Method for calculating hot spot stress at end part of horizontal rod piece for supporting transverse bulkhead

Abstract

The invention relates to a method for calculating the hot spot stress at the end part of a horizontal rod piece for supporting a transverse bulkhead, which belongs to the field of ship engineering structure design, and comprises the following steps of: calculating through a coarse mesh finite element to obtain node displacement, and determining the hot spot position at the end part of the rod piece; relative displacements of all the horizontal rod pieces are calculated, and then nominal stresses of all the horizontal rod pieces are calculated; or the nominal stress is obtained directly according to the coarse mesh finite element calculation result; combining each stress concentration coefficient corresponding to each hot spot; and calculating the hot spot stress. The invention provides a hot spot stress simplified calculation method based on a coarse grid calculation result (nominal stress) and a stress concentration coefficient, which is beneficial to improving the evaluation efficiency.

Description

Technical Field

[0001] This invention discloses a simplified calculation method for hot spot stress at the ends of horizontal members supporting transverse bulkheads in container ships, which can serve as a reference for the design of supporting transverse bulkhead structures and belongs to the field of marine engineering structural design. Background Technology

[0002] Container ship cargo hold transverse bulkheads are divided into two types: watertight transverse bulkheads and supporting transverse bulkheads. Supporting transverse bulkheads are located between two watertight transverse bulkheads. Watertight transverse bulkheads consist of complete watertight panels, while supporting transverse bulkheads are fully open truss systems. Vertical guide rails are installed on the fore and aft sides of the transverse bulkhead to support the containers within the cargo hold. Supporting transverse bulkheads are mainly composed of several vertical and horizontal trusses. If the spacing between the vertical and horizontal trusses is equal to or exceeds the dimensions of two containers, horizontal members are needed to support the guide rails. Figure 1 As shown, a certain ultra-large container ship has transverse horizontal angle steel connected to the vertical girders between adjacent horizontal girders, and struts are installed between adjacent vertical girders to connect the front and rear angle steels to support the guide rails.

[0003] The horizontal bars in this article refer to Figure 1 The horizontal members (in the beam direction) are the most common type of horizontal members. Their connection to the vertical girder may be lapped, posing a fatigue risk under overall deformation in waves. The key to assessing fatigue strength is obtaining hot-spot stresses. These hot-spot stresses can typically be obtained using a fine-mesh finite element method in a model of a section under fatigue loading conditions. However, fine-mesh finite element modeling is time-consuming, and there are many locations to assess.

[0004] Currently, there are no standards or guidelines from domestic or international classification societies for assessing hot spot stress and fatigue at the ends of horizontal members supporting transverse bulkheads in container ships. While each classification society has simplified calculation methods (nominal stress and stress concentration factor) for longitudinal girder stress in the hull, there are no simplified calculation methods for the stress at the ends of horizontal members supporting transverse bulkheads.

[0005] There are two methods to calculate hot spot stress: (1) directly calculate hot spot stress based on fine mesh finite element method; (2) calculate hot spot stress based on nominal stress and stress concentration factor. Method (1) needs to establish fine mesh finite element model, and if the load of the refined region is transmitted, it is time-consuming; method (2) can quickly obtain nominal stress based on coarse mesh finite element model or simplified method, and then hot spot stress can be obtained by combining stress concentration factor, which is more efficient. If there is no ready-made stress concentration factor, it needs to be obtained by fine mesh finite element method. For the case of needing to calculate many similar structure nodes, method (2) is still more time-saving. At present, method (2) is more used in the ship structure fatigue evaluation of the hull longitudinal. However, the end node form of the longitudinal is quite different from that of the end node form of the horizontal rod of the supporting transverse bulkhead of the container ship, and the load mode is also different. The longitudinal mainly considers axial tension and compression and bending in one direction, while the horizontal rod of the supporting transverse bulkhead needs to consider axial tension and compression and bending in two directions, that is, three deformation modes. The nominal stress of the longitudinal can be obtained by beam theory, while the nominal stress of the horizontal rod of the supporting transverse bulkhead needs to be obtained by coarse mesh finite element method. Therefore, the hot spot stress calculation method of the longitudinal cannot be directly applied to the horizontal rod of the supporting transverse bulkhead. The existing ship classification society specifications do not have a hot spot stress calculation method (method (2)) for the horizontal rod of the supporting transverse bulkhead, so a targeted hot spot stress calculation method based on method (2) needs to be developed.

