Zastosowanie Szeregów Trygonometrycznych do Obliczania Zamkniętych Powłok Walcowych

This paper is concerned with the application of the common method of trigonometric series to the computation of cylindrical shells of small thickness. Solutions are given for a tube of finite length simply supported or clamped along the edges, and acted on by any load symmetric in relation to the axis of the tube. Solutions are given for the problem of a tube supported along three circles and the problem of a very long tube supported along many circles spaced by the distance Z and loaded in a periodic manner. The equations for tubes apply also to a plate strip, if the radius of the tube increases solving the problem of indefinitely. A method is also given for a tube of variable thickness by reducing it to a Fredholm integral equation of the second kind and determining the expansion coefficients of the deflection. Examples are included for simple loads such as a constant load or a concentrated load on the periphery.