Novel cloaking lamellar structures for a screw dislocation dipole, a circular Eshelby inclusion and a concentrated couple

Using conformal mapping techniques, we design novel lamellar structures which cloak the influence of any one of a screw dislocation dipole, a circular Eshelby inclusion or a concentrated couple. The lamellar structure is composed of two half-planes bonded through a middle coating with a variable thickness within which is located either the dislocation dipole, the circular Eshelby inclusion or the concentrated couple. The Eshelby inclusion undergoes either uniform anti-plane eigenstrains or uniform in-plane volumetric eigenstrains. As a result, the influence of any one of the dislocation dipole, the circular Eshelby inclusion or the concentrated couple is cloaked in that their presence will not disturb the prescribed uniform stress fields in both surrounding half-planes.

Internal uniform hydrostatic stresses in a three-phase non-elliptical inclusion subjected to a nearby concentrated couple

We apply conformal mapping techniques with analytic continuation to study the existence of a uniform hydrostatic stress field inside a non-elliptical inclusion bonded to an infinite matrix via a finite thickness interphase layer when the matrix is simultaneously subjected to a concentrated couple as well as uniform remote in-plane stresses. We show that the desired internal uniform hydrostatic stress field is possible for given material and geometric parameters provided a certain constraint is placed on the remote loading. Subsequently, when the single loading parameter, five material parameters and three geometric parameters are prescribed, all of the unknown complex coefficients appearing in the series representing the corresponding conformal mapping function can be uniquely determined from a set of nonlinear recurrence relations. We find that the internal uniform hydrostatic stress field, the constant mean stress in the interphase layer and the hoop stress along the inner interface on the interphase layer side are all unaffected by the existence of the concentrated couple whereas the non-elliptical shape of the (three-phase) inclusion is attributed solely to the influence of the nearby concentrated couple.

Configurational Forces on Elastic Line Singularities

Configurational forces acting on two-dimensional (2D) elastic line singularities are evaluated by path-independent J-, M-, and L-integrals in the framework of plane strain linear elasticity. The elastic line singularities considered in this study are the edge dislocation, the line force, the nuclei of strain, and the concentrated couple moment that are subjected to far-field loads. The interaction forces between two similar parallel elastic singularities are also calculated. Self-similar expansion force, M, evaluated for the line force shows that it is exactly the negative of the strain energy prelogarithmic factor as in the case for the well-known edge dislocation result. It is also shown that the M-integral result for the nuclei of strain and the L-integral result for the line force yield interesting nonzero expressions under certain circumstances.

Research on the Selecting Control Sections of Internal Force Envelope by Simulation

The simulation optimization of internal force envelope in plane bar structure subjected to complex moving loads, including arbitrary concentrated force, concentrated couple, linearly distributed force and etc, was mainly discussed. By means of Vsap2011, the plane bar structure analyzing software, the effects of internal force envelope’s control sections on the solving precision of internal force envelope were analyzed. The research had reached to some important conclusions that in order to the obtain higher solving precision of internal force envelope, the element passed by moving loads should be divided by steps; more than enough dividing points should be inserted between load acting points for the element arbitrarily distributed with live loads; the element without any loads should be divided by defined interval when its both ends are rigid-jointed, while it should not be divided when its single or both ends are hinged-jointed.

The Carothers Paradox in the Case of a Nonclassical Couple

The Carothers solution for a wedge loaded by a concentrated couple at its vertex is known to be valid for the wedge angles 2α<2α*≈257 deg only. Moreover, for π<2α<2α* it exists for antisymmetric loading only. The more realistic model of the concentrated couple of the arbitrary orientation is examined by the approach of Dundurs-Markenscoff. It is shown that the Carothers type solution holds for the edge angles 2α<π.[S0021-8936(00)00402-5]

Singular Solutions in Second-Order Elasticity

The problems of a concentrated point force in an infinite medium (Kelvin's problem), or applied normal to the boundary of a half-space (Boussinesq's problem), as well as the corresponding problems for a concentrated couple, are solved to second order for incompressible isotropic elastic solids. The solutions are based on a simplified form of the second-order equations, obtained previously, and use of the Love's function representation for axisymmetric problems in the linear theory.

Critical Angles in Bending of Rotationally Inhomogeneous Elastic Wedges

An anisotropic rotationally inhomogeneous wedge bent by either a concentrated couple applied at the tip (Carothers problem) or uniform surface loadings (Levy problem) is considered. The existence criteria for homogeneous solutions describing stresses and strains in both problems are established. In the Levy problem there are two types of critical wedge angles, at which homogeneous solutions break down and become infinite. The first type critical wedge angles of Levy’s problem are shown to be critical also for Carothers’problem whatever the rotational inhomogeneity. Particular solutions to both problems are obtained at the critical wedge angle. The form of these solutions is established to depend on two factors: the multiplicity degree of roots of some eigenvalue equation and the number of independent eigenvectors of some real matrix. It is shown also that the eigenvalue equation does not provide an alternative way to calculate the critical angles and in the first-order perturbation theory results in just the same equations for the critical angles.