Axisymmetric Theory Of Elasticity Research Articles

Active vibration control of rotating smart bidirectional FGPTC subjected to internal mechanical shock

This study considers the active vibration control of a sandwich truncated cone, whose intermediate layer is made of bidirectional functionally graded (FG) porous material bonded with integrated piezoelectric actuator and sensor layers on its outer and inner surfaces. The material properties of the bidirectional functionally graded porous truncated cone (FGPTC), with even and uneven porosity distributions along the length and thickness directions, are changed using a power law function. The governing motion equations utilize the two-dimensional (2D) axisymmetric theory of elasticity rather than simple shell theories. The solving of the governing motion equations is accomplished through the utilization of graded finite element and Newmark methods. The study investigates the impact of dimensions, parameters, and porosity types on transient response behavior, including the semi-vertex angle and the ratio of truncated cone length to outer radius. Furthermore, the effects of power index, porosity volume fractions, rotational velocities, and boundary conditions are examined. Active vibration control (AVC) of the piezoelectric FGPTC is achieved by employing a closed-loop control algorithm based on velocity feedback. Several numerical simulations are conducted to evaluate the effectiveness of the proposed active vibration control system in reducing structural vibrations. The results demonstrate significant reductions in vibration amplitudes and improved structural stability achieved through the active control approach.

Meshless finite block method with infinite elements for axisymmetric cracked solid made of functionally graded materials

Axisymmetric cracked solid structures in functionally graded materials (FGMs) under static and dynamic loading are analysed by using the Finite Block Method (FBM). Based on the axisymmetric elasticity theory, the equilibrium equations inside the rotating section of FGMs in the cylinder coordinate system are formulated in strong form. The shape functions in the FBM are constructed by Lagrange polynomial interpolation with mapping techniques for the irregular finite or semi-infinite physical domains. A special approximation technique is proposed to avoid singularities in the traction boundary conditions on the axis of symmetry. The stress intensity factor is obtained by the crack opening displacement. The time-dependent problems are addressed using the Laplace transform and Durbin's inverse approach. Several numerical examples are investigated in order to illustrate the accuracy and convergence of the proposed method, and the numerical solutions are compared with analytical solutions, the finite element method and other methods.

Dynamic analysis of functionally graded rotating thick truncated cone made of saturated porous materials

In the current article, dynamic behavior of functionally graded saturated porous rotating thick truncated cone is investigated for the first time. It is assumed that porosity distributions along the thickness are (1) symmetric nonlinear, (2) nonlinear asymmetric and (3) uniform distributions. The Biot poroelastic law instead of Hooke’s law is used to model the constitutive equations. Also, 2D axisymmetric theory of elasticity instead of simple shell theories is used for the governing motion equations. Graded finite element and Newmark methods have been used to solve the governing motion equations. First, natural frequencies of stationary functionally graded saturated porous cone are obtained, and then by considering the effect of centrifugal force and spin softening effect, dynamic response of porous cone in an undrained condition for different variables such as porosity and Skempton coefficients, rotational velocity, semi vertex angle of the cone and different distribution of porosity has been investigated. Obtained results denote that by increasing Skempton coefficient, natural frequencies are increased, and natural frequencies of PUD distribution are lower than other distributions. Also, rotational velocity and semi-vertex angle have significant effect on the displacement and stress field.

Stress analysis of functionally graded saturated porous rotating thick truncated cone

In this article, static response of functionally graded saturated porous rotating truncated cone is investigated for the first time. Three different patterns are considered for porosity distribution along with the thickness of the cone, which are symmetric nonlinear, nonlinear asymmetric and uniform distributions. The relationship between stress and strain is based on the Biot constitutive law instead of simple Hook’s law. 2D axisymmetric elasticity theory and finite element method based on Rayleigh-Ritz energy formulation are used to model the problem. The effect of various parameters such as: rotational velocity, porosity and Skempton coefficients, semi vertex angle of the cone, different boundary conditions and different distribution of porosity on displacements and stresses of the cone has been investigated.

