Axisymmetric Loading Research Articles

IDENTIFICATION OF AN ARBITRARY MOVING AXISYMMETRIC LOAD ACTING ON A CYLINDRICAL SHELL

Various types of external non-stationary loads can act on various structural elements and cylindrical shells of finite length in particular distributed and concentrated, stationary and moving load. When using various external load identification methods, the type of external load is usually known. In prac- tice this is not always the case. The purpose of the study is to develop a method for identifying an arbitrary axisymmetric load acting on an elastic cy- lindrical shell of finite length, which can be used to identify a moving load. To model the non-stationary load of a cylindrical shell, a system of differ- ential equations of the refined Timoshenko theory for medium thickness shells was used. The solution to this system of differential equations is ob- tained by expanding the unknown functions into Fourier series and applying the integral Laplace transform. The solution of the inverse problem was obtained using the theory of integral equations and the Tikhonov regularization method. As a result of the study, a solution of the inverse problem of solid mechanics to identify an arbitrary axisymmetric non-stationary load was obtained. A numerical experiment was carried out to use the developed method to identify a moving non-stationary load acting on a simply supported cylindrical shell of medium thickness. The simulation results indicate a fairly accurate identification of both the change in time and the distribution along the shell of a non-stationary axisymmetric moving load. A method has been developed for identifying an external non-stationary load randomly distributed along a cylindrical shell, which makes it possible to identify a moving load without preliminary information about the type of this load. The developed method allows us to reproduce moving non-stationary loads, which are often encountered in practice, and expand it to other types of structural elements.

Frequency-domain axisymmetric and thermomechanical viscoelastic analysis of thermoplastic composite pipe

ABSTRACT Thermoplastic composite pipe (TCP), composed of polymers and composite laminates, shows significant potential for deep-water offshore oil field development due to its lightweight and high strength. However, current mechanical studies primarily focus on the elastic domain, ignoring the critical viscoelasticity of non-metallic materials. To solve this, we introduce a comprehensive theoretical model that incorporates viscoelastic properties under both axisymmetric and thermal loads, considering radial convective thermal gradients and axial heat conduction. This model accurately predicts TCP's mechanical behavior by using stiffness coefficients, differential geometry, and radial-axial temperature transfer curves. By applying the principle of elastic-viscoelastic correspondence, we obtain viscoelastic solutions in the frequency domain, showing strong agreement with Finite Element (FE) models particularly under cyclic loading. Viscoelasticity introduces larger equivalent axial stiffness and viscoelastic damping within complex structures, which become more obvious with temperature fluctuations.

Analysis of axisymmetric thermoelastic diffusive half-space with variable material properties using hyperbolic two-temperature model

The aim of the current study is to investigate the variable thermal conductivity and diffusivity impact on the transient response of an axisymmetric thermodiffusive elastic half-space under axisymmetric thermal, mechanical, and concentration loads in the light of hyperbolic two-temperature generalized fractional thermoelastic diffusion model. With the help of Kirchhoff’s transform, the governing equations are converted into linear form. The resulting equations are solved by imposing the combined Laplace–Hankel transform. In converted space, the solutions for different field quantities are presented in compact form. The copper material is considered for numerical computation. By employing a mathematical inversion procedure, the solutions are converted into the original space. Numerically computed solutions for various physical quantities are illustrated in the form of graphs to show the impact of variable thermal conductivity and diffusivity, hyperbolic two temperature, and fractional parameters. Validation of the obtained results is also presented.

Theoretical and numerical methods for predicting the structural stiffness of unbonded flexible riser for deep-sea mining under axial tension and internal pressure

Composite materials have received great attention in the design of flexible risers for deep-sea mining due to their significant advantages of high strength and lightweight. However, under the influence of various nonlinear factors, the cross-sectional response of composite flexible risers is extremely complex, and the prediction of their structural stiffness is greatly challenged. This paper focuses on a new type of composite flexible riser applied in deep-sea mining. The nonlinearity of materials and detailed geometric features of structures are fully considered. Theoretical and numerical models for predicting structural stiffness under axisymmetric loads are constructed. By iteratively solving the equilibrium equation, the strain and displacement fields of the flexible riser are obtained. Firstly, the accuracy of theoretical and numerical methods is verified based on a 5-layer 8-inch unbonded flexible riser as a case study. Secondly, the influence of fiber volume fraction (FVF) on the structural stiffness and weight of flexible risers is discussed. Finally, the influence of structural design parameters of the reinforcement layer on its axial tensile stiffness and radial stiffness is explored. The research results can provide parameter inputs for the design and dynamic analysis of flexible risers.

