ABAQUS-based shipping coil steel liner checking method

Abstract

The invention relates to the technical field of ship transportation engineering and structural strength checking, in particular to a ship transportation coil steel liner checking method based on ABAQUS, which comprises the following steps: determining coil steel parameters and cargo hold structure parameters; based on the coil steel parameters and the cargo hold structure parameters, a finite element model is established in ABAQUS software, and meanwhile, material attributes are set for the finite element model in the ABAQUS software; grid division is carried out on the finite element model, and meanwhile boundary conditions and loads are set in ABAQUS software; submitting the finite element model of which the parameters are set to ABAQUS software for calculation to obtain stress distribution of a bottom plate and a double-layer bottom framework in the cargo hold; and comparing the maximum stress in the stress distribution of the bottom plate and the double-layer bottom framework in the cargo hold with a preset allowable stress by taking the Mirse stress as a failure judgment index to finish the strength check of the liner. On the premise that the structural strength of the ship is guaranteed, the economic benefit of shipping the coil steel is maximized.

Description

Technical Field

[0001] The present invention relates to the technical field of ship transportation engineering and structural strength verification, and in particular to an ABAQUS-based method for verifying a shipping coil steel liner. Background Art

[0002] Current research and methods address stowage, dunnage, and structural strength issues associated with bulk carriers carrying heavy cargo during transport of coiled steel. The article "Research on Securing Methods for Coiled Steel in General Cargo Ships" examined the stowage locations of coiled steel on general cargo ships from the perspective of vertical inertial acceleration, noting that stowage of coiled steel in the fore and aft cargo holds is more likely to exceed allowable standards, while other locations are relatively safe. The article "Optimization Analysis of Dunnage Schemes for Dry-Towing Semi-Submersible Platforms" used finite element analysis to examine the stress changes caused by machining errors in the spacing of the dunnage timbers and the resulting variations in thickness when semi-submersible platforms are stowed using glulam dunnage. The finite element analysis results showed that the stress differences between the two spacing schemes and those with and without machining errors were not significant. The article "Calculation and Application of Dunnage Required for Ships Carrying Coiled Steel and Other Heavy Cargo" summarized empirical formulas for estimating the required dunnage thickness for transporting coiled steel based on the experience of the Norwegian and Nippon Kaiji Kaiji Classification Societies. However, this method treats the dunnage timbers as simply supported beams with concentrated loads in the middle, resulting in a less reliable solution than direct finite element analysis. In "Study on the Local Strength of Handysize Bulk Carriers Carrying Coiled Steel Based on ANSYS," direct finite element calculations were used to compare the maximum stresses and allowable stresses for several typical operating conditions when bulk carriers are loaded with coiled steel. However, the paper did not examine factors such as padding, and the number of operating conditions covered was relatively small. In "Study on the Local Strength of Cargo Units Carrying General Carriers Carrying Heavy Cargo Based on ANSYS," direct finite element calculations were used to study the maximum stress magnitude and distribution in cargo holds when general carriers are loaded with heavy cargo, and the differences in effective load-bearing area under different operating conditions were compared. The article "Several Suggestions for Ships Carrying Coiled Steel Cargo" lists some precautions for stowage and securing when loading coiled steel, as well as methods for estimating the maximum number of shipping layers. In "Study on Combined Modeling of Solid and Shell Elements Based on ABAQUS," the effectiveness of shell-solid element modeling was verified by comparing the calculation results of shell-solid element contact modeling with those of full solid element modeling. In his article "On Padding of Coiled Steel and Steel Plates on Ships," Xue Yingchun discussed precautions for stowing coiled steel cargo by sea, as well as the current shortcomings of padding in maritime shipping, emphasizing the importance of padding in distributing and transmitting loads. In his article "Local Strength Verification of Ships Carrying Tracked Vehicles," Chen Yiping established a mathematical model for securing heavy cargo and verifying local strength, taking into account the ship's deck plate structure.

[0003] In the prior art, when the coil steel is stowed in the cabin, it cannot be calculated as a uniform load, but due to factors such as the liner, it cannot be directly regarded as a concentrated load for calculation according to the actual contact area, and the current specific bulk cargo ship loading manual and other materials generally only give the allowable value of the uniform load on the bottom of the cargo cabin. In the face of such a situation, shipping companies generally choose to develop a stowage plan more conservatively to avoid excessive burden on the cargo cabin support structure and inner bottom plate. However, this approach not only wastes shipping capacity to some extent, but also does not completely avoid accidents caused by insufficient structural strength when transporting coil steel. The current research is relatively less on the effectiveness of the liner in transmitting load when stowing coil steel, and less on direct calculation of common coil steel stowage conditions using the finite element method to verify safety. In actual operation, not only is there a lack of relevant specifications for the use of liners, but also there is a lack of understanding among crew members and port operators regarding the use of liners and the safety of the structural strength of common coil steel stowage conditions.

[0004] Based on the above technical problems, the present method can maximize the economic benefits of shipping coil steel while ensuring the structural strength of the ship. SUMMARY

[0005] In view of the above-mentioned technical problems in the existing coil steel transportation, such as the lack of accurate calibration method for liner parameters, insufficient safety verification of stowage conditions, and limited reliability of traditional estimation methods and empirical formulas, which lead to waste of shipping capacity or structural safety hazards, a method for calibrating liners for shipping coil steel based on ABAQUS is provided. The present application mainly uses ABAQUS to establish a refined finite element model of the cargo cabin, coil steel and liner, and combines dynamic load calculation to simulate the stress of different stowage positions and liner parameters. By comparing the Mises stress with the allowable stress, the calibration is realized, thereby achieving the technical effects of accurately determining the optimal parameters of the liner, quantifying the structural safety of different stowage conditions, and improving the utilization rate of shipping capacity while ensuring the strength of the cargo cabin.

