Self-adaptive collaborative optimization method for multi-constraint topological morphology of ship plate shell structure
By employing a multi-constraint topology adaptive collaborative optimization method, combined with a two-way evolution strategy and topology optimization, the problem of simultaneous optimization of multiple mechanical properties in ship plate and shell structures was solved, achieving structural lightweighting and performance improvement, and simplifying manufacturing.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-01
- Publication Date
- 2026-04-03
AI Technical Summary
Existing topology optimization methods struggle to simultaneously meet multiple mechanical performance requirements in ship plate and shell structures, and there is interference between topology and morphology optimization, leading to decreased structural performance and increased production difficulty.
A multi-constraint topology adaptive collaborative optimization method is adopted. Through a two-way evolution strategy, combined with a multi-performance comprehensive evolution matrix and a topology elimination and expansion matrix, the synchronous collaboration between topology and topology optimization is achieved, ensuring a high degree of uniformity in topology features and regularity in shape.
It has achieved lightweighting of ship hull structures and improved multiple mechanical properties, solved manufacturability issues, and enhanced the practical application value and production efficiency of the design results.
Smart Images
Figure CN121786955A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of structural optimization, particularly to the design of ship plate and shell structures, and to a multi-constraint topology adaptive collaborative optimization method that can further improve multiple mechanical properties of the structure while achieving overall structural lightweighting. Background Technology
[0002] To reduce structural weight and save materials, conceptual optimization methods such as topology optimization and morphology optimization have been proposed. Compared with detailed optimization methods such as shape and size optimization, topology and morphology optimization rely less on the initial structural layout and the designer's subjective experience. They can solve for the optimal mechanical transmission path within a given optimization space using optimization algorithms, and generate innovative structural configurations, thereby producing greater economic benefits.
[0003] As research deepens, various types of structural topology optimization methods have been proposed. Representative methods include evolutionary approaches based on the "survival of the fittest" principle, which gradually eliminate inefficient units to retain efficient unit layouts. Further, bidirectional evolutionary algorithms have been developed that can restore or add necessary units based on feedback from structural mechanical properties. Meanwhile, morphology optimization techniques, another popular conceptual optimization design method, have been widely applied in various plate and shell structures such as battery pack casings and automotive shells.
[0004] However, existing evolutionary or bidirectional evolutionary topology methods generally only include single constraints, making it difficult to simultaneously use multiple mechanical properties as design constraints for structural optimization. In real-world engineering environments, however, various plate and shell structures such as ships, aircraft, and automobiles are subject to various loads and operating environments. Designers, while pursuing lightweight structures, also have high requirements for multiple mechanical properties such as displacement deformation, stress, strain energy, and natural frequencies.
[0005] Furthermore, there is currently no invention patent that integrates bidirectional evolutionary topology and morphology optimization technology and applies them together to the design of ship plate and shell structures, so as to effectively improve their lightweighting and improve multiple mechanical properties through the synchronous cooperation of the two methods.
[0006] Furthermore, inefficient structural units are removed during bidirectional evolutionary topology optimization. When morphology optimization and topology optimization are performed simultaneously, topology optimization will also remove the morphological features generated on inefficient units, thus destroying the morphology optimization results. The remaining incomplete morphological features not only fail to strengthen the structure but also lead to a decrease in the load-bearing capacity and other mechanical properties of the original topology layout.
[0007] Furthermore, the morphological features generated by morphological optimization, such as protrusions or rolling ribs, are uneven in height along the direction perpendicular to the plane of the sheet, exhibiting significant irregularities. This makes the production of morphologically optimized structures more difficult during stamping and casting, and the design results are difficult to apply in practice. Summary of the Invention
[0008] The purpose of this invention is to provide a multi-constraint topology adaptive collaborative optimization method for ship plate and shell structures. This method achieves lightweighting and improved local mechanical properties of ship plate and shell structures through a two-way evolution strategy, while ensuring high uniformity of topological features and regular shape, thereby solving manufacturability problems and adapting to production needs.
