A ship variable thickness steel plate optimization design method based on simulated annealing algorithm

Abstract

The application discloses a kind of ship variable thickness steel plate optimization design method based on simulated annealing algorithm, belong to ship structure design technical field.The existing technology in traditional ship steel plate optimization design method is solved because of the stiffness mutation resulting in the problem of poor optimization effect;The application is defined to the continuous change thickness field for ship grid division unit and node set, the ship node finite element model is established by finite element solver, and the stress distribution of each node under design condition is extracted;Define and simplify design variable, construct objective function and constraint condition;Combined with the stress distribution of each node under design condition, the ship node finite element model is optimized and iterated using simulated annealing algorithm;Through the optimized ship node finite element model, the optimal thickness distribution scheme is output, and the thickness between nodes in the scheme is smoothly transitioned by linear interpolation.The application avoids the structural redundancy caused by ship steel plate optimization design, and can be applied to ship structure lightweight.

Description

Technical Field

[0001] This invention relates to an optimization design method for variable thickness steel plates in ships, and more particularly to an optimization design method for variable thickness steel plates in ships based on simulated annealing algorithm, belonging to the field of ship structural design technology. Background Technology

[0002] The shipbuilding industry is a modern comprehensive industry, providing essential technical equipment for marine development, water transportation, energy transportation, and economic construction. It is an indispensable and crucial component of the manufacturing sector. The development direction of the shipbuilding industry is green and intelligent, aiming to enhance the modernization level of the industrial chain and supply chain, promote the optimization and upgrading of the manufacturing industry, and comprehensively drive economic development. Currently, efforts are being made to build an advanced ship assembly and construction system, accelerate the digital transformation of ship assembly and construction, increase the market promotion of high-end, green, and intelligent ship types, consolidate and enhance the market share of high-tech, high-value-added products, deepen lean shipbuilding, follow the path of new industrialization, and improve the overall competitiveness of the shipbuilding industry.

[0003] To improve shipbuilding efficiency, reduce structural weight, promote green, low-carbon, and high-quality development in the shipbuilding industry, and enhance the overall competitiveness of the shipbuilding sector, longitudinally profiled steel plates (LP plates) hold significant importance in future shipbuilding. Through special rolling and controlled cooling processes, LP plates achieve different thicknesses at both ends while maintaining uniform and stable performance. LP plates exhibit more uniform performance along the longitudinal direction, reducing weld seams and improving shipbuilding efficiency compared to welding methods for transitioning between different thickness sections in the structure. Furthermore, their linear matching of structural loads reduces structural weight, making them an effective choice for lightweight shipbuilding.

[0004] Ship structure optimization, as a crucial link in lightweight design, has gradually highlighted its importance. Ship structure optimization has gradually developed based on the lightweight needs, performance assurance requirements, cost control objectives, and technological development support of the shipbuilding industry. Its core is to reasonably reduce the thickness of steel plates under the premise of meeting the safety performance of ship strength, stiffness, corrosion resistance, etc., so as to maximize the benefits of the ship's entire life cycle. According to the ship type, node stress characteristics and manufacturing process requirements, the traditional ship node steel plate thickness design methods include the empirical analogy method and the partition thickness design method. The specific problems are as follows: (1) The empirical analogy method is based on the node thickness data of similar ships. It is suitable for simple nodes of conventional ships. Although it is convenient to operate and has a short design cycle, it lacks scientific theoretical support and the design reliability depends on experience. This method is entirely based on the past experience of designers and lacks systematic mechanical analysis and numerical calculation as support. If the subjectivity is strong and the randomness is large, if the designer is not experienced or does not fully understand the actual operation and failure cases of similar ships, it is easy to cause the thickness parameter selection deviation; (2) The partition thickness design method divides several thickness partitions according to the overall stress level of the area where the node is located. It is suitable for nodes with relatively regular structural forms. Although it simplifies the manufacturing process, the thickness transition is not reasonable and the numerical calculation stability is poor. The partition thickness change method often adopts the "step-like" thickness change design. The thickness difference between adjacent partitions directly leads to the discontinuity of the node stiffness matrix. In finite element analysis, it is easy to cause numerical singularity, convergence difficulty and other problems, which distort the calculation results and cannot reflect the real stress state of the structure. Although the fixed gradient thickness method attempts to achieve thickness transition, the gradient value is preset by human and lacks mechanical basis. There may still be stress concentration or stiffness change in the transition area. It cannot adapt to the characteristics of local stress concentration of the node and has the risk of weight waste and fatigue.

