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Analysis of a penny-shaped crack in magneto-elastic medium.
(Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej, 2009) Rogowski, Bogdan
The problem of a crack in a piezomagnetic material under magneto-mechanical loading is considered. The exact solution, obtained in this work, includes the unknown a priori normal component of the magnetic induction vector inside the crack. Several different physical assumptions associated with limited magnetic permeability of the crack are utilized to determine those unknown magnetic inductions through the crack boundaries. Analytical formulae for the stress and magnetic induction in- tensity factors are derived. The effects of magnetic boundary conditions (limited permeability) at the crack surface on the basic parameters of fracture mechanics are analysed and some features of the solution are discussed. If the permeability of the medium inside the crack tends to zero or is very large, extreme results i.e. impermeable or permeable crack solutions are obtained.
Exact solution of mode III crack in elastic half-space
(Wydawnictwo Politechniki Łódzkiej, 2011) Rogowski, Bogdan
The elastic half-space contains a straight - line crack which lies in some distance from the tangentially loaded boundary. Fourier transform technique is used to reduce the problem to the solution of the Fredholm integral equation of the second kind. This equation is solved exactly. Field intensity factors of stress, crack displacement and the energy release rate are determined explicitly. Accordingly to exact analytical solution, obtained here, which is new to the author's best knowledge, the behaviour of a crack which is located in the neighbourhood of the boundary of a half-space may be investigated exactly.
Inclusion problems for elastic anisotropic media
(Wydawnictwo Politechniki Łódzkiej, 2006) Rogowski, Bogdan; Red. nauk. Wydziału: Urban, Tadeusz; Olesiak, Zbigniew; Matysiak, Stanisław
lnclusion mechanics appeared later then contact mechanics. The main reason for creating that branch of mechanics was the appearance and development of the new materials called composites. But not only. In real materials inclusions are always present. This book is about inclusion problems, which are solved by means of complex mathematical analysis. Although methods of the solutions, presented here, may seem difficult at the beginning, obtainedfinal results are simple and usefuL This book is intended for scientists and engineers who specialize in the field of inclusion mechanics and materiał science. ft can be also usefal to academic teachers, post-graduate students and students specializing in mechanics of solids. I hope they may draw from this book inspiration for farther elaborations of these problems. Perhaps it would be possible for them to simplify some results and prove the essential thesis.
On the contact problem for a smooth punch in piezoelectroelasticity.
(Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej, 2005) Dyka, Ewa; Rogowski, Bogdan
The problem of electroelasticity for piezoelectric materials is considered. For axially symmetric states, three potentials are introduced, which determine displacements, electric potential, stresses, components of the electric field vector and electric displacements in the piezoelectric body. These fundamental solutions are utilized to solve a smooth contact problem. Exact solutions are obtained for elastic and electric fields in the contact problem. The numerical results are presented graphically to show the influence of applied mechanical and electrical loading on the analyzed quantities and to clarify the effect of anisotropy of piezoelectric materials. It is also shown that the influence of anisotropy of the materials on these fields is significant.
On the stress intensity factors for transient thermal loading in an orthotropic thin plate with a crack.
(Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej, 2004) Rogowski, Bogdan
This paper is concerned with an orthotropic thin plate containing a crack perpendicular to its surfaces. It is assumed that the transient thermal stress is set up by the application of a heat flux as a function of time and position along the crack edge and the heat flow by convection from the plate surfaces. The exact analytical solutions for the stress intensity factor and crack-opening displacement are derived. Numerical examples show, among others, a dependence of the stress intensity factor on the thermal and elastic constants of the orthotropic material.