The nonlinear analysis of ship plating with flat bar stiffners has been carried out by the finite element method based on the load incremental approach. The large deflection analysis has been done by using the Lagrangian description. The elastoplastic analysis has been performed by adopting the flow theory of plasticity and the von Mises yield condition. The layered elements are used to show the process of yielding through the plate thickness in the elasto-plastic analysis. The following results are obtained; 1) According to the large deflection analysis, it is shown that the small deflection theory to the plate is applicable in the range of the lateral deflection-the thickness ratio $w/h{\leqq}0.3$ and ship plating in the range of $w/h{\leqq}0.5$. 2) By means of the elasto-plastic analysis, it is found that the maximum load-carrying capacity of the plate increases as much as 1.8 times of the initial yield load in the case of the simply supported condition and 2.2 times in the clamped condition. It is also shown that the maximum load-carrying capacity of ship plating increase as much as 4.3 times in the simply supported condition and 4.2 times in the clamped condition. This method would be applied and extended to solve combined nonlinear problems which involve both material nonlinearity and geometric nonlinearity.

In the conventional ship's structures, the stiffeners with asymmetric sections have been widely used, in spite of the disadvantage on the point of strength, compared to those with symmetric sections. So far, the stiffened plating was usually analyzed not considering the geometric unsymmetry characteristics of the section, including only the cross sectional area and moment of inertia. In this paper, the stiffened plating is devided into the strips having a thin-walled open cross section by using the concept of the effective width. The geometric characteristics of the sections are also included. The governing equations are derived, which can be applied to the arbitrary cross section beams, and the symmetric and the asymmetric section beams which have the same cross sectional areas are analyzed by using the finite element method. From that result, we obtain the allowable load of the two sections, and compared them.

From the singularity distribution which obtained by minimum wave resistance condition, optimum hull form is obtained by stream line trancing method as Inui and Pien did. Thus obtained hull form has a extruded bottom along a keel line. Therefore the hull form must be modified to have flat bottom. This modification process is conducted by putting a fictitious bottom. It is found out that the wave resistance does not significantly alter at design speed even though the hull form has remarkably changed at the bottom. Therefore flattening the bottom by the effect of depth may be more rational for practical hull form design than ordinary manual hull-form modification.

For the preliminary estimation of the vertical hull natural frequency, the Schlick's or Schlick-type formulae have been traditional ones and are still in common use today. Some investigators have made their efforts, based on statistical data of ships' system parameters, to extend the applicability of Schlick-type formulae to higher modes, or to utilize the Rayleigh method. For instance, the work done by Dinsenbacher et al.[5] belongs to the former and that of Nagamoto et al.[6] to the latter. In a part of his previous paper[7], the author, investigating the case of a cargo ship of medium size, suggested that provided statistically simplified curves such as trapezoid of system parameter distributions are available in hands, direct utlization of an ordinary computer program can be also an another convenient method by which we can obtain both natural frequencies and normal mode shapes. In this paper, to confirm the feasibility of the above suggestion, four high speed boats are investigated. The system parameters of them are originally given in [5]. The computer program used here is one confiled based on a calculation method derived from Myklestal-Prohl modeling of hull, transfer matrix formulation and an extended Gumbel's initial value method for solving frequency equation. The results of the investigation show that the direct calculation based on statistically oriented and reasonably assumed trapezoidal mean curves of system parameter distributions can give us natural frequencies within about 5% deviation up to several-noded modes and normal mode shapes serviceable at least up to 4- or 5-noded modes in comparision with those based on actual distributions of system parameters. For this simplified method the actual data required for input are only of ship length, displacement, total added mass, bending and shear rigidity at amidship. They are available at the early stage of design. By this method we can also easily trace variations of vibration characteristics in the course of ship design cycles.

Herein the flow past a submerged circular cylinder with a free surface is mapped onto a reference plane, in which the free surface is transformed to a straight line and the cylinder to a certain shape. A global mapping function between two planes is sought in a manner that linear free-surface elevation is generated in the physical plane. Hereby the Froude mumber $F_h$, based on the submergence depth h', is assumed to be of order 0(1) and the ratio a'/h'(a'=cylinder radius) of order o(1). Wave thus obtained are slightly different in magnitude and phase from usual linear solution. The resulting free wave starts advanced ahead compared to the classical result and its amount depends on Froude number. Based on the present concept wave forces are calculated. In this type of approach the body boundary condition gives more influence on wave resistance than that by the free surface in the speed range $F_h>1$.