Non-axisymmetric Loading Research Articles

Effects of Electric Potential on Thermo-Mechanical Behavior of Functionally Graded Piezoelectric Hollow Cylinder under Non-Axisymmetric Loads

Effects of Electric Potential on Thermo-Mechanical Behavior of Functionally Graded Piezoelectric Hollow Cylinder under Non-Axisymmetric Loads

An Analytic Solution of Length-Limited Thin-Walled Cylindrical Shells under Non-Axisymmetric Uniform Line Load and Concentrated Load

Solution for length-limited thin-walled cylindrical shells' deformation and stress state under non-axisymmetric uniform line load and concentrated load conditions, such as containments of rail guns, is a common engineering problem. Based on fundamental equations of the above problem, load function and displacement function are presented, and displacement and stress analytic solutions are obtained by Galerkin Method in this paper. The analytical solutions are verified by comparing them with ANSYS numerical solutions of an example problem. The results of this paper can be served as a reference for analytic solutions and engineering designs of non-axisymmetric cylindrical shells.

Failure of cylindrical steel silos composed of corrugated sheets and columns and repair methods using a sensitivity analysis

The paper deals with failure of large cylindrical steel silos composed of horizontally corrugated sheets with vertical stiffeners. The failure reasons were discussed. A linear buckling and a non-linear analysis with geometric and material non-linearity were carried out with a perfect and an imperfect silo shell (with different initial geometric imperfections) by taking into account axisymmetric and non-axisymmetric loads imposed by a bulk solid following Eurocode 1. The 3D FE calculations were carried out with the commercial finite element code “Abaqus”. The calculated buckling forces were compared with the allowable one given by Eurocode 3. Repair methods of silos against buckling were proposed. A sensitivity analysis was performed for a silo to predict the location and profile type of strengthening elements.

3D buckling analysis of a cylindrical metal bin composed of corrugated sheets strengthened by vertical stiffeners

The paper presents 3D results of a quasi-static buckling analysis of a funnel-flow cylindrical metal bin composed of horizontally corrugated sheets strengthened by vertical columns. A linear buckling and a non-linear analysis with geometric and material non-linearity were carried out with a perfect and an imperfect real silo shell by taking into account axisymmetric and non-axisymmetric loads imposed by a bulk solid following Eurocode 1 and different initial geometric imperfections and load non-uniformities around the circumference. The calculated buckling forces were compared with the permissible one given by Eurocode 3.

Analysis of disc brake temperature distribution during single braking under non-axisymmetric load

This paper aims to study and compare the temperature distributions caused by mutual sliding of two members of the disc brake system basing on two- and three-dimensional FE modelling techniques and complexity of the phenomenon. First step of the analysis based on the previously developed model where the intensity of heat flux was assumed to be uniformly distributed on the friction surface of disc during braking process, and the heat is transferred exclusively in axial direction, whereas during the second, the three-dimensional rotor is subjected to the non-axisymmetric thermal load to simulate realistic thermal behaviour of the brake action. Operation conditions, thermo-physical properties of materials and dimensions of the brake system were adopted from the real representation of the braking process of the passenger vehicle. Arbitrarily selected four values of the velocities at the moment of brake engagement were applied to the models so as to investigate theirs influence on the obtained solutions of the temperature evolutions on the contact surface of the disc volume referring to two separated finite element analysis. The large amount of heat generated at the pad/disc interface during emergency braking indisputably evokes non-uniform temperature distributions in the domain of the rotor, whereas the pad element is constantly heated during mutual sliding. The obtained results of the original code of three-dimensional modelling technique implemented to the conventional FE software revel high agreement with the solution of simplified process of friction heating.

Dynamical Behaviors of Asphalt Pavement under Vehicle Loads

The dynamical responses of asphalt pavement structures subjected to the vehicles are studied considering the effect of horizontal forces. Based on the elasticity, the stress distribution and deformations of asphalt pavement structures under nonaxisymmetric loads are investigated. Integral transform method is used to obtain the stress response function. And the maximum shear stress distribution and Mises stress is studied analytically and numerically. The influence of the horizontal forces and material parameters of the pavement structures on the dynamic behaviors of the structure is analyzed. The results show that the horizontal force plays important roles on the maximum shear stress and Mises stresses in structures.

