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1

Three-phase parabolic inhomogeneities with internal uniform stresses in plane and anti-plane elasticity

Wang X., Schiavone P.

Archives of Mechanics

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2020

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Vol. 72, nr 1

27--38

EN

We examine the in-plane and anti-plane stress states inside a parabolic inhomogeneity which is bonded to an infinite matrix through an intermediate coating. The interfaces of the three-phase parabolic inhomogeneity are two confocal parabolas. The corresponding boundary value problems are studied in the physical plane rather than in the image plane. A simple condition is found that ensures that the internal stress state inside the parabolic inhomogeneity is uniform and hydrostatic. Furthermore, this condition is independent of the elastic properties of the coating and the two geometric parameters of the composite: in fact, the condition depends only on the elastic constants of the inhomogeneity and the matrix and the ratio between the two remote principal stresses. Once this condition is met, the mean stress in the coating is constant and the hoop stress on the coating side is also uniform along the entire inhomogeneity-coating interface. The unconditional uniformity of stresses inside a three-phase parabolic inhomogeneity is achieved when the matrix is subjected to uniform remote anti-plane shear stresses. The internal uniform anti-plane shear stresses inside the inhomogeneity are independent of the shear modulus of the coating and the two geometric parameters of the composite.

2

Neutrality of coated holes in the presence of screw dislocation dipoles or circular thermal inclusions

Wang X., Schiavone P.

Archives of Mechanics

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2018

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Vol. 70, nr 5

405--427

EN

In this paper, we consider the design of neutral coated holes in two particular cases when the thick coating itself is altered by the presence of some form of material imperfection. In the first case we consider anti-plane deformations of a linearly elastic solid when the thick coating applied to the hole includes a screw dislocation dipole. In the second case, we investigate the design of neutral coated holes in plane elasticity when the thick coating contains a circular thermal inclusion and the surrounding linearly elastic solid is subjected to uniform remote hydrostatic stresses. The design is achieved by constructing particular forms of the conformal mapping function for the coating itself. Several examples are presented to demonstrate the resulting solutions. Our numerical results show that the existence of the screw dislocation dipole or the circular thermal inclusion in the coating exerts a significant influence on the shape of the neutral coated hole.

3

Effects of boundary reinforcement on local singular fields in linearly elastic materials

Kim C. I., Schiavone P., Ru C.-Q.

Archives of Mechanics

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2013

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Vol. 65, nr 4

289-–300

EN

We consider the local deformation near a point at the interface between free and fixed boundary segments in an elastic half-plane undergoing plane strain deformations. Using asymptotic analysis, we show that the addition of a reinforcement along the free boundary effectively eliminates the well-known oscillatory behavior of the displacement and stress fields in the vicinity of the point leading to a strong square-root stress singularity. In addition, we demonstrate that the reinforcement induces a deformation field which is smooth locally and bounded at the point of interest.

4

New results concerning the identification of neutral inhomogeneities in plane elasticity

Vasudevan M., Schiavone P.

Archives of Mechanics

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2006

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Vol. 58, nr 1

45-58

EN

Using the concept of a spring-layer (imperfect) interface, we develop the series methods to determine the corresponding interface functions which ensure the (stress) neutrality of an elastic inhomogeneity. We assume that the inhomogeneity occupies a simply-connected domain with a regular boundary and that the inhomogeneity-matrix system is subjected to linear plane deformations. Of particular interest is the fact that the prescribed stress field inside the matrix is assumed to be non-uniform.

5

A sector inplane finite element in polar coordinates with rotational degree of freedom

Bouzrira C., Sabir A., Nemouchi Z.

Archives of Civil Engineering

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2005

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Vol. 51, nr 4

471-483

EN

In the present paper the strain based approach is applied to the development of a new sector element for general plane elasticity. It is developed in a system of polar coordinates and is based on dependent strains insofar as it is allowed by the compatibility equation. The displacement function for the element represent the rigid body modes and are associated with the three degrees of freedom per node namely the radial and the circumferential displacement and the inplane rotation. Numerical results from two selected test examples involving rotationally symmetric as well as rotationally unsymmetric type of deformation show that good accuracy is available for practical applications.

PL

Zastosowano podejście odkształceniowe celem stworzenia nowego elementu przekrojowego w płaskim zagadnieniu sprężystości. Zastosowano ujęcie odkształceń zależnych w biegunowym układzie współrzędnych w takim stopniu jak jest to możliwe spełniając warunki zgodności równania nierozdzie!ności. Funkcja przemieszczeń elementu opisuje ruchy sztywne i jest związana z trzema stopniami swobody na punkcie węzłowym, tj, radialnymi i obwodowymi przemieszczeniami jak również obrotem w płaszczyźnie. Rozwiązania numeryczne dwóch wybranych zadań uwzględniających rotacyjną symetryczną i asymetryczną postać deformacji pokazują możliwość uzyskania dobrych wyników w praktycznych zastosowaniach.