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Chapter 1
Mechanical Engineering and Manufacturing Technologies
Total Longitudinal Moment Calculation and Reliability Analysis of Yacht Structures
Wenzheng ZHI
Marine Engineering Institute
Jimei University
Xiamen, China
e-mail: [email protected]
Shaofen LIN
Marine Engineering Institute
Jimei University
Xiamen, China
Abstract—in order to check the reliability of the yacht in FRP (Fiber Reinforce Plastic) materials, in this paper, the vertical force and the calculation method of the overall longitudinal bending moment on yacht was analyzed. Specially, this paper focuses on the impact of speed on the still water bending moment on yacht. Then considering the mechanical properties of the cap type stiffeners in composite materials, the ultimate bearing capacity of the yacht has been worked out, finally the reliability of the yacht was calculated with using response surface methodology. The reasult can be uesd in yacht design and yacht driving.
Keywords—yacht; longitudinal bending moment; ultimate load; reliability
I. INTRODUCTION
The longitudinal strength relates directly to the safety and the life of the yachts, according to the rules for the construction and classification of coastal boats (here after referred to as The Rule), the yachts with a length more than 15 meters must be checked. The external load on the ship and the bearing capacity of the ship structure is random, but traditional means consider it as a constant value, ignore the impact of randomness, in fact, the ships built according to The Rule still take safety risk. Since 80’s last century the view of the reliability has been introduced into the strength check computation about steel vessels, in order to analyze the safety risk quantitatively. But rare researches focus on the yacht. On the one hand, the yacht usually is different from steel vessels in high speed, small size and light weight, the hydrodynamic and wave have a significant influence on bending moment, that increase the variability of the force on the yacht, in the other hand, the mechanical property of FRP structures is more random than steel structures. Thus it can be seen that it is necessary to check the reliability of the yachts[1].
II. FAILURE FUNCTION OF THE HULL
The hull girder’s failure function to be utilized for the reliability analysis for ultimate Longitudinal Strength of the yacht can be calculated based on resistance-load model. The external load on the hull of yachts cosists of still water load and wave load. The ultimate load-carrying of the hull relate with the structure style, material properties and the weight of the hull. The failure function can be expressed as[1]:
Here Mu is the ultimate bearing moment of the hull, Mg is the general bending moment, Cu and Cg are the uncertainties of the calculation model.
Because of the quite complex structure of the hull, the failure function can’t be expressed explicitly, in this paper I introduce the response surface method for calculation. The principle of the response surface method is to design a series of variables, which can be made into a group of exploratory points, figure out the corresponding values of the performance function, then we can make up a polynomial to fit and instead of the failure function. The reliability index, which is commonly used to measure the reliability in many project fields, is a quantity, the geometric significance of which is the minimum distance between the origin and the limit state surface. According to this, the reliability can be calculated based on optimization method. The calculation model can be defined as follow [3]:
The constraint condition is the failure function of the hull structure.
III. CALCULATION OF TOTAL LONGITUDINAL BENDING MOMENT
According to the rules for the construction and classification of coastal boats, two kinds of working conditions should be considered when we calculate the overall longitudinal bending moment of the hull structure. In one case, in one case, if the yacht keeps a stable navigation state, the overall longitudinal bending moment can be divided into still-water bending moment and wave-induced bending moment, in the other case, if the yachts sail under severe sea state, the stress on the hull possess obvious impact characteristic, the overall longitudinal bending moment now approximate the wave fustigation bending moment.
The hull can be considered as a hollow beam with unconstrained boundary, the shear and bending moment distribution can be obtained by calculating the vertical load distribution. The hull mainly under the influence of the gravity, buoyancy and hydrodynamic lift, when the yachts sail at low speed, the hydrodynamic lift is so small that it usually can be ignored. With the improvement of the speed, the hydrodynamic lift increases and supports the yacht instead of the buoyancy. According to the analyses above, it is necessary to consider the effects of speed, when we calculate the still-water bending moment.
Owing to the complicated sea state, wave-induced bending moment and wave fustigation bending moment can not be worked out by theoretical calculation or numerical simulation. They usually be calculated by taking empirical formulas. The design value of wave-induced bending moment can be calculated under the formula which is on the basis of the rules for the construction and classification of coastal boats.
Where : LWL is ship length, Lf is ship length coefficient, Lf = 0.0412LWL + 4, B is the ship breadth, Cb is the block coefficient, C1 is the reduction factor of design category.
The design value can only expresses the maximum moment in a cycle of wave, the moment used in checking reliability should be calculated based on the model of long-term wave statistics. According to the literature[2], the result calculated based on the model of long-term wave statistics is about 90% of the design value.
According to the rule, the design value of wave fustigation bending moment on the yacht can be calculated by the empirical formula as
Where nca is the vertical overload coefficient at the yacht’s center of gravity, ncg = acg/g, here acg is the Vertical acceleration at the center of gravity, nFE and nAE are the vertical overload coefficient at both ends of the designed waterline, respectivel...