Discontinuous Solutions of Axisymmetric Elasticity Theory for a Piecewise Homogeneous Layered Space with Periodical Interfacial Disk-Shape Defects

Discontinuous Solutions of Axisymmetric Elasticity Theory for a Piecewise Homogeneous Layered Space with Periodical Interfacial Disk-Shape Defects

Determination of stresses in concrete lining with rock-bolt in case of exhaustion of rock-bolt supporting strength

The article deals with the solution of analytical problem of flat axisymmetric elasticity theory, when rock-bolt supporting strength is exhausted. Expression for determination of stresses in concrete lining is deduced, where pressure increasing at exploitation have regarded. This methodology can be used at blueprint stage and preliminary calculation during mining operations. Further evaluation of concrete lining strength and geophysical probe of rock is needed for the preliminary calculation.

Time Domain Dynamic Analysis of Floating Piles under Impact Loads

In this study, the differential quadrature method (DQM), a mathematically simple, accurate, and computationally efficient numerical tool, was employed to analyze the response of single piles under dynamic axial loading. The dynamic behavior of the piles and surrounding soil were modeled using the one-dimensional (1D) or three-dimensional (3D) axisymmetric elasticity theory, respectively. The governing equations subjected to the related boundary and initial conditions were discretized in both the spatial and temporal domains via DQM. The behavior of the floating piles embedded in a half-space layer of homogeneous and Gibson soils under uniform and sinusoidal impact loads was studied. The piles and the soil behavior were assumed to be linear elastic and linear viscoelastic, respectively. To compare and verify the results obtained from the DQM approach, the problems were also solved via a finite-element-based commercial software program in some cases. The approach was found to have high accuracy and numerical stability. Finally, the effects of the different parameters of the soil and pile on the pile-head settlement time history were investigated.

Nonlinear analysis of functionally graded nanocomposite rotating thick disks with variable thickness reinforced with carbon nanotubes

In this paper the nonlinear elasticity solution of functionally graded nanocomposite rotating thick disks with variable thickness reinforced with single-walled carbon nanotubes (SWCNTs) is presented. Four distribution types of uniaxial aligned SWCNTs are considered: uniform and three types of functionally graded (FG) distributions along radial direction of the disk. The effective material properties of the nanocomposite disk are estimated by a micro-mechanical model. The governing nonlinear equations are based on the axisymmetric theory of elasticity with the geometric nonlinearity in axisymmetric complete form. The nonlinear graded finite element method (NGFEM) based on Rayleigh–Ritz energy formulation with the Picard iterative scheme is employed to solve the nonlinear equations. The solution is considered for four different thickness profiles, namely constant, linear, concave and convex. The effects of different types of distributions and volume fractions of CNTs and various types of thickness profiles on the displacement and stresses of the rotating disks as well as comparison between linear and nonlinear responses are investigated. The achieved results show that the displacement and stress fields can be controlled by changing the type of distribution and volume fraction of CNTs as well as the thickness profile. Moreover, the difference between linear and nonlinear results are noticeable in high angular velocities; thus, for obtaining accurate results, the geometric nonlinearity must be considered.

Influence of the geometry of coaxial adhesive joints on the transmitted load under tensile and compression loads

More and more accurate models have been developed for describing the mechanical behavior of an adhesive in an assembly which allow to numerically optimize the design of bonded assemblies. This paper deals with stress analysis in coaxial bonded joints. The objective was to analyze the effect of various geometries of the different parts of the assembly in order to optimize the maximal transmitted load of such joints. In the case of tensile loads, the stress distributions were analyzed using axisymmetric theory of elasticity. A pressure-dependent elastic limit of the adhesive was used, in order to accurately represent the difference between tensile-shear and compression-shear loads in the mechanical response of the adhesive. In adhesively bonded joints, stress concentrations can contribute to the initiation and propagation of cracks in the adhesive. Therefore, designing adhesively bonded assemblies which strongly limit stress concentrations can significantly increase the load transmitted by the assembly. Moreover, cylindrical joints are associated with high substrate strength in the radial direction, meaning that peel and cleavage forces have different effects compared to single lap joints. A comparison between the mechanical behavior of these two joints is proposed, starting from 2D simulations in the case of tensile and compressive loads. Furthermore, the influence of the angle of conical geometries of the bonded area, which can easily be used for such assemblies, is analyzed with respect to the stress distributions. It is shown that several geometries allow a large reduction of stress concentrations and thus lead to stronger assemblies. Moreover the influences of several geometries which strongly limit stress concentrations are presented.