Finite Element Axisymmetric Models for Conical Wedge Anchorage Used in the Production of Prestressed Steel Reinforced Concretes

The anchor system plays a very important part of the prestressed structure, that contacts and transmits force to the cables when stretching to create residual stress. The operating conditions of the anchor system in general and the anchor core in particular are extremely harsh. In this paper, <I>ABAQUS</I> software was applied to model and numerically simulate the axisymmetric loading process of the anchor core in manufacturing prestressed concrete sleepers, to study the effects of tensile forces to the pressure resistance of the cylinder. To verify the analytical results, a Finite Element (<I>FE</I>)-model with the same material and geometrical properties was created. The difference is the assumption of plane stress in the analytical solution, can be solved using two - dimensional finite elements, which are most conveniently described in cylindrical (<i>r, θ, z</i>) coordinates. This articles also especially focused on calculating the change of stress on the edges of the anchor core teeth with different tensile forces. We also refered to experimental results to get data on traction force and working conditions to build a calculation model and select input parameters. Comparison of the stress generated on the teeth of the anchor core was performed with three different tensions of <i>171, 181</i> and <i>191 kN</i>. The maximum and concentrated stress at the top and root of the anchor core when tensioning the cable has been calculated.

Theoretical study on 3D elastic response and first layer failure strength of composite cylinders subjected to axisymmetric loadings

The traditional Lekhnitskii 3D elastic theory can obtain the exact stress and strain response of the composite cylinder under the axially symmetric loadings. However, when the cylinder contains 0° winding layers or isotropic layers, some calculation parameters corresponding to the two kinds of special layers will become singular. By analyzing the continuity of singular parameters and calculating their limits, the problem of singular parameters can be effectively solved and the Lekhnitskii theory can be extended to composite thick-walled cylinders with arbitrary winding angles. Furthermore, based on the Chang-Chang strength criterion of composite layers and the ideal elastic-plastic assumption of isotropic metal layers, the theoretical calculation method of first layer failure strength and the corresponding failure modes of the composite cylinders subjected to axisymmetric loadings was proposed. Then, the composite cylinder with metal liner was fabricated by fiber winding process. The experimental blasting pressure of the cylinder was 52.8 MPa with a major failure mode of fiber tensile fracture. Based on the proposed theoretical method, the cylinder's first layer failure strength of internal pressure was 44.1 MPa, and the initial failure mode was also fiber tensile fracture. The predicted result of the first layer failure strength was lower than the experimental results. The result proved the safety and economy of the proposed theoretical method for the initial design of the composite cylinder.

Development of governing partial differential equations of reinforcing thin films

In this paper, a novel interface model for elastic isotropic thin films perfectly bonded to the surrounding elastic media is introduced. Considering an average stress and displacement through the thin film thickness, the shear stress discontinuity across the interface is expressed in terms of spatial and time derivatives of displacement components. The derived interfacial equations are presented in a general form. As such, they are applicable to asymmetric elastodynamic problems of anisotropic solids with thin film interfaces. Employing the introduced interface model and Hankel transform technique, static Green's functions of an elastic isotropic half-space reinforced by a buried thin film are obtained. Results of some special cases, including axisymmetric loading, inextensible membrane, unreinforced half-space, and surface-coated half-space, are also presented. The robustness and effectiveness of the proposed interface model are shown by two solved numerical examples, and some elastic responses are plotted to show the impact of thin film stiffness. According to the numerical results, modeling elastic thin films as inextensible membranes can significantly alter the elastic responses.

Численное моделирование процессов деформирования и потери устойчивости многослойных оболочек вращения при комбинированных квазистатических и динамических осесимметричных нагружениях с кручением

Численное моделирование процессов деформирования и потери устойчивости многослойных оболочек вращения при комбинированных квазистатических и динамических осесимметричных нагружениях с кручением

Axisymmetric Pressing Problem of Discrete Metal Materials

The paper presents an analytically closed solution to the problem of axisymmetric pressing of discrete metal materials by the method of jointly solving the differential equations of equilibrium of the metal and the plasticity conditions of the porous body, taking into account all pressing factors without exception: the type and properties of the charge, loading conditions, porosity, temperature, friction, etc. The purpose of this work is to develop the foundations of the engineering theory of pressure processing of discrete materials using the example of solving the problem of axisymmetric pressing of structurally inhomogeneous metal chips in a movable closed matrix. The basis for constructing a physical and mathema-tical model of the process is the idealized case of uniform compaction of a porous body with the subsequent determination of the lateral pressure coefficient corresponding to the actual degree of compaction at various stages of loading. The resulting equation for the relationship between the stress tensor components and the yield stress and relative compaction density represents the cylindrical Mises plasticity condition, which in the limit at zero porosity transforms into the plasticity condition for compact metals. The boundary value problem is solved for tangential stresses, taking into account the magnitude and direction of action of contact friction forces, which in their physical nature do not differ from the friction forces in the depth of the pressed material. The physico-mathematical model makes it possible to calculate the stress fields and density of the body according to the coordinates of the deformation zone, as well as energy-power parameters (pressure, force, work of deformation) provided that three structural and rheological characteristics are determined: the yield strength, relative compression and the degree of deformation compaction. Due to the fact that the problem is solved in relation to bodies of rotation in a general form and in a general formulation, the solution itself should be considered as methodological for any axisymmetric loading scheme.

