Method and system for evaluating ultimate strength of ship structure based on variable thickness steel plate

Abstract

This invention provides a method and system for assessing the ultimate strength of ship structures based on variable-thickness steel plates, belonging to the field of material strength assessment technology. The method includes: discretizing the cross-section of the hull beam into multiple structural units; determining the thickness value of each structural unit according to a preset variable-thickness design rule; determining the effective cross-sectional area and buckling stress parameter of each structural unit based on the thickness value and structural parameters; and using the effective cross-sectional area and buckling stress parameter as mechanical parameters, determining the ultimate bending moment of the hull beam using an incremental iteration method. This invention enables accurate assessment of the ultimate bending moment of variable-thickness ship structures.

Description

Technical Field

[0001] This invention relates to the field of material strength assessment technology, and more specifically, to a method and system for assessing the ultimate strength of ship structures based on variable thickness steel plates. Background Technology

[0002] In related technologies, the ultimate strength assessment methods for ship structures (such as the Smith method based on the CSR-H standard) are mainly based on the geometric assumption of "equal thickness columnar bodies". For example, the "minimum thickness method" is used to treat the steel plates at each location as plates of equal thickness.

[0003] With the application of longitudinally variable thickness (LP) steel plates in lightweight ship design, the characteristic of their continuously varying thickness along the longitudinal direction results in a highly geometrically nonlinear coupling in the structure. Related technologies for handling LP steel plate structures, such as the "minimum thickness method," are conservatively reliable in terms of safety. However, the ultimate strength calculated by this method is far lower than the actual load-bearing capacity of the structure. This means there is a significant deviation between the ultimate strength assessment result and the actual value, potentially leading to material waste and loss of lightweight advantages in practical design. Summary of the Invention

[0004] The problem that this invention aims to solve is that, when related technologies assess the ultimate strength of ship structures, the assessment results deviate significantly from the actual situation, resulting in inaccurate assessments.

[0005] To address the aforementioned problems, in a first aspect, the present invention provides a method for evaluating the ultimate strength of ship structures based on variable thickness steel plates, comprising: The cross section of the hull beam is discretized into multiple structural units, and the thickness value of each structural unit is determined according to a preset variable thickness design rule. Based on the thickness value and structural parameters of each structural unit, determine the effective cross-sectional area and buckling stress parameters of each structural unit; Using the effective cross-sectional area and the buckling stress parameter as mechanical parameters, the ultimate bending moment of the hull beam is determined by an incremental iteration method.

[0006] Optionally, determining the thickness value of each structural unit according to a preset variable thickness design rule includes: Based on the position coordinates of the structural unit in the cross section of the hull beam and the preset position-thickness correspondence, the thickness value of the corresponding structural unit is determined. The preset position-thickness correspondence includes a position-thickness correspondence that is continuously and gradually changed and / or stepped.

[0007] Optionally, determining the thickness value of the corresponding structural unit based on its position coordinates in the cross-section of the hull beam and a preset position-thickness correspondence includes: Obtain the centroid height coordinates of the structural unit, the bottom height of the hull beam and the corresponding bottom plate design thickness, as well as the deck height and the corresponding deck design thickness; Based on the relative position ratio of the centroid height coordinates within the range formed by the bottom height and the deck height, the bottom plate design thickness and the deck design thickness are linearly interpolated to determine the thickness value, and this thickness value is determined as the thickness value of the corresponding structural unit.

[0008] Optionally, determining the thickness value of the corresponding structural unit based on its position coordinates in the cross-section of the hull beam and a preset position-thickness correspondence includes: Based on the design layout drawing of the cross section of the hull beam, the one-to-one correspondence between each constant thickness value in the thickness list and the transverse coordinate interval is determined; wherein, the transverse coordinate interval is a number of continuous coordinate ranges divided in the transverse width, and each transverse coordinate interval corresponds to a constant thickness value. Obtain the lateral coordinates of the structural unit; Based on the horizontal coordinate range into which the horizontal coordinate falls, the corresponding constant thickness value is read from the thickness list, and the constant thickness value is determined as the thickness value of the corresponding structural unit.

[0009] Optionally, the structural unit types include plate units, stiffener units, and stiffener units with plates; The step of determining the effective cross-sectional area and buckling stress parameters of each structural unit based on its structural parameters and thickness includes: For the plate element, the effective cross-sectional area and plate flexibility coefficient of the plate element are determined based on the thickness value of the plate element, and then the buckling critical stress of the plate element is determined. For the reinforcing element, the cross-sectional properties of the reinforcing element are determined based on its thickness value. The cross-sectional properties include cross-sectional area and moment of inertia, thereby determining the Euler critical stress of the reinforcing element. For the plate-stiffening element unit, the effective cross-sectional area of ​​the plate portion and the effective cross-sectional area of ​​the stiffening element are determined according to their thickness values. The effective cross-sectional area of ​​the plate portion is reduced by the effective width and then summed with the effective cross-sectional area of ​​the stiffening element to obtain the effective cross-sectional area of ​​the combined unit. The axial stress of the plate portion and the axial stress of the stiffening element are determined according to the buckling critical stress of the plate portion and the Euler critical stress of the stiffening element, respectively. The combined stress of the combined unit is then obtained by weighted summation of the effective cross-sectional areas.

[0010] Optionally, the step of using the effective cross-sectional area and buckling stress parameters as mechanical parameters and employing an incremental iteration method to determine the ultimate bending moment of the hull beam includes: Based on the effective cross-sectional area of ​​each structural unit and the centroid position of each structural unit, the elastic section modulus of the hull beam cross section is determined, and the initial neutral axis position of the hull beam cross section is determined based on the elastic section modulus. Starting from the preset initial curvature of the cross section of the hull beam, the preset curvature increment of the cross section of the hull beam is gradually increased to enter the next curvature. Under each curvature, based on the effective cross-sectional area and the buckling critical stress of each structural unit, the neutral axis position of the cross section of the hull beam is iteratively adjusted until the total axial force of the cross section of the hull beam is balanced, and the section bending moment of the cross section of the hull beam corresponding to the curvature is determined. Record the curvature and section bending moment of the cross section of the hull beam under each curvature to generate the bending moment-curvature curve of the hull beam; When the curvature of the cross section of the hull beam reaches or exceeds the preset maximum required curvature of the cross section of the hull beam, the peak value of the bending moment-curvature curve is extracted as the ultimate bending moment of the hull beam.

[0011] Optionally, the step of iteratively adjusting the neutral axis position of the hull beam cross section until the total axial force of the hull beam cross section is balanced under each curvature, based on the effective cross-sectional area and the buckling critical stress of each structural unit, and determining the section bending moment of the hull beam cross section corresponding to that curvature includes: Based on the current curvature and the current neutral axis position, determine the axial strain of each structural unit; Based on the buckling critical stress, the axial strain, and the preset stress-strain curve of each structural unit, the corresponding axial stress is determined; based on the axial stress and the effective cross-sectional area, the unit reaction force of the structural unit is determined. The total axial force is obtained by summing the unit reaction forces of all the structural units, and it is determined whether the total axial force is less than a preset threshold. If so, determine the section bending moment corresponding to the current curvature based on the converged unit reaction force and the neutral axis position; If not, adjust the position of the neutral axis and redetermine the axial strain of each structural unit, and determine the unit reaction force of the structural unit until the total axial force of all structural units is less than a preset threshold, so as to determine the section bending moment under the corresponding curvature.

[0012] Optionally, in a preset stress-strain curve, For each of the structural units, under tension, the preset stress-strain curve adopts a bilinear model that includes an elastic segment and a plastic hardening segment; For each of the structural units, under compression, the stress-strain curve of the structural unit is determined based on the buckling stress parameter corresponding to the structural unit; Wherein, when the axial strain of the structural unit exceeds a preset ultimate strain threshold, the axial stress of the structural unit decreases to a preset residual strength threshold.

[0013] Optionally, the adjustment of the neutral axis position of the hull beam cross section adopts the Newton-Raphson iterative method, wherein the correction amount of each iteration is determined according to the ratio of the total axial force of the current hull beam cross section to the total tangential stiffness of the hull beam cross section, the total tangential stiffness is obtained by weighted summation of the current tangential stiffness of each structural unit, and the current tangential stiffness is determined according to the buckling critical stress and the effective cross-sectional area of ​​the structural unit.