Elasto-Plastic Stress and Deformation Analyses of the Bearing Surfaces in Hollow Cylindrical Bolted Joints under External Axial Loads

An important issue is how to determine a bolt preload of a bolted joint taking an external axial load into account. The following two methods for determining the bolt preload are discussed in the present paper. In the first method, the bolt preload is determined such that the stress at the bearing surfaces is lower than the yield stress of the clamped parts taking account of the load factor. In the second method it is determined such that the stress at the bearing surfaces is higher than the yield stress of clamped parts. Thus, firstly the load factor to obtain the increment Ft in the axial bolt force when an external load is applied to a bolted joint is investigated using axi-symmetrical theory of elasticity, FEM analyses and experiments. The analytical results are in a fairly good agreement with the FEM and the experimental results. Then, the contact stress distributions and the plastic displacement distributions at the bearing surfaces under external loads are examined using elasto-plastic FEM analyses. Experiment to measure the load factor and the reduction in the axial bolt forces were carried out. The prediction for the reduction in axial bolt force of the joint under external load is fairly consistent with the experimental result. In addition, in the first method for determining the bolt preload, it is found that no plastic deformation is occurring at the bearing surfaces and no reduction is occurring. It is noticed that a higher bolt preload according to the second method shows a small reduction in axial bolt force. Discussion is made on the critical stress at the bearing surfaces.

G030162 軸方向外力を受ける中空円筒ねじ締結体の内力係数と座面永久変形にっいて([G03016]材料力学部門一般セッション(16):応力分布)

An important issue is how to determine a bolt preload of a bolted joint taking an external axial load into account. One method for determining the bolt preload is such that the stress at the bearing surfaces is less than the yield stress of the clamped parts taking account of the load factor. Another method is such that the stress at the bearing surfaces is higher than the yield stress of clamped parts. Firstly the load factor to obtain the increment F, in the axial bolt force is investigated using axi-symmetrical theory of elasticity, FEM analyses and experiments. Then, the contact stress distributions and the plastic displacement distributions at the bearing surfaces under external loads are examined using elasto-plastic FEM analyses. The prediction for the reduction in axial bolt force of the joint under external load is fairly consistent with the experimental result. It is noticed that a higher bolt preload according to the second method shows a small reduction in axial bolt force. Discussion is made on the critical stress at the bearing surfaces.

Axisymmetrical Stress and Strength Analyses of Epoxy-Steel Composite Cylinders under Push-off Loads

The interface stress distributions in composite cylinders of steel (solid cylinder) and epoxy (hollow cylinder) under push-off loads are analyzed using axisymmetrical theory of elasticity as a three-body contact problem. In the numerical calculations, the effects of Young’s modulus and the diameter of solid cylinder on the interface stress distribution are examined. In addition, the effects of the diameter of supported hollow cylinder and the stress distribution due to the applied push-off loads are also examined. It is found that the normal stress at the interfaces increases as Young’s modulus of solid cylinder decreases, the diameter of solid cylinder and the diameter of supported hollow cylinder increase. It is also found that the shear stress at the interfaces increases as the diameter of supported hollow cylinder increases, Young’s modulus and the diameter of solid cylinder decrease. Singular stresses occur at the edges of the interfaces. A valid method for estimating the singularity is proposed and the discussion is made. Using the interfaces stresses obtained from the numerical analysis and analogous tests, the push-off strength of composite cylinders is estimated. The experiments to measure composite cylinders strength are carried out. It is seen that a rupture initiates at the lower edge of the interface area when the push-off loads are applied to the upper end of solid cylinder. For verification of the present analysis of the interface stress distributions, finite-element method (FEM) is also carried out. The numerical results of the interface stress distributions and the strength are in fairly good agreement with the experimental results and the FEM results. The axisymmetrical theory of elasticity is more rational compared to the shear lag theory in examining the stress singularity and considering the normal stress and shear stress at the interfaces at the same time. Finally, as an example, it is observed that the weight of composite cylinders is lighter by 48.1% than that of the structure with the same of steel material for obtaining the same strength.