[0005] Variable thickness optimization is a refined structural design technology developed based on constant thickness design, combined with the stress differences, functional requirements, and manufacturing processes of different parts of the hull. Its core goal is to achieve "thickness as needed, thicker in strong areas, and thinner in weak areas," maximizing the benefits of lightweighting while ensuring structural safety. Using finite element software such as Abaqus, a full-scale or local fine model of the hull is established to simulate the stress distribution of the ship under various working conditions such as still water, waves, and collisions, clarifying the stress level and failure risk of each plate unit, and providing a quantitative basis for variable thickness zoning. Unit nodes are the core hubs for load transfer in the hull. The stress levels in node areas such as longitudinal skeleton-outer plate and deck-side are much higher than in ordinary plate and shell areas. Traditional constant thickness design cannot adapt to this local high stress characteristic, which easily leads to stress concentration and then structural fatigue cracking. Variable thickness node design allows for targeted thickening of high-stress node-related units while thinning of low-stress node areas, achieving precise thickness distribution with "thicker in strong areas and thinner in weak areas." This keeps node stress within acceptable limits, significantly reducing the risk of structural fatigue failure. Compared to "regional equal thickness" optimization, variable thickness node design represents unit-level refined optimization. It allows for precise thinning of non-critical node areas while ensuring the strength of critical nodes, avoiding weight redundancy from overall thickening. The reduction in hull weight directly increases cargo capacity and range, while reducing fuel consumption, aligning with the shipping industry's energy conservation and emission reduction policies, achieving a dual reduction in construction costs (reduced steel usage) and operating costs (reduced fuel consumption). Variable thickness node design treats the thickness of each node-related unit as an independent design variable, which, combined with simulated annealing intelligent optimization algorithms, achieves multi-objective collaborative optimization of "strength-stiffness-lightweighting-cost." Compared to the variable dimensional limitations of traditional regional optimization, node-level thickness variables can more flexibly explore the design space, finding better Pareto solutions and meeting the high-performance design requirements of special-purpose vessels.

[0006] In summary, a method for optimizing the design of variable thickness steel plates for ships based on simulated annealing algorithms is needed. Summary of the Invention

[0007] A brief overview of the invention is given below to provide a basic understanding of certain aspects of it. It should be understood that this overview is not an exhaustive summary of the invention. It is not intended to identify key or essential parts of the invention, nor is it intended to limit the scope of the invention. Its purpose is merely to present certain concepts in a simplified form as a prelude to the more detailed description that follows.

[0008] In view of this, in order to solve the problem that the optimization effect of traditional ship steel plate optimization design methods in the prior art is poor due to the sudden change in stiffness, the present invention provides a ship variable thickness steel plate optimization design method based on simulated annealing algorithm.

[0009] The technical solution is as follows: A method for optimizing the design of variable thickness steel plates for ships based on simulated annealing algorithm, comprising the following steps:

[0010] S1. For the ship mesh generation unit and node set, define the continuously changing thickness field, establish the ship node finite element model through the finite element solver, and extract the stress distribution of each node under the design conditions.

[0011] S2. Taking into account production process constraints, define and simplify the design variables of the ship node finite element model, construct the objective function of the ship node finite element model and the constraints for optimizing the ship node finite element model;

[0012] S3. Initialize the simulated annealing algorithm parameters. Based on the objective function and constraints, and combined with the stress distribution of each node under the design conditions, the simulated annealing algorithm is used to optimize and iterate the finite element model of the ship nodes.

[0013] S4. After the iteration terminates, the optimal thickness distribution scheme is output through the optimized ship node finite element model, and the thickness between nodes in the scheme is smoothly transitioned through linear interpolation.

