| Because most offshore structures have comparable length and breadth,transverse stability is not sufficient to estability the safety of the floating structure.This has been resolved by following conventional transverse stability methodology to any orientation.Various axis directions are to be investigated to arrive at the most weakest one.The analysis for all orientation ceates high longitudinal moments,longitudinally balanced at each heel angle reduce righting arms of structures,which is more reasonable.However,the different lonngitudinally balance methods manifested in various difinitions of the floating parameters,resulting in different righting arm curves.Second,some provisions in code for the stability of the offshore platform exist ambiguity,such as angel of inclination,most critical axes.The validity of the stability calculation results should be judged by the information such as the trim angle,the transverse axis direction and the stability criterion of the platform floating state.Therefore,it is necessary to explore a set of geometric definitions,hydrostatic elements and static stability curves for offshore engineering structures.Offshore structure is characterized by a combination of multiple unit,using Constructive Solid Geometry and triangular mesh surface to establish three dimensional wireframe model.The polygon clipping algorithm is used to deal with the intersection of the structure and the waterplane.The geometric properties of the structure after intersection are calculated using the Green's formula and the tangential tetrahedron.The Euler angles are used as the floating parameters of the structure,and the three kinds of longitudinal balance cases are divided according to the different rotation order of the Euler angle.Based on the vector operation,the hydrostatic elements such as the center of buoyancy,center of floatation,and the stability elements such as metacenter radius,right arm and trim angle stiffness coefficient are deduced.The heel angle of the structure under different heel axis directions is clearly defined by the plane of rotation and angle of rotation.Angle of rotation has simple geometrical interpretation in oblique free trim and free twist.The iterative method is used to solve the floating equations of the structure,to obtain the right arm curves.However,for some heel axis directions,the oblique free trim will cause the problem of stopping the calculation due to can not longitudinal balance.Whilst free twist approach,when during progressive heel an unstable position is reached,the structure will suddenly change axis direction such that a new stable position is attained.Righting arm curve is discontinuous.Using the potential energy surface and the trim angle stiffness coefficient to analyse those cases.The geometric calculation method based on the triangular mesh surface model and the polygon clipping algorithm satisfies the hydrostatic calculation requirement of the offshore structure preliminary design.The introduction of the plane of rotation and angle of rotation unify the different longitudinal balance cases of the heel angle,with a clear physical meaning.The trim angle stiffness coefficient can be used as the stability criterion of the offshore structure floating state.Oblique free trim or free twist is sensible as this lead to the slowest build up of potential energy for increasing heel angle when the structure remain stable.At this moment there does not seem to be a robust way to calculate stability other than using fixed trim and a fixed axis direction.If the floating state of the structure is stable during the process of calculating the righting arm curve,the calculated righting arm curve by free twist is called the minimum righting arm curve.The most critical axis can be viewed as the axis direction for which a given heel angle is reached with the least effort.Establishing potential energy surface,Application of the lowest gain in energy approach is an unambiguous way to define the most critical or weakest axis. |
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