsion is applied to the upper end of the shaft. The numerical results show more conservative values than the experimental results. It is found that the joint strength of bonded shrink-fitted joints is greater than that of shrink-fitted joints.

Axisymmetric Stress Analysis and Strength of Joints Combining Adhesives with Bolts Subjected to Torsions.

The stress distributions in joints combining adhesives with bolts are analyzed by using axisymmetric theory of elasticity as a three-body contact problem when torsions are applied to the joints. The joints consist of two hollow cylinders and they are fastened by a bolt and nut after being joined with an adhesive. When an external torsion is applied to a combination joint, an increment/decrement of torsion occurs in the bolt. A method for estimating the variation of torsion in the bolt is proposed. In addition, using the interface stress distribution, a method for predicting strength of the combination joint is proposed. The torsional load occurred in the bolt was measured using strain gauges. Strength of the combination joint was also measured. A fairly good agreement was seen between the analytical and the experimental results. It is shown that the increment of torsional load occurred in the bolt is small substantially. It is observed that the strength of combination joint is greater than that of adhesive joints. It is also found that the combination joint strength increases as the intial clamping force increases and that it is greater than that of bolted joints without adhesives.

Superheater minimum stress unit start-up option of coal-fired power plant

In the operation of coal-fired power plants, the provision of selecting the superheater minimum stress unit start-up option is presented in this paper. This stress minimization is necessary for tomorrow's business climate, of the electric-supply industry, with expanding deregulation and competition both domestic arid global. The start-up option recommended in the present paper is meant to influence the power plant automation in start-up and firing temperature controls. The stress temperatures characteristics for final superheater outlet temperatures are approximated and three selected unit start-up options are identified. The paper presents a practical mathematical formulation of the superheater heat transfer equilibrium. This is done for the unit start-up segment that is the low boiler continuous maximum rating (C.M.R.) range (0–20%). The mathematical formulation of the matrix equilibrium is modelled in the paper as a conductivity spring and a capacity spring opposed by heat fluxes. The heat flow equilibrium equation derived in the present paper is a nonlinear system in which the thermal properties vary with the superheater temperatures. A detailed solution is presented in the paper. Consequently, the paper presents two superheater axisymmetric finite element heat transfer and stress analysis models along with heat transfer and stress analysis results. The paper suggests that automation should include faster plant start-up according to the unit start-up option with the fastest firing rate, which yields minimum stress.

Axisymmetric Stress Analysis and Strength of Bonded Shrink-fitted Joints of Solid Shafts Subjected to Torsional Loads.

Axisymmetric Stress Analysis and Strength of Bonded Shrink-fitted Joints of Solid Shafts Subjected to Torsional Loads.

The influence of specimen size on the surface stress distribution induced by indentation testing

The stress state in an elastic cylindrical coupon of finite dimensions on a rigid, frictionless foundation under axisymmetric contact loading is studied. The axisymmetric stress analysis is devoted to an investigation of the effects of the free surfaces of the plate on the surface radial tensile stress field, which is particularly important for an assessment of crack initiation in brittle materials. Attention is focused on cases where the ratio of plate thickness ( h) and plate radius ( W) to contact radius ( a) fall in the range 0.5 < h a < 10, and 1 < w a < 5 , respectively, which is the region of both experimental and theoretical interest.

Axisymmetric Stress Analysis and Strength of Bonded Shrink-Fitted Joints Subjected to Push-Off Forces.

Shrink fit has been used commonly for joining the cylindrical components such as shaft and gears. It is noted recently the shrink fitted joint with anaerobic adhesives is adopted in order to improve it's joint strength. In a reliable design of bonded shrink fitted joints, it is necessary to know the contact stress distributions at the interfaces. In this paper, the interface stress distribution of bonded shrink fitted joint under push-off force is analyzed by using axisymmetric theory of elasticity as four-body contact problem. Analogical test is conducted to determine the relationship between the normal stress and the shear stress. Using the interface stress distribution and analogical test results, a method for estimating the joint strength is proposed. In the numerical calculations, the effect of the outer diameter and Young's modulus of the rings and the engagement length on the contact stress distributions at the interfaces are clarified. Push-off force measurement was carried out for bonded shrink fitted joints. In the experiments, the effect of shrink fit interference and the outer diameter of ring on the joint strength are examined. The numerical results are in a fairly good agreement with the experimental results. It is found that the strength of the bonded shrink fitted joint is greater than that of shrink fitted joint.

Axisymmetric Stress Analysis and strength of Bonded Shrink-Fitted Joints of Solid Shafts Subjected to Push-Off Forces.

This paper deals with analysis of stress in the adhesive layer of bonded shrink-fitted joints subjected to push off forces. The stress distributions in the adhesive layer of bonded shrink-fitted joints and those when the joints are subjected to push-off forces are analyzed as a four-body contact problem using the axisymmetrical theory of elasticity. The effects of the outer diameter and the stiffness of rings on the stress distributions in the adhesive layer are clarified by numerical calculation. Using the stress distributions in the adhesive layer, a method for predicting joint strength is proposed. It is seen that a rupture initiates from the lower edge of the outside surface in an adhesive layer. Experiments on joint strength were performed. The numerical results are in fairly good agreement with the experimental results. It is found that the joint strength increases as the outer diameler and Young's modulus of rings increase. In addition, it is found that the joint strength of bonded shrink-fitted joints is greater than that of unbonded shrink fitted joints.

P-version hierarchical axisymmetric shell element

A hierarchical formulation for a three-node axisymmetric shell element based on p-version for linear elastic axisymmetric stress analysis is presented. The element displacement field can be of arbitrary polynomial orders p ξ and p η in the longitudinal (ξ) and the transverse (η) directions of the element. The element approximation functions and the corresponding nodal variables are derived by first constructing the one-dimensional hierarchical approximation functions of order p ξ and p η and the corresponding nodal variables operators in the ξ and η directions and then taking their products (also known as tensor products). The element displacement approximation is hierarchical, i.e. the approximation functions and the nodal variables corresponding to the polynomial orders p ξ and p η are a subset of those corresponding to the polynomial orders ( p ξ + 1) and ( p η + 1). Since the displacement approximation is hierarchical, the resulting element stiffness matrix and the equivalent nodal load vectors are hierarchical also. The formulation ensures C 0 continuity. The element properties are derived using the principal of virtual work and the hierarchical element approximation. In developing the element properties all four components of the stress ( σ θ , σ r , τ rz , σ z ) and strain ( ε θ , ε r , γ rz , ε z ) are retained, i.e. the stress normal to the middle surface of the element is not neglected (an assumption commonly used in developing axisymmetric shell elements) in the present formulation. The element formulation also permits non-differentiable geometries (sharp corners). The stress concentrations at such locations can be calculated accurately due to the presence of a complete state of stress (and strain) and a non-differentiable geometry feature. Numerical examples are presented to demonstrate the accuracy, efficiency, modeling convenience and overall superiority of the present formulation as well as its applications to pressure vessel stress analysis. The results obtained from the present formulation are also compared with those available in the literature as well as with the analytical solutions. The numerical results from the h- models using isoparametric axisymmetric solid elements are also presented for comparison purposes