[0014] The present invention provides a method for assessing the ultimate strength of ship structures based on variable-thickness steel plates. This method embeds pre-defined variable-thickness design rules into the discretization stage, assigning a thickness value independently to each structural unit. This overcomes the limitations of traditional methods that rely on assumptions such as moderate thickness, enabling the discrete model to accurately reproduce the thickness distribution characteristics of the variable-thickness steel plate and avoiding evaluation biases caused by thickness simplification in subsequent calculations. Based on the actual thickness value of each structural unit, its effective cross-sectional area and buckling stress parameters are determined, ensuring an accurate correspondence between the mechanical properties of each unit and its actual thickness. Using the determined effective cross-sectional area and buckling stress parameters as input, the ultimate bending moment of the hull beam is solved using an incremental iteration method. During the incremental iteration process, the unit reaction force of each unit is determined by multiplying its axial stress by its effective cross-sectional area, while the magnitude and evolution path of the axial stress are directly affected by the buckling stress parameters. Because the thickness value carried by each unit is a simulated value of the actual thickness determined according to the variable-thickness design rules, the effective cross-sectional area and buckling stress parameters differ between units. This leads to different unit reactions at the same strain level, and the starting points for stiffness degradation in the compressive units also differ. This differentiated internal force response drives a corresponding shift in the neutral axis during the total axial force balance iteration, which is ultimately reflected in the calculation results of the section bending moment. Through the above steps, the effective cross-sectional area and buckling stress parameters fully transmit the differentiated characteristics of the thickness distribution to the entire process of bending moment calculation, achieving an accurate assessment of the ultimate bending moment of a variable-thickness hull structure.

[0015] Secondly, the present invention also provides a ship structure ultimate strength assessment system based on variable thickness steel plates, applying the ship structure ultimate strength assessment method based on variable thickness steel plates as described in any of the above claims, including: The variable thickness determination module is used to: discretize the cross section of the hull beam into multiple structural units, and determine the thickness value of each structural unit according to the preset variable thickness design rules; The parameter determination module is used to: determine the effective cross-sectional area and buckling stress parameters of each structural unit based on the thickness value and structural parameters of each structural unit; The ultimate bending moment assessment module is used to determine the ultimate bending moment of the hull beam by using the effective cross-sectional area and the buckling stress parameter as mechanical parameters and employing an incremental iteration method.

[0016] Thirdly, the present invention provides an electronic device, including a memory and a processor; The memory is used to store computer programs; The processor is configured to, when executing the computer program, implement the method for assessing the ultimate strength of ship structures based on variable thickness steel plates as described in the first aspect.

[0017] Fourthly, the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method for evaluating the ultimate strength of ship structures based on variable thickness steel plates as described in the first aspect.

[0018] The ship structure ultimate strength assessment system, electronic equipment, and computer-readable storage medium based on variable thickness steel plates provided by this invention have the same beneficial effects as the ship structure ultimate strength assessment method based on variable thickness steel plates compared to the prior art, and will not be repeated here. Attached Figure Description

[0019] Figure 1 A flowchart illustrating a method for evaluating the ultimate strength of ship structures based on variable thickness steel plates, according to an embodiment of the present invention, is shown. Figure 2 This invention illustrates a flowchart of determining the ultimate bending moment of a ship's beam using the effective cross-sectional area and buckling stress parameters as mechanical parameters and an incremental iteration method, as shown in an embodiment of the invention. Figure 3 A schematic diagram of the ultimate strength assessment system for ship structures based on variable thickness steel plates is shown in an embodiment of the present invention. Figure 4 A schematic diagram of the structure of an electronic device according to an embodiment of the present invention is shown. Detailed Implementation

[0020] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0021] It should be noted that relational terms such as "first" and "second" in this invention are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0022] In the description of this specification, references to terms such as "embodiment," "one embodiment," and "one implementation" indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or implementation is included in at least one embodiment or illustrative implementation of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or implementation. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or implementations.

[0023] Reference Figure 1 As shown in the figure, this invention proposes a method for evaluating the ultimate strength of ship structures based on variable thickness steel plates, including: The cross-section of the hull beam is discretized into multiple structural units, and the thickness value of each structural unit is determined according to a preset variable thickness design rule.

[0024] Specifically, in the ultimate strength assessment of ship structures, the hull beam cross-section is first discretized into multiple structural units. The purpose of discretization is to transform the continuous cross-section into a computational model composed of a finite number of independent components, each component being called a structural unit. Types of structural units may include plate units, stiffener units, and plate-stiffener composite units (plate units with stiffeners), etc. According to a pre-defined variable thickness design rule, a thickness value is independently assigned to each structural unit. The core of this rule lies in establishing a mapping relationship between the position coordinates of the structural unit and its thickness value. This mapping relationship can be a continuous, gradual change (e.g., linear interpolation of thickness with height) or a stepped change (e.g., a thickness list corresponding to transverse intervals), applicable respectively to gradually changing areas such as side plates and segmented plate areas such as decks and bottom plates.

[0025] Based on the thickness value and structural parameters of each structural unit, the effective cross-sectional area and buckling stress parameters of each structural unit are determined.

[0026] Specifically, for each structural element, its effective cross-sectional area and buckling stress parameters are determined based on its thickness and structural parameters. The effective cross-sectional area characterizes the load-bearing area of ​​the element, while the buckling stress parameters describe the element's instability characteristics under compression. Different types of elements correspond to different buckling stress parameters. For example, for plate elements, the buckling stress parameters may include the critical buckling stress, determined by referring to the standard formula based on the plate compliance coefficient; for stiffener elements, the buckling stress parameters may include the Euler critical stress, determined based on the cross-sectional properties and effective length; for plate-stiffener composite elements, the buckling stress parameters may include the combined stress obtained through weighted summation. This step transforms the thickness value into the mechanical parameters required for subsequent mechanical calculations.

[0027] Using the effective cross-sectional area and the buckling stress parameter as mechanical parameters, the ultimate bending moment of the hull beam is determined by an incremental iteration method.

[0028] Specifically, the incremental iterative method is a classic numerical method (such as the Smith method) in the field of ultimate strength assessment of ship structures. It is widely used in the calculation of the ultimate bearing capacity of various ship hull structures and has universality. This method uses curvature as a control parameter and simulates the complete process of the hull beam from elasticity to ultimate strength and then to failure by gradually increasing the curvature. It iteratively solves the internal force balance at each curvature step to obtain the bending moment-curvature curve and extracts the peak value as the ultimate bending moment.

[0029] However, the traditional incremental iterative method is based on the geometric assumption that all structural elements have equal thickness, meaning that elements of the same type have the same thickness value. When this method is directly applied to variable thickness steel plate structures, the following problems arise: if minimum thickness simplification is used, the evaluation results are too conservative and cannot take full advantage of the lightweight properties of variable thickness steel plates; if average thickness simplification is used, weak points may be masked, the ultimate bearing capacity may be overestimated, and safety hazards may exist; if piecewise discrete simplification is used, the number of elements increases dramatically and stress transfer deviations occur at abrupt changes in the cross-section.

[0030] Based on the aforementioned universal incremental iterative method, this invention introduces two key steps: first, assigning a thickness value to each structural unit independently according to the variable thickness design rules, breaking the assumption of medium thickness in traditional methods; second, determining the effective cross-sectional area and buckling stress parameters of each unit based on the thickness value, so that subsequent mechanical calculations are based on the actual thickness distribution.

[0031] Theoretically, the effective cross-sectional area directly determines the magnitude of the reaction force generated by an element under stress, while the buckling stress parameter determines the stress-strain evolution path of the element under compression. Since the thickness of each element follows a variable thickness design rule, the effective cross-sectional area and buckling stress parameter exhibit differentiated characteristics consistent with the thickness distribution. This differentiation has the following effects in the incremental iterative method: at the element reaction force calculation level, the difference in effective cross-sectional area leads to different reaction force contributions from each element under the same strain; at the equilibrium iteration level, the difference in buckling stress parameters among elements results in different starting points for stiffness degradation in the compression elements, driving the neutral axis to shift in line with the actual stiffness distribution; at the bending moment calculation level, these differences are ultimately reflected in the differentiated composition of the cross-sectional bending moment, enabling the calculation results to reflect the true mechanical behavior of the variable thickness structure.