[0006] The nominal stress of the horizontal rod of the supporting transverse bulkhead is divided into three stress components (torsional stress is ignored): axial stress and bending stress in two directions. The horizontal rod in the coarse mesh finite element model is simulated by beam element, but the three stress components of the beam element cannot be directly obtained, so the commonly used method of directly reading the nominal stress may not be applicable. At this time, the nominal stress can be calculated based on relative displacement and beam theory.

[0007] The CSR specification has a calculation method for the stress concentration factor of the hull longitudinal, but it is not applicable to the end of the horizontal rod of the supporting transverse bulkhead; the DNV ship structure fatigue evaluation guide has a stress concentration factor table for various node forms, but it does not have a method for the end of the horizontal rod of the supporting transverse bulkhead (lap and complex deformation state). Therefore, a stress concentration factor calculation method for the horizontal rod of the supporting transverse bulkhead needs to be given, which needs to consider the lap condition and three stress components. SUMMARY

[0008] The purpose of the present application is to provide a simplified hot spot stress calculation method based on coarse mesh calculation results (nominal stress) and stress concentration factor, so as to improve the evaluation efficiency.

[0009] In order to achieve the above object, the technical scheme of the present application provides a kind of support transverse bulkhead horizontal bar end hot spot stress calculation method, it includes the following steps: The node displacement is obtained by coarse mesh finite element calculation, and the hot spot position of the bar end is determined; Calculate the relative displacement of each horizontal bar, and then calculate the nominal stress;Or directly obtain the nominal stress from the coarse mesh finite element calculation result; Combine each hot spot with each stress concentration coefficient; Calculate hot spot stress.

[0010] Preferably, the node displacement obtained by coarse mesh finite element calculation includes: The coarse mesh finite element model of the cabin section where the support transverse bulkhead is located is subjected to fatigue load condition; Carry out finite element calculation to obtain the displacement result of each condition.

[0011] Preferably, the relative displacement of the horizontal bar across the span of both ends includes axial relative displacement and bending direction relative displacement.

[0012] Preferably, the axial relative displacement refers to the difference between the distance between the nodes at both ends of the horizontal bar before and after deformation of the finite element model.

[0013] Preferably, the bending direction relative displacement includes horizontal and vertical relative displacement, which is calculated by projecting the coordinates of the deformed nodes onto the specified straight line.

[0014] Preferably, the nominal stress includes: calculating the axial nominal stress and the bending nominal stress in two directions.

[0015] Preferably, the axial nominal stress is calculated by the following formula:

[0016] Wherein, E The elastic modulus of the material is The axial relative displacement of the horizontal bar where the hot spot is located is l The length of the horizontal bar where the hot spot is located is

[0017] Preferably, the bending nominal stress is calculated by the following formula:

[0018]

[0019] Wherein, the subscripts h And v Horizontal and vertical, subscript i And j The bar where the hot spot is located and the other side of the bar,σ is the nominal stress at the hot spot, E is the elastic modulus of the material, η is the sign coefficient (1 or -1), δ is the relative displacement of the member, l is the span length of the member, I is the moment of inertia of the cross section of the member, Z is the modulus of the cross section of the member at the hot spot, x e is the distance from the hot spot to the vertical web.

[0020] Preferably, the stress concentration factor is calculated by: K a σ hs-a σ a K h σ hs-h σ h K v σ hs-v σ v wherein, σ hs-a σ hs-h σ hs-v are the axial hot spot stress, the horizontal bending hot spot stress, the vertical bending hot spot stress, σ a σ h σ v are the axial nominal stress, the horizontal bending nominal stress, the vertical bending nominal stress.

[0021] Preferably, if the connection between the horizontal member panel and the vertical web panel is a lap weld, both panels are simulated by shell elements and are staggered by a certain distance, and the shell elements are connected at the end of the connection, and the thickness of the connection element can be taken as the sum of the thicknesses of the two panels.