[0009] To achieve the above objectives, the present invention provides an adaptive collaborative optimization method for multi-constraint topology of ship plate and shell structures, which includes the following steps: Step 100: Establish a finite element model of the ship's plate and shell structure, and use multiple mechanical properties as constraints, with minimizing the plate and shell mass as the objective function; Step 200: Calculate the sensitivity information of each element of the finite element model under various mechanical properties; Step 300: Perform bidirectional evolutionary topology optimization under multiple mechanical performance constraints to construct a unit multi-performance comprehensive evolutionary matrix under multiple constraints; Step 400: Apply the topological element solution set to the surface nodes of the shell element and calculate the bidirectional evolution matrix of each node; Step 500: Establish the morphology optimization equation and perform morphology co-optimization solution; Step 600: Eliminate or enlarge the morphological features; Step 700: Determine whether the optimization result meets the constraints and convergence requirements. If not, update the unit change rate and iterate the optimization.
[0010] Preferably, in step 100, the ship's plate and shell structure is taken as the object, and a geometric mesh is divided by two-dimensional shell elements to establish a finite element model. The displacement deformation, stress, strain energy, and first-order natural frequency of the structure during the design of the ship's plate and shell are used as multiple key design mechanical performance indicators as constraints.
[0011] Preferably, in step 300, the topology optimization mathematical model of the plate and shell finite element model covering multiple mechanical performance constraints is as follows: (1) In the formula, It is the value of evolution or degradation of the structural material unit; It is the finite element design domain of the structure; It is the volume objective of topology optimization; It is an external load term; It is the overall stiffness matrix; It is the displacement term of the structure; It is the maximum displacement deformation response of the structure. It is a displacement constraint condition; It is the maximum stress response of the structure. It is a stress constraint condition; It is the maximum strain energy of the structure. It is a compliance constraint condition; It is the first-order natural frequency response of the structure. It is a first-order natural frequency constraint condition.
[0012] Preferably, in step 300, the rate of change of the j-th constraint under the k-th optimization iteration is used. Construct a multi-performance comprehensive evolution matrix of units under multiple constraints, and analyze the sensitivity information of each unit under different constraints. The results are summarized, and the overall sensitivity is calculated. The established multi-performance comprehensive evolution matrix of the unit is as follows: (2) In the formula, The multi-constraint integrated sensitivity of the i-th unit; Let J be the rate of change of the j-th constraint in the k-th optimization iteration; For the i-th unit The j-th constraint Sensitivity information below; This represents the maximum sensitivity of all elements under the j-th constraint. Combining equations (1) and (2), we obtain the topological solution sets of efficient and inefficient units during the k-th iteration. .
[0013] Preferably, in step 400, the topological unit set is decomposed. Apply the algorithm to the surface nodes of the shell element, construct and compute the bidirectional evolution matrix for each node. Its expression is as follows: (3) in, Let be the bidirectional evolution value of the p-th node, whose size is equal to the maximum value among all bidirectional evolution values of all units containing that node; This represents the bidirectional evolution value for all units containing this node.
[0014] Preferably, in step 500, the node bidirectional evolution matrix is used. The morphological change equations for the surface nodes of the current plate and shell element are established as follows: (4) in, Let p be the shape stretching and shifting variable for the p-th node; A vector representing the overall shape of the deck structure; It is the initial vector, set to 0; and These are the lower and upper limits of the node's stretching and moving range, respectively.
[0015] Preferably, in step 500, based on the morphology change equation (4), further morphology optimization is carried out synchronously in the current topology iteration step to solve for the morphology design variables of the deck shell element nodes. Its mathematical expression is as follows: (5).
[0016] Preferably, in step 600, the morphology elimination and expansion matrix is established using a hyperbolic tangent function as follows: (6) in, This represents the result of shape elimination and expansion for the p-th node; The desired stamping height for the desired shape; It is the defined morphology generation threshold.
[0017] Preferably, in step 600, the morphology design variables obtained by solving equation (5) are... By inputting the shape elimination and expansion matrix established by equation (6), shape features below the threshold can be eliminated, making them approach 0; for shape features equal to or above the threshold, they can be further expanded to approach the desired stamping height. ...
