Obliczanie Sprężystej i Sprężysto-Plastycznej Stateczności Płyt Kołowych o Zmiennej Sztywności Metoda Odwrotna

The aim of the present paper is to obtain accurate solutions of the stability problem of circular and annular plates with variable rigidity, subjected to uniform compression by a constant force N. Various (statically determinate) support conditions are analysed both in the elastic and the elastic-plastic range. Some solutions are obtained by means of the inverse method of «assumed accurate solution».
In the elastic range the problem is stated in a general manner in the second part. The third part contains a number of accurate solutions for circular (3.9) and (3.10) and annular plates (3.28), (3.29), (3.31), (3.32), (3.40) and (3.41) obtained by assuming the deflection angle in the form of solution of Euler's equation I, (3.2). All the solutions obtained in this part determine plates with zero rigidity at a free or simply supported edge. The fourth part discusses solutions not having this feature. They are also obtained by assuming the deflection angle in the form of an Euler's equation but having a somewhat different form (Euler's equation II), (4.2). The equations (4.21) and (4.22) are sufficiently general to enable theoretical obtainment of an arbitrary number of forms of plates (and the relevant critical forces).
Solutions are obtained for full plates (4.26), (4.27), (4.37) and (4.38) and annular plates (4.47), (4.48), (4.54) and (4.55). They are illustrated by some simple examples.
In the fifth part an essential simplification of the general equation (2.8) is obtained by assuming the deflection function in the form of the solution of the Bessel equation (5.8). Similarly to the third part the rigidity at a free or simply supported edge must be zero (5.18), (5.19).
The sixth part is devoted to elastic-plastic buckling of circular and annular plates with variable rigidity. It is based on the simple buckling theory of elastic plastic plates given by RoS and Eichinger, the Kármán modulus being replaced by the tangent modulus E (o) = do|de, and the A. Ylinen formula (6.1) being used. Practical procedure for the determination of the form of the plate in the elastic-plastic is described as well as the method of finding the critical force in this range for a prescri- bed form of the plate. In conclusion (part 7) the material economies are determined in percents if a constant rigidity plate is replaced by a plate of variable rigidity, the critical force remaining the same, (7.6). For the example under consideration these economies are considerable and amount to 12 percent.