Axisymmetrical Stress and Strength Analysis of Epoxy-Steel Composite Cylinders under Torsional Loads

The interface stress distributions in composite cylinders of steel (solid cylinder) and epoxy (hollow cylinder) under push-off loads are analyzed using axisymmetrical theory of elasticity as a three-body contact problem. In the numerical calculations, the effects of Young’s modulus and the diameter of solid cylinder on the interface stress distribution are examined. In addition, the effects of the diameter of supported hollow cylinder and the stress distribution due to the applied push-off loads are also examined. It is found that the normal stress at the interfaces increases as Young’s modulus of solid cylinder decreases, the diameter of solid cylinder and the diameter of supported hollow cylinder increase. It is also found that the shear stress at the interfaces increases as the diameter of supported hollow cylinder increases, Young’s modulus and the diameter of solid cylinder decrease. Singular stresses occur at the edges of the interfaces. A valid method for estimating the singularity is proposed and the discussion is made. Using the interfaces stresses obtained from the numerical analysis and analogous tests, the push-off strength of composite cylinders is estimated. The experiments to measure composite cylinders strength are carried out. It is seen that a rupture initiates at the lower edge of the interface area when the push-off loads are applied to the upper end of solid cylinder. For verification of the present analysis of the interface stress distributions, finite-element method (FEM) is also carried out. The numerical results of the interface stress distributions and the strength are in fairly good agreement with the experimental results and the FEM results. The axisymmetrical theory of elasticity is more rational compared to the shear lag theory in examining the stress singularity and considering the normal stress and shear stress at the interfaces at the same time. Finally, as an example, it is observed that the weight of composite cylinders is lighter by 48.1% than that of the structure with the same of steel material for obtaining the same strength.

21510 内圧を受けるガスケット付き閉止型フランジ締結体の応力解析と密封性能評価(一般講演 応力解析)

The stresses of a blind flange connection with a spiral wound gasket under internal pressure are analyzed taking account a hysteresis of the gasket using axisymmetric theory of elasticity as a four-body contact problem. The leakage tests were also conducted using an actual blind flange connection with a spiral wound gasket. Using the contact gasket stress distribution of the blind flange connections with 3" nominal diameter under internal pressure, the values of the new gasket constants proposed by PVRC were estimated by taking account the changes in the contact gasket stress. A difference in the new gasket constants was small between the PVRC values and the estimated values that were obtained by using the actual contact gasket stress. In addition, a method for determining the bolt preload for a given tightness parameter was demonstrated. The discrepancy of the bolt preload was increased between the estimated values and those by the PVRC as the given tightness parameter was increased.

Effect of fitted position on stress distribution and strength of a bonded shrink fitted joint subjected to torsion

Recently, joints combining shrink fit with anaerobic adhesives (bonded shrink fitted joint) have been appeared in order to increase the joint strength. This paper deals with stress analysis and strength estimation of the bonded shrink fitted joints in which a ring is fitted at the end of a hollow shaft subjected to torsion. The objective of the paper is to examine the effect of fitted position on the characteristics of the bonded shrink fitted joints. The stress distributions at the interface of the joints are analyzed using axisymmetric theory of elasticity. The effects of outer diameter, height and stiffness of the ring on the interface stress distributions are examined in the numerical calculations. In numerical calculations, it is found that a rupture of adhesive layer initiates from the edge of the interfaces close to the end of the shaft to which a torsional load is applied. Using the interface stress distributions, joint strength was predicted. Furthermore, experiments to measure the joint strength were carried out. The numerical results of the joint strength show more conservative values than the experimental results. In addition, the stress distributions in the present study are compared with those in which a ring is fitted at the middle of a shaft. It is found that the effect of shrink fitted position is negligibly small and the strength of the bonded shrink fitted joints is greater than that of shrink fitted joints without adhesives.