Conceptual Design of a New Outer Divertor for C-Mod

The next generation outer divertor target proposed for C-Mod is intended to operate with edge physics behavior that is ’Demo-like’, i.e., it will be capable of operating at a bulk tile and structure temperature of 600C. The proposed design exposes a vertical cylinder covered with tungsten lamellae tiles to the divertor heat flux. Heat load variation along the height of the cylindrical target has been specified and is being considered in the tile design. The design must allow for differential radial thermal expansion of the cylindrical structure. It is intended to be toroidally continuous with a high tolerance on axisymmetry to improve alignment with the plasma and limit interactions of disruption induced currents with the toroidal field. Inductively driven axisymmetric disruption currents are calculated using electromagnetic transient simulations previously employed for RF antennas and the cryopump. Disruption-induced halo currents are expected to flow though the structure, which have proved troublesome for the old outer divertor structure. The new toroidally continuous structure will be intrinsically strong with respect to axisymmetric mechanical loads, although the support hardware will also need to be robust to resist movement during non-axisymmetric halo loads. Halo current specifications for the outer divertor have been developed, and halo current paths that minimize loading are “forced” with appropriate use of insulation and grounding straps. Radiative energy transfer to other components in the vessel makes sustained operation of the outer divertor at elevated temperatures difficult.

Nonaxisymmetric Thermomechanical Analysis of Functionally Graded Hollow Cylinders

Analytical solutions for nonaxisymmetric, thermomechanical response of functionally graded hollow cylinders are obtained in this article. The hollow cylinders are assumed to be subjected to nonaxisymmetric mechanical and transient thermal loads. Properties of functionally graded material are considered as temperature-independent and continuously varying in radial direction. Employing complex Fourier series and Laplace transform techniques, analytical solutions of time-dependent temperature and thermomechanical stresses are obtained. Numerical values of temperature and stresses of a FGM hollow cylinder under assumed thermomechanical loads are presented in graphical form.

The Thermoelastic Behavior of Thrust Washer Bearings Considering Mixed Lubrication, Asperity Contact, and Thermoviscous Effects

A comprehensive numerical model is developed to investigate the behavior of a tilted thrust washer bearing. The goal of this work is to investigate the physical phenomena that distress the bearing system. This work includes thermoelastic deformations, which have been neglected in previous studies. The thrust washer bearing is subjected to non-axisymmetric loads within the planetary gear sets of automatic transmissions and consists of flat-faced washers placed between an idle helical gear and an adjacent carrier face. Various coupled numerical schemes model sliding friction, boundary lubrication, asperity contact, thermo-mechanical deformation, thermoviscous effects, and full-film lubrication. The model provides predictions of frictional torque, bearing temperature, hydrodynamic lift, and other indicators of bearing performance. The numerical model and theoretical predictions confirm the experimental results, showing that the bearing under consideration is very susceptible to the mechanisms of thermoelastic instability (TEI) and thermoviscous distress (TVD).

A technique for calculating large deflections of nonshallow elastoplastic shells of revolution under nonaxisymmetric loading

A technique for calculating the geometrically and physically nonlinear stress strain state of nonshallow shells of revolution under the nonaxisymmetric wind-like loading is proposed. The calculation results for a semispherical shell with the central hole and rigidly fixed edges depending on the loading nonaxisymmetry, material characteristics and thickness are presented. We demonstrate not only quantitative but also qualitative influence of taking into account the factor of joint nonlinearity on the process of shell deformation.

Thick shells of revolution: Derivation of the dynamic stiffness matrix of continuous elements and application to a tested cylinder

This paper describes a procedure for calculating the dynamic stiffness matrix of tubular shells with free edge boundary conditions. Such an analysis forms the basis for the Continuous Element Method. The method is used to formulate a thick axisymmetric shell element which takes into account rotatory inertia, transverse shear deformation and non-axisymmetric loadings.

Stress state of compound solids of revolution made of damaged orthotropic materials with different tensile and compressive moduli

A technique is proposed to allow for damages and different tensile and compressive moduli of orthotropic materials in stress-strain analysis of compound bodies of revolution under nonaxisymmetric loading and heating. The technique combines the semi-analytic finite-element method and the method of successive approximations

The Behavior of Thrust Washer Bearings Considering Mixed Lubrication and Asperity Contact

The behavior and life of a tilted flat thrust washer bearing is modeled by a comprehensive numerical code. The goal is to investigate the conditions that distress thrust washer bearings through numerical techniques. The thrust washer bearing supports non-axisymmetric loads within the planetary gear sets of automatic transmissions and consists of flat-faced washers placed between an idle helical gear and its contacting face. Because of non-axisymmetric loading, the gears and washers tilt in relation to the carrier, forming a converging gap that may produce hydrodynamic lift. Various coupled numerical schemes model sliding friction, boundary lubrication, asperity contact, thermo-viscous effects, and full film lubrication. The model provides predictions of frictional torque, bearing temperature, hydrodynamic lift, and other indicators of bearing performance. The results show that the bearing operates in the regimes of boundary lubrication, mixed lubrication, and full-film lubrication, and that the bearing can distress at high loads and speeds. Presented at the STLE Annual Meeting in Toronto, Ontario, Canada May 17-20, 2004 Review led by Jane Wang