Elastic Equilibrium of a Hollow Cylinder of Finite Length Under Axisymmetric Force Loading

Elastic Equilibrium of a Hollow Cylinder of Finite Length Under Axisymmetric Force Loading

A MICRO APPROACH TO VALIDATE THE GURSON YIELD CRITERIA AT MACRO LEVEL

In the present work, an effort has been made to validate Gurson yield criteria at the macro level with an equivalent numerical model at the micro level. The continuum body at macroscale has been assumed as periodically arranged stackable unit cells each containing a single void at microscale. A hexagonal cylinder containing a spherical void is considered as the shape of the unit cell; for simplicity, the hexagonal cylinder is modeled as a circular cylinder which allows simpler axisymmetric loading. Furthermore, due to symmetry, only a quarter of the geometry is required to model. A good comparison between both models is obtained for the different void radii.

Finite Element In-Depth Verification: Base Displacements of a Spherical Dome Loaded by Edge Forces and Moments

Nowadays, engineers possess a wealth of numerical packages in order to design civil engineering structures. The finite element method offers a variety of sophisticated element types, nonlinear materials, and solution algorithms, which enable engineers to confront complicated design problems. However, one of the difficult tasks is the verification of the produced numerical results. The present paper deals with the in-depth verification of a basic problem, referring to the axisymmetric loading by edge forces/moments of a spherical dome, truncated at various roll-down angles, φo. Two formulations of analytical solutions are derived by the bibliography; their results are compared with those produced by the implementation of the finite element method. Modelling details, such as the finite element type, orientation of joints, application of loading, boundary conditions, and results’ interpretation, are presented thoroughly. Four different ratios of the radius of curvature, r and shell’s thickness, and t are examined in order to investigate the compatibility between the implementation of the finite element method to the “first-order” shell theory. The discussion refers to the differences not only between the numerical and analytical results, but also between the two analytical approaches. Furthermore, it emphasizes the necessity of contacting even linear elastic preliminary verification numerical tests as a basis for the construction of more elaborated and sophisticated models.

Review of elasto-static models for three-dimensional analysis of thick-walled anisotropic tubes

Most shell or beam models of anisotropic tubes under bending have no validity for thick-walled structures. As a result, the need to develop three-dimensional formulations which allow a change in the stress, strain and displacement distributions across the radial component arises. Basic formulations on three-dimensional anisotropic elasticity were made either stress- or displacement-based by Lekhnitskii or Stroh on plates. Lekhnitskii also was the first to expand these analytical formulations to tubes under various loading conditions. This paper presents a review of the stress and strain analysis of tube models using three-dimensional anisotropic elasticity. The focus lies on layered structures, like fiber-reinforced plastics, under various bending loads, although the basic formulations and models regarding axisymmetric loads are briefly discussed. One section is also dedicated to the determination of an equivalent bending stiffness of tubes.

Hidden ring crack in a rotating hollow cylinder under torsion

We consider the impact of a ring crack within a rotating hollow cylinder of fixed height under axisymmetric (torsion) loading. The form of the displacement is obtained from the equation of motion using the Fourier sin transform. The displacement jump over the crack is obtained from the boundary condition on the tangential stress, formulated as a singular integral equation which is solved by the method of orthogonal polynomials. The stress intensity factors on the opposing crack surfaces are calculated. The dependence of the crack extension on the problem geometry is investigated, including the impact of the crack’s location, cylinder’s height, torsion loading and rotation frequency. Possible extensions of the model to cover fatigue cracking are considered. Whether the presented model can be used to develop a practical test for detecting cracks is investigated.