[0022] Preferably, the boundary conditions are: the upper and lower ends of the model are rigid, the front and rear end nodes of the vertical web at the horizontal member plane are simply supported; the calculation conditions include: the nodes at the outer end of the horizontal member are constrained in all degrees of freedom except axial tension and compression, and a unit displacement is applied in the axial direction outward; ​​​​​​​​​​​​The horizontal rod outer end node is constrained in other degrees of freedom except around the vertical corner, and a unit displacement forward is applied; The horizontal rod outer end node is constrained in other degrees of freedom except around the vertical corner, and a unit displacement forward is applied.

[0023] Preferably, the hot spot stress is calculated by multiplying the nominal stress by the stress concentration coefficient and calculating the hot spot stress by the following formula:

[0024] Wherein, k is a correction coefficient, and is taken as 1.25, K a 、 K h 、 K v is a stress concentration coefficient, σ a 、 σ h 、 σ v is a nominal stress.

[0025] In summary, the present application includes the following beneficial technical effects: The method of the present application combines coarse grid finite element calculation and stress concentration coefficient, avoids the cumbersome process of fine grid finite element modeling, significantly reduces the calculation time and resource consumption, and is especially suitable for large-scale fatigue evaluation scenarios, can quickly obtain the hot spot stress, and improves the evaluation efficiency.

[0026] In view of the complex stress characteristics of the support transverse bulkhead horizontal rod, the axial tension and compression and two direction bending deformation modes are considered, the nominal stress is calculated by relative displacement, and then the hot spot stress is accurately restored by combining the stress concentration coefficient, so that the reliability and accuracy of the calculation result are ensured, and a strong basis is provided for fatigue strength evaluation.

[0027] The present application is specially designed for the lap joint of the container ship support transverse bulkhead horizontal rod, fills the gap in this field of the existing ship classification society standard, and provides the designer with the selection and technical support for the fatigue evaluation of such structure node.

[0028] The present application can quickly fatigue screen a large number of structure nodes, thereby improving the efficiency of large-scale fatigue evaluation. The present application can calculate the nominal stress based on the relative displacement, can consider each component of the stress and the corresponding stress concentration coefficient, has good applicability to such structure nodes whether it is a conventional angle steel connection or a special lap joint form. The present application provides a universal and flexible hot spot stress calculation tool for ship structure design and optimization, and helps the technical progress in the field of ship engineering. BRIEF DESCRIPTION OF DRAWINGS

[0029] Figure 1 Typical support transverse bulkhead structure schematic diagram of super large container ship; Figure 2 Support transverse bulkhead horizontal bar hot spot stress calculation flow chart; Figure 3 Typical hot spot position schematic diagram; Figure 4 Node selection schematic diagram for calculating relative displacement in bending direction; Figure 5 Fine mesh finite element model schematic diagram; Figure 6 Modeling method schematic diagram of angle steel panel and vertical web panel lap joint node. DETAILED DESCRIPTION

[0030] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of protection of the present application.

[0031] The embodiments of the present application disclose a support transverse bulkhead horizontal bar end hot spot stress calculation method.

[0032] The present application is based on the finite element method and the beam theory considering relative displacement, and the support transverse bulkhead horizontal bar end hot spot stress calculation is performed according to the steps shown in the figure, that is, first, the node displacement results are obtained by coarse mesh finite element calculation and the hot spot position of the bar end is determined, then the relative displacement of each horizontal bar is calculated on the basis of the coarse mesh calculation results, and then the nominal stress is calculated, or the nominal stress is directly obtained from the coarse mesh finite element calculation results, and finally the hot spot stress of each hot spot position is obtained in combination with the stress concentration coefficients corresponding to each hot spot. Figure 2

[0033] The specific description of each step is as follows (in the following directions, the front direction refers to the direction towards the bow, and the rear direction refers to the direction towards the stern): (1) Coarse mesh finite element calculation and determination of hot spot position According to the fatigue load case of the coarse mesh finite element model of the cabin section where the support transverse bulkhead is located, the fatigue load case is applied to the cabin section according to the ship classification society standard, and the finite element calculation is performed to obtain the displacement results of each case.

