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Antiplane deformation of a bimaterial with thin interfacial nonlinear elastic inclusion

Sulym H., Piskozub Y., Polanski J.

Acta Mechanica et Automatica

2018

Vol. 12, no. 3

190--195

The problem of longitudinal shear of bimaterial with thin nonlinear elastic inclusion at the interface of matrix materials is considered. Solution of the problem is constructed using the boundary value problem of combining analytical functions and jump functions method. The model of the thin inclusion with nonlinear resilient parameters is built. Solution of the problem is reduced to a system of singular integral equations with variable coefficients. The convergent iterative method for solving such a system is offered for various nonlinear strain models, including Ramberg-Osgood law. Numerical calculations are carried out for different values of non-linearity characteristic parameters for the inclusion material. Their parameters are analysed for the tensely-deformed matrix under loading a uniformly distributed shear stresses and for a balanced system of the concentrated forces.

On the sums of unilaterally continuous functions

Grande M.

Demonstratio Mathematica

2002

Vol. 35, nr 4

743-748

In this article we prove that each jump function f : R-R is the sum of two unilaterally continuous jump functions. Moreover we observe that there are jump functions g : R - R, which are not the products of any finite family of unilaterally continuous jump functions.