[0032] In summary, this invention does not change the solution framework of the incremental iterative method itself. Instead, by introducing variable thickness assignment and thickness-based mechanical parameter determination steps at the front end, the universal method is able to accurately handle variable thickness structures, thus solving the technical problem that traditional methods cannot accurately evaluate the ultimate strength of variable thickness steel plate structures.

[0033] In practical application, this embodiment embeds pre-defined variable thickness design rules into the discretization stage, assigning a thickness value independently to each structural unit. This breaks through the limitations of traditional methods that rely on assumptions such as moderate thickness, enabling the discrete model to accurately reproduce the thickness distribution characteristics of the variable thickness steel plate and avoiding evaluation deviations caused by thickness simplification in subsequent calculations. Based on the actual thickness value of each structural unit, its effective cross-sectional area and buckling stress parameters are determined, ensuring an accurate correspondence between the mechanical properties of each unit and its actual thickness. Using the determined effective cross-sectional area and buckling stress parameters as input, the ultimate bending moment of the hull beam is solved using an incremental iteration method. During the incremental iteration process, the unit reaction force of each unit is determined by multiplying its axial stress by its effective cross-sectional area, while the magnitude and evolution path of the axial stress are directly affected by the buckling stress parameters. Since the thickness value carried by each unit is a simulated value of the actual thickness determined according to the variable thickness design rules, each unit has a different effective cross-sectional area and buckling stress parameters, resulting in different unit reactions at the same strain level, and the starting point of stiffness degradation in the compression unit is also different for each unit. This differentiated internal force response drives a corresponding shift in the neutral axis during the total axial force balance iteration, which is ultimately reflected in the calculation results of the section bending moment. Through the above steps, the effective cross-sectional area and buckling stress parameters fully transmit the differentiated characteristics of the thickness distribution to the entire process of bending moment calculation, achieving an accurate assessment of the ultimate bending moment of a variable-thickness hull structure.

[0034] As an optional embodiment of the present invention, determining the thickness value of each structural unit according to a preset variable thickness design rule includes: Based on the position coordinates of the structural unit in the cross section of the hull beam and the preset position-thickness correspondence, the thickness value of the corresponding structural unit is determined. The preset position-thickness correspondence includes a position-thickness correspondence that is continuously and gradually changed and / or stepped.

[0035] Specifically, the core of the variable thickness design rule lies in establishing a mapping relationship between the position coordinates and thickness values ​​of structural units. For any structural unit in the cross section of the hull beam, its thickness value is not fixed in advance, but is determined in real time based on the position coordinates of the structural unit in the cross section. The position coordinates include the centroid height coordinate z_i (used to characterize the position of the structural unit in the vertical direction) and the transverse coordinate y_i (used to characterize the position of the structural unit in the horizontal direction). Depending on different design requirements, the position-thickness correspondence can take two forms: the first is a continuous gradual correspondence, where the thickness changes continuously with the position coordinates, suitable for areas such as side outer plates and longitudinal bulkheads where the thickness gradually changes along the height direction, usually described using linear interpolation or nonlinear interpolation functions; the second is a stepped correspondence, where the thickness changes in steps with the position coordinates, suitable for areas such as decks and bottom plates designed as "segmented plates," usually described using a tabular mapping method. In practical engineering applications, the cross section of a ship's hull beam may simultaneously contain continuous gradient regions (such as the outer side plating) and stepped change regions (such as the deck and bottom plating). Therefore, the preset position-thickness correspondence can be used alone or both at the same time.

[0036] In practical applications, this embodiment directly associates thickness values ​​with position coordinates, achieving parametric modeling of variable thickness sections and avoiding the tedious manual assignment of thickness values ​​to each unit in traditional methods. The continuous gradient correspondence can accurately simulate the physical law of the continuous change of thickness of structures such as side plates with water pressure gradient, while the step change correspondence can restore the "layout diagram" logic in shipbuilding, making the stiffness distribution of the calculation model consistent with the actual ship height. The two correspondences can be used alone or in combination, covering various variable thickness design forms commonly found in hull structures, and have good versatility and adaptability. This rule is executed in the cross section discretization stage, and the subsequent ultimate strength calculation process can begin after the thickness value is assigned.

[0037] As an optional embodiment of the present invention, determining the thickness value of the corresponding structural unit based on the position coordinates of the structural unit in the cross-section of the hull beam and a preset position-thickness correspondence includes: Obtain the centroid height coordinates of the structural unit, the bottom height of the hull beam and the corresponding bottom plate design thickness, as well as the deck height and the corresponding deck design thickness; Specifically, for any structural unit in the cross-section of the hull beam, the centroid height coordinates z_i of that structural unit need to be obtained first (z_i represents the coordinate value of the geometric center of the i-th structural unit in the vertical direction, usually with the hull baseline as the origin and upward as positive). Simultaneously, the bottom height z_bottom (the vertical coordinate value of the bottom plating) and its corresponding bottom plating design thickness t_bottom (the design thickness of the bottom area) of the hull beam cross-section, as well as the deck height z_deck (the vertical coordinate value of the deck) and its corresponding deck design thickness t_deck (the design thickness of the deck area) need to be obtained. These parameters are directly read from the ship design drawings or design specifications. For the side plating structure, the thickness usually follows a continuous linear gradient from the bottom to the deck along the height direction, i.e., thicker at the bottom and thinner at the deck, to meet the requirements of water pressure varying with depth.

[0038] Based on the relative position ratio of the centroid height coordinates within the range formed by the bottom height and the deck height, the bottom plate design thickness and the deck design thickness are linearly interpolated to determine the thickness value, and this thickness value is determined as the thickness value of the corresponding structural unit.

[0039] Specifically, let the bottom height be z_bottom, and the corresponding bottom plate design thickness be t_bottom; let the deck height be z_deck, and the corresponding deck design thickness be t_deck. For a structural unit with centroid height coordinate z_i, first calculate its relative position ratio r, i.e., r = (z_i - z_bottom) / (z_deck - z_bottom). This ratio reflects the relative position of the structural unit within the section from the bottom to the deck. When z_i = z_bottom, r = 0; when z_i = z_deck, r = 1. Then, calculate the thickness value t_i of the structural unit (t_i represents the thickness value of the i-th structural unit) using the following linear interpolation formula: t_i = t_bottom + r × (t_deck - t_bottom) = t_bottom × (1 - r) + t_deck × r. Using this formula, the thickness at the bottom (r=0) is t_bottom, the thickness at the deck (r=1) is t_deck, and the thickness at the mid-height section varies linearly with the height. Finally, the calculated thickness value t_i is assigned to this structural unit.

[0040] When applied in practice, this embodiment establishes a linear mapping relationship between the centroid height coordinate and the thickness, with a clear physical meaning. The thickness value is calculated using a linear interpolation formula, which is simple and efficient, and does not require pre - defining a complex thickness list. It can accurately simulate the continuously varying thickness characteristics of structures such as side outer plates and longitudinal bulkheads, avoiding the accuracy loss caused by using average thickness or discrete segmentation in traditional methods. As a continuous function of the height coordinate, the thickness ensures the smoothness of the thickness change between adjacent structural units, avoiding stress transfer deviation caused by cross - section mutation. This method has a high degree of parameterization. Designers only need to define the thickness values at both ends of the bottom and deck, and then the thickness assignment of all structural units on the entire side can be automatically completed, greatly improving the modeling efficiency.