[0034] There are several fatigue hot spots at the connection between the horizontal bar and the vertical web, which need to be determined according to the specific structure drawing. Generally, they include the connection between the upper edge or lower edge (free edge) of the horizontal bar and the edge of the vertical web panel, the connection between the front edge or rear edge (free edge) of the horizontal bar and the edge of the vertical web stiffener or knee plate. The typical hot spot position of a certain container ship is as shown in the figure​Figure 3 As shown in Fig. 2, each bar has two hot spots, which are located at the free end of the bar, close to the connection with the adjacent member.

[0035] (2) Calculation of relative displacement The relative displacement refers to the difference between the displacements of the two ends of a span of the horizontal bar (the connection with the brace and the connection with the vertical girder). The horizontal bar only bears the force from the guide rail at the ends of the span and the overall deformation of the ship, and does not bear other loads, so the nominal stress at the hot spot can be calculated using the relative displacement. The relative displacement can be divided into three components: the axial relative displacement along the horizontal bar and the relative displacement in two bending directions perpendicular to the horizontal bar. The relative displacement of each horizontal bar under each load condition is calculated separately.

[0036] a) Axial relative displacement Axial relative displacement δ a It can be taken as the difference between the distances between the nodes at the two ends of the span of the horizontal bar before and after the deformation of the finite element model. If the axial nominal stress can be directly obtained from the model, the axial relative displacement does not need to be calculated.

[0037] b) Bending direction relative displacement The bending direction relative displacement includes the relative displacement in the horizontal direction δ h and the relative displacement in the vertical direction δ v If the bending nominal stress in a certain direction can be directly obtained from the model, the bending relative displacement in that direction does not need to be calculated.

[0038] In order to consider the overall deformation of the model, the initial coordinates and the displacement results in each direction of four nodes (A, B, C, D, as shown in Figure 4 Fig. 3) are obtained from the finite element model. The coordinates of each point after deformation are calculated according to the above data, and then B is projected onto the straight lines AC and AD, respectively, to obtain the sizes of δ h and δ v The signs of the relative displacements are determined according to the direction of B relative to A after deformation.

[0039] (3) Calculation of nominal stress The nominal stress at each hot spot of the horizontal bar can be divided into three components: the axial nominal stress and the two bending nominal stresses. The nominal stress of each hot spot under each load condition should be calculated separately.

[0040] a) Axial nominal stress Axial nominal stress σ a It can be calculated as follows:

[0041] where: E — Elastic modulus of the material, MPa — Axial relative displacement of the horizontal member where the hot spot is located, mm, see (2) a) l — Span length of the horizontal member where the hot spot is located, mm, from the vertical web to the brace If the axial nominal stress can be directly obtained from the model, it is not necessary to calculate it by the above method.

[0042] b) Bending nominal stress For Figure 3 the bending nominal stress of a hot spot on the member i (i is 1 or 2) in two directions (x and y) can be calculated as: σ h and σ v

[0043]

[0044] where: subscript h , v — Horizontal direction (h) and vertical direction (v) subscript i , j — Member where the hot spot is located (i) and the other side member (j) σ — Bending nominal stress at the hot spot, MPa E — Elastic modulus of the material, MPa η — Symbol coefficient (1 or -1), so that the stress calculated is positive when the hot spot is subjected to tensile stress and negative when it is subjected to compressive stress.

[0045] δ — Relative displacement of the member, mm, see (2) b) l — Span length of the member (from the vertical web to the brace), mm I — Moment of inertia of the section of the member, cm 4 Z — Section modulus of the section of the member at the hot spot, cm 3 ​x e — distance of hot spot from vertical web, mm If the span length of member i and member j l and cross-sectional properties (A, I, J) are all the same, respectively, the nominal bending stresses in two directions at the hot spot can be simplified as: I h , I v , Z h , Z v ) are all the same, respectively, the nominal bending stresses in two directions at the hot spot can be simplified as:

[0046]

[0047] If the bending nominal stress in a certain direction can be directly obtained from the model, there is no need to calculate the nominal stress by the above method.

