Axisymmetric Mechanical Loads Research Articles

Optimization on Elastoplasticity of Functionally Graded Shells of Revolution under Axisymmetric Loading

Depending on the load level, structures can experience a material nonlinearity known as elastoplasticity, which has an important role in the behaviour of structures. In order to avoid the elastoplastic behaviour, it is necessary to find the optimal thickness distribution, which corresponds to the minimum mass that provides an elastic behaviour for a certain load level. The elastoplasticity analysis of functionally graded axisymmetric shells under axisymmetric mechanical loading, and the subsequent optimization, was performed by using a simple conical frustum finite element model with two nodal circles; three degrees of freedom per node, which was based on Kirchhoff’s theory allowing for shear deformation; and using a reduced numerical integration procedure that is essential for its success when applied to thin shells. The formulation accounts for the calculation of the displacements and through-thickness stress distribution, including the effective stress. In this work, the thickness was the design variable in the optimization procedure and the mass was the objective function that needed to be minimized subject to a constraint imposed on the effective stress. The optimization solutions were obtained by using a feasible arc interior point gradient-based algorithm. Some illustrative examples were performed, and the corresponding results are presented and discussed.

Investigation of displacement and stress fields in pressurized thick-walled FGM cylinder under uniform magnetic field

In this paper, an analytical solution is presented for computing mechanical displacements and stresses in a thick-walled cylindrical pressurized vessel made of functionally graded materials (FGM). The pressure vessel is subject to axisymmetric mechanical loading within a uniform magnetic field. The analytical model of the pressurized vessel was constructed, where the radial continuous varying of elastic modulus and permeability along the thickness was assumed. It has been assumed that the elastic modulus and permeability are varying through thickness of the FG material according to a nonlinear general distribution along the thickness. Navier’s equation, which is a second-order ordinary differential equation, was derived from the mechanical equilibrium equation with the consideration of the Lorentz force resulting from the magnetic field. The distributions of the displacement and stresses were determined by the exact solution to Navier’s equation. Numerical results clarify the influence of the magnetic field, non-homogeneity parameter and internal pressure on the magneto-elastic response of the functionally graded cylindrical vessel. Thus, these parameters have remarkable effects on the distributions of radial displacement and radial and circumferential stresses.

Strip yield zone of a penny-shaped crack in a magnetoelectroelastic material under axisymmetric loadings

The strip yield zone ahead of a penny-shaped crack in a magnetoelectroelastic material, subjected to electric, magnetic and axisymmetric mechanical loadings, is evaluated analytically. Hankel transform is employed to reduce the mixed boundary value problem of the penny-shaped crack to dual integral equations, which are solved exactly under the assumption of electrically and magnetically permeable crack face conditions and the plastic strip yield zone crack model. An analytic solution to the mixed boundary problem has been obtained to predict the relationship between the length of the strip yield zone and the applied loadings. The distribution of mechanical, electric and magnetic fields in and outside of the strip yield zone in the cracked magnetoelectroelastic material has been derived analytically, and the crack opening displacement has been investigated. The effects of the mechanical, electric and magnetic loadings on the size of the yield zone are discussed in detail.

Electroelastic response of a piezoelectric cylinder with D∞ symmetry under axisymmetric mechanical loading

To understand the electroelastic field in fibers made of biodegradable polymers such as poly-l-lactic acid, we theoretically analyze the axisymmetric electroelastic field in a solid and infinitely long cylinder with D∞ symmetry, when subjected to a combined pressure and torsional shear stress. By introducing two kinds of displacement potential functions and an electric potential function and applying a Fourier transform technique, we derive the formulae for the electroelastic field quantities inside the body. Moreover, by performing numerical calculations, we elucidate the field both qualitatively and quantitatively, and investigate the possibility of using fibers made of poly-l-lactic acid for medical engineering applications.

Dugdale plastic zone of a penny-shaped crack in a piezoelectric material under axisymmetric loading

The Dugdale plastic zone ahead of a penny-shaped crack in a piezoelectric material, subjected to electric and axisymmetric mechanical loadings, is evaluated analytically. Hankel transform is employed to reduce the mixed boundary-value problem of the penny-shaped crack to dual integral equations, which are solved exactly under the assumption of electrically permeable crack face conditions. A closed-form solution to the mixed boundary-value problem is obtained to predict the relationship between the length of the plastic zone and the applied loading. The stress distribution in and outside of the yield zone has been derived analytically, and the crack opening displacement has been investigated. The electric displacement has a constant value in the strip yield zone. The current Dugdale crack model leads to non-singular stress and electric fields near the crack front, and it is observed that the material properties affect the crack opening displacement.

Nonlinear viscoelastic analysis of thick-walled cylindrical composite pipes

This paper analyzes the effect of the polymer matrix non-viscoelastic behaviour in the mechanical behaviour of thick multilayered cylinders. The original contribution of this work is to provide novel approximate analytical solutions to compute the time-dependent internal stress state through the pipe thickness within the framework of nonlinear viscoelasticity theory. The structures considered are thick, multilayered anisotropic infinitive long cylinders subjected to axisymmetric mechanical loading. Under such conditions there is an exact elastic solution which naturally satisfies equilibrium, strain-displacement, compatibility and boundary conditions for the stated constitutive equations and loading. Due to the continuous stress variations through the cylinder thickness, the proposed nonlinear viscoelastic solution assumes the averaged stress state to calculate the nonlinear elastic and viscoelastic factors in each layer. Furthermore, the solution is obtained assuming that the creep strains, within each layer, are constant through the thickness. The proposed algorithm converges to the exact solution when the number of layers is artificially increased. For the linear viscoelastic case, the proposed solution proved to match the exact known solution for isotropic viscoelastic materials. Finally several invented cases are run to illustrate the importance of the viscoelasticity phenomenon on the internal stress field in thick-laminated cylinders.

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.

Elastic-plastic behavior of fibrous composites

T he elastic-plastic behavior of fibrous composites is explored with self-consistent models. The overall and local yield surfaces, instantaneous moduli, thermal coefficients, plastic strains and thermal microstresses are calculated for selected material systems, using R. Hill's (1965) model, and a modified scheme. Axisymmetric mechanical loads and uniform thermal changes are considered and the extension to shear loads is discussed. A limited comparison of the calculated microstresses is made with available experimental results.