[0041] As an optional embodiment of the present invention, the determining the thickness value of the corresponding structural unit according to the position coordinates of the structural unit in the cross - section of the hull girder and a preset position - thickness correspondence relationship includes: According to the designed layout drawing of the hull girder cross - section, determine the one - to - one correspondence between each constant thickness value in the thickness list and the lateral coordinate interval; wherein, the lateral coordinate interval is a plurality of continuous coordinate ranges divided in the lateral width, and each lateral coordinate interval corresponds to one constant thickness value; Specifically, the designed layout drawing is a detailed drawing in ship structure design, which stipulates the plate thickness adopted at different lateral positions of the hull girder cross - section. According to the designed layout drawing, the lateral width of the hull girder cross - section is divided into several continuous lateral coordinate intervals, and each interval corresponds to a constant thickness value. Arranging these constant thickness values in the order of the lateral coordinate intervals constitutes the thickness list. For example, for the deck structure, the lateral width from the midship to the side can be divided into three intervals: Interval I (0 ≤ y < y1) corresponds to thickness t1, interval II (y1 ≤ y < y2) corresponds to thickness t2, interval III (y2 ≤ y ≤ y3) corresponds to thickness t3, then the thickness list is [t1, t2, t3].

[0042] Obtain the lateral coordinate of the structural unit; Specifically, for any structural unit in the hull girder cross - section, during discretization, it is necessary to determine the lateral position of the structural unit in the hull girder cross - section. The lateral coordinate yi of the structural unit (yi represents the coordinate value of the ith structural unit in the lateral direction, usually with the mid - longitudinal section of the hull girder cross - section as the origin, and the left - hand or right - hand side direction as positive) is determined according to the position of its geometric center in the hull girder cross - section. Usually, the mid - longitudinal section of the hull girder cross - section is taken as the origin (y = 0), and the left - hand or right - hand side direction is positive. For symmetric structures, only the units on one side need to be calculated, and the other side can be obtained by symmetry.

[0043] According to the horizontal coordinate interval in which the horizontal coordinate falls, read the corresponding constant thickness value from the thickness list, and determine this constant thickness value as the thickness value of the corresponding structural unit.

[0044] Specifically, compare the horizontal coordinate yi of the structural unit with the preset horizontal coordinate intervals to determine the interval to which yi belongs.

[0045] For example, if the horizontal coordinate intervals are divided into interval I: [0, y1), interval II: [y1, y2), interval III: [y2, y3], and the thickness list is [t1, t2, t3].

[0046] When yi is in interval II, that is, y1 ≤ yi < y2, read the second thickness value t2 from the thickness list and assign it to this structural unit, that is, ti = t2. This thickness value will be used for subsequent calculations of the effective cross-sectional area, buckling stress parameters, etc. of this structural unit. ti represents the thickness value of the i-th structural unit.

[0047] When this embodiment is applied in practice, directly generate the corresponding relationship between the thickness list and the horizontal coordinate intervals based on the ship design panel plan, fully restoring the actual design logic in the shipbuilding process. The calculation model is consistent with the actual ship. By matching the horizontal coordinates with the intervals, the correct thickness values can be quickly assigned to a large number of structural units, with high calculation efficiency. It supports any number of horizontal coordinate interval divisions and can accurately simulate stepped variable thickness distributions from simple to complex. It forms a complement with the continuous gradient variable thickness method in the previous embodiment, jointly covering two common variable thickness design forms in the hull structure, enabling this method to adapt to different variable thickness design requirements of various ship types (such as bulk carriers, oil tankers, container ships).

[0048] As an optional embodiment of the present invention, the types of the structural units include plate units, stiffener units, and plate-stiffener units; Specifically, in the assessment of the ultimate strength of the ship structure, the cross-section of the hull girder consists of various types of members.

[0049] The plate unit represents the pure steel plate area in the cross-section of the hull without the support of stiffeners, or a wide plate whose buckling characteristics need to be considered separately in the mechanical model. In ship structures, this usually refers to the hull plating, bulkhead plating, or the solid floor area in the double bottom. Its main parameters include thickness and width. The failure mode is mainly controlled by plate buckling. During analysis, calculate the reduction of the buckling bearing capacity before reaching the yield limit.

[0050] Stiffening members (also known as reinforcing ribs) are steel sections welded to a plate to enhance its stability. Geometry: Common cross-sectional shapes include flat steel, bulb flat steel, angle steel, or T-beams. Stiffening members are considered as independent beam models with specific cross-sectional areas and moments of inertia. Key parameters also include effective length, which determines the critical force at which column buckling occurs.

[0051] The plate-stiffened element is the most commonly used plate-stiffened element in hull structure assessment, simulating the actual working state of the ship's strong components. A large portion of the ship's longitudinal strength is provided by the plate frame with longitudinal stiffeners. Components include: bottom longitudinal stiffeners, side longitudinal stiffeners, deck longitudinal stiffeners, and their associated plates. Geometrically, it consists of a single stiffener and its associated plates. It is the standard representation of the hull's longitudinal skeleton (such as longitudinal stiffeners). In calculations, the initial area is allocated as follows: 70% to plates and 30% to stiffeners. The effective width is the core of this element. When the element is under compression, the plates near the stiffeners continue to bear the load, while the central area of ​​the plate grid fails due to buckling. Effective area reduction is achieved through dynamic calculation of strain effects. It comprehensively considers plate buckling and stiffener column buckling, making it the element type that contributes the most to the calculation of the hull's ultimate bending moment.

[0052] The step of determining the effective cross-sectional area and buckling stress parameters of each structural unit based on its structural parameters and thickness includes: For the plate element, the effective cross-sectional area and plate flexibility coefficient of the plate element are determined based on the thickness value of the plate element, and then the buckling critical stress of the plate element is determined. Specifically, for a plate element, let its thickness be t and its width be b, then the effective cross-sectional area of ​​the plate element is A_plate = b × t. The plate flexibility coefficient β is calculated as follows: β = (b / t) × (σ_y / E)^(1 / 2), where σ_y is the yield strength of the material and E is the elastic modulus. Based on the value of β, the buckling critical stress σ_c of the plate element is calculated according to the piecewise formula in Clause 6.2.1 of the CSR-H standard. .

[0053] When β ≤ 0.525, σ_c = σ_y; When 0.525 < β ≤ 0.8, σ_c = σ_y × (1.08 - 0.16 / β); When β > 0.8, σ_c = σ_y × (2.25 / β - 1.25 / β²), and the calculated result should not exceed σ_y.

[0054] For the reinforcing element, the cross-sectional properties of the reinforcing element are determined based on its thickness value. The cross-sectional properties include cross-sectional area and moment of inertia, thereby determining the Euler critical stress of the reinforcing element. Specifically, for the stiffening element, its cross-sectional area A_st and moment of inertia I are determined based on its geometry and thickness. The effective length L of the stiffening element is determined according to its end constraints, usually taken as the distance between adjacent support points. The Euler critical stress σ_E is calculated using the following formula: σ_E = π² × E × I / (A_st × L²). Then, the relative compliance is calculated using the material yield strength σ_y, and the buckling critical stress σ_c of the stiffening element is determined according to the formula in Clause 6.3 of the CSR-H standard. .

[0055] For the plate-stiffening element unit, the effective cross-sectional area of ​​the plate portion and the effective cross-sectional area of ​​the stiffening element are determined according to their thickness values. The effective cross-sectional area of ​​the plate portion is reduced by the effective width and then summed with the effective cross-sectional area of ​​the stiffening element to obtain the effective cross-sectional area of ​​the combined unit. The axial stress of the plate portion and the axial stress of the stiffening element are determined according to the buckling critical stress of the plate portion and the Euler critical stress of the stiffening element, respectively. The combined stress of the combined unit is then obtained by weighted summation of the effective cross-sectional areas.

[0056] Specifically, for a stiffener unit with a plate, let the effective cross-sectional area of ​​the plate portion be A_ p The effective cross-sectional area of ​​the reinforcing member is A_ s The effective width ratio is ψ (ψ is a coefficient between 0 and 1; ψ=1 in the elastic segment and gradually decreases after buckling). The effective cross-sectional area of ​​the composite element is A_c = A_ p × ψ + A_ s .

[0057] Under compression, calculate the axial stress σ_ of the plate portion separately. p Axial stress σ_ of the reinforcing member s Among them, σ_ p Based on the buckling critical stress σ_c of the plate element The axial strain ε is determined by calling the stress-strain curve of the plate element; σ_ s The stress-strain curve of the stiffening element is used to determine the stress. The combined stress σ_c of the composite element is calculated using the following formula: σ_c = (σ_ p × A_ p × ψ + σ_ s × A_ s ) / (A_ p× ψ + A_ s ).