[0048] (4) Stress concentration factor a) Overview The stress concentration factor is the ratio of the hot spot stress to the nominal stress. The stress concentration factor at the hot spot of a horizontal member can be divided into three components: the axial stress concentration factor (K K a ) and two bending stress concentration factors (K K h and K K v ), which are used with three nominal stress components (N σ a , σ h and N σ v , respectively. The stress concentration factor for each hot spot location of the same type of structural joint needs to be calculated separately. The stress concentration factor can be used for hot spot stress calculation in similar structural fatigue assessment.

[0049] If there is no corresponding stress concentration factor data, it can be calculated as follows: K a = σ hs-a / σ a ; K h = σ hs-h / σ h ; K v = σ hs-v / σ v wherein: σ hs-a 、 σ hs-h 、 σ hs-v —Axial hot spot stress, horizontal bending hot spot stress, vertical bending hot spot stress, obtained by fine mesh finite element method, see b), c), d) below; σ a 、 σ h 、 Figure 5 v —Axial nominal stress, horizontal bending nominal stress, vertical bending nominal stress, calculated from relative displacement corresponding to (4)c) and (3).

[0050] The signs of hot spot stress and nominal stress should be the same.

[0051] b) Finite element model for stress concentration factor calculation The model range is: longitudinal (ship length direction) including the whole support bulkhead (not including horizontal bar at one end), transverse (ship width direction) one span of horizontal bar on both sides of vertical girder (end at support bar), vertical one layer box height (or to adjacent horizontal member) above and below the analyzed horizontal bar.

[0052] The fine mesh model is shown in Figure 6 The refined area adopts 10mm x 10mm mesh to consider the fatigue strength of the weld toe at the free edge of the plate; the bar and stiffener in the refined area and transition area are simulated by plate elements.

[0053] If the connection between the panel (vertical wing plate) of the horizontal bar and the panel of the vertical girder is a lap weld, both panels are simulated by shell elements and staggered by a certain distance (the distance between the mid-surfaces of the two panels), and at the end of the connection, the two panels are connected by shell elements, and the thickness of the connection element can be taken as the sum of the thicknesses of the two panels. Figure 3 is the modeling method of the lap joint between the horizontal bar and the panel of the vertical girder when the horizontal bar is an angle steel.

[0054] c) Boundary conditions and calculation conditions for stress concentration factor calculation: The upper and lower ends of the model are taken as rigid, and the nodes of the vertical girder web plate at the front and rear ends of the horizontal bar plane are taken as simply supported; each calculation condition also has additional boundary constraints.

[0055] The calculation conditions include the following three: i) LC-a: the outboard end node of the horizontal member is restrained in all degrees of freedom except axial tension and compression, and a unit displacement is applied in the axial direction outward; ii) LC-h: the outboard end node of the horizontal member is restrained in all degrees of freedom except rotation about the vertical angle, and a unit displacement is applied in the forward direction; iii) LC-v: the outboard end node of the horizontal member is restrained in all degrees of freedom except rotation about the longitudinal angle, and a unit displacement is applied in the upward direction.

[0056] d) Stress reading and hot spot stress calculation for stress concentration factor calculation The stress reading and hot spot stress calculation of the fine mesh model can refer to the ship classification society standard. Taking the China Classification Society container ship standard as an example, for the hot spot shown in σ , the hot spot stress is read and calculated according to the method of type "b" hot spot.

[0057] The hot spot stress calculated by the working condition LC-a is σ hs-a ; the hot spot stress calculated by the working condition LC-h is σ hs-h ; and the hot spot stress calculated by the working condition LC-v is σ hs-v .

[0058] (5) Calculation of hot spot stress The hot spot stress can be obtained by multiplying the nominal stress by the corresponding stress concentration factor. The final hot spot stress σ hs is obtained by superimposing the hot spot stresses of each component

[0059] In the formula: k - correction coefficient, considering the error brought by the simplified formula and other uncertain factors, taken as 1.25; K a , K h , K v - stress concentration factor, obtained from (4); σ a , σ h , ​ v - nominal stress, obtained from (3).

[0060] The hot spot stress calculation method can be used for fatigue screening evaluation of a large number of structural nodes. If the fatigue life obtained does not meet the evaluation criterion, it is recommended to select the most serious area to perform hot spot stress calculation and fatigue evaluation by using the traditional fine mesh finite element method.