[0018] Preferably, in step 700, the morphology optimization structure after elimination and expansion is re-input into the bidirectional evolutionary topology optimization, and it is determined whether the constraints of the current iteration step are satisfied and whether the optimization objective has converged. If it has not converged, the update rate is used according to the topology evolution criterion. Update the rate of change of the unit Then return to step 200 until convergence; where the expression for the rate of change of the updated cell is as follows: (7).
[0019] In summary, the present invention has the following beneficial technical effects: This invention enables lightweight and high-performance structural design during the ship hull design phase through collaborative bidirectional evolutionary optimization of topology. By constructing a multi-performance integrated evolutionary matrix for elements, the bidirectional evolutionary topology optimization problem under multiple mechanical performance constraints is solved. This method effectively integrates topology optimization and morphology optimization techniques, avoiding mutual interference between the two and achieving simultaneous optimization, significantly improving the efficiency and effectiveness of structural design.
[0020] This invention derives a bidirectional evolution matrix for nodes, enabling shell nodes to adaptively evolve or degenerate synchronously with the topological elements. This synchronization mechanism ensures that morphological features are generated only on efficient retained elements, avoiding performance degradation caused by inefficient elements, thus fully leveraging the advantages of topology and morphology optimization in reducing structural weight and enhancing mechanical properties. Simultaneously, this method adaptively enhances the local mechanical properties of the structure through morphology optimization, further eliminating redundant material and achieving efficient and lightweight construction.
[0021] Furthermore, this invention, through a morphology elimination and expansion matrix, eliminates or expands the generated morphology features based on a threshold, ensuring that features such as morphological protrusions or rolled ribs appear at the same stamping and casting height, effectively solving the manufacturability problem of the structure. This not only improves the practical engineering application value of the design results but also significantly reduces the complexity and cost of manufacturing. It is easy to implement, highly adaptable, and provides an innovative and practical solution for the design of ship plate and shell structures. Attached Figure Description
[0022] Figure 1 This is a schematic diagram of the deck structure's geometric model; Figure 2 This is a schematic diagram of the load conditions on the deck; Figure 3 A schematic diagram of the deck structure obtained by adaptive collaborative optimization of multi-constraint topology. Figure 4 A schematic diagram of the deck structure obtained by traditional topology optimization; Figure 5 The strain energy cloud map is for both traditional topology optimization and topology co-optimization. Detailed Implementation
[0023] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0024] This invention discloses an adaptive collaborative optimization method for multi-constraint topology of ship plate and shell structures, comprising the following steps: Step 100: Taking the ship's plate and shell structure as the object, establish a finite element model, and simultaneously use multiple acceptable limit mechanical properties (such as maximum withstandable displacement deformation, stress, overall strain energy, first natural frequency, etc.) as constraints, and take minimizing the plate and shell mass as its objective function to carry out optimization design. Step 200: Calculate the sensitivity information of each element of the deck finite element model under various mechanical properties using the difference algorithm; Step 300: Perform bidirectional evolutionary topology optimization under multiple mechanical performance constraints on the finite element model of the ship plate and shell. Based on the set current rate of change, construct the multi-performance comprehensive evolution matrix of the elements under multiple constraints, and transform the multi-constraint bidirectional evolutionary topology optimization problem into a single-constraint bidirectional evolutionary topology optimization problem, thereby obtaining the topology solution set of efficient and inefficient elements under multiple mechanical performance constraints in each iteration. Step 400: Apply the topological element solution set of the current iteration step to the surface nodes of the shell element to calculate the bidirectional evolution matrix of each node, so that the node can adaptively evolve into a morphology co-deformation node or degenerate into an elimination node that is removed along with inefficient elements. Step 500: Based on the bidirectional evolution matrix of nodes, establish the morphology optimization equation of the surface nodes of the plate and shell unit, and perform topological morphology co-optimization solution under the current topology iteration step. Step 600: Establish a shape elimination and expansion matrix through a hyperbolic tangent function, eliminate shape features below the defined shape generation threshold according to the defined shape generation threshold, and further expand shape features equal to or higher than the threshold to the set stamping height. Step 700: The morphology optimization results after elimination and expansion are re-input into the bidirectional evolutionary topology optimization, and it is determined whether the constraints and optimization objectives of the current iteration step are satisfied and converged. If they do not converge, the unit change rate is updated according to the topology evolution criterion and the process returns to step 200 until convergence is achieved. Finally, a ship plate shell topology morphology co-optimization design structure that simultaneously meets the requirements of structural performance and lightweighting and is easy to produce in practice is obtained.