[0058] In practical application, this embodiment rationally divides the cross-section of the hull beam into three types: plate elements, stiffener elements, and composite elements, covering all major components of the hull structure. Different buckling stress calculation methods are used for different element types: plate elements consider local buckling, stiffener elements consider overall instability, and composite elements reflect the collaborative work of the plate and stiffener through weighted summation. Accurate calculation of the effective cross-sectional area provides accurate mechanical parameters for subsequent element reaction and bending moment calculations. Accurate determination of buckling stress ensures that the stress-strain curve under compression truly reflects the post-buckling behavior of each element, thereby improving the overall accuracy of the ultimate bending moment assessment. This classification and parameter determination method fully complies with the CSR-H standard requirements and has good engineering applicability.

[0059] like Figure 2 As shown, in an optional embodiment of the present invention, the step of using the effective cross-sectional area and buckling stress parameters as mechanical parameters and employing an incremental iteration method to determine the ultimate bending moment of the hull beam includes: Based on the effective cross-sectional area of ​​each structural unit and the centroid position of each structural unit, the elastic section modulus of the hull beam cross section is determined, and the initial neutral axis position of the hull beam cross section is determined based on the elastic section modulus. Specifically, for the discretized cross-section of the hull beam, the effective cross-sectional area of ​​each structural element i is A_i (A_i represents the effective cross-sectional area of ​​the i-th structural element), and the centroid height coordinate is z_i. First, the elastic section modulus W of the hull beam cross-section is calculated (W represents the elastic section modulus of the hull beam cross-section), and its calculation formula is W = I / z_max (z_max represents the distance from the farthest fiber of the section to the neutral axis), where I is the moment of inertia of the cross-section, and it conforms to the following formula: I = Σ[A_i × (z_i - z_NA_elastic)²], where z_NA_elastic (representing the position of the elastic neutral axis) is the position of the elastic neutral axis, determined by the area moment equilibrium condition: Σ(A_i × z_i) / ΣA_i. Then, the initial neutral axis position z_NA_0 (representing the initial neutral axis position) is determined according to the elastic profile modulus, and is usually taken as the elastic neutral axis position z_NA_elastic.

[0060] Starting from the preset initial curvature of the cross section of the hull beam, the preset curvature increment of the cross section of the hull beam is gradually increased to enter the next curvature. Under each curvature, based on the effective cross-sectional area and the buckling critical stress of each structural unit, the neutral axis position of the cross section of the hull beam is iteratively adjusted until the total axial force of the cross section of the hull beam is balanced, and the section bending moment of the cross section of the hull beam corresponding to the curvature is determined. Specifically, the initial curvature κ_0 is set (usually zero or a minimum value), the curvature increment Δκ (Δκ represents the preset curvature increment, preset according to the calculation accuracy requirements, generally taken as 1 / 20 to 1 / 50 of the elastic limit curvature), and the maximum required curvature κ_max (κ_max represents the preset maximum required curvature, usually taken as 2 to 5 times the estimated limit curvature). Starting from κ = κ_0, at each curvature step κ_j = κ_{j-1} + Δκ (κ_j represents the curvature value of the j-th curvature step), the following sub-steps are executed: First, assume an initial neutral axis position z_NA_current (z_NA_current represents the neutral axis position of the current iteration step; the first curvature step uses z_NA_0, and subsequent curvature steps use the neutral axis position of the previous convergence step). Then, based on the current curvature κ_j and the current neutral axis position z_NA_current, calculate the axial strain ε_i of each structural element using the formula ε_i = κ_j × (z_i - z_NA_current). Next, determine the axial stress σ_i based on the stress-strain curve of each element (a bi-segment hardening model is used for the tensile state, and an appropriate model is used for the compressive state depending on the element type), and then calculate the element reaction F_i = σ_i × A_i.

[0061] The total axial force F_total = ΣF_i is obtained by summing the reactions of all elements (F_i represents the reaction force of the i-th structural element). If |F_total| is less than the preset axial force tolerance threshold ε_tol, the current neutral axis position has met the equilibrium condition; otherwise, the neutral axis position is adjusted using the Newton-Raphson iterative method, with a correction amount Δz_NA = -F_total / K_total, where K_total is the total tangential stiffness. The neutral axis position is updated z_NA_new = z_NA_current + Δz_NA, and the strain, stress, and reaction force of each element are recalculated until |F_total| < ε_tol, where z_NA_new represents the updated neutral axis position.

[0062] Once the total axial force has reached equilibrium and converged, calculate the section bending moment M_j corresponding to the current curvature κ_j according to the formula M = Σ[F_i × (z_i - z_NA)], and record the point (κ_j, M_j).

[0063] Record the curvature and section bending moment of the cross section of the hull beam under each curvature to generate the bending moment-curvature curve of the hull beam; Specifically, for each curvature step κ_j, after completing the aforementioned iterative equilibrium calculation and obtaining the corresponding cross-sectional bending moment M_j, the point (κ_j, M_j) is recorded in the data sequence. Connecting the points obtained from all curvature steps in ascending order of curvature yields the moment-curvature curve M(κ) of the hull beam. This curve typically starts from the origin, first passing through an elastic segment (where the bending moment and curvature have an approximately linear relationship), then entering an elastoplastic segment (where the curve slope gradually decreases), and finally reaching a peak and possibly entering a descending segment.

[0064] When the curvature of the cross section of the hull beam reaches or exceeds the preset maximum required curvature of the cross section of the hull beam, the peak value of the bending moment-curvature curve is extracted as the ultimate bending moment of the hull beam.

[0065] Specifically, continuously increase the curvature κ, repeating the curvature step calculation process described above, until κ ≥ κ_max. Among all recorded (κ, M) points, find the maximum bending moment M_u (M_u represents the ultimate bending moment of the hull beam), i.e., M_u = max{M(κ)}. This maximum value is the ultimate bending moment of the hull beam under the current load condition (camber or sag). If the curve is still in the rising segment at κ_max without a peak, increase κ_max and continue the calculation until a clear peak is captured.

[0066] In practical applications, this embodiment simulates the entire process of a ship's hull beam from elastic to plastic, and from buckling to failure, by gradually increasing the curvature, providing a clear understanding of the physical process. The effective cross-sectional area and buckling stress parameters of the elements calculated based on the variable thickness discrete model make the internal force response at each curvature step more accurate. The Newton-Raphson iterative method is used to ensure the balance of the total axial force at each curvature step, resulting in high calculation accuracy. The final generated moment-curvature curve fully reflects the evolution of the hull beam's load-bearing capacity, and the accurately extracted ultimate bending moment provides a reliable basis for ship structural strength assessment and lightweight design.

[0067] like Figure 2 As shown, in an optional embodiment of the present invention, the step of iteratively adjusting the neutral axis position of the hull beam cross section based on the effective cross-sectional area and the buckling critical stress of each structural unit under each curvature until the total axial force of the hull beam cross section is balanced, and determining the section bending moment of the hull beam cross section corresponding to the curvature includes: Based on the current curvature and the current neutral axis position, determine the axial strain of each structural unit; Specifically, let the current curvature be κ and the current neutral axis position be z_NA. For the i-th structural element in the cross section of the hull beam, with centroid height coordinate z_i, the axial strain ε_i of this structural element is calculated as follows: ε_i = κ × (z_i - z_NA). A positive value for ε_i indicates that the element is under tension, and a negative value indicates that the element is under compression. This formula is based on the plane section assumption, that is, the cross section of the hull beam remains planar after bending, and the strain of each element is linearly distributed along the section height.

[0068] Based on the buckling critical stress, the axial strain, and the preset stress-strain curve of each structural unit, the corresponding axial stress is determined; based on the axial stress and the effective cross-sectional area, the unit reaction force of the structural unit is determined. Specifically, the stress state of the i-th structural element is determined by the sign of its axial strain ε_i: if ε_i ≥ 0, the element is in a tensile state, and the axial stress σ_i is determined by calling the stress-strain curve under tensile conditions; if ε_i < 0, the element is in a compressive state, and the axial stress σ_i is determined by calling the corresponding stress-strain curve under compressive conditions according to the element type. The stress-strain curve under tensile conditions uses a bi-linear elastoplastic hardening model, the plate element under compressive conditions uses a Smith model correction curve, the stiffening element uses a linear transition model, and the combined element uses a weighted summation method. Then, the element reaction F_i is calculated using the following formula: F_i = σ_i × A_i, where A_i is the effective cross-sectional area of ​​the i-th structural element.