Elastic response of transversely isotropic and non-homogeneous geomaterials under circular ring concentrated and axisymmetric distributed loads

This paper first develops the closed-form solution of a layered halfspace subject to circular ring concentrated loads. The layered halfspace consists of finite layers and a lower halfspace. All the layers in the layered halfspace are homogeneous and transversely isotropic. Integral transform techniques are utilized to derive the solution in cylindrical polar coordinates. Then, the closed-form solution is used to develop the numerical method of axisymmetric distributed loads over circular areas. The numerical method involves integration along the radius direction and discretization of a loading circular area into one-dimensional elements. Finally, the elastic responses of non-homogeneous geomaterial halfspaces under axisymmetric distributed loads over circular areas are analyzed in detail.

NUMERICAL MODELING OF DYNAMIC DEFORMATION OF A THREE-LAYER RIBBED CYLINDRICAL SHELL UNDER AXISYMMETRIC IMPULSE LOADS

The non-stationary vibrations of three-layer composite cylindrical shell under axisymmetric impulse loads have been researched. The mathematical model and method for calculating the dynamic deformation of the shell system under consideration is based on the geometrically nonlinear theory of Timoshenko’s type shells and ribs. The results of numerical analysis of the problem are presented.

A method to analyze the axisymmetric problem of FRP laminated tubes based on singularity correction

In order to solve the problem of singularity in the stress and strain calculation process of FRP laminated tubes with arbitrary layer angles under axisymmetric thermomechanical loading, a three-dimensional elasticity theory analysis method based on singularity correction by modifying the stiffness matrix coefficients is proposed. Firstly, the basic three-dimensional elasticity theory model for FRP laminated tubes under axisymmetric thermomechanical loading is established through the displacement method. Then, the singularity plies in the laminate are determined, and the stiffness matrix coefficients of the singularity plies are modified respectively. Modifications to the displacement function coefficients, stiffness coefficients, boundary condition, and interlayer continuous condition equilibrium equations are also conducted subsequently. Verifications of the present approach are conducted by comparing the stress distributions calculated by the singularity correction method with those extracted by traditional isotropic elasticity models and then with numerical results provided by finite element analysis. Good consistency was obtained; thus, the correctness of the theory is proved from both theoretical and numerical aspects.

Dynamic response of cylindrical deep buried tunnels in unsaturated soil under axisymmetric explosion loading

This study established a calculation model for a cylindrical tunnel subjected to internal explosion loading in an unsaturated medium, assuming that the transient load exponentially decays along the tunnel direction. The governing equations for the lining tunnel and the surrounding unsaturated soil under explosion load were derived based on continuum mechanics and the theory of porous media mixtures. Laplace inverse transformation and Fourier inverse transformation were employed to derive the dynamic response of the lining and soil in the time-space domain. Furthermore, the effects of unsaturated medium saturation on the explosion response of the lining and the surrounding region were investigated. The results demonstrate that the analytical solution can be used to explain the dynamic response of an underground tunnel surrounded by unsaturated soil, during an internal explosion. The solutions can be extended to further advancements considering different boundary conditions.

Circular Nanoplate on Elastic Nanolayer under Axisymmetric Loading and Surface Effects

Influence of surface energy on an interaction problem between a flexible circular nanoplate and a nanolayer is examined by using a variational formulation and the GM surface theory. The nanoplate is resting in smooth contact on the supporting nanolayer, and subjected to axisymmetric vertical loadings. The normal traction at the plate–layer interface is written in terms of generalized coordinates obtained from the flexibility equations derived from Green’s function and Hankel integral transform technique. A numerical solution scheme is then implemented into a computer code, and the convergence and accuracy of the proposed solution are verified with existing solutions. A set of numerical solutions is illustrated to present an impact of the surface energy effects on this interaction problem. Both deflection and bending moment of the nanoplate show a considerable dependence on the relative plate stiffness and the surface material properties, and demonstrate the size-dependent behaviors.

New insight into large deformation analysis of stretch-based and invariant-based rubber-like hyperelastic elastomers

A nonlinear finite element formulation for large deformation analysis of hyperelastic membranes in Total Lagrangian framework is developed. In many cases, it is convenient to utilize the invariant-based strain energy density function to analyze the structures when employing the finite element method. However, in this contribution, both invariant-based and stretch-based formulations are developed. Formulations are completely general and not restricted to axisymmetric loading and geometry of membrane. Furthermore, initially flat and non-flat membrane can be investigated by this method. Incompressible as well as compressible materials can be modeled. A method for imposing the plane stress condition to the formulation for compressible materials is presented. Moreover, isotropic and anisotropic materials can be considered. Some problems are analyzed and results compared to the available ones in the literature. The comparison between solution based on invariant-based method and stretch-based method with exact fourth-order elasticity tensor obtained in this work demonstrates that the stretch-based method derived in this paper works very well. The presented examples demonstrate that the developed formulations have no restriction or simplification with respect to the modeled object geometry and inherent anisotropy.