[0025] In a specific embodiment of the present invention, an adaptive collaborative optimization method for multi-constraint topology of a ship plate and shell structure is disclosed. The specific steps of the method include: In step 100, taking the ship's plate and shell structure as the object, a finite element model is established by dividing the geometric mesh using two-dimensional shell elements. Several key design mechanical performance indicators of the ship's plate and shell structure, such as displacement deformation, stress, strain energy, and first-order natural frequency, are simultaneously used as constraints. The objective function is to minimize the plate and shell mass, and high-performance optimization design is carried out.
[0026] In step 200, the finite element software is called to calculate the sensitivity information of each element under each mechanical constraint condition of the deck finite element model.
[0027] In step 300, bidirectional evolutionary topology optimization of the finite element model is performed to obtain the topological solution set of efficient and inefficient elements considering multiple mechanical performance constraints in each iteration. The topology optimization mathematical model for the plate-shell finite element model, which encompasses multiple mechanical performance constraints, can be expressed in the following form: (1) In the formula, It is the value of evolution or degradation of the structural material unit; It is the finite element design domain of the structure; It is the volume objective of topology optimization; It is an external load term; It is the overall stiffness matrix; It is the displacement term of the structure; It is the maximum displacement deformation response of the structure. It is a displacement constraint condition; It is the maximum stress response of the structure. It is a stress constraint condition; It is the maximum strain energy (compliance) of the structure. It is a compliance constraint condition; It is the first-order natural frequency response of the structure. It is a first-order natural frequency constraint condition.
[0028] Based on this, according to the rate of change of the j-th constraint under the k-th optimization iteration... Construct a multi-performance comprehensive evolution matrix of units under multiple constraints, and analyze the sensitivity information of each unit under different constraints. The results are summarized, and the overall sensitivity is calculated. The established multi-performance comprehensive evolution matrix of the unit is shown in the following equation (2): (2) In the formula, The multi-constraint integrated sensitivity of the i-th unit; Let J be the rate of change of the j-th constraint in the k-th optimization iteration; For the i-th unit The j-th constraint Sensitivity information below; This represents the maximum sensitivity of all elements under the j-th constraint.
[0029] Based on the established multi-performance comprehensive evolutionary matrix of the unit, by combining equations (1) and (2), the multi-constraint bidirectional evolutionary topology optimization problem can be equivalently transformed into a single-constraint bidirectional evolutionary topology optimization problem, and the topological solution sets of efficient and inefficient units in the k-th iteration can be obtained. .
[0030] In step 400, the topological unit solution set of the current iteration step is... Apply the algorithm to the surface nodes of the shell element, construct and compute the bidirectional evolution matrix for each node. Its expression is shown in equation (3): (3) in, Let be the bidirectional evolution value of the p-th node, whose size is equal to the maximum value among all bidirectional evolution values of all units containing that node; This represents the bidirectional evolution value for all units containing this node.
[0031] Therefore, when the p-th node is located on an efficient unit, its bidirectional evolution value is... As the value approaches 1, the node will evolve and be preserved along with the efficient unit, participating in subsequent morphological deformation; however, when the p-th node is entirely located on an inefficient unit, its bidirectional evolution value... The value will approach 0, causing the node to degenerate and be eliminated along with the inefficient unit.
[0032] In step 500, based on the node bidirectional evolution matrix The morphological change equation of the surface nodes of the current plate and shell unit is established, as shown in equation (4).
[0033] (4) in, Let p be the shape stretching and shifting variable for the p-th node; A vector representing the overall shape of the deck structure; It is the initial vector, which is usually set to 0; and These are the lower and upper limits of the node's stretching and moving range, respectively.