[0006] The technical means adopted by the present application are as follows: A method for calibrating liners for shipping coil steel based on ABAQUS, comprising the following steps: S1. Determine the coil steel parameters and cargo cabin structure parameters, wherein the coil steel parameters include coil steel weight, coil steel inner diameter, coil steel outer diameter, and coil steel width, and the cargo cabin structure parameters include cargo cabin width, cargo cabin length, rib spacing, transverse strong rib plate spacing, and maximum uniform load bearing capacity of the inner bottom plate; S2. Based on the coil steel parameters and cargo cabin structure parameters, establish a finite element model in ABAQUS software, wherein the finite element model includes a cargo cabin structure finite element model, a coil steel finite element model, and a liner finite element model, and set material properties for the finite element model in the ABAQUS software; S3. Grid partitioning is performed on the finite element model, and boundary conditions and loads are set in the ABAQUS software, the boundary conditions including line displacement constraints and angular displacement constraints on the cargo hold bottom shell plate, the front and rear end surfaces of the cargo hold, and the loads including the self weight and dynamic load of the coil steel, to obtain a single-coil-steel finite element model; S4. The single-coil-steel finite element model is submitted to the ABAQUS software for calculation to obtain the stress distribution of the cargo hold inner bottom plate and double-layer bottom frame corresponding to the single coil steel, and the law of variable influence on the stress distribution; S5. Based on the law of variable influence on the stress distribution, an entire-cargo-stowage finite element model is constructed, and the entire-cargo-stowage finite element model is submitted to the ABAQUS software for calculation to obtain the stress distribution of the cargo hold inner bottom plate and double-layer bottom frame corresponding to the entire-cargo-stowage; S6. According to the fourth strength theory, the maximum stress in the stress distribution of the cargo hold inner bottom plate and double-layer bottom frame corresponding to the entire-cargo-stowage is compared with a preset allowable stress by taking the Mises stress as a failure criterion, and the strength check of the liner pad is completed.

[0007] Further, the working conditions of the single-coil-steel finite element model include: 2-liner-pad working conditions for cross-solid-rib-stowage, 3-liner-pad working conditions for cross-solid-rib-stowage, 2-liner-pad working conditions for stowage between solid ribs, and 3-liner-pad working conditions for stowage between solid ribs.

[0008] Further, the working conditions of the entire-cargo-stowage finite element model include: 10-ton-coil-steel working conditions for three-layer stowage, 15-ton-coil-steel working conditions for two-layer stowage, 20-ton-coil-steel working conditions for two-layer stowage, and 25-ton-coil-steel working conditions for single-layer stowage.

[0009] Further, the dynamic load is calculated based on a vertical synthetic acceleration, and the vertical synthetic acceleration is calculated by combining a heave acceleration, a roll angular acceleration, and a pitch angular acceleration, and the calculation formula of the vertical synthetic acceleration is:

[0010]

[0011] wherein, is the vertical synthetic acceleration, is a first vertical synthetic acceleration, is a second vertical synthetic acceleration, is the heave acceleration, is the roll angular acceleration, is a longitudinal distance from a calculation point to a tail vertical line, is a transverse distance from the calculation point to a longitudinal center section, is the pitch angular acceleration, is a ship length.

[0012] Further, the calculation formula of the heave acceleration is:

[0013] wherein, is a square coefficient, is an acceleration coefficient, and the calculation formula of the acceleration coefficient is:

[0014] wherein, is a navigation area coefficient, is a correlation coefficient of the acceleration coefficient, is a speed similarity ratio, the calculation formula of the roll angle acceleration is: the calculation formula of the roll angle acceleration is:

[0015] wherein, is a maximum roll angle, is a roll period, and the calculation formula of the roll period is:

[0016] wherein, is an initial stability height under a calculation working condition, is a roll rotation radius, the calculation formula of the maximum roll angle is:

[0017] wherein, is a correlation coefficient of the maximum roll angle, is a ship width, the calculation formula of the pitch angle acceleration is:

[0018] wherein, is a maximum pitch angle, is a pitch period, and the calculation formula of the pitch period is:

[0019] the calculation formula of the maximum pitch angle is: .

[0020] Further, when the three-layered cargo is 10 tons of steel coils, and the cushion thickness is greater than or equal to 90 mm, the allowable stress requirement is met. When the two-layered 15-ton coil steel working condition or the two-layered 20-ton coil steel working condition is used, the gasket thickness reaches 50 mm or more, and the allowable stress requirement is met; When the single-layered 25-ton coil steel working condition is used, the gasket thickness reaches 50 mm or more, and the allowable stress requirement is met.

[0021] Further, in the boundary condition, the line displacement constraint of the cargo hold bottom shell plate is x=0, y=0, z=0, and the angular displacement constraint is 0, 0, 0; the line displacement constraint of the cargo hold front and rear end surface is x=0, and the angular displacement constraint is 0, 0.

