A Simplified Racking Analysis of a Car Carrier by Using Symbolic Calculations

Abstract

Recently detailed three-dimesional finite element analyses have commonly been performed for the structural design of the middle part, or sometimes of the whole part of a ship. The computer aided design of this kind is effective for the rational determination of scantlings of established ship structural systems. It should be contrasted for newly developed ships that difficulties may arise because of the various constraints accompanying to the present CAE-system as to examine the feasibility of the wide variations of possible structural systems at the initial stage of the structural design.
It has been a controversial issue whether the rapid development of computer hardwares and structural analysis softwares will soon accomplish the level which will enable the structural synthesis including the selection of an optimum structural system. Since we have not yet had the definite answer to the question whether a machine could think design strategies, it seems appropriate to pursuit not only complex but accurate CAE-system, but also simple but approximate methods in order to assist skilled structural designers at the very begining of ship design.
In the present paper a simplified analysis is proposed for the proper selection of structural systems of a car carrier, whose transverse structural system has wide variations such as partial bulkhead system and strong web frame system depending on the relevant design philosophies. Introducing a simple beam model, which can be solved by a symbolic manipulation procedure, one can observe that the racking deformation of transverse section is mainly influenced by the non-dimensional shearing rigidity defined in the present analysis. Comparing the partial bulkhead and strong web frame systems, the shearing rigidities at the bulkhead sections having the latter system is considerably small, and correspondingly its racking deformation obtained by the simplified analysis is several times larger than that of the former system.
In order to predict the racking deformation of actual ships having various transverse rigidities, an effective method is proposed, where the simple beam analysis using symbolic calculations is combined with the numerical data obtained by precise three-dimensional structural analyses of ships having similar principal dimensions. The validity of the proposed method is confirmed by comparing the predicted values with the precise numerical results.