[0034] Based on the morphology change equation shown in equation (4), morphology optimization can be further carried out synchronously under the current topology iteration step to solve for the morphology design variables of the deck shell element nodes. Its mathematical expression is as follows: (5) In step 600, based on the defined morphology generation threshold, a hyperbolic tangent function is used to establish the morphology elimination and expansion matrix, as detailed in equation (6): (6) in, This represents the result of shape elimination and expansion for the p-th node; The desired stamping height for the desired shape; It is the defined morphology generation threshold.
[0035] The morphological design variables obtained by solving equation (5) By inputting the shape elimination and expansion matrix established by equation (6), shape features below the threshold can be eliminated, making them approach 0 (i.e., no protrusion occurs); for shape features equal to or above the threshold, they are further expanded to approach the desired stamping height. This facilitates actual production and manufacturing.
[0036] In step 700, the optimized morphology structure after elimination and expansion is re-input into the bidirectional evolutionary topology optimization, and it is determined whether the constraints of the current iteration step are satisfied and whether the optimization objective has converged. If it has not converged, the update rate is used according to the topology evolution criterion. Update the rate of change of the unit (As shown in the following formula) and return to step 200 until convergence, finally obtaining the optimized design structure of the ship plate shell structure topology that simultaneously meets the requirements of structural performance and lightweighting and is easy to produce in practice.
[0037] (7) In the design of ship plate and shell structures, this invention simultaneously uses multiple mechanical properties such as maximum displacement deformation, stress, strain energy, and natural frequency as constraints, and combines them with the set current rate of change. By constructing a multi-performance comprehensive evolution matrix for the unit, a two-way evolutionary topology optimization design under multiple mechanical performance constraints is carried out.
[0038] Subsequently, by deriving a bidirectional evolution matrix for nodes, nodes on the plate and shell surface can evolve or degenerate based on the topology element results. Nodes located on highly efficient retained elements can evolve into nodes with morphological co-deformation, assisting in the simultaneous topology optimization to locally enhance the morphology of the ship's plate and shell surface; while nodes located on inefficient elements will degenerate and be eliminated along with the inefficient elements. This ensures that morphological features are generated only on highly efficient retained elements and are not removed along with inefficient elements, effectively avoiding mutual interference between topology and morphological optimization. Based on this, a morphological elimination and expansion matrix is further established, eliminating morphological features below a threshold and expanding morphological features equal to or above the threshold to a set stamping height. This ensures that generated morphological protrusions or rolling ribs appear at the same height, effectively solving the manufacturability problem.
[0039] This optimization method enables structural lightweighting through bidirectional evolutionary topology optimization, while simultaneously using morphology optimization to adaptively enhance the local mechanical properties of the structure, further eliminating redundant material. It achieves simultaneous integration of topology and morphology optimization, effectively avoiding destructive interference between the two. Furthermore, the resulting morphological features are all located at the same height and have relatively regular shapes, making them suitable for practical manufacturing and possessing significant potential for widespread application.
[0040] The method of the present invention will be further described below with reference to the accompanying drawings and specific embodiments. During the service life of critical plate and shell structures of ships, multiple mechanical properties such as maximum displacement deformation, stress, strain energy, and first-order natural frequency are closely related to the overall structural safety. Therefore, this specific embodiment will perform multi-constraint topology adaptive collaborative optimization on a typical ship open deck plate and shell structure. The implementation process is as follows: 1. Establish the geometric model of the open deck structure, such as... Figure 1 As shown, the deck length L = 3360 mm, width B = 2240 mm, opening radius R = 200 mm, and deck thickness t = 15 mm. The geometric mesh was generated using two-dimensional quadrilateral shell elements through finite element software.
[0041] 2. Define the material of the structure as steel, with an elastic modulus of... Poisson's ratio is Based on the actual working conditions of the deck, load conditions are applied to the finite element model, including concentrated loads generated by cargo and equipment on the deck, and uniformly distributed loads at both ends of the deck during bending and compression of the deck frame, such as... Figure 2 As shown.
[0042] 3. Define optimization constraints. Considering the four important mechanical properties of the open deck, namely displacement deformation, stress, overall strain energy, and first natural frequency, the four constraints are set as follows: (1) the maximum displacement deformation does not exceed 40 mm; (2) the maximum stress does not exceed 235 MPa; (3) the overall strain energy (compliance) of the deck does not exceed 6*10 5 Nmm; (4) The first natural frequency of the structure is higher than 10Hz.