[0022] Further, the establishment of the cargo hold structure finite element model includes the processing of component openings and the idealization processing of bulb flat steel structures, the component openings are modeled by using equivalent plate thickness or geometry according to the scale condition, and the bulb flat steel is converted into equivalent angle steel by a formula for modeling.

[0023] Compared with the prior art, the present application has the following advantages: 1. The present application establishes a refined finite element model by ABAQUS, accurately simulates the contact relationship between the coil steel, the gasket and the cargo hold and the influence of dynamic load, overcomes the limitations of traditional estimation methods and empirical formulas, can capture stress concentration areas, avoids damage to the cargo hold structure caused by insufficient gasket parameters, and significantly reduces transportation risks.

[0024] 2. The present application quantifies the influence of gasket material, quantity, thickness, length and stowage position on structural stress, clearly defines the critical gasket parameters for different coil steel weights, reduces gasket material consumption under the premise of meeting strength requirements, and reduces transportation costs.

[0025] 3. The present application provides an operable finite element checking process to address the problem of lack of specific coil steel gasket checking methods in the current bulk cargo ship loading manual, clearly defines the safety criteria under different working conditions, provides quantitative guidance for ship crew and port operators, avoids waste of transport capacity caused by conservative stowage, and provides technical basis for revision of ship loading manual and development of industry standards.

[0026] Based on the above reasons, the present application can be widely popularized in the fields of ship transportation engineering and structural strength checking. BRIEF DESCRIPTION OF DRAWINGS

[0027] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or the prior art description will be briefly introduced as follows. Obviously, the drawings in the following description are some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative labor.

[0028] Figure 1A flowchart of a method for checking a coil steel cushion based on ABAQUS.

[0029] Figure 2 A schematic diagram for defining an embodiment wood orthotropic coordinate system and elastic parameters.

[0030] Figure 3 A schematic diagram for an embodiment meshing.

[0031] Figure 4 A stress cloud chart of a three-layer 10-ton coil steel in a cargo hold.

[0032] Figure 5 A stress cloud chart of a two-layer 15-ton coil steel in a cargo hold.

[0033] Figure 6 A stress cloud chart of a two-layer 20-ton coil steel in a cargo hold.

[0034] Figure 7 A stress cloud chart of a one-layer 25-ton coil steel in a cargo hold.

[0035] Figure 8 A stress cloud chart of a one-layer 25-ton coil steel in a cargo hold with a replaced cushion material. DETAILED DESCRIPTION

[0036] In order to make the personnel in the art better understand the present application scheme, the technical scheme in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor should belong to the scope of protection of the present application.

[0037] It should be noted that the terms "first", "second", and the like in the specification and claims of the present application and the above-described drawings are used to distinguish similar objects, and do not necessarily have to be used to describe a specific order or sequence. It should be understood that the data thus used can be interchanged under appropriate circumstances, so that the embodiments of the present application described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "include" and "have" and any variations thereof are intended to cover non-exclusive inclusion, for example, a process, method, system, product or device including a series of steps or units does not have to be limited to those steps or units clearly listed, but can include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0038] As Figure 1As shown, the present application provides a shipping coil steel liner checking method based on ABAQUS, comprising the following steps: S1. Determine the coil steel parameters and cargo hold structure parameters, the coil steel parameters including coil steel weight, coil steel inner diameter, coil steel outer diameter, coil steel width, the cargo hold structure parameters including cargo hold width, cargo hold length, rib spacing, transverse strong rib spacing, and inner bottom plate maximum uniform load bearing capacity.

[0039] Specifically, the coil steel parameters are shown in Table 1: Table 1

[0040] The cargo hold adopts a single side longitudinal frame double bottom structure, with a width of 30.104m, a length of 29.52m, a rib spacing of 0.82m, a transverse strong rib spacing of 2.46m, and an inner bottom plate maximum uniform load bearing capacity of 20t / m 2 . According to the actual production situation, 10t, 15t, 20t, and 25t coils are established at equal weight intervals.

[0041] S2. Based on the coil steel parameters and cargo hold structure parameters, a finite element model is established in ABAQUS software, the finite element model including a cargo hold structure finite element model, a coil steel finite element model, and a liner finite element model, and material properties are set for the finite element model in ABAQUS software.

[0042] Specifically, the selection of material parameters in the model is as follows: The inner bottom plate of the hull and the main double bottom frame material are made of AH32 high-strength steel, with a density of 7.85×103kg / m 3 , a Young's modulus of 210000MPa, a Poisson's ratio of 0.3, and a yield limit of 315MPa.

[0043] The liner wood is selected from eastern poplar wood, abbreviated as cw, and yellow birch wood, abbreviated as yb. The two hardwoods have densities of 0.4×103kg / m 3 and 0.62×103kg / m 3 , respectively. The wood is orthotropic and transversely isotropic material, with different material properties in the longitudinal, radial, and tangential directions.

[0044] As shown in Figure 2 , the longitudinal axis L is parallel to the wood fibers, the radial axis R is perpendicular to the annual rings, and the tangential axis T is perpendicular to the wood fibers but tangent to the annual rings. Generally, the liner wood needs to be placed in the direction of the wood compression resistance. Due to the different material properties of wood and steel, the engineering constant function in the ABAQUS material setting is used to set the elastic properties of the wood and define the material direction during modeling. The wood elastic parameter settings are shown in Table 2.

