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1

On 3D symmetrical thermoelastic anticrack problems

Kaczyński A.

Archives of Mechanics

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2016

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Vol. 68, nr 2

99--112

EN

A potential theory method is developed to solve a symmetrical thermoelastic problem of a cooling temperature field applied over the faces of a rigid sheet-like inclusion (an anticrack) in an elastic space. The governing boundary two-dimensional (2D) singular integral equations for an arbitrarily shaped anticrack are derived in terms of unknown thermal shear stress jumps. As an illustration, a complete solution expressed in elementary functions to the problem of a circular rigid inclusion subjected to a uniform temperature is presented and interpreted from the point of view of fracture theory.

2

On the contact problem in piezoelectroelasticity

Kaliński W., Rogowski B.

International Journal of Applied Mechanics and Engineering

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2009

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Vol. 14, no 1

157-174

EN

The problem of electroelasticity for piezoelectric materials is considered. The fundamental solutions for the axi-symmetric problem of piezoelasticity are utilized to solve a smooth contact problem. Exact solutions are obtained for elastic and electric fields in the contact problem. If the contact region is an annular three-part then the mixed boundary value problem is considered. In this case the solution is approximated as series solution.

3

On the thermoelastic problem of uniform heat flow disturbed by a circular rigid lamellate inclusion

Kaczyński A., Monastyrskyy B.

Archives of Mechanics

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2009

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Vol. 61, nr 3-4

309-324

EN

A complete solution in elementary functions is given for the three-dimensional thermoelastic ?eld in an elastic space, containing an absolutely rigid circular inclusion (anticrack) under a normally incident uniform heat ?ow. The inclusion is assumed to be slightly conducting, with a certain thermal resistance. The analysis is based on the potential theory method. The resulting boundary-value problems are reduced to classical mixed problems of the potential theory. The temperature, ?uxes, thermal stresses and displacements in the inclusion plane are given in closed forms and interpreted from the point of view of the failure theory.

4

On the contact problem for a smooth punch in piezoelectroelasticity

Dyka E., Rogowski B.

Journal of Theoretical and Applied Mechanics

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2005

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Vol. 43 nr 4

745--761

EN

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.

PL

Rozpatrzono osiowo symetryczne zagadnienie clektrosprężystości dla materiałów piezoelektrycznych. Wprowadzono trzy potencjały opisujące przemieszczenia, naprężenia, elektryczny potencjał, składowe wektora pola elektrycznego i elektrycznych przemieszczeń. Znalezione fundamentalne rozwiązania wykorzystano do analizy zagadnienia kontaktowego gładkiego stempla. Znaleziono ścisłe rozwiązania opisujące sprężyste i elektryczne pola w rozpatrywanym zagadnieniu kontaktowym. Wyniki obliczeń przedstawiono na wykresie w celu pokazania wpływu mechanicznych i elektrycznych obciążeń na analizowane wielkości. Efekt anizotropii materiałów piezoelektrycznych w omawianym zagadnieniu jest znaczący.