[0014] Furthermore, in S1, based on the theory of variable thickness shell elements, the shape, nodes, and corresponding thickness values ​​of the variable thickness shell elements used in the ship mesh are defined, and interpolation is performed within the elements using the shape functions used by the variable thickness shell elements to obtain a continuously changing thickness field. ;

[0015] Continuously changing thickness field Represented as:

[0016]

[0017] in, For shape functions, For the first The thickness value of each node, Let any point be within the variable thickness shell element;

[0018] Reference continuously varying thickness field The stiffness matrix is ​​calculated using a finite element solver. During the process, ,in, The strain-displacement matrix, Let T be the material constitutive matrix, and T be the matrix transpose, so that the thickness value changes continuously with the coordinates. The finite element solver completes the construction of the ship node finite element model.

[0019] Furthermore, in S2, considering the production process limitations of variable thickness steel plates for ships, the thickness of the same column of nodes perpendicular to the rolling direction is set to a uniform value, and only the thickness of different columns of nodes in the rolling direction is retained as an independent design variable. Based on the n columns of nodes along the rolling direction of the variable thickness steel plate for ships, the design variable vector X is defined.

[0020] The design variable vector X is represented as:

[0021]

[0022] in, Indicates the first The thickness of the steel plate at the column node;

[0023] Combined with continuously varying thickness field This will minimize the total weight of the ship's variable thickness steel plates. As the objective function of the ship node finite element model;

[0024] The objective function of the ship node finite element model is expressed as:

[0025]

[0026] in, This represents the total number of elements in the ship's nodal finite element model. For material density, Let be the thickness function at any point within the variable thickness shell element. This is the integration region for the variable thickness shell element;

[0027] By combining mechanical performance constraints and manufacturing process constraints, constraints are constructed to optimize the finite element model of ship nodes;

[0028] Constraints Represented as:

[0029]

[0030] in, For the allowable stress of steel, This is the maximum displacement limit. This represents the distance between adjacent nodes along the rolling direction. This represents the maximum thickness variation rate during the rolling process. Minimum wall thickness, For the maximum wall thickness, For the first The thickness of the steel plate for the column nodes.

[0031] Furthermore, in S3, initializing the simulated annealing algorithm parameters involves generating a new solution through small-amplitude local perturbations, increasing the node thickness in high-stress regions, and thinning the node thickness in low-stress regions, while ensuring the thickness is not less than the minimum wall thickness. This forms the initial thickness scheme;

[0032] During the initial thickness scheme generation process, the constraints of the ship node finite element model are satisfied, ensuring that the thickness change rate of adjacent columns of nodes does not exceed the maximum allowable thickness gradient, and that the node thickness perpendicular to the rolling direction remains consistent. After the strength and stiffness are verified by the finite element solver and the constraints are satisfied, the lighter feasible solution is preferentially accepted according to the objective function of the ship node finite element model. At high temperatures, a heavier feasible solution is accepted to escape local optima. The energy difference obtained is determined using the Metropolis criterion. The reception probability is calculated. According to the reception probability The process is iterated until the temperature drops to the termination value, at which point the iteration stops, and all received feasible solutions are identified and recorded.

[0033] Energy difference Represented as:

[0034]

[0035] in, For the newly generated feasible solution, This is the current feasible solution;

[0036] Receive probability The calculation formula is:

[0037]

[0038] in, Boltzmann's constant, s This refers to the current annealing temperature parameter.

