Calculation of non-conservative stability problems using “analytical” finite elements

Article type: Research Article

Authors: Lehmann, E.^{a; *} | Fricke, W.^b

Affiliations: [a] Flender Werft AG, Lübeck, Germany | [b] Thyssen Nordseewerke GmbH, Emden, Germany

Note: [*] Formerly Lecturer of matrix methods in ship structural analysis, Hamburg University, Institut für Schiffbau.

Abstract: The calculation of non-conservative stability problems is feasible by using the “kinetic stability criterion” according to Ziegler [1] . This means that a natural frequency analysis is performed at variable non-conservative load for obtaining evidence on the stability of the system. Solutions are found either for relatively simple systems by solving the differential equation being valid over the entire range of calculation ([2] , [3] , [4] , [5] , [6]) or for more complicated systems by approximating with finite elements on the basis of hermitical polynominals [7] . In this paper, however, non-conservative stability problems are treated with “analytical” finite elements in which the assumed displacement function exactly satisfies the differential equation. A discretisation error only appears due to the pointwise introduction of distributed non-conservative loads.

DOI: 10.3233/ISP-1978-2528503

Journal: International Shipbuilding Progress, vol. 25, no. 285, pp. 127-137, 1978