Engineering Transactions, 4, 4, pp. 525-541, 1956

O Odkształceniach i Naprężeniach Termicznych w Cienkich Płytach Prostokątnych i Kołowych o Zmiennej Grubości

Z. Thrun

Differential equations of deflection are derived in Cartesian and polar coordinates for plates of arbitrarily variable thickness, subjected to temperature arbitrarily distributed oved both faces of the plates and linearly variable over the thickness. Rectangular plates of linearly variable thickness clamped or simply supported on two edges are also investigated. Solution in the case of thickness constituting a quadratic function is obtained for circular plates.
The results obtained for a numerical example are compared with the corresponding results for a plate of constant mean thickness, subjected to a constant temperature difference. Finally, a solution for a circular
plate of axially symmetrical rigidity and temperature distribution is obtained by means of the method of finite differences.

Full Text: PDF
Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).


R. Gran Olsson, Biegung der Rechteckplatte bei linear veründerlicher Biegungssteifigkeit, Ing.-Archiv 5 (1934).

R. Gran Olsson, Unsymmetrische Biegung der Kreisringplatte von quadratischveränderlicher Steifigkeit, Ing.-Archiv 10 (1939).

S. Timoshenko, Theory of Plates and Shells, New York 1940.

N. J. Nielsen, Wyznaczanie odkształceń w płytach za pomocą równań różnicowych (w jez. duńskim), Kopenhaga 1920.

O. Pichler, Die Biegung kreissymmetrischer Platten von veränderlicher Dicke, Berlin 1928.

E. Melan i H. Parkus, Wärmespannungen infolge stationärer Temperaturfelder, Wieden 1935.

Z. Thrun, Odkształcenia i naprężenia termiczne w cienkich płytach, Arch. Mech. Stos. 4 (1954).