Structural Optimization 15, 187-200 (~) Springer-Verlag 1998 Automated optimization of transverse frame layouts for ships by elastic-plastic finite element analysis M.K. Rahman* Department of Marine Technology, University of Newcastle Upon Tyne, NE1 7P~U, UK Abstract This paper presents a model for the optimum de- sign of ship transverse frames. An elastic-plastic finite element analysis algorithm for plane frames has been incorporated in the model to evaluate the ultimate strength of the overall frame, and different effects of design loads. Using these strengths and load effects, appropriate design constraints are then formulated to pre- vent different failure categories; the overall collapse, ultimate limit state failures and serviceability failures. Possible instabilities and effects of combined loads are accounted for in formulating these constraints. Scantlings of the frame structure have been modelled as free design variables. The weight function and different con- straint functions are then derived relating design variables in such a way that once parameters for finite element analysis are input, the scheme automatically forms the objective function and all con- straints, and then interacts with the simplex algorithm through sequential linearization to find the optimum solution. Thus the scheme is almost automatic. Different layouts of the frame struc- ture have been designed by executing this scheme, which demon- strates the capability of the model and the possibility of weight savings by choosing the appropriate layout. Finally, it is suggested how this model would interact with the design of longitudinal ma- terials to ensure the overall optimality in ship hull module design, to prevent grillage buckling and to validate underlying assump- tions in analysis. 1 Introduction The optimum design of the whole ship structure as a single design problem is still acknowledged as being an infeasible task from the point of view of modelling complexities and as being computationally cumbersome, when limit-based theo- ries of structural engineering are used as the basis for such a design. However, the current trend of rationalizing the ship structural design procedure often integrates such theo- ries in the process of achieving efficient and innovative design. To make such a process analytically and computationally vi- able, several recent research activities have been devoted to contributing different approaches. Hughes (1983) presented comprehensive theories for such design emphasizing mainly approximate analysis. Through the appropriate utilization of such approximate analyses, a rationally-based methodology was developed by Rahman (1991) for the optimum design of ship structures. This methodology was used to demonstrate the improvement in design switching over from design rules * Current address: Centre for Petroleum Engineering, University of New South Wales, Australia supplied by a leading classification society to very approx- imate structural engineering theories (Rahman 1992),. and successive improvements using more rigorous analysis (Rah- man and Caldwell 1995). The main philosophy behind this methodology is to de- compose the whole ship structure into a number of manage- able hull modules. The length of such a module should ex- tend over at least one complete cargo hold. This hull mod- ule is decoupled conceptually into a number of transverse frames and hull girders (longitudinal materials between two adjacent transverse frames). When appropriate measures are taken to validate such decoupling, the ultimate longitudinal strength (Rahman and Chowdhury 1996) and the ultimate transverse strength (Rahman 1997) can be evaluated inde- pendently. Such decoupling is validated by maintaining rela- tive sizes of transverse frames such that the overall longitudi- nal collapse occurs between adjacent transverse frames with- out involving several frames. This philosophy of interframe longitudinal collapse has permitted the multilevel optimiza- tion scheme to design hull girders (Rahman 1994) through decomposed design of deck, side and bottom substructures by a panel optimization scheme for each (Rahman 1996). Similarly, the evaluation of transverse strength indepen- dently has been the basis for designing the transverse frames of ships. These transverse frames are approximately orthog- onal to the longitudinal structure, and the shell and deck platings prevent sway (large deformations) in the longitu- dinal direction. Neglecting any contribution of longitudinal stiffeners to the transverse strength, the transverse structure of a ship can be considered as a plane frame having a plate flange whose breadth is equal, or nearly equal, to the spacing of these frames. Components of these plane frames are beam elements under predominant bending loads arising from lat- eral pressure caused by cargo and hydrostatic distributions. However, this permits the use of basic theories of plane frame analysis in the design of the transverse structures of the ship. Nonlinear finite element analysis (Chen et al. 1983) has never been a candidate to be included in the design scheme in- volving optimization because of its prohibitive computation, in spite of its accuracy. Direct plastic analysis (Neal 1985; Hodge 1959; Horne 1971) has been extensively used (Green- berg and Prager 1952; Neal and Symonds 1952; Harrison 1970) to design civil engineering type structures where the instability is not of primary concern. Because of its sim- plicity, there were attempts (Chowdhury 1977; Kim 1982) to use this method to design optimum ship frames. How-