[0045] Table 2

[0046] E1, E2, E3, G1, G2, G3 in the table represent longitudinal, tangential and radial modulus of elasticity and shear modulus respectively; U1, U2, U3 represent longitudinal, tangential and radial Poisson's ratio respectively, the above data are based on material parameters of wood at 12% moisture content.

[0047] The coordinate system adopts the right-hand coordinate system required by the specification for dynamic load calculation, the x-axis is positive in the bow direction, the y-axis is positive in the port side direction, and the z-direction is positive in the upward direction. However, the finite element analysis results are irrelevant to this coordinate system. When modeling, the ABAQUS global coordinate system is used as the reference for the position of each component, making the position coordinates of each assembly part more simple and easy to use.

[0048] The cargo hold structure finite element model is processed as follows: 1. The finite element grid of the hull structure is divided along the ship transverse direction according to the longitudinal frame spacing, the longitudinal direction according to the frame spacing or reference frame spacing, and the side according to the same size. The principle is to make the grid shape as close to a square as possible.

[0049] 2. Generally, the various types of plate and shell structures of the hull, strong frames, longitudinal girders, web plates of flat bulkhead girders, frames, etc., as well as channel bulkheads and wall benches are simulated by 4-node plate and shell elements, and triangular elements are used as little as possible. In high stress areas and high stress change areas, triangular elements are avoided as much as possible, such as lightening holes, manholes, bulkhead and bench connections, adjacent knees or discontinuous structures.

[0050] 3. For deck plates, inner and outer shell plates, inner and outer bottom plates, longitudinal frames on top and bottom edge cabin inclined plates, bulkhead stiffeners, etc. that bear water pressure and cargo pressure, beam elements can be used to simulate, considering the influence of eccentricity. The face plates and stiffeners of main components such as longitudinal girders, rib plates, frames and knees can be simulated by bar elements. If the arrangement and size division of the grid are difficult, the secondary components in these areas are merged into an equivalent bar element to simulate.

[0051] 4. The vertical direction of the bottom longitudinal girders and rib plates should be arranged with not less than 3 units. The bottom unit of the bulkhead should be a square unit as much as possible under normal circumstances.

[0052] 5. An independent point is built at each intersection of the fore and aft end faces and the shaft and centerline section, and the node degrees of freedom of each longitudinal component in the end face , , , are related to the independent point.

[0053] 6. The structural dimensions shall be based on the shipbuilding scantlings and shall adequately reflect the stiffening required for strength reasons, but shall not take into account any special design requirements of the shipowner.

[0054] Because of the coil steel stowage in the centerline of the cargo hold, the full-width model of the No. 3 cargo hold double bottom of the bulk carrier is established by shell elements according to the target ship's transverse and longitudinal section drawings. Because the main research object is the stress of the cargo hold double bottom components, the coil steel mass is large, and the stowage height is low, which will not directly contact with the cargo hold side bulkhead. Therefore, except for the cargo hold double bottom, the component models such as the side bulkhead, hatch, and hatch cover plate, which have little effect on the stress of the cargo hold double bottom, are not established. At the same time, the model of part of the components is idealized.

[0055] The establishment of the finite element model of the cargo hold structure includes the processing of component openings and the idealization of bulb flat steel structures. The component openings are modeled by equivalent plate thickness or geometry according to the scale conditions, and the bulb flat steel is converted to equivalent angle steel by formula.

[0056] Specifically, in the process of establishing a finite element model according to the actual ship structure, some structures are relatively complex. If the actual modeling is completely followed, the pre-processing and calculation workload will be increased. Therefore, the model idealization can be processed to make it more meet the requirements of finite element calculation, while still ensuring the accuracy and reliability of the simulation results.

[0057] The longitudinal of the bulk carrier is usually bulb flat steel. In order to simplify the modeling and calculation process, the longitudinal bulb flat steel is modeled as equivalent angle steel according to the following formula:

[0058]

[0059]

[0060]

[0061] wherein, is the height of the equivalent angle steel, is the net height of the bulb flat steel, is the length of the wing plate, is the net thickness of the bulb flat steel, is the thickness of the wing plate, is the thickness of the web.

[0062] is the relevant coefficient of the equivalent angle steel, and the calculation formula is:

[0063] For the cargo hold full-width model, the boundary conditions are set according to Table 3. Among them, the end faces A and B are the front and rear ends of the cargo hold.

[0064] Table 3

[0065] S3. The finite element model is meshed, and boundary conditions and loads are set in the ABAQUS software. The boundary conditions include linear displacement constraints and angular displacement constraints on the outer shell plate of the cargo hold bottom and the front and rear end surfaces of the cargo hold, and the loads include the self-weight and dynamic load of the coil steel, to obtain a single coil steel finite element model.