Stress Analysis and Determination of Bolt Preload in Pipe Flange Connections With Gaskets Under Internal Pressure

The stresses of a pipe flange connection with a spiral-wound gasket under internal pressure are analyzed taking account a nonlinearity and a hysteresis of the gasket by using an axisymmetric theory of elasticity and the finite element method (FEM). The leakage tests were also conducted using an actual pipe flange connection with a spiral-wound gasket. Using the contact stress distribution of the pipe flange connection with 3-in. nominal diameter under internal pressure and the tightness parameter, the values of the new gasket constants are obtained by taking into account the changes in the contact stress. A difference in the new gasket constants between the estimated values obtained from the actual pipe flange connection and the values obtained by the PVRC procedure is small. In addition, a method to determine the bolt preload for a given tightness parameter is demonstrated. The obtained results of the bolt preload for the pipe flange connection are in a fairly good agreement with those obtained by the PVRC procedure under a lower pressure application. However, a difference in the bolt preload is about 10% when an internal pressure is increased.

Stress Analysis and an Estimation of the Sealing Performance in Pipe Flange Connections with Spiral Wound Gasket Subjected to Internal Pressure.

The stresses of a pipe flange connection with a spiral wound gasket under internal pressure are analyzed taking account a non-linearity and a hysteresis of the gasket by using axisymmetric theory of elasticity and finite element method (FEM). The leakage tests were also conducted using the actual pipe flange connections with spiral wound gaskets. Using the contact stress distribution of the pipe flange connections with 3 nominal diameter under internal pressure, the values of the new gasket constants proposed by PVRG are estimated by taking account the changes in the contact stress. A difference in the new gasket constants is substantial between the PVRC values and the estimated results, which are obtained by using the initial clamping stress. However, the difference is small between the PVRC values and the estimated values which are obtained by using the actual gasket stress. In addition, a method for determining the bolt preload for a given tightness parameter is demonstrated. The obtained results for the pipe flange connection are in a fairy good agreement with those obtained by PVRG procedure.

Stress analysis and strength evaluation of bonded shrink fitted joints subjected to torsional loads

This paper deals with the stress analysis and strength evaluation of bonded shrink fitted joints subjected to torsion. The stress distributions in the adhesive layer of bonded shrink fitted joints are analyzed by 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 clarified by numerical calculations. Using the interface stress distributions, the joint strength is predicted. In addition, the joint strength was measured experimentally. It is seen that rupture of the adhesive layer is initiated from the upper edge of the interface when torsion is applied to the upper end of the shaft. The numerical results are in fairly good agreement with the experimental results. It was found that the joint strength of bonded shrink fitted joints is greater than that of shrink fitted joints.

Some primal problems of the axisymmetric theory of elasticity for space with a flat slit bounded by a circle

We consider the first and second primal problems of the axisymmetric theory of elasticity for space with a round slit and a mixed problem in which forces are specified on one side of the slit and displacements are specified on the other side. The problems reduce to conjugation problems for generalized analytic functions on rectilinear segments, whose solution is obtained in closed form.

Thermal Stress Analysis of Pipe Flange Connections Combining Bolts with Adhesive Subjected to Heat Conduction from Contained Fluid.

Thermal stress distribution of adhesively bonded pipe flange connections subjected to heat conduction in steady state are analyzed by using the thermoelastic displacement potential and Michell's stress functions based on the axisymmetrical theory of elasticity. In the analysis, pipe flanges, hubs of pipe flange and an adhesive are replaced by finite hollow cylinders, respectively. In the numerical calculations, the effects of the ratios of linear thermal expansion coefficients, Young's moduli between the pipe flange and the adhesive layer and the adhesive thickness on the stress distribution at the interface between the flange and the adhesive layer are examined. As a result, it is seen that the thermal stress (compressive) at the inner and the outer surfaces of the adhesive layer increases with a decrease of Young's moduli ratio, the linear thermal expansion coefficient ratio and the adhesive thickness. In addition, stress analysis by using FEM (Finite Element Method) was also carried out. Fairly good agreement is seen between the numerical and FEM results. The characteristics are compared with those of the connections with gaskets. It is found that the stress at hub of the joint with adhesive is smaller than that of the joint with gasket.