Guided wave inspection of long steel pipe using non-axisymmetric end loading transducer

In order to overcome the conventional guided wave transducer's unsuitability for piled pipe inspection, a non-axisymmetric end loading (NEL) transducer is designed and studied in this paper. Propagation of guided waves in a hollow cylinder and the circumferential distribution of echoes from notches are studied by using the finite element (FE) method under different end loading conditions. The simulated results show that when the radial angle between the first notch on a pipe and the NEL transducer is zero, the energy distribution from notch echoes is a maximum, even if there are different direction notches on the pipe. A specially designed clamp is developed to fix the NEL transducer to the pipe. Finally, the simulated and experimental results show that the circumferential and axial location of the notch on pipe can be located by rotating the NEL transducer during the process of inspection.

General Three-Dimensional Analysis of Transient Elastic Waves in a Multilayered Medium

AbstractThe propagation of transient elastic waves in a three-dimensional multilayered medium subjected to general dynamic loadings is analyzed in this study. One of the objectives of this study is to develop an effective analytical method for determining transient full-field solutions in the multilayered medium subjected to nonaxisymmetric dynamic loadings. The wave field is decomposed into two parts; one is the P-SV system of waves and the other is the SH system, each of which propagates independently in a horizontally layered medium. A simple relationship between solutions of two- and three-dimensional problems in the Fourier transform domain is also presented. A matrix solution in the triple transform domain is obtained by Brownwich expansion and the inverse transform is inverted by Cagniard’s method. The matrix representation of the solution can be easily used to calculate the transient response of the multilayered medium without tracing the ray path manually. The formulas presented in this study enable us to calculate the long-time transient responses of the multilayered medium for three-dimensional configuration. The theoretical transient solution for a layer overlaying a half-space subjected to an arbitrarily oriented point force is presented in detail. The numerical calculations are compared with experimental measurements for the surface displacement response on a plate and a layer overlaying a half-space subjected to an axisymmetric point force. The numerical investigation is also carried out for nonaxisymmetric loading problem of a layer overlaying a half-space.

Nonaxisymmetric Deformation of Solids of Revolution Made of Elastic Orthotropic Materials with Different Tensile and Compressive Moduli

A method is proposed to allow for the difference of the tensile and compressive moduli of compound orthotropic bodies of revolution subject to nonaxisymmetric loading and heating. The compliance matrix is symmetrized by introducing weighting coefficients that take into account the influence of the sign of stresses in two mutually perpendicular directions on the corresponding coefficients of this matrix

Numerical Nonaxisymmetric Thermostress Analysis of Compound Solids of Revolution with Damage

A technique is proposed to allow for deformation damage of cylindrically orthotropic elastic materials in a thermoelastoplastic stress–strain analysis of composite bodies of revolution under nonaxisymmetric loading and heating

Exact formulation of interface stiffness matrix for axisymmetric bodies under non-axisymmetric loading

Based on the concept of the zero-thickness joint element, a new and accurate formulation of the stiffness matrix for an axisymmetric interface element is presented. This element was formulated to model soil-structures interfaces in semi-analytical analysis of axisymmetric solids of revolution subjected to non-axisymmetric loading. The advantages of the closed-form solution of the interface stiffness matrix are manifold. First of all, it is exact and accurate under all conditions. Secondly, it can be easily used in a finite element code. This formulation requires only the angle of the interface element inclination, thus eliminating the need for numerical integration for each orientation of interface element. Thirdly, it is compatible with the commonly used continuum isoparametric elements such as the six-noded triangle or the eight-noded quadrilateral elements. Two example problems involving a rigid footing and a pile subjected to lateral loading are used to show the advantages of using this new exact formulation.

Influence of the Direction of the Principal Anisotropy Axes in a Rectilinearly Orthotropic Material on the Stress State of a Compound Solid of Revolution Subject to Nonaxisymmetric Heating

A technique for analysis of the temperature fields and the stress state of isotropic and orthotropic laminated bodies of revolution under nonaxisymmetric loading is described. The influence of the direction of the principal anisotropy axes in a rectilinearly orthotropic material on the stress state of a three-layer body of revolution under nonaxisymmetric loading is studied

Model of Plastic Deformation at the Front of a Circular Crack Under Nonaxisymmetric Loading

The constrained plastic deformation at the front of a circular mode I crack under nonaxisymmetric loading in the crack plane is studied. It is shown that the normal stresses in the plastic zone depend on the polar angle and external stresses. The constraint is maximum at those points on the crack front along tangents to which the maximum external tensile stresses act