[0066] Specifically, Figure 3 Fig. 1 is a schematic diagram of meshing of a double-bottom grid model and a coil steel and cushion combination grid model, and the shell elements of the main components of the cargo hold mainly adopt 4-node quadrilateral elements. To ensure that the grid in the key area is relatively fine, the main element grid size is controlled at about 175 mm. The cargo hold model contains 144,120 nodes and 150,244 elements, of which only 1,496 triangular S3 elements are used. HYPERMESH is used to divide the grid, ensuring that the grids at the connection of different components are connected to each other, and most of the grid shapes are close to squares, meeting the modeling requirements of the ship classification society and ensuring the accuracy and effectiveness of the model. The cargo hold double-bottom grid model is shown in Fig. 1. An eight-node solid element is used to establish the cushion wood and coil steel model. Since the stress distribution on the coil steel is not analyzed, and the number of elements involved in the coil steel stowage in the hold is extremely large, to control the number of elements and save calculation time, the coil steel model is planned to be divided into three layers of elements along the radial direction, and the approximate global size of the cushion solid element is taken as 33 mm. Further grid independence verification is carried out on this basis. Figure 3

[0067] When the coil steel is stowed in the cargo hold, the inner bottom plate of the cargo hold is not only subjected to the weight load of the coil steel itself, but also subjected to the influence of the dynamic load. To calculate the stress condition of the coil steel stowed in the cargo hold for a long time, static analysis instead of dynamic analysis is adopted. The vertical synthetic acceleration is calculated according to the following formula:

[0068]

[0069] wherein, is the vertical synthetic acceleration, is the first vertical synthetic acceleration, is the second vertical synthetic acceleration, is the heave acceleration, is the roll angular acceleration, is the longitudinal distance from the calculation point to the vertical line at the stern, is the transverse distance from the calculation point to the longitudinal center plane, is the pitch angular acceleration, is the ship length.

[0070] The calculation formula of the heave acceleration is:​

[0071] wherein, is a square coefficient, is an acceleration coefficient.

[0072] The calculation formula of the acceleration coefficient is:

[0073] wherein, is a navigation area coefficient, and 1 is taken for the whole navigation area, is a correlation coefficient of the acceleration coefficient, and 9.6 is taken for the selected example ship, is a speed similarity ratio, and the value is not greater than 0.2.

[0074] The calculation formula of the roll angle acceleration is:

[0075] wherein, is a maximum roll angle, and is not greater than 0.523 rad, is a roll period.

[0076] The calculation formula of the roll period is:

[0077] wherein, is an initial stability height under the calculation condition, and 0.12 times the ship width can be taken for the bulk carrier when there is no accurate value, is a roll rotation radius, and 0.39 times the ship width can be taken for the bulk carrier when there is no accurate value.

[0078] The calculation formula of the maximum roll angle is:

[0079] wherein, is a correlation coefficient of the maximum roll angle, and 1.2 is taken for the example ship, is a ship width.

[0080] The calculation formula of the pitch angle acceleration is:

[0081] wherein, is a maximum pitch angle, is a pitch period.

[0082] The calculation formula of the pitch period is:

[0083] The calculation formula of the maximum pitch angle is:

[0084] Due to the close packing of the coil steel in the cargo hold, the weight distribution is relatively symmetrical, and the heave acceleration is calculated to be 2.69 m / s 2 , the roll acceleration is 0.32 rad / s 2 , the pitch acceleration is 0.07 rad / s 2 , and the combined vertical acceleration of the cargo is 13.99 m / s 2 . The acceleration will be set as the gravity load in the coil steel entity.

[0085] Since the ship high-strength steel is a plastic material, yield failure often occurs, according to the fourth strength theory, Von Mises stress is used as the failure criterion, and stress mentioned in the following refers to Von Mises stress , which is calculated as follows.

[0086]

[0087] wherein, is the stress in the x direction of the unit, is the stress in the y direction of the unit, is the shear stress in the XY plane of the unit.

[0088] S4. Submit the single coil steel finite element model to the ABAQUS software for calculation to obtain the stress distribution of the single coil steel corresponding to the cargo hold inner bottom plate and double bottom frame, and obtain the rule of variable influence on stress distribution.

[0089] The working conditions of the single coil steel finite element model include: 2 spacer conditions across the solid ribbed plate, 3 spacer conditions across the solid ribbed plate, 2 spacer conditions between the solid ribbed plates, and 3 spacer conditions between the solid ribbed plates.

[0090] The simulation results of the working conditions of the single coil steel finite element model are as follows: (1) The results of the cross-solid ribbed plate loading are as follows: 2 spacers: when the thickness is 50 mm, the maximum stress of the inner bottom plate of the cw material is 123.9 MPa, and the yb material is 121.4 MPa; as the thickness increases to 140 mm, the inner bottom plate stress decreases to 69.45 MPa (cw) and 61.41 MPa (yb) respectively, and the inner bottom plate is the main stress position. 3 spacers: when the thickness is 50 mm, the maximum stress of the inner bottom plate of the cw material is 10.20 MPa, and the yb material is 11.75 MPa; the stress is significantly lower than that of the 2 spacer condition, and the maximum stress position shifts to the double bottom frame (the stress of the cw material frame is 48.41 MPa).

[0091] (2) The result of the stowage between the solid floor is: 2 pads: 50mm thick, the maximum stress of the inner bottom plate of cw material is 130.7MPa, and that of yb material is 134.3MPa; when the thickness increases to 140mm, the stress of the inner bottom plate decreases to 74.89MPa (cw) and 67.21MPa (yb) respectively. 3 pads: 50mm thick, the maximum stress of the inner bottom plate of cw material is 111.5MPa, and that of yb material is 105.9MPa; when the thickness increases to 120mm, the stress of the inner bottom plate and the skeleton is close (70.12MPa and 70.68MPa for cw material respectively). Length effect: the stress of 700mm pad increases by 4.7% compared with that of 1500mm inner bottom plate, and the stress of 2000mm pad decreases by 3.4% compared with that of 1500mm inner bottom plate, and the influence range is less than 10%.