[0069] The total axial force is obtained by summing the unit reaction forces of all the structural units, and it is determined whether the total axial force is less than a preset threshold. Specifically, the total axial force F_total is equal to the algebraic sum of the reactions of all structural elements, that is: F_total = F1 + F2 + ... + F_n, where n is the total number of structural units. The absolute value of the total axial force F_total is checked against a preset axial force tolerance threshold ε_tol. This tolerance threshold is typically taken as one-thousandth to one-ten-thousandth of the total yield axial force in the cross section of the hull beam. If |F_total| < ε_tol (ε_tol represents the preset axial force tolerance threshold), the currently assumed neutral axis position is considered to meet the equilibrium condition; otherwise, the neutral axis position needs to be adjusted.

[0070] If so, determine the section bending moment corresponding to the current curvature based on the converged unit reaction force and the neutral axis position; Specifically, when the total axial force satisfies the equilibrium condition, the section bending moment M corresponding to the current curvature is calculated by the following formula: M = Σ [F_i × (z_i - z_NA)], which is the sum of the unit reaction force F_i of all structural elements multiplied by the distance (z_i - z_NA) from the centroid of the element to the neutral axis, where z_i is the height coordinate of the centroid of the i-th structural element, z_NA is the position of the neutral axis after convergence, and F_i represents the unit reaction force of the i-th structural element.

[0071] If not, adjust the position of the neutral axis and redetermine the axial strain of each structural unit, and determine the unit reaction force of the structural unit until the total axial force of all structural units is less than a preset threshold, so as to determine the section bending moment under the corresponding curvature.

[0072] Specifically, if the equilibrium condition is not met, the Newton-Raphson iterative method is used to adjust the neutral axis position. The correction Δz_NA is calculated as follows: Δz_NA = -F_total / K_total, where K_total is the total tangential stiffness, which is equal to the sum of the current tangential stiffnesses of all structural elements, i.e., K_total = Σ k_i, where k_i is the current tangential stiffness of the i-th structural element. The neutral axis position is updated: z_NA_new = z_NA_current + Δz_NA. Then, under the new neutral axis position, the axial strain, axial stress, and element reaction of each structural element are recalculated, and the total axial force is recalculated. The above iterative process is repeated until |F_total| < ε_tol, at which point the neutral axis position has converged, and the section bending moment corresponding to the current curvature is calculated according to the above formula.

[0073] In practical applications, this embodiment directly correlates curvature κ with strain ε_i of each element through the plane section assumption, providing a clear physical meaning. The conversion between strain ε_i and stress σ_i is based on the constitutive model recommended by the CSR-H standard, with corresponding processing methods for each element type, resulting in high calculation accuracy. The Newton-Raphson iterative method is used to adjust the neutral axis position, and the total tangential stiffness K_total is used for correction, resulting in fast convergence speed, typically requiring only three to five iterations to satisfy the equilibrium condition. The setting of the total axial force tolerance threshold ε_tol allows for flexible control of calculation accuracy, meeting practical engineering needs. The final obtained cross-sectional bending moment M reflects the true bending moment response of the hull beam cross-section under the current curvature κ, laying the foundation for subsequent generation of complete bending moment-curvature curves and extraction of ultimate bending moments.

[0074] like Figure 2 As shown, in an optional embodiment of the present invention, in a preset stress-strain curve, For each of the structural units, under tension, the preset stress-strain curve adopts a bilinear model that includes an elastic segment and a plastic hardening segment; Specifically, the stress-strain curve under tension is divided into two stages: the first stage is the elastic segment, when the axial strain ε does not exceed the yield strain ε. (ε) = σ / E, where σ When E is the yield strength of the material and E is the elastic modulus, the axial stress σ and axial strain ε satisfy Hooke's law, i.e., σ = E·ε; the second stage is the plastic hardening stage, when the axial strain ε exceeds the yield strain ε. Afterward, the material enters the plastic hardening stage, and the axial stress σ increases according to the linear hardening law, that is, σ = σ ·[1 + α·(ε-ε ) / ε ], where α is the strain hardening coefficient. To prevent the stress from increasing indefinitely, the maximum axial stress is limited to a preset multiple of the yield strength, typically not exceeding 1.1 times σ. .

[0075] For each of the structural units, under compression, the stress-strain curve of the structural unit is determined based on the buckling stress parameter corresponding to the structural unit; Specifically, the stress-strain curve under compression is determined using different methods depending on the element type: For a plate element, the plate flexibility coefficient β is first calculated based on the plate element thickness t and the plate width b. The calculation formula is as follows: ; Then, the critical buckling stress σ_c of the plate element is calculated according to the segmented formula in the CSR-H standard. The compressive stress-strain curve of the plate element adopts the modified curve of the Smith model, which is divided into three stages: the pre-buckling stage, when the axial strain ε is less than the critical buckling strain ε_c. (ε_c) = σ_c When / E), the axial stress σ = E·ε; in the post-buckling transition stage, when the axial strain ε is at ε_c To yield strain ε Between these points, the axial stress σ follows a parabolic form from σ_c Transition to σ In the post-yield stage, when the axial strain ε exceeds ε Afterwards, the axial stress remains at σ. .

[0076] For the stiffening element, firstly, based on the cross-sectional properties (cross-sectional area A, moment of inertia I) and effective length L of the stiffening element, calculate the Euler critical stress σ_E using the Euler formula, i.e., σ_E = π²·E·I / (A·L²). Then, combine this with the material yield strength σ The relative compliance is calculated, and then the critical buckling stress σ_c of the stiffening element is determined according to the CSR-H standard. The compressive stress-strain curve of the reinforcing element adopts a simplified linear transition model, which is divided into two stages: the pre-buckling stage, when the axial strain ε is less than the critical buckling strain ε_c. At that time, the axial stress σ = E·ε; during the post-buckling curve transition stage, when the axial strain ε exceeds ε_c Afterwards, the axial stress σ is at the buckling critical stress σ_c With yield stress σ The distance between them is determined by linear interpolation.

[0077] For reinforced member elements with plates, the stress-strain curve under compression is not determined by a single formula, but by a weighted summation method. Specifically, the axial stress σ_ of the plate portion is calculated separately. p Axial stress σ_ of the reinforcing member s The effective width ratio ψ of the calculation plate is used to reduce the effective area of ​​the plate. Then, the axial stress σ_c of the composite element is obtained by weighted summation. The calculation formula is: σ_c = (σ_ p ·A_ p ·ψ + σ_ s ·A_ s ) / (A_ p ·ψ + A_ s ).

[0078] Wherein, when the axial strain of the structural unit exceeds a preset ultimate strain threshold, the axial stress of the structural unit decreases to a preset residual strength threshold.

[0079] Specifically, a unified failure criterion is defined for all types of structural elements: when the absolute value of the axial strain ε of the structural element exceeds a preset ultimate strain threshold ε_ l When the residual stress drops to 0.15 (typically 15%), the element is considered to have failed. A failed element does not completely lose its load-bearing capacity but retains a certain residual strength, i.e., the axial stress decreases to the residual strength threshold multiplied by the material's yield strength. The residual strength coefficient is typically taken as 0.2, i.e., σ_ = 0.2·σ .

[0080] In practical applications, this embodiment employs a bilinear hardening model for the tensile state, accurately simulating the strain hardening behavior of steel after yielding, while avoiding overly optimistic estimations by limiting the maximum stress. For the compressive state, different element types are modeled separately. Plate elements use a parabolic post-buckling model to reflect their high load-bearing capacity after buckling, while stiffener elements use a linear transition model to represent the rapid decrease in load-bearing capacity after overall instability. Combined elements accurately simulate the mechanical behavior of the plate and stiffener working together through weighted summation. The failure criteria use ultimate strain and residual strength thresholds, considering both the material's ultimate deformation capacity and avoiding numerical instability caused by complete element failure. This stress-strain curve system fully complies with the CSR-H specification requirements and provides accurate mechanical constitutive relationships for subsequent incremental iterative calculations.