[0061] Finally, it should be noted that the above only for the preferred embodiments of the present application, and is not intended to limit the present application, although the foregoing embodiments of the present application have been described in detail, for those skilled in the art, it still can be modified, or part of the technical features of the equivalent replacement, within the spirit and principles of the present application, any modification, equivalent replacement, improvement, etc., should be included within the scope of the present application.

Claims

1. A method of calculating hot spot stresses at the end of a transverse bulkhead horizontal member, characterized in that, The method comprises the following steps: The node displacement is obtained by coarse grid finite element calculation, and the hot spot position of the end of the rod is determined; The relative displacement of each horizontal rod is calculated, and then the nominal stress is calculated; or the nominal stress is directly obtained from the coarse grid finite element calculation result; The stress concentration coefficient corresponding to each hot spot is combined; The hot spot stress is calculated.

2. The method of claim 1, wherein the method is characterized by: The node displacement obtained by coarse grid finite element calculation is based on the displacement results of each working condition obtained by finite element calculation after the fatigue load working condition is applied to the coarse grid finite element model of the support transverse bulkhead.

3. The method of claim 1, wherein the method is characterized by: The relative displacement of the horizontal rod at both ends of the span includes axial relative displacement and bending direction relative displacement.

4. The method of claim 1, wherein, The nominal stress includes: calculating the axial nominal stress and the bending nominal stress in two directions.

5. The method of claim 4, wherein the method further comprises: The axial nominal stress is calculated by the following formula: wherein, E E is the modulus of elasticity of the material, is the axial relative displacement of the horizontal member at the hot spot, l is the span length of the horizontal member at the hot spot.

6. The method of claim 4, wherein the method is characterized by: The bending nominal stress is calculated by the following formula: where subscript h and v are horizontal and vertical directions, respectively, subscript i and j are the rod member where the hot spot is located and the other side rod member, respectively, Stress concentration coefficient is calculated by the following method: is the nominal bending stress at the hot spot, E is the material elastic modulus, The hot spot stress used for stress concentration coefficient calculation is obtained by using the fine grid finite element method, wherein if the connection between the horizontal rod panel and the vertical web panel is a lap weld, both panels are simulated by shell elements and are staggered by a certain distance, and the shell elements are connected at the connection end, and the thickness of the connection element can be the sum of the thicknesses of the two panels. is a symbol coefficient (1 or -1), The hot spot stress used for stress concentration coefficient calculation is obtained by using the fine grid finite element method, wherein the boundary conditions of the model are: the upper and lower ends of the model are rigidly fixed, and the nodes at the front and rear ends of the vertical web in the horizontal rod plane are simply supported; the calculation working conditions include: is the relative displacement of the rod member, l is the span length of the rod member, I is the section modulus of the rod member, Z is the section modulus of the rod member at the hot spot, x e is the distance from the hot spot to the vertical web.

7. The method of claim 1, wherein, The horizontal rod outer end node is constrained in addition to the axial tension and compression, and the unit displacement is applied in the axial direction outward; a = The horizontal rod outer end node is constrained in addition to the rotation around the vertical angle, and the unit displacement is applied forward; hs-a / The horizontal rod outer end node is constrained in addition to the rotation around the longitudinal angle, and the unit displacement is applied upward. a ； K h = The hot spot stress is calculated by multiplying the nominal stress by the stress concentration coefficient, and the hot spot stress is calculated by the following formula: hs-h / ​ h ； K v = ​ hs-v / ​ v wherein ​ hs-a , ​ hs-h , ​ hs-v are the axial hot spot stress, the horizontal bending hot spot stress, the vertical bending hot spot stress, respectively, ​ a , ​ h , ​ v are the axial nominal stress, the horizontal bending nominal stress, the vertical bending nominal stress, respectively.

8. The method of calculating the hot spot stress of the end of the horizontal transverse bulkhead beam according to claim 7, characterized in that, ​ 9. The method of claim 7, wherein the method further comprises: ​ ​ ​ ​ 10. The method of claim 1, wherein, ​ wherein k is a correction factor taken as 1.25, K a , K h , K v is a stress concentration factor, ​ a , ​ h , ​ v is a nominal stress.

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