[0092] Due to the use of single coil steel stowage model, the coil steel load is small, and the maximum stress of each working condition is less than the allowable stress of each component. Within the allowable stress range, the difference in stress transmission effect caused by the two types of wood on the pad is limited, indicating that within the range of hardwood materials, the type of wood has little effect on the effect of the pad. Each coil steel uses three pads and is the safest working condition when stowed across the solid floor, and there is little significance in increasing the thickness of the pad under this condition. In other working conditions, factors affecting stress size include the number of pads, thickness, and length. Except for the condition of stowing three pads per group above the solid floor, the increase in pad thickness has a significant effect on the maximum stress of the inner bottom plate, with a stress reduction of more than 20%, while the effect on the double bottom skeleton stress is generally less than 10%. The maximum stress reduction of the three working conditions changing the length of the pad is also less than 10%, and it cannot change the stress distribution, so increasing the length of the pad also has a general effect on improving the stress condition of the double bottom. For a 50,000-ton bulk carrier similar to this structure, first of all, attention should be paid to stowing coil steel in a position with sufficient support as much as possible. If it is not possible to stow according to the double bottom structure design due to the need for tight packing during the transportation of coil steel, sufficient thickness and number of pads should be used. Especially when stowing 20 tons or more of heavy coil steel, the commonly used 50mm thick hardwood pad can ensure effective load distribution in well-supported positions, but in areas below the actual contact position that lack solid floor support, it may not meet the pad requirements, resulting in deformation or even damage to the inner bottom plate structure. At this time, it should be ensured that three hardwood pads with sufficient length of 100mm thickness or even thicker can be used to ensure safety.

[0093] S4. Based on the law of variable stress distribution, an integral stowage finite element model is constructed, and the integral stowage finite element model is submitted to ABAQUS software for calculation, and the stress distribution of the inner bottom plate and the double bottom skeleton corresponding to the integral stowage.

[0094] The working conditions of the whole-hold stowage finite element model include: 10-ton coil steel stowage of three layers, 15-ton coil steel stowage of two layers, 20-ton coil steel stowage of two layers, 25-ton coil steel stowage of two layers, and 25-ton coil steel stowage of single layer.

[0095] The simulation results of the working conditions of the whole-hold stowage finite element model are as follows: (1), as Figure 4 shown, Figure 4 (a) is the inner bottom plate stress nephogram of 10-ton coil steel stowage of three layers in the cargo hold, Figure 4 (b) is the double-layer bottom frame stress nephogram of 10-ton coil steel stowage of three layers in the cargo hold. The results of 10-ton coil steel (three layers of stowage) are: Model parameters: inner diameter 510 mm, outer diameter 1370 mm, width 1300 mm, whole-hold stowage three layers; Key results: 50mm thick cw gasket: inner bottom plate maximum stress 264.9MPa (exceeds allowable value 282.1MPa), unsafe 90mm thick cw gasket: inner bottom plate stress reduced to 162.4MPa (safe); 60mm thick yb gasket: inner bottom plate stress 201.7MPa (safe), better than the same thickness cw material.

[0096] (2), as Figure 5 shown, Figure 5 (a) is the inner bottom plate stress nephogram of 15-ton coil steel stowage of two layers in the cargo hold, Figure 5 (b) is the double-layer bottom frame stress nephogram of 15-ton coil steel stowage of two layers in the cargo hold. The results of 15-ton coil steel (two layers of stowage) are: Model parameters: inner diameter 510 mm, outer diameter 1370 mm, width 1500 mm, whole-hold stowage two layers; Key results: 50mm thick cw / yb gasket: inner bottom plate maximum stress is 219.2MPa, 215.9MPa respectively (both ≤282.1MPa), safe; when the thickness increases to 100mm, the yb material inner bottom plate stress is reduced to 159.3MPa, the frame stress is 165.6MPa, and the load dispersion effect is significant.

[0097] (3), as Figure 6 shown, Figure 6 (a) is the inner bottom plate stress nephogram of 20-ton coil steel stowage of two layers in the cargo hold, Figure 6 (b) is the double-layer bottom frame stress nephogram of 20-ton coil steel stowage of two layers in the cargo hold. The results of 20-ton coil steel (two layers of stowage) are: Model parameters: inner diameter 510 mm, outer diameter 1510 mm, width 1600 mm, whole-hold stowage two layers; Key results: 50mm thick cw cushion: inner bottom stress 220.9 MPa, skeleton stress 247.1 MPa (both are not exceeding the allowable value); stress is concentrated in the middle beam of the cargo hold, and the centerline load is superimposed due to the symmetrical stacking of the coil steel.

[0098] (4), as Figure 7 shown, Figure 7 (a) is the inner bottom stress nephogram of one layer of 25-ton coil steel in the cargo hold, Figure 7 (b) is the double bottom skeleton stress nephogram of one layer of 25-ton coil steel in the cargo hold. The results of 25-ton coil steel (one layer of stacking) are: Model parameters: same as 25-ton two-layer condition, only one layer of stacking; Key results: 50mm thick cw cushion: inner bottom stress 220.9 MPa, skeleton stress 247.1 MPa (both are not exceeding the allowable value); stress is concentrated in the middle beam of the cargo hold, and the centerline load is superimposed due to the symmetrical stacking of the coil steel.