[0081] like Figure 2 As shown, in an optional embodiment of the present invention, the adjustment of the neutral axis position of the hull beam cross section adopts the Newton-Raphson iterative method, wherein the correction amount of each iteration is determined according to the ratio of the total axial force of the current hull beam cross section to the total tangential stiffness of the hull beam cross section. The total tangential stiffness is obtained by summing the current tangential stiffness of each structural unit, and the current tangential stiffness is determined according to the buckling critical stress and the effective cross-sectional area of ​​the structural unit.

[0082] Specifically, at each curvature step, the process of iteratively adjusting the position of the neutral axis until the total axial force is balanced is as follows: Let the total axial force at the current curvature step be F_total, which is a function of the neutral axis position z_NA. The Newton-Raphson iterative method is used to find the neutral axis position that makes the total axial force zero. In the Kth iteration, the correction Δz_NA is equal to the negative total axial force of the Kth step divided by the total tangential stiffness of the Kth step, that is: Δz_NA=-F_total_K / K_total_K.

[0083] Where F_total_K is the total axial force calculated at the current neutral axis position z_NA_K during the Kth iteration; K_total_K is the total tangential stiffness of the hull beam cross section during the Kth iteration.

[0084] The total tangential stiffness K_total is equal to the sum of the current tangential stiffness k_i of all structural elements, that is: K_total=Σk_i.

[0085] For each structural element, its current tangential stiffness is defined as the derivative of the axial stress σ with respect to the axial strain ε, that is: k_i = dσ_i / dε_i, which is the slope of the tangent line on the stress-strain curve of this element. Depending on the type of structural element, the current tangent stiffness is determined according to the following rules: For a plate element, the current tangential stiffness is determined by the buckling critical stress σ_cr, which is determined by the thickness of the plate element, and the effective cross-sectional area. In the elastic stage, the current tangential stiffness is equal to the elastic modulus E; in the post-buckling parabolic transition stage, the current tangential stiffness gradually decreases with increasing strain; in the yield plateau stage, the current tangential stiffness approaches zero.

[0086] For a stiffening element, the current tangential stiffness is determined by the Euler critical stress σ_E, which is determined by the thickness of the stiffening element, and the effective cross-sectional area. In the elastic stage, the current tangential stiffness is equal to the elastic modulus E; in the post-buckling elastic transition stage, the current tangential stiffness gradually decreases with increasing strain.

[0087] For a plate-stiffening element, its current tangential stiffness is obtained by weighted summation of the tangential stiffness of the plate portion and the tangential stiffness of the stiffening element based on the effective cross-sectional area, wherein the effective cross-sectional area of ​​the plate portion needs to be reduced by the effective width.

[0088] Update the neutral axis position: The neutral axis position z_NA_{K+1} at step K+1 is equal to the neutral axis position z_NA_K at step K plus the correction amount Δz_NA at step K, that is: z_NA_{K+1}=z_NA_K+Δz_NA.

[0089] Repeat the above iterative process until the absolute value of the total axial force is less than the preset axial force tolerance threshold ε_tol, i.e., |F_total| < ε_tol. This tolerance threshold is usually taken as one-thousandth to one-ten-thousandth of the total yield axial force of the hull beam cross section.

[0090] In practical applications, this embodiment employs the Newton-Raphson iterative method to adjust the neutral axis position, offering advantages such as fast convergence, strong adaptability, synergistic optimization with variable thickness models, and good engineering feasibility. Correction using the total tangent stiffness typically requires only three to five iterations to reach equilibrium; it effectively handles nonlinear behavior where tangent stiffness approaches zero near the limit state, stably tracks the buckling descent segment, and ensures complete capture of the peak value of the moment-curvature curve; synergistic optimization with variable thickness models precisely drives the offset of regions with stronger neutral axis stiffness based on non-uniform stiffness distribution, resulting in a neutral axis position and ultimate bending moment that better reflect physical reality; this method is stable, reliable, easy to program, and meets the accuracy and efficiency requirements of engineering design.

[0091] To evaluate the rationality and reliability of the hull beam ultimate strength calculation method and software developed in this paper, the ultimate strength calculation of the midship section structure of a bulk carrier was performed using the hull beam ultimate strength calculation software developed in this paper; see Tables 1 and 2 for details.

[0092] Table 1 - Structural Unit Parameter Table

[0093] Table 2 - Calculation results and comparison of ultimate strength of a bulk carrier (*10) 7 kNm)

[0094] To verify the rationality and reliability of the proposed method for assessing the ultimate strength of ship structures based on variable thickness steel plates, this invention uses a cross-section of a bulk carrier's midship section as a specific example. A discrete structural unit model (as shown in Table 1) containing 14 different types (flat steel, T-beams, and angle steel) and corresponding yield strength parameters was constructed, and ultimate strength calculations were performed based on this model. The calculation results (as shown in Table 2) indicate that the ultimate bending moment of the midship arch calculated by the method of this invention (original structure 1.48 × 10⁻⁶) is within the acceptable range. 7 kN·m, variable thickness 1.44×10 7 kN·m) and the vertical ultimate bending moment (both 1.35×10) 7 kN·m), compared with the results reported by Chen, Cho, Masaoka, Rigo, etc. (medium arch 1.71~1.91×10). 7 kN·m, sag 1.37~1.60×10 7 The overall trend of the bending moment (kN·m) is consistent. Meanwhile, the ultimate bending moment of the variable thickness structure (1.44) is slightly lower than that of the original structure (1.48), indicating that the present invention can accurately capture the mechanical performance differences brought about by the variable thickness design, avoid the risk of overestimation that may be brought about by traditional simplification methods (such as the average thickness method), and verify the reliability and accuracy of the method of the present invention in engineering applications.

[0095] like Figure 3 As shown, the present invention also provides a ship structure ultimate strength assessment system 200 based on variable thickness steel plates, which applies the ship structure ultimate strength assessment method based on variable thickness steel plates as described in the above embodiments, including: The variable thickness determination module 210 is used to: discretize the cross section of the hull beam into multiple structural units, and determine the thickness value of each structural unit according to the preset variable thickness design rules. The parameter determination module 220 is used to: determine the effective cross-sectional area and buckling stress parameters of each structural unit based on the thickness value and structural parameters of each structural unit; The ultimate bending moment assessment module 230 is used to: use the effective cross-sectional area and the buckling stress parameter as mechanical parameters, and adopt an incremental iteration method to determine the ultimate bending moment of the hull beam.

[0096] The specific implementation method of this embodiment can be referred to the corresponding implementation method described above, and will not be described again here.

[0097] like Figure 4 As shown, an electronic device 300 provided in this embodiment of the invention includes a memory 310 and a processor 320; the memory 310 is used to store a computer program; the processor 320 is used to implement the above-described method for evaluating the ultimate strength of ship structures based on variable thickness steel plates when the computer program is executed.

[0098] Alternatively, an electronic device 300 includes a memory 310 and a processor 320 coupled to the memory 310; the memory 310 is configured to store a computer program; and the processor 320 is configured to perform the following operations when the computer program is executed: The cross section of the hull beam is discretized into multiple structural units, and the thickness value of each structural unit is determined according to a preset variable thickness design rule. Based on the thickness value and structural parameters of each structural unit, determine the effective cross-sectional area and buckling stress parameters of each structural unit; Using the effective cross-sectional area and the buckling stress parameter as mechanical parameters, the ultimate bending moment of the hull beam is determined by an incremental iteration method.

[0099] This invention provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it implements the above-described method for evaluating the ultimate strength of ship structures based on variable thickness steel plates.

[0100] Alternatively, a non-volatile computer-readable storage medium storing a computer program that, when executed by a processor, causes the processor to perform the following operations: The cross section of the hull beam is discretized into multiple structural units, and the thickness value of each structural unit is determined according to a preset variable thickness design rule. Based on the thickness value and structural parameters of each structural unit, determine the effective cross-sectional area and buckling stress parameters of each structural unit; Using the effective cross-sectional area and the buckling stress parameter as mechanical parameters, the ultimate bending moment of the hull beam is determined by an incremental iteration method.

