A trimaran connecting bridge fine design method based on a topology optimization method

Abstract

A refined design method for trimaran connecting bridges based on topology optimization is presented, belonging to the field of ship structural optimization design. S1: Construct the design domain and finite element discrete model of the trimaran connecting bridge. S2: Construct a multi-mesh, matrix-free method, and GPU parallel solution strategy corresponding to the topology optimization mathematical model. S3: Perform iterative topology optimization calculations and output the converged topology optimization density field results. S4: Automatedly reconstruct the topology optimization density field results to obtain a manufacturable 3D solid structure of the connecting bridge. S5: Perform finite element verification on the 3D connecting bridge solid model; if the verification results meet preset indicators, output the final design scheme; otherwise, return to S2 to S4 to adjust optimization parameters and iterate again. This invention overcomes the limitations of existing large-scale topology optimization designs on computer memory capacity, achieving efficient topology configuration design for desktop-level structures with hundreds of millions of nodes, and is easily extended to the design and lightweight design of other ship engineering structures.

Description

Technical Field

[0001] This invention belongs to the field of ship and marine engineering structural design, and relates to a refined design method for trimaran connecting bridges based on topology optimization. Specifically, it relates to a refined design method for trimaran connecting bridges on a scale of hundreds of millions of units, which is particularly applicable to innovative configuration design and lightweight design of unmanned trimaran. Background Technology

[0002] Trimaraners have garnered significant attention in the field of high-performance ships due to their advantages such as high speed, excellent seakeeping, and large deck area. As a crucial load-bearing structure connecting the main hull to the two side hulls, the connecting bridge not only serves to link the main hull to the hulls but also directly participates in the transmission of the overall ship load. Its structural strength, stiffness, and stability have a significant impact on the safety, reliability, and service performance of the trimaran.

[0003] Current trimaran bridge structure designs typically rely heavily on designer experience, involving iterative revisions and adjustments based on empirical formulas, regulatory requirements, and finite element analysis results. This approach generally involves first defining an initial structural form, then verifying the structural response through finite element calculations, and finally adjusting local structural dimensions, frame arrangements, or reinforcement methods based on the verification results. While this method can meet general engineering design needs, it suffers from high reliance on design experience, low design efficiency, unclear optimization objectives, and limited ability to find optimal solutions.

[0004] Topology optimization is an advanced design method that, given loads, boundary conditions, and volume fraction constraints, achieves optimal structural performance by rationally distributing materials within the design domain. It has broad application prospects in aerospace, shipbuilding and ocean engineering, mechanical equipment, and the automotive industry. However, existing topology optimization methods typically require repeated finite element analysis, sensitivity analysis, and design variable updates during the optimization iteration process. When dealing with large and complex structures in shipbuilding and ocean engineering, detailed finite element models with millions to hundreds of millions of degrees of freedom are often required to characterize local structural details and complex boundary features. In this case, traditional finite element calculation methods suffer from the following problems: (1) High memory consumption: Traditional finite element method requires explicit assembly and storage of large-scale sparse stiffness matrix, which is difficult to support hundreds of millions of calculations under the condition of limited memory capacity of desktop computer. (2) Low computational efficiency: Topology optimization requires multiple iterations, and each round requires finite element solution (which takes up more than 90% of the total optimization time), making it difficult to meet the efficiency requirements of engineering design. (3) It is difficult to balance design accuracy and computational scale. Due to limitations in computing resources, existing methods usually cannot simultaneously take into account the overall topological layout of complex structures and the characterization of local details, which limits the application effect of topology optimization in high-resolution fine design; (4) Insufficient engineering adaptability: Existing topology optimization methods rarely conduct large-scale, refined design research for complex structures such as multihull ships in the field of shipbuilding and ocean engineering, which is difficult to meet the comprehensive requirements of unmanned trimaran ships and other structures in terms of lightweight, high rigidity and engineering manufacturability.

[0005] In recent years, GPUs have demonstrated significant advantages in numerical computation due to their massive parallel computing capabilities. However, existing GPU acceleration methods mostly focus on accelerating local computation processes or single solution stages, with less emphasis on collaborative optimization across the entire process of topology optimization, including finite element analysis, sensitivity analysis, and design variable updates. Furthermore, traditional topology optimization methods are often limited by computational scale, making it difficult to balance the overall topological layout of complex structures with the detailed characterization of local features. Moreover, the optimization results often require extensive manual post-processing before being transformed into engineering-usable structural solutions, limiting their application in the innovative design of complex structures in fields such as shipbuilding and marine engineering.