[0099] On this basis, two kinds of material cushions with dimensions of 100mmx50mmx1500mm are replaced for verification. As Figure 8 shown, Figure 8 (a) is the inner bottom stress nephogram of one layer of 25-ton coil steel in the cargo hold with the replaced cushion material, Figure 8 (b) is the double bottom skeleton stress nephogram of one layer of 25-ton coil steel in the cargo hold with the replaced cushion material. The maximum stress of the inner bottom plate using yb cushion material is 163.6 MPa, and the maximum stress of the double bottom plate is 187.5 MPa. The inner bottom plate and double bottom plate stress nephograms are shown in Figure 8 . The maximum stress of the inner bottom plate using cw cushion material is 169.3 MPa, and the maximum stress of the double bottom plate is 196.8 MPa. By comparing the allowable stress values of each component, it can be seen that the two conditions after the thickness is reduced also do not exceed the allowable stress, proving that this stacking method is relatively safe, and the cushion thickness can be appropriately reduced to reduce costs.

[0100] The above data show that in the case of 10-ton coil steel stacking 3 layers, a wood cushion with a thickness of 90mm or more is required to ensure safety. The 15-ton and 20-ton coil steel stacking 2 layers are relatively safe, and a hardwood wood cushion with a thickness of 50mm or more can ensure that the allowable stress is not exceeded. The 25-ton coil steel stacking 2 layers is relatively extreme and difficult to ensure the safety of structural strength. In transportation, similar conditions should be avoided as much as possible, and only one layer of stacking is relatively safe, and the cushion quality can be appropriately weakened to reduce costs. This shows that under the premise of ensuring the safety of ship structural strength, economic benefits are also maximized, and it is also given how to use what kind of cushion material. In the current research, there is no specific method for the selection of sediment materials.

[0101] S5. According to the fourth strength theory, taking the von Mises stress as the failure criterion, the maximum stress in the stress distribution of the corresponding cargo hold inner bottom plate and double bottom frame under the whole-cabin stowage is compared with the preset allowable stress to complete the strength check of the liner.

[0102] When the liner thickness is greater than or equal to 90 mm under the 10-ton coil steel stowage of three layers, the allowable stress requirement is met.

[0103] When the liner thickness is greater than or equal to 50 mm under the 15-ton coil steel stowage of two layers or the 20-ton coil steel stowage of two layers, the allowable stress requirement is met.

[0104] When the liner thickness is greater than or equal to 50 mm under the 25-ton coil steel stowage of single layer, the allowable stress requirement is met.

[0105] Under the three-layer stowage of 10-ton coil steel, when the liner thickness of cw material is greater than or equal to 90 mm, the maximum stress value is less than the allowable stress value of the inner bottom plate. When the liner thickness of yb material is greater than or equal to 60 mm, the maximum stress value is less than the allowable stress value of the inner bottom plate. Since part of the conditions of this case do not meet the allowable stress requirement, the estimated uniform load P = Q / S = 16.81 t / m 2 , which is less than the allowable uniform load 20 t / m 2 of the cargo hold inner bottom plate. However, according to the direct calculation method, if the liner thickness or material pressure resistance is insufficient, this stowage condition is not always safe. Therefore, in actual transportation, attention should be paid to ensure that the liner meets the prerequisite assumptions when applying the estimation method for strength check.

[0106] Under the two-layer stowage of 15-ton coil steel, even a 50 mm thick liner can meet the allowable stress requirement. Although the equivalent weight of the lowermost layer of a single coil steel under the two-layer stowage of 15-ton coil steel is about 30 tons compared to the three-layer stowage of 10-ton coil steel, the volume of 15-ton coil steel is larger, and the number of coils per row is smaller. The total cabin load and weight are less than those of the three-layer stowage of 10-ton coil steel. The final stress result is smaller compared to the three-layer stowage of 10-ton coil steel. Unlike the single stowage condition, when the liner thickness reaches 90 mm, the double bottom frame becomes the main force position, indicating that the longitudinal and transverse frames can more fully distribute and transfer the load brought by each coil under the condition of close stowage in the whole cabin. The stress on the inner bottom plate is relatively concentrated, similar to the single stowage condition.

[0107] Under the two-layer stowage of 20-ton coil steel, the maximum stress position under this condition is the cargo hold central beam. The main reason is that the coil steel is generally tightly packed from both sides to the center, and the two sides of the cargo hold are symmetrical along the central line of the cargo hold. The weight of the coil steel stacked along the central line increases continuously with the working condition setting, so the load on the central frame also increases.

[0108] 25 tons of steel coil stowage one layer of work conditions, the replacement of 100mm x 50mm x 1500mm size two kinds of material pad to verify. The use of yb material pad inner bottom plate maximum stress is 163.6MPa, double layer bottom skeleton maximum stress is 187.5MPa, the stress nephogram of inner bottom plate and double layer bottom skeleton is shown in Figure 8 The use of cw material pad inner bottom plate maximum stress is 169.3MPa, double layer bottom skeleton maximum stress is 196.8MPa. By comparing the allowable stress value of each component, it can be seen that the two kinds of working conditions after the thickness reduction also do not exceed the allowable stress, which proves that the stowage mode is relatively safe, and the thickness of the pad can be appropriately reduced to reduce the cost.

