船体梁极限强度英文文献和中文翻译(3)
The further research on the interaction between the vertical and horizontal bending was undertaken by the Hu, Y. et al, (2001). It was found that the interaction curve is asymmetrical because the hull cross-section is not symmetrical about the horizontal axis and the behavior of the structural members under compression is different from that under tension due to the non-linearity caused by buckling. An interaction equation suitable for bulk carriers is proposed based on the results of the analyzed ship. As it is well know the basic equation that relates the applied vertical and horizontal bending moments to the longitudinal stress are very simple and may be resumed as followed: yi yxi xiIx MIy M . .− = σ (1) or it may be expressed as a function of the total moment by: yixi iIxIyMϕ ϕ σ sin . cos .− = (2) Where ϕ is the angle that the bending moment vector makes with the baseline and xi and yi are the coordinates of the point in the referential located in any point of the neutral axis. For a given points of the cross section this relation is constant until the yield stress of the material is reached in any point of the section or the local structure of hull section is damaged during operation. Once the cases mentioned above occur the neutral axis moves away from its original position and thus the constancy of the relation may be broken. Due to the same reason the relation between the angle of the moment vector ϕ and the angle of the neutral axis θ is constant in the linear elastic range but is changed when some damage of section is already present. This relation may be expressed by: θ ϕ tgIItgxy= (3) The Calculation Steps The assessment of moment-curvature relationship is obtained by imposing a sequence of increasing curvature to the hull girder. For each curvature, the average strain of element is determined assuming that plane section remains plane after the curvature is applied. The values of strain are introduced in the model that represents the load-shortening behavior of each element. The bending moment resisted by the cross section is obtained from the summation of the contributions from the inpidual elements. The calculated set of values defines the desired moment-curvature relation. The most general case corresponds to that in which the ship is subjected to curvature in the x and y directions respectively denoted as Cx , Cy. The overall curvature C is related to these two components by: 2 2y x C C C + = (4) or θ cos . C x C = and θ sin . C y = C (5) adopting the right-hand rule, where θ is the angle between the neutral axis and the x axis and is related to the components of the curvature by: xyCCtg = θ (6) The strain at the centroid of an element i is iε which depends on its position and on the hull curvature, as given by: y gi x gi iC x C y . . − = ε (7) Where (xgi , ygi) are the coordinates of centroid of the element i referred to the central point at each curvature. Once the state of strain in each element is determined, the corresponding average stress may be calculated according to the method described above, and consequently the components of the bending moment for a curvature C are given by: i i gi x A y M σ ∑ = .. (8) ∑ = i i gi y A x M . .σ (9) Where iσ represents the stress of element i at (xgi , ygi). Ai represent the cross sectional area of element i. This is the bending moment on the cross section after calculating properly the instantaneous position of the intersection of the neutral axis associated with each curvature and the centerline (it is be called as center of force.). The condition to determine the correct position of neutral axis is: 0 = ∑ i iA σ (10) The a trial-and error process has to be used to estimate correctly its position. The total net load in the section, NL, or the error in the shift estimate ΔG should be less than or equal to sufficiently low value (Gord, J. M. , 1996). In this paper, the following equation is used. ∑ ∑ −≤ = i i i iA A NL 0610 σ σ (11) Where i 0 σ is the material yield stress of element i . The relationship of element strain—stress An applied curvature to the section induces compression in one side of the axis of the section and tension in the other side. According to the algorithm described earlier, for a particular magnitude of applied curvature, the induced strains are calculated for all elements in the section. The corresponding stresses are calculated by using the stress-strain relationship for inpidual panels.