[0039] The beneficial effects of the present invention are as follows: (1) Achieving precise thickness matching at the node level, significantly improving structural safety and durability: Traditional methods use "partitioning" or "empirical values" as design basis, which cannot match the stress distribution of highly concentrated local nodes, and are prone to the contradiction of "thin where strong and thick where weak". The present invention takes unit nodes and associated plate units as the minimum optimization objects, sets the thickness of each node as an independent design variable, and combines the global search capability of simulated annealing algorithm to specifically thicken high stress nodes and thin low stress nodes, so that the node stress is completely controlled within the allowable range, eliminating the hidden danger of stress concentration at nodes, reducing the risk of fatigue cracking of the hull structure, greatly improving the service durability of ship nodes, and avoiding structural redundancy caused by over-design in traditional methods; (2) Ensuring the stability of finite element calculation and improving the reliability of simulation results: The "step-like" thickness mutation of traditional partitioned thickness design is prone to problems such as numerical singularity, negative eigenvalues, and convergence difficulties in finite element models, resulting in distortion of simulation results. By embedding thickness gradient approximation in the neighborhood search strategy of simulated annealing algorithm, the present invention can achieve the desired results. The bundle automatically generates a smooth thickness transition scheme for linear / spline interpolation between nodes, ensuring that the thickness difference between adjacent elements meets the mechanical continuity requirements. This invention can avoid numerical calculation anomalies from the design source, improve the calculation stability and result accuracy of finite element software such as Abaqus, reduce calculation interruptions caused by numerical problems, and reduce the time cost of simulation verification; (3) Maximize the lightweight benefits and reduce ship construction costs and operating energy consumption: Traditional gradient optimization algorithms are prone to getting trapped in local optima and are difficult to achieve self-weight minimization under strength constraints; the empirical analogy method often retains too much thickness redundancy to ensure safety. This invention relies on the global optimization characteristics of the simulated annealing algorithm to explore the optimal thickness distribution scheme in the whole domain under multiple constraints. Under the premise of meeting the strength, stiffness, and classification society specifications, it can achieve precise reduction of the self-weight of the hull node area. This invention reduces the amount of steel used and reduces the ship construction cost; at the same time, it reduces the overall self-weight of the hull, increases the ship's cargo capacity and endurance, and reduces fuel consumption, which meets the requirements of energy conservation and emission reduction in the shipping industry.

[0040] In summary, this invention takes the unit nodes and associated plate units of the ship node as the minimum optimization object, and sets the thickness of different columns of nodes in the steel plate rolling direction as an independent design variable, thereby achieving "precise thickness matching at the node level". Attached Figure Description

[0041] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings:

[0042] Figure 1 This is a flowchart illustrating an optimization design method for variable thickness steel plates in ships based on simulated annealing algorithms.

[0043] Figure 2 is a simplified schematic diagram of the steel plate node, where (a) is a schematic diagram of the bottom side compartment node and (b) is a simplified schematic diagram of the bottom side compartment node.

[0044] Figure 3 This is a schematic diagram of the optimal solution for the thickness of each node in the optimized steel plate;

[0045] Figure 4 shows the stress diagrams of the steel plate before and after optimization, where (a) is the stress diagram of the steel plate before optimization and (b) is the stress diagram of the steel plate after optimization. Detailed Implementation

[0046] To make the technical solutions and advantages of the embodiments of the present invention clearer, the exemplary embodiments of the present invention will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not an exhaustive list of all embodiments. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0047] refer to Figure 1 Figure 4 illustrates this embodiment, a method for optimizing the design of variable thickness steel plates for ships based on simulated annealing algorithms, specifically including the following steps:

[0048] S1. For the ship mesh generation unit and node set, define the continuously changing thickness field, establish the ship node finite element model through the finite element solver, and extract the stress distribution of each node under the design conditions.

[0049] S2. Taking into account production process constraints, define and simplify the design variables of the ship node finite element model, construct the objective function of the ship node finite element model and the constraints for optimizing the ship node finite element model;

[0050] S3. Initialize the simulated annealing algorithm parameters. Based on the objective function and constraints, and combined with the stress distribution of each node under the design conditions, the simulated annealing algorithm is used to optimize and iterate the finite element model of the ship nodes.

[0051] S4. After the iteration terminates, the optimal thickness distribution scheme is output through the optimized ship node finite element model, and the thickness between nodes in the scheme is smoothly transitioned through linear interpolation.

[0052] Specifically, referring to Figure 2, the Y-axis direction is the steel plate rolling direction, and the X-axis direction is the direction perpendicular to the rolling direction. Ensure that the node thickness in the X-axis direction is equal, and the numbers are the node numbers automatically generated by Abaqus.

[0053] refer to Figure 3 Nodal-Thickness represents the node thickness, with units of meters (m), and Node represents a node.