[0043] 4. Create optimization objectives and design variables. Set the optimization objective as minimizing the overall volume of the open deck as its lightweight objective. Use each unit as a bidirectional evolutionary topology optimization variable, and the morphology stretching distance of each node as a morphology optimization variable, and specify the upper limit of morphology stretching as 15mm (i.e., the maximum depth of stamping casting).
[0044] 5. By calling the finite element software, calculate the sensitivity information of each element under each constraint condition of the deck finite element model. .
[0045] 6. Set the initial element change rate under each constraint condition. Both are 0.02, update rate All values are 0.02. The sensitivity information of each element under each constraint condition is... By combining this with the multi-performance comprehensive evolution matrix of the unit under multiple constraints constructed according to equation (2), the comprehensive sensitivity of each unit can be obtained. Furthermore, by combining equations (1) and (2), the multi-constraint bidirectional evolutionary topology optimization problem can be equivalently transformed into a single-constraint bidirectional evolutionary topology optimization problem, and the efficient and inefficient unit topology solution sets of the k-th bidirectional evolutionary topology optimization iteration can be obtained. .
[0046] 7. During each iteration of bidirectional evolutionary topology optimization, the topology solution set is simultaneously updated. The bidirectional evolution matrix of each node is calculated by applying the matrix to the nodes on the surface of the shell element. As shown in equation (3), nodes on efficient units are preserved through evolution and participate in subsequent morphological co-deformation; nodes entirely on inefficient units are degenerated and eliminated.
[0047] 8. Node-based bidirectional evolutionary matrix The morphological change equation of the surface nodes of the current shell element is established, as shown in Equation (4). Furthermore, morphological optimization is carried out synchronously under the current topology iteration step (see Equation (5)) to solve for the optimal morphological design variables of the deck element nodes under the current iteration step's topology configuration. .
[0048] 9. Define the morphology generation threshold The desired stamping height is 7.5mm. The value is 15mm. A hyperbolic tangent function is used to establish the morphology penalty and enhancement matrix, as detailed in equation (6). The generated optimal morphology design variables are then applied. Further normalization processing is performed, which involves penalizing morphological features below a threshold to prevent them from protruding, while morphological features equal to or above the threshold are further enhanced to the desired stamping height. This facilitates actual production and manufacturing.
[0049] 10. Re-input the penalized and enhanced morphology optimization structure into the bidirectional evolutionary topology optimization, determine whether it meets the constraints, and calculate the relative change of the optimization objective between the current iteration step and the previous iteration step. As shown in equation (8) below.
[0050] (8) 11. Set the convergence tolerance to 0.1% at this point. When If the convergence tolerance is greater than or equal to the threshold or the structure does not meet the constraints, then the update rate is used according to the topological evolution criterion. Update the rate of change of the unit (as shown in equation (7)), and return to step 5; until convergence, when When the convergence tolerance is less than the limit and the structure meets the constraints, a final design structure for optimizing the ship deck topology that simultaneously satisfies structural performance and lightweight requirements, and is easy to produce in practice, is obtained. Figure 3 As shown.
[0051] In this embodiment, a multi-constraint topology adaptive collaborative optimization method is used to achieve lightweight and high-performance optimization design of ship open decks. Figure 3 The co-evolutionary structure of the topology reveals that features such as protrusions and rolling ridges are located on the retained efficient topological units, with intact edges that are not destroyed by the removed inefficient topological units. This demonstrates that the proposed bidirectional evolutionary topology optimization effectively avoids mutual interference between topology optimization and morphology optimization techniques, achieving successful integration of the two.