[0109] The above research is carried out by simulation to directly calculate the structural strength, and different pad conditions are changed to obtain the pad that meets the structural strength. After the ship type and the size of the coil steel are determined, the coil steel stowage and structural strength analysis can be carried out by simulation to obtain the allowable range of the pad. On the premise of ensuring the structural strength, the space utilization rate is maximized, the most number of coil steels are stowed, and the transportation benefit is ensured.

[0110] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, but not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for verifying the liner of shipping coil steel based on ABAQUS, characterized in that: The following steps are involved: S1. Determine the coil parameters and cargo hold structural parameters, including coil weight, coil inner diameter, coil outer diameter, and coil width; and cargo hold structural parameters including cargo hold width, cargo hold length, rib spacing, transverse rib spacing, and maximum uniformly distributed load bearing capacity of the inner bottom plate; S2. Based on the coil steel parameters and cargo hold structure parameters, a finite element model is established in ABAQUS software. The finite element model includes a cargo hold structure finite element model, a coil steel finite element model, and a liner finite element model. At the same time, material properties are set for the finite element model in ABAQUS software. S3. Mesh the finite element model and set boundary conditions and loads in ABAQUS software. The boundary conditions include linear and angular displacement constraints on the cargo hold bottom shell plate and the front and rear end surfaces of the cargo hold. The loads include the deadweight of the steel coil and dynamic loads. A finite element model of a single steel coil is obtained. S4. Submit the single coil steel finite element model to ABAQUS software for calculation to obtain the stress distribution of the cargo hold inner bottom plate and double bottom frame corresponding to the single coil steel, and obtain the law of variables affecting the stress distribution; S5. Based on the influence of variables on stress distribution, a finite element model of full-hold stowage was constructed and submitted to ABAQUS software for calculation of the stress distribution of the cargo hold inner bottom plating and double-bottom frame corresponding to full-hold stowage. The operating conditions of the finite element model for full-hold stowage included: three-layer stowage of 10 tons of steel coils, two-layer stowage of 15 tons of steel coils, two-layer stowage of 20 tons of steel coils, and a single-layer stowage of 25 tons of steel coils. Specifically, in the three-layer stowage condition of 10 tons of coiled steel, the allowable stress requirement is met when the liner thickness reaches 90 mm or more; in the two-layer stowage condition of 15 tons of coiled steel or two-layer stowage condition of 20 tons of coiled steel, the allowable stress requirement is met when the liner thickness reaches 50 mm or more; in the single-layer stowage condition of 25 tons of coiled steel, the allowable stress requirement is met when the liner thickness reaches 50 mm or more; S6. Based on the fourth strength theory and taking the Mises stress as the failure judgment index, the maximum stress in the stress distribution of the cargo hold inner bottom plate and double bottom frame corresponding to the entire hold loading is compared with the preset allowable stress to complete the strength verification of the liner.

2. The ABAQUS-based verification method for shipping coil steel lining according to claim 1 is characterized in that: The working conditions of the single coil steel finite element model include: a working condition of 2 liners stowed across solid floors, a working condition of 3 liners stowed across solid floors, a working condition of 2 liners stowed between solid floors, and a working condition of 3 liners stowed between solid floors.

3. The ABAQUS-based verification method for shipping coil steel lining according to claim 1 is characterized in that: The dynamic load is calculated based on the vertical composite acceleration, which is calculated by combining the heave acceleration, roll angular acceleration, and pitch angular acceleration. The calculation formula for the vertical composite acceleration is: in, is the vertical resultant acceleration, is the first vertical resultant acceleration, is the second vertical resultant acceleration, is the heave acceleration, is the roll angular acceleration, is the longitudinal distance from the calculation point to the tail perpendicular, is the transverse distance from the calculation point to the longitudinal midsection, is the pitch angular acceleration, For the captain.

4. The ABAQUS-based verification method for shipping coil steel lining according to claim 3 is characterized in that: The calculation formula of the heave acceleration is: in, is the square coefficient, is the acceleration coefficient, and the calculation formula of the acceleration coefficient is: in, is the navigation area coefficient, is the correlation coefficient of the acceleration coefficient, is the speed similarity ratio, The calculation formula of the roll angular acceleration is: in, is the maximum roll angle, is the rolling period, and the calculation formula of the rolling period is: in, To calculate the initial stability height under working conditions, is the rolling rotation radius, The calculation formula of the maximum roll angle is: in, is the correlation coefficient of the maximum roll angle, For the width of the ship, The calculation formula of the pitch angular acceleration is: in, is the maximum pitch angle, is the pitch period, and the calculation formula of the pitch period is: The calculation formula of the maximum pitch angle is: 。 5. The ABAQUS-based verification method for shipping coil steel lining according to claim 1 is characterized in that: In the boundary conditions, the linear displacement constraints of the cargo hold bottom outer shell plate are x=0, y=0, z=0, and the angular displacement constraints are 0, 0, 0; the linear displacement constraints of the front and rear end surfaces of the cargo hold are x=0, and the angular displacement constraints are 0, 0.

6. The ABAQUS-based verification method for shipping coil steel lining according to claim 1, characterized in that: The establishment of the finite element model of the cargo hold structure includes the processing of component openings and the idealization of the bulb flat steel structure. The component openings are modeled using equivalent plate thickness or geometry according to scale conditions, and the bulb flat steel is converted into equivalent angle steel through a formula for modeling.

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