[0054] Referring to Figure 4, S, Mises represents Von Mises stress, i.e., equivalent stress;

[0055] The optimal thickness scheme includes: the node thickness values ​​corresponding to each independent design variable (arranged by rolling direction); finite element analysis results: total structural weight, stress distribution cloud maps of key parts (deck, longitudinal girder, keel, etc.), and displacement data of key parts; constraint satisfaction verification report: clearly defining the degree of satisfaction of the maximum principal stress, maximum displacement, and process constraints, and explaining the safety and feasibility of the optimal scheme.

[0056] Furthermore, in S1, based on the theory of variable thickness shell elements, the shape, nodes, and corresponding thickness values ​​of the variable thickness shell elements used in the ship mesh are defined, and interpolation is performed within the elements using the shape functions used by the variable thickness shell elements to obtain a continuously changing thickness field. ;

[0057] Continuously changing thickness field Represented as:

[0058]

[0059] in, For shape functions, For the first The thickness value of each node, Let any point be within the variable thickness shell element;

[0060] Reference continuously varying thickness field The stiffness matrix is ​​calculated using a finite element solver (such as Abaqus). During the process, ,in, The strain-displacement matrix, The material constitutive matrix is ​​T, which is the matrix transpose. This allows the thickness value to change continuously with the coordinates, achieving a smooth physical transition and avoiding abrupt changes in stiffness at the nodes. The finite element model of the ship's nodes is then constructed using a finite element solver.

[0061] Specifically, in this embodiment, by introducing node thickness variables, a numerical model of the transverse section of a bulk carrier is established in finite element software. The stress distribution of key parts such as the deck, longitudinal girder, and keel of the bulk carrier under the condition of full-load departure is analyzed, and weak areas of the structure are identified, providing a numerical simulation basis and stress state assessment for subsequent variable thickness optimization.

[0062] In a standard equal-thickness shell element, the degrees of freedom of a node typically include only translational displacements. and rotational displacement ,in, This represents the translational displacement along the X-axis. This represents the translational displacement along the Y-axis. This represents the translational displacement along the Z-axis. This represents the rotational displacement along the X-axis. The rotational displacement is along the Y-axis. The rotational displacement is along the Z-axis. The variable-thickness shell element theory treats thickness as a field variable that needs to be defined. This is achieved by discretizing the shell element thickness and assigning different thickness values ​​to each node of the shell element, rather than giving the entire element or section a constant value. In this embodiment, the bulk carrier mesh uses standard quadrilateral shell elements. A standard quadrilateral shell element has four nodes, and corresponding thickness values ​​are assigned to nodes 1, 2, 3, and 4 respectively. Thickness value Thickness value Thickness value The thickness value can come from the node thickness set during mesh generation, or be defined through a subroutine.

[0063] Furthermore, in S2, considering the limitations of the production process of ship variable thickness steel plates—current rolling technology can only achieve continuous thickness variation in a single direction—the selection of design variables can be simplified. The thickness of the same column of nodes perpendicular to the rolling direction is set to a uniform value, and only the thickness of different columns of nodes in the rolling direction is retained as independent design variables. This not only conforms to the actual industrial production, but also significantly reduces the number of design variables and reduces the complexity of optimization calculations. Based on the n columns of nodes along the rolling direction of the ship variable thickness steel plate, the design variable vector X is defined.

[0064] The design variable vector X is represented as:

[0065]

[0066] in, Indicates the first The thickness of the steel plate at the column node;

[0067] Combined with continuously varying thickness field This will minimize the total weight of the ship's variable thickness steel plates. As the objective function of the ship node finite element model;

[0068] The objective function of the ship node finite element model is expressed as:

[0069]

[0070] in, This represents the total number of elements in the ship's nodal finite element model. For material density, Let be the thickness function at any point within the variable thickness shell element. This is the integration region for the variable thickness shell element;

[0071] By combining mechanical performance constraints and manufacturing process constraints, constraints are constructed to optimize the finite element model of ship nodes;

[0072] Constraints Represented as:

[0073]

[0074] in, For the allowable stress of steel, To standardize the maximum allowable displacement limit, This represents the distance between adjacent nodes along the rolling direction. The maximum allowable thickness change rate (gradient) for the rolling process is used to ensure that excessive abrupt changes do not lead to stress concentration. Minimum wall thickness, For the maximum wall thickness, For the first The thickness of the steel plate for the column nodes.