[0052] If the traditional topology optimization method is used, the result is as follows: Figure 4 As shown in the table below, the maximum displacement deformation, maximum stress, overall strain energy, first-order natural frequency, and other mechanical properties, as well as structural volume parameters, of the topology-optimized deck and the traditional topology-optimized deck are summarized:
[0053] Therefore, it can be seen that the present invention significantly reduces the maximum displacement deformation and overall strain energy of the designed deck compared with the traditional topology optimization structure; the first-order natural frequency is greatly improved; and at the same time, it takes into account the maximum stress of the structure, keeping the maximum stress of the structure at the same level as the traditional topology optimization structure. Figure 5 The differences in element strain energy distribution cloud maps between traditional topology optimization and the topology-morphology co-optimization structure of this invention are shown. From Figure 5 It can be seen that in the traditional topology-optimized layout, the open deck, due to the influence of uniformly distributed compressive loads and concentrated loads at both ends, results in a high element strain energy distribution in a large area along the x-axis in the middle of the deck. However, in the structure with integrated topology optimization, the generation of raised vertical (y-axis) rolled ribs effectively slows down the diffusion and propagation of high element strain energy along the x-axis in the middle of the deck, and the element strain energy along the x-axis near the deck opening is significantly reduced. This demonstrates that the related topology features generated by topology optimization can effectively enhance the stiffness of the structure and improve its various mechanical properties, thereby enabling the open deck to better meet the optimization constraints under the four working conditions.
[0054] Furthermore, it is noteworthy that the volume of the deck co-optimized by topology and morphology is reduced by 16.2% compared to the traditional topology-optimized structure, demonstrating a superior lightweight effect. This illustrates that simultaneous morphology optimization, while enhancing structural mechanical performance, allows topology optimization technology to further eliminate more redundant material, thereby achieving the given constraints with less material cost. This demonstrates that the invention, through the integration of topology optimization and morphology optimization techniques, further leverages the advantages of both to obtain a more favorable ship deck design structure.
[0055] At the same time, Figure 3 In the final design results, the morphological protrusions are all uniformly generated at the artificially set stamping height, and the structure is more regular and simple, thus ensuring structural performance while being easier to construct in actual engineering and mass production.
[0056] Compared with traditional topology optimization, this invention provides an adaptive and collaborative optimization method for multi-constraint topology morphology of ship plate and shell structures. This method enables lightweight and high-performance design of the structure through collaborative bidirectional evolutionary optimization of topology morphology during the design phase of the ship plate and shell. By constructing a multi-performance comprehensive evolutionary matrix for elements, the bidirectional evolutionary topology optimization problem under multiple mechanical performance constraints is solved. Furthermore, a bidirectional evolutionary matrix for nodes is derived, allowing plate and shell nodes to adaptively evolve or degenerate synchronously with the topology elements, effectively avoiding interference between topology and morphology optimization. A morphology collaborative optimization model corresponding to the current topology iteration is established, fully leveraging the advantages of both in terms of lightweighting and enhanced mechanical performance. Simultaneously, through morphology elimination and expansion matrices, generated morphology features are eliminated or expanded based on thresholds, ensuring that morphology protrusions or rolling ribs appear at the same stamping and casting height, effectively solving the manufacturability problem of the structure. This method is easy to implement and highly adaptable.
[0057] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A method for adaptive collaborative optimization of multi-constraint topology of ship plate and shell structures, characterized in that, Includes the following steps: Step 100: Establish a finite element model of the ship's plate and shell structure, and use multiple mechanical properties as constraints, with minimizing the plate and shell mass as the objective function; Step 200: Calculate the sensitivity information of each element of the finite element model under various mechanical properties; Step 300: Perform bidirectional evolutionary topology optimization under multiple mechanical performance constraints to construct a unit multi-performance comprehensive evolutionary matrix under multiple constraints; Step 400: Apply the topological element solution set to the surface nodes of the shell element and calculate the bidirectional evolution matrix of each node; Step 500: Establish the morphology optimization equation and perform morphology co-optimization solution; Step 600: Eliminate or enlarge the morphological features; Step 700: Determine whether the optimization result meets the constraints and convergence requirements. If not, update the unit change rate and iterate the optimization.
2. The adaptive collaborative optimization method for multi-constraint topology of ship plate and shell structures according to claim 1, characterized in that, In step 100, taking the ship's plate and shell structure as the object, a finite element model is established by dividing the geometric mesh using two-dimensional shell elements, and multiple key design mechanical performance indicators of the ship's plate and shell structure, such as displacement deformation, stress, strain energy, and first-order natural frequency, are simultaneously used as constraints.