[0006] Therefore, there is an urgent need to propose a refined design method for trimaran connecting bridges with a scale of hundreds of millions of units based on GPU parallel acceleration and matrix-free methods. This method aims to achieve low-memory, high-efficiency computation and low-manual-cost automated structural reconstruction throughout the topology optimization process, thereby breaking through the limitations of traditional desktop computing platforms in terms of solution scale, computational efficiency, design accuracy, and engineering applicability. Summary of the Invention

[0007] To address the shortcomings of existing methods, this invention provides a refined design method for trimaran connecting bridge structures on a scale of hundreds of millions of units, based on topology optimization. This invention combines density-based topology optimization, multi-grid conjugate gradient solving, matrix-free methods, and GPU parallel acceleration to construct a computational framework. This enables refined finite element analysis and iterative topology optimization on a desktop computer for structures on a scale of hundreds of millions of units, without requiring explicit assembly of the global stiffness matrix. Furthermore, through geometric post-processing and automated reconstruction with low manual costs, a trimaran connecting bridge structural solution that balances lightweight design, high stiffness, and manufacturability is obtained.

[0008] To achieve the above objectives, the present invention adopts the following technical solution: A refined design method for trimaran connecting bridges based on topology optimization, comprising the following steps: Step S100: Construct the design domain and three-dimensional finite element discretization model of the trimaran connecting bridge. Based on the geometry, boundary constraints, and stress conditions of the trimaran connecting bridge, a design domain is established. This design domain is then finely meshed to form a finite element discretization model, and material parameters, non-design domains, load application areas, and initial configuration are defined. Specifically: Step S101: Establish the three-dimensional geometric model of the connecting bridge and the design domain boundary. Based on the connection relationship between the main hull and the sheet hull of the trimaran, establish the three-dimensional geometric model of the connecting bridge, and define the design domain boundary using a cuboid envelope or an envelope body matching the shape of the connecting bridge.

[0009] Step S102: Divide the design domain and non-design domain. Based on the assembly interface, constraint area, load application area, and the engineering structural area that must be retained, the entire connecting bridge is divided into an optimizable design domain and a non-optimizable non-design domain; among which, the non-design domain is used to retain the connection boundary, installation area, or local reinforcement area.

[0010] Step S103: Establish a three-dimensional finite element discretization model. The design domain is finely discretized using eight-node hexahedral elements to obtain a three-dimensional finite element discretization model containing node information, element information, element volume information, and element node connection relationships.

[0011] Step S104: Set material parameters. Set the elastic modulus of the connecting bridge material. Poisson's ratio .

[0012] Step S105: Define the initial configuration. Construct an initial configuration formed by stretching two elliptical cross sections along the length of the connecting bridge, and convert the initial configuration into an initial relative density field as the initial design variable distribution for subsequent topology optimization iterations.

[0013] Step S200: Based on the three-dimensional finite element discrete model obtained in Step S100, a topology optimization mathematical model is established. Furthermore, a multigrid, matrix-free method, and GPU parallel solution strategy corresponding to this topology optimization mathematical model are constructed, resulting in a matrix-free GPU parallel solution strategy for the multigrid conjugate gradient method (MGCG). Specifically: Step S210: Establish a topology optimization mathematical model based on the density method. (The text abruptly ends here.) The design variable for each unit is defined as relative density. The SIMP interpolation method is used to establish the first The elastic modulus of each element is: (1) In the formula, For the first The elastic modulus of each unit; It is the minimum elastic modulus, used to avoid singularity problems; The elastic modulus of a solid material, and ; For the first with punishment Relative density of each unit This is the penalty factor, which is usually 3. For the Each element has an element stiffness matrix. Determined by both material parameters and element geometry information, it can be specifically expressed as: (2) In the formula, For the first The volume region of each unit; For the first The strain-displacement matrix of each element; For the first The material elasticity matrix of each unit.

[0014] When the connecting bridge material is an isotropic linear elastic material, the material elasticity matrix From the elastic modulus of the material Compared to Poisson Determined; during the topology optimization process, the first Material elasticity matrix of each unit By the elastic modulus of each unit Compared to Poisson The global stiffness matrix of the structure is determined jointly. All element stiffness matrices are assembled according to the element-node connection relationships to obtain the global stiffness matrix of the structure. Its expression is: (3) in, The design variable vector is composed of the relative densities of all elements; Total number of design variables; For the first Assembly matrix from individual units to global degrees of freedom.

[0015] With minimum compliance as the optimization objective, the objective function is established as follows: (4) In the formula, Let compliance be the objective function; This is the global load vector; This is the global displacement vector.

[0016] Material usage is controlled using volume fraction constraints: (5) in, and These represent the volume of each unit and the total volume of the structure, respectively. The target volume fraction; ρ is the relative density, and its value ranges from 0 to 1.

[0017] This yields the mathematical model for topology optimization, whose mathematical expression is as follows: (6) Step S220: Equilibrium equations in the topology optimization mathematical model established in step S210 Using the global stiffness matrix Due to the sparsity property, MGCG is used to solve the global displacement vector. The multi-mesh system is constructed by hierarchically coarsening the three-dimensional finite element discrete model obtained in step S103, forming a multi-layer mesh system from fine mesh to coarse mesh. The V-cycle strategy is preferably adopted to eliminate high-frequency errors on the fine mesh layer and correct low-frequency errors on the coarse mesh layer.