[0075] Specifically, with the lightweighting of the transverse compartment structure of bulk carriers as the core objective, while also considering structural strength balance, under the condition of full-load departure, the maximum principal stress of all structural units of the steel plate shall not exceed the allowable stress of the steel; the maximum vertical displacement of the steel plate shall not exceed the displacement limit allowed by the specification; the node thickness variation rate shall meet the requirements of the steel plate rolling process, and the thickness difference between adjacent columns of nodes shall not exceed the maximum allowable thickness gradient. Considering the rolling process limitations of ship variable thickness steel plates (LP steel plates), that is, the cross-sectional thickness perpendicular to the rolling direction must be consistent, this method does not directly use the thickness of all nodes as variables, but defines it by the column along the rolling direction.

[0076] Furthermore, in S3, the process proceeds according to the steps of "generating a new solution → constraint verification → calculating the objective function → judging by the Metropolis criterion → cooling cycle". The initial solution must be a feasible solution and have a certain degree of rationality to shorten the optimization iteration cycle. Initializing the simulated annealing algorithm parameters involves generating a new solution through small-amplitude local perturbations, increasing the node thickness in high-stress areas and thinning the node thickness in low-stress areas, while ensuring that the thickness is not less than the minimum wall thickness. This forms the initial thickness scheme;

[0077] The initial thickness scheme generation process strictly satisfies the constraints of the ship node finite element model, ensuring that the thickness variation rate of adjacent columns of nodes does not exceed the maximum allowable thickness gradient, and that the node thickness perpendicular to the rolling direction remains consistent. After the strength and stiffness are verified by the finite element solver and the constraints are met, the lighter feasible solution is prioritized according to the objective function of the ship node finite element model. At high temperatures, a heavier feasible solution is accepted to escape local optima. The energy difference is determined using the Metropolis criterion. (Including constraint penalty terms), the acceptance probability is calculated. According to the reception probability The process is iterated until the temperature drops to the termination value, at which point the iteration stops, and all received feasible solutions are identified and recorded.

[0078] Energy difference Represented as:

[0079]

[0080] in, For the newly generated feasible solution, This is the current feasible solution;

[0081] Receive probability The calculation formula is:

[0082]

[0083] in, Boltzmann's constant, s This refers to the current annealing temperature parameter.

[0084] Specifically, during the optimization iteration of the simulated annealing algorithm, the neighborhood search strategy generates new solutions and embeds thickness gradient constraints using the following formula:

[0085] For the current node thickness Generate new candidate thickness The basic state perturbation is represented as:

[0086]

[0087] in, A random number between [-1, 1] The set search step size;

[0088] To ensure that the thickness of adjacent elements meets the mechanical continuity requirement, this invention directly embeds the thickness smooth transition constraint into the above search process, i.e., the new candidate thickness. The thickness gradient constraint formula must be satisfied: ,in, For nodes The adjacent nodes, For nodes With nodes The distance between them The maximum allowable thickness gradient;

[0089] During the simulation annealing algorithm iteration, if the new solution generated according to the perturbation formula violates the above thickness gradient constraint or extreme value constraint, the solution is rejected or truncated and corrected until a smooth thickness transition scheme that satisfies the constraints is generated. Then, the calculation of the objective function and the acceptance judgment of the Metropolis criterion are carried out.

[0090] Although the invention has been described with reference to a limited number of embodiments, those skilled in the art will understand from the foregoing description that other embodiments are conceivable within the scope of the invention described herein. Furthermore, it should be noted that the language used in this specification has been chosen primarily for readability and instructional purposes, and not for the purpose of interpreting or limiting the subject matter of the invention. Therefore, many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the appended claims. The disclosure of the invention is illustrative and not restrictive, and the scope of the invention is defined by the appended claims.