[0101] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided by this invention can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0102] The above description is merely a specific embodiment of the present invention, enabling those skilled in the art to understand or implement the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the present invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features of the invention herein.

[0103] While the present invention has been disclosed above, its scope of protection is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention, and all such changes and modifications will fall within the scope of protection of the present invention.

Claims

1. A method for evaluating ultimate strength of a ship structure based on a variable thickness steel plate, characterized by, include: The cross section of the hull beam is discretized into multiple structural units, and the thickness value of each structural unit is determined according to a preset variable thickness design rule. Based on the thickness value and structural parameters of each structural unit, determine the effective cross-sectional area and buckling stress parameters of each structural unit; Using the effective cross-sectional area and the buckling stress parameter as mechanical parameters, the ultimate bending moment of the hull beam is determined by an incremental iteration method.

2. The method for evaluating the ultimate strength of a variable thickness steel plate based ship structure according to claim 1, characterized in that, The step of determining the thickness value of each structural unit according to the preset variable thickness design rules includes: Based on the position coordinates of the structural unit in the cross section of the hull beam and the preset position-thickness correspondence, the thickness value of the corresponding structural unit is determined. The preset position-thickness correspondence includes a position-thickness correspondence that is continuously and gradually changed and / or stepped.

3. The method for evaluating the ultimate strength of ship structures based on variable thickness steel plates according to claim 2, characterized in that, The step of determining the thickness value of the corresponding structural unit based on the position coordinates of the structural unit in the cross section of the hull beam and a preset position-thickness correspondence includes: Obtain the centroid height coordinates of the structural unit, the bottom height of the hull beam and the corresponding bottom plate design thickness, as well as the deck height and the corresponding deck design thickness; Based on the relative position ratio of the centroid height coordinates within the range formed by the bottom height and the deck height, the bottom plate design thickness and the deck design thickness are linearly interpolated to determine the thickness value, and this thickness value is determined as the thickness value of the corresponding structural unit.

4. The method for evaluating the ultimate strength of ship structures based on variable thickness steel plates according to claim 2, characterized in that, The step of determining the thickness value of the corresponding structural unit based on the position coordinates of the structural unit in the cross section of the hull beam and a preset position-thickness correspondence includes: Based on the design layout drawing of the cross section of the hull beam, the one-to-one correspondence between each constant thickness value in the thickness list and the transverse coordinate interval is determined; wherein, the transverse coordinate interval is a number of continuous coordinate ranges divided in the transverse width, and each transverse coordinate interval corresponds to a constant thickness value. Obtain the lateral coordinates of the structural unit; Based on the horizontal coordinate range into which the horizontal coordinate falls, the corresponding constant thickness value is read from the thickness list, and the constant thickness value is determined as the thickness value of the corresponding structural unit.

5. The method for assessing the ultimate strength of ship structures based on variable thickness steel plates according to any one of claims 1-4, characterized in that, The structural units include plate units, stiffening member units, and stiffening member units with plate reinforcement. The step of determining the effective cross-sectional area and buckling stress parameters of each structural unit based on its structural parameters and thickness includes: For the plate element, the effective cross-sectional area and plate flexibility coefficient of the plate element are determined based on the thickness value of the plate element, and then the buckling critical stress of the plate element is determined. For the reinforcing element, the cross-sectional properties of the reinforcing element are determined based on its thickness value. The cross-sectional properties include cross-sectional area and moment of inertia, thereby determining the Euler critical stress of the reinforcing element. For the plate-stiffening element unit, the effective cross-sectional area of ​​the plate portion and the effective cross-sectional area of ​​the stiffening element are determined according to their thickness values. The effective cross-sectional area of ​​the plate portion is reduced by the effective width and then summed with the effective cross-sectional area of ​​the stiffening element to obtain the effective cross-sectional area of ​​the combined unit. The axial stress of the plate portion and the axial stress of the stiffening element are determined according to the buckling critical stress of the plate portion and the Euler critical stress of the stiffening element, respectively. The combined stress of the combined unit is then obtained by weighted summation of the effective cross-sectional areas.

6. The method for assessing the ultimate strength of ship structures based on variable thickness steel plates according to any one of claims 1-4, characterized in that, The step of using the effective cross-sectional area and buckling stress parameters as mechanical parameters and employing an incremental iteration method to determine the ultimate bending moment of the hull beam includes: Based on the effective cross-sectional area of ​​each structural unit and the centroid position of each structural unit, the elastic section modulus of the hull beam cross section is determined, and the initial neutral axis position of the hull beam cross section is determined based on the elastic section modulus. Starting from the preset initial curvature of the cross section of the hull beam, the preset curvature increment of the cross section of the hull beam is gradually increased to enter the next curvature. Under each curvature, based on the effective cross-sectional area and the buckling critical stress of each structural unit, the neutral axis position of the cross section of the hull beam is iteratively adjusted until the total axial force of the cross section of the hull beam is balanced, and the section bending moment of the cross section of the hull beam corresponding to the curvature is determined. Record the curvature and section bending moment of the cross section of the hull beam under each curvature to generate the bending moment-curvature curve of the hull beam; When the curvature of the cross section of the hull beam reaches or exceeds the preset maximum required curvature of the cross section of the hull beam, the peak value of the bending moment-curvature curve is extracted as the ultimate bending moment of the hull beam.

7. The method for evaluating the ultimate strength of ship structures based on variable thickness steel plates according to claim 6, characterized in that, Under each curvature, based on the effective cross-sectional area and the critical buckling stress of each structural unit, the neutral axis position of the hull beam cross section is iteratively adjusted until the total axial force of the hull beam cross section is balanced. The section bending moment of the hull beam cross section corresponding to that curvature is determined by: The axial strain of each structural unit is determined based on the current curvature and the current neutral axis position. Based on the buckling critical stress, the axial strain, and the preset stress-strain curve of each structural unit, the corresponding axial stress is determined; based on the axial stress and the effective cross-sectional area, the unit reaction force of the structural unit is determined. The total axial force is obtained by summing the unit reaction forces of all the structural units, and it is determined whether the total axial force is less than a preset threshold. If so, determine the section bending moment corresponding to the current curvature based on the converged unit reaction force and the neutral axis position; If not, adjust the position of the neutral axis and redetermine the axial strain of each structural unit, and determine the unit reaction force of the structural unit until the total axial force of all structural units is less than a preset threshold, so as to determine the section bending moment under the corresponding curvature.

8. The method for evaluating the ultimate strength of ship structures based on variable thickness steel plates according to claim 7, characterized in that, In the preset stress-strain curve, For each of the structural units, under tension, the preset stress-strain curve adopts a bilinear model that includes an elastic segment and a plastic hardening segment; For each of the structural units, under compression, the stress-strain curve of the structural unit is determined based on the buckling stress parameter corresponding to the structural unit; Wherein, when the axial strain of the structural unit exceeds a preset ultimate strain threshold, the axial stress of the structural unit decreases to a preset residual strength threshold.

9. The method for evaluating the ultimate strength of ship structures based on variable thickness steel plates according to claim 6, characterized in that, The adjustment of the neutral axis position of the hull beam cross section adopts the Newton-Raphson iterative method, wherein the correction amount of each iteration is determined according to the ratio of the total axial force of the current hull beam cross section to the total tangential stiffness of the hull beam cross section. The total tangential stiffness is obtained by weighted summation of the current tangential stiffness of each structural unit. The current tangential stiffness is determined according to the buckling critical stress and the effective cross-sectional area of ​​the structural unit.

10. A system for assessing the ultimate strength of ship structures based on variable thickness steel plates, characterized in that, The method for assessing the ultimate strength of ship structures based on variable thickness steel plates as described in any one of claims 1-9 includes: The variable thickness determination module is used to: discretize the cross section of the hull beam into multiple structural units, and determine the thickness value of each structural unit according to the preset variable thickness design rules; The parameter determination module is used to: determine the effective cross-sectional area and buckling stress parameters of each structural unit based on the thickness value and structural parameters of each structural unit; The ultimate bending moment assessment module is used to determine the ultimate bending moment of the hull beam by using the effective cross-sectional area and the buckling stress parameter as mechanical parameters and employing an incremental iteration method.

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