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Non-local Kirchhoff–Love plates in terms of fractional calculus

Sumelka W.

Archives of Civil and Mechanical Engineering

2015

Vol. 15, no. 1

231--242

Modern continuum mechanics needs new mathematical techniques to describe the complexity of real physical processes. Recently fractional calculus, a branch of mathematical analysis that studies differential operators of an arbitrary (real or complex) order, emerged as a powerful tool for modelling complex systems. It is due to the fact that fractional differential operators introduce non-locality to the description considered in a natural way. In this sense they generalize classical (local) formulations and make the description more realistic. This paper deals with the generalisation of the Kirchhoff–Love plates theory using fractional calculus. This new formulation in non-local, thus all common fields like e.g. internal forces or displacements at a specific point contain somehow information from its finite surroundings, which is in agreement with experimental observations.

Testovacie merania fyzikalnych procesov v rekuperacnej streche bytoveho domu

Perecinsky M.

Budownictwo o Zoptymalizowanym Potencjale Energetycznym

2004

nr (2)

293--298

This paper deals with some possibilities of the realization of the recuperational flat roofs, which use the refuse warmth of air from the object ventilation system. This warmth due to its continuos flow in the roof space gives up a part of its thermical energy. The theoretic knowledge and results presented in this paper are the result of research work of the whole collective at the Department of Construction at the Faculty of Civil Engineering TU Kosice.