Claims

1. A method for optimizing the design of variable thickness steel plates for ships based on simulated annealing algorithm, characterized in that, Includes the following steps: S1. For the ship mesh generation unit and node set, define the continuously changing thickness field, establish the ship node finite element model through the finite element solver, and extract the stress distribution of each node under the design conditions. S2. Taking into account production process constraints, define and simplify the design variables of the ship node finite element model, construct the objective function of the ship node finite element model and the constraints for optimizing the ship node finite element model; S3. Initialize the simulated annealing algorithm parameters. Based on the objective function and constraints, and combined with the stress distribution of each node under the design conditions, the simulated annealing algorithm is used to optimize and iterate the finite element model of the ship nodes. S4. After the iteration terminates, the optimal thickness distribution scheme is output through the optimized ship node finite element model, and the thickness between nodes in the scheme is smoothly transitioned through linear interpolation.

2. The method for optimizing the design of ship variable thickness steel plates based on simulated annealing algorithm according to claim 1, characterized in that, In S1, based on the theory of variable thickness shell elements, the shape, nodes, and corresponding thickness values ​​of the variable thickness shell elements used in the ship mesh are defined. Interpolation is then performed within the elements using the shape functions employed by the variable thickness shell elements to obtain a continuously varying thickness field. ; Continuously changing thickness field Represented as: in, For shape functions, For the first The thickness value of each node, Let any point be within the variable thickness shell element; Reference continuously varying thickness field The stiffness matrix is ​​calculated using a finite element solver. During the process, ,in, The strain-displacement matrix, Let T be the material constitutive matrix, and T be the matrix transpose, so that the thickness value changes continuously with the coordinates. The finite element solver completes the construction of the ship node finite element model.

3. The method for optimizing the design of ship variable thickness steel plates based on simulated annealing algorithm according to claim 2, characterized in that, In S2, considering the production process limitations of variable thickness steel plates for ships, the thickness of the same column of nodes perpendicular to the rolling direction is set to a uniform value, and only the thickness of different columns of nodes in the rolling direction is retained as an independent design variable. Based on the n columns of nodes along the rolling direction of the variable thickness steel plate for ships, the design variable vector X is defined. The design variable vector X is represented as: in, Indicates the first The thickness of the steel plate at the column node; Combined with continuously varying thickness field This will minimize the total weight of the ship's variable thickness steel plates. As the objective function of the ship node finite element model; The objective function of the ship node finite element model is expressed as: in, This represents the total number of elements in the ship's nodal finite element model. For material density, Let be the thickness function at any point within the variable thickness shell element. This is the integration region for the variable thickness shell element; By combining mechanical performance constraints and manufacturing process constraints, constraints are constructed to optimize the finite element model of ship nodes; Constraints Represented as: in, For the allowable stress of steel, This is the maximum displacement limit. This represents the distance between adjacent nodes along the rolling direction. This represents the maximum thickness variation rate during the rolling process. Minimum wall thickness, For the maximum wall thickness, For the first The thickness of the steel plate for the column nodes.

4. The method for optimizing the design of ship variable thickness steel plates based on simulated annealing algorithm according to claim 3, characterized in that, In step S3, initializing the simulated annealing algorithm parameters involves generating a new solution through small-amplitude local perturbations. This increases the node thickness in high-stress regions and thins the node thickness in low-stress regions, ensuring the thickness is not less than the minimum wall thickness. This forms the initial thickness scheme; During the initial thickness scheme generation process, the constraints of the ship node finite element model are satisfied, ensuring that the thickness change rate of adjacent columns of nodes does not exceed the maximum allowable thickness gradient, and that the node thickness perpendicular to the rolling direction remains consistent. After the strength and stiffness are verified by the finite element solver and the constraints are satisfied, the lighter feasible solution is preferentially accepted according to the objective function of the ship node finite element model. At high temperatures, a heavier feasible solution is accepted to escape local optima. The energy difference obtained is determined using the Metropolis criterion. The reception probability is calculated. According to the reception probability The process is iterated until the temperature drops to the termination value, at which point the iteration stops, and all received feasible solutions are identified and recorded. Energy difference Represented as: in, For the newly generated feasible solution, This is the current feasible solution; Receive probability The calculation formula is: in, Boltzmann's constant, s This refers to the current annealing temperature parameter.

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