Elastic and Thermoelastic Responses of Orthotropic Half-Planes

Yuriy V Tokovyy; Anatoliy V Yasinskyy; Sebastian Lubowicki; Dariusz M Perkowski

doi:10.3390/ma15010297

Elastic and Thermoelastic Responses of Orthotropic Half-Planes

Materials (Basel). 2021 Dec 31;15(1):297. doi: 10.3390/ma15010297.

Authors

Yuriy V Tokovyy^{1

2}, Anatoliy V Yasinskyy¹, Sebastian Lubowicki³, Dariusz M Perkowski³

Affiliations

¹ Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, 79060 Lviv, Ukraine.
² Department of Applied Mathematics, Institute of Applied Mathematics and Fundamental Sciences, National University Lviv Polytechnic, 79013 Lviv, Ukraine.
³ Faculty of Mechanical Engineering, Bialystok University of Technology, 15-351 Bialystok, Poland.

Abstract

A unified approach is presented for constructing explicit solutions to the plane elasticity and thermoelasticity problems for orthotropic half-planes. The solutions are constructed in forms which decrease the distance from the loaded segments of the boundary for any feasible relationship between the elastic moduli of orthotropic materials. For the construction, the direct integration method was employed to reduce the formulated problems to a governing equation for a key function. In turn, the governing equation was reduced to an integral equation of the second kind, whose explicit analytical solution was constructed by using the resolvent-kernel algorithm.

Keywords: elastic half-plane; explicit solutions; integral equation of second kind; orthotropic material; plane elasticity and thermoelasticity problems; resolvent-kernel algorithm.

Abstract

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