[0018] Step S230: Based on the solution of the equilibrium equations in step S220, the matrix-free finite element solution process is accelerated using GPU parallelism. A matrix-free GPU parallel finite element solution strategy is constructed to reduce memory usage and improve iteration efficiency. Specifically: Step S231: For the equilibrium equations in the topology optimization mathematical model in step S220... Explicitly assemble the global stiffness matrix Instead, it directly performs matrix-vector multiplication during the iterative solution process based on the element-node connection relationship, thus forming a finite element solution process based on the matrix-free method.

[0019] Step S232: The local matrix-vector multiplication operation and multigrid conjugate gradient method calculation in the finite element solution process based on the matrix-free method formed in step S231 are accelerated in parallel using GPU, and a GPU parallel accelerated finite element solution process is constructed, which is used as the parallel solution strategy for topology optimization iterative calculation in step S300.

[0020] Step S300: Based on the initial relative density field obtained in step S100 and the topology optimization mathematical model and parallel solution strategy established in step S200, perform iterative topology optimization calculations and output the converged topology optimization density field results. Specifically: Step S301: Use the initial relative density field obtained in step S105 as the initial design variable distribution, and set the iteration count. k .

[0021] Step S302: In the firstk In this iteration, the MGCG matrix-free GPU parallel solution strategy established in steps S220 to S232 is used to complete the finite element analysis and obtain the global displacement vector under the current design variable distribution. And calculate the compliance objective function value under the current design variable distribution according to equation (4). and its relation to the relative density of the unit Sensitivity: (7) In the formula, and The first The element displacement vector and element stiffness matrix corresponding to each element.

[0022] Step S303: Filter the relative density field or the sensitivity obtained in step S302 to suppress the checkerboard phenomenon and grid dependence; then, under the volume fraction constraint (Equation (3)), update the design variables using the optimal criterion method (OC method) to obtain the relative density field for the next iteration.

[0023] Step S304: Determine if the convergence criterion is met; when the rate of change of the compliance objective function value between two adjacent iterations meets the convergence criterion... And the maximum change in relative density among all elements satisfies When the topology optimization process is considered converged, the final topology optimization density field result is output; where, The compliance convergence threshold, Set the design variable convergence threshold; otherwise, the topology optimization process has not converged. Use the updated relative density field as the design variable distribution for the next iteration, and let... k = k +1, return to step S302 to continue iteration.

[0024] Step S400: Perform geometric post-processing and low-manual-cost automated reconstruction on the topology optimization density field results output in step S300 to obtain a manufacturable 3D solid structure for the connecting bridge. Specifically: Step S401: Perform volume-preserving threshold truncation on the topology optimization density field results, according to the threshold. λ Extract entity candidate regions; the threshold λ Determined based on the target volume fraction, so that the truncated solid volume matches the target volume fraction. f Maintain consistency or be largely consistent.

[0025] Step S402: Smooth the boundaries of the candidate entity regions obtained in step S401 to eliminate the jagged boundaries caused by the discretization of the hexahedral mesh.

[0026] Step S403: Output the smoothed candidate solid region as an intermediate geometry format file, and perform surface-sculpting and solidification reconstruction to obtain a manufacturable 3D connecting bridge solid model.

[0027] Step S500: Perform finite element analysis on the 3D connecting bridge solid model obtained in step S400; if the analysis result meets the preset indicators, output the final design scheme; otherwise, return to steps S200 to S400 to adjust the optimization parameters and iterate again. Specifically: Step S501: Import the three-dimensional connecting bridge solid model obtained in step S400 into the finite element analysis software, and perform strength and stiffness checks under the same boundary conditions and load conditions as in step S100 to obtain the maximum equivalent stress. σ max and maximum displacement δ max .

[0028] Step S502: Apply the maximum equivalent stress σ max With the allowable stress of the material σ allow Compare and determine the maximum displacement. δ max With allowable displacement δ allow Compare; when σ max ≤ σ allow and δ max ≤ δ allow If the three-dimensional connecting bridge solid model meets the preset indicators, the final design scheme is output; if it does not meet the indicators, the target volume fraction, non-design domain range, and threshold are adjusted. λ Alternatively, iterate through the control parameters and return to steps S200 to S400 to re-execute. The allowable stress of the material... σ allow The allowable stress value, determined based on the mechanical properties of the connecting bridge material, is preferably no greater than the material's yield strength. σ y The allowable displacement δ allow This is the upper limit of allowable deformation pre-set based on the stiffness requirements and service conditions of the connecting bridge.

[0029] Further, in step S102, the fixed end region corresponds to the connection area between the connecting bridge and the main hull's strength deck, and the stressed end region corresponds to the connection area between the connecting bridge and the sheet body. The filtering process in step S303 uses density filtering or sensitivity filtering. The intermediate geometry file in step S403 is an STL