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Frictionless contact between a rigid indentor and a transversely isotropic functionally graded layer

Patra R., Barik S. P., Chaudhuri P. K.

International Journal of Applied Mechanics and Engineering

2018

Vol. 23, no. 3

655--671

This article is concerned with the study of frictionless contact between a rigid punch and a transversely isotropic functionally graded layer. The rigid punch is assumed to be axially symmetric and is supposed to be pressing the layer by an applied concentrated load. The layer is resting on a rigid base and is assumed to be sufficiently thick in comparison with the amount of indentation by the rigid punch. The graded layer is modeled as a non-homogeneous medium. The relationship between the applied load P and the contact area is obtained by solving the mathematically formulated problem through using the Hankel transform of different order. Numerical results have been presented to assess the effects of functional grading of the medium and the applied load on the stress distribution in the layer as well as on the relationship between the applied load and the area of contact.

Eigen value approach in micropolar elastic medium with voids

Singh R., Singh K.

International Journal of Applied Mechanics and Engineering

2013

Vol. 18, no. 2

521--536

The eigen value approach, following the Laplace and Hankel transformation has been employed to find a general solution of the field equations in a micropolar elastic medium with voids for an axisymmetric problem. An infinite space with the mechanical source has been applied to illustrate the utility of the approach. The integral transformations has been inverted by using a numerical inversion technique to get the result in physical domain. The results in the form of normal displacement, volume fraction, normal force stress, tangential force stress and tangential couple stress components have been obtained numerically and illustrated graphically.

The elasticity problem for a stratified semi-infinite medium containing a penny-shaped crack filled with a gas

Monastyrskyy B., Kaczyński A.

Acta Mechanica et Automatica

2007

Vol. 1, no. 1

63-66

This paper deals with a periodic two-layered elastic half-space weakened by an interface penny-shaped crack tilled with a gas. The study is based on the approximate treatment by using the linear elasticity with microlocal parameters in the axisymmetric case. Applying the Hankel integral transforms, we obtain a system of dual integral equations. It is reduced to a set of two integral equations which are solved numerically. Some results concerning the variation of the internal gas pressure and the stress intensity factors of mode I and mode II are illustrated graphically.

Niniejsza praca poświęcona jest zagadnieniu periodycznej dwuwarstwowej półprzestrzeni sprężystej osłabionej międzywarstwową szczeliną kołową wypełnioną gazem. Zastosowano przybliżone podejście oparte na liniowej teorii sprężystości z parametrami mikrolokalnymi w osiowo-symetrycznym przypadku. Używając transformacji Hankela, otrzymano układ dualnych równań całkowych, który sprowadzono do numerycznego rozwiązania równań całkowych. Zależności dotyczące wewnętrznego ciśnienia gazu i współczynników intensywności naprężeń zilustrowano graficznie.