3. The adaptive collaborative optimization method for multi-constraint topology of ship plate and shell structures according to claim 2, characterized in that, In step 300, the topology optimization mathematical model of the plate and shell finite element model, which covers multiple mechanical performance constraints, is as follows: (1) In the formula, It is the value of evolution or degradation of the structural material unit; It is the finite element design domain of the structure; It is the volume objective of topology optimization; It is an external load term; It is the overall stiffness matrix; It is the displacement term of the structure; It is the maximum displacement deformation response of the structure. It is a displacement constraint condition; It is the maximum stress response of the structure. It is a stress constraint condition; It is the maximum strain energy of the structure. It is a compliance constraint condition; It is the first-order natural frequency response of the structure. It is a first-order natural frequency constraint condition.
4. The adaptive collaborative optimization method for multi-constraint topology of ship plate and shell structures according to claim 3, characterized in that, In step 300, the rate of change of the j-th constraint under the k-th optimization iteration is used. Construct a multi-performance integrated evolution matrix of units under multiple constraints, and analyze the sensitivity information of each unit under different constraints. The results are summarized, and the overall sensitivity is calculated. The established multi-performance comprehensive evolutionary matrix of the unit is as follows: (2) In the formula, The multi-constraint integrated sensitivity of the i-th unit; Let J be the rate of change of the j-th constraint in the k-th optimization iteration; For the i-th unit The j-th constraint Sensitivity information below; This represents the maximum sensitivity of all elements under the j-th constraint. Combining equations (1) and (2), we obtain the topological solution sets of efficient and inefficient units during the k-th iteration. .
5. The adaptive collaborative optimization method for multi-constraint topology of ship plate and shell structures according to claim 4, characterized in that, In step 400, the topological unit set is solved. Apply the algorithm to the surface nodes of the shell element, construct and compute the bidirectional evolution matrix for each node. Its expression is as follows: (3) in, Let be the bidirectional evolution value of the p-th node, whose size is equal to the maximum value among all bidirectional evolution values of all units containing that node; This represents the bidirectional evolution value for all units containing this node.
6. The adaptive collaborative optimization method for multi-constraint topology of ship plate and shell structures according to claim 5, characterized in that, In step 500, based on the node bidirectional evolution matrix The morphological change equations for the surface nodes of the current plate and shell element are established as follows: (4) in, Let p be the shape stretching and shifting variable for the p-th node; A vector representing the overall shape of the deck structure; It is the initial vector, set to 0; and These are the lower and upper limits of the node's stretching and moving range, respectively.
7. The adaptive collaborative optimization method for multi-constraint topology of ship plate and shell structures according to claim 6, characterized in that, In step 500, based on the morphology change equation (4), further morphology optimization is carried out synchronously in the current topology iteration step to solve for the morphology design variables of the deck shell element nodes. Its mathematical expression is as follows: （5）。 8. The adaptive collaborative optimization method for multi-constraint topology of ship plate and shell structures according to claim 7, characterized in that, In step 600, the hyperbolic tangent function is used to establish the topography elimination and expansion matrix as follows: (6) in, This represents the result of morphology elimination and expansion for the p-th node; The desired stamping height for the desired shape; It is the defined morphology generation threshold.
9. The adaptive collaborative optimization method for multi-constraint topology of ship plate and shell structures according to claim 8, characterized in that, In step 600, the morphology design variables are obtained by solving equation (5). By inputting the shape elimination and expansion matrix established by equation (6), shape features below the threshold can be eliminated, making them approach 0; for shape features equal to or above the threshold, they can be further expanded to approach the desired stamping height. ...
10. The adaptive collaborative optimization method for multi-constraint topology of ship plate and shell structures according to claim 9, characterized in that, In step 700, the optimized morphology structure after elimination and expansion is re-input into the bidirectional evolutionary topology optimization, and it is determined whether the constraints of the current iteration step are satisfied and whether the optimization objective has converged. If it has not converged, the update rate is used according to the topology evolution criterion. Update the rate of change of the unit And return to step 200 until convergence; where the expression for the rate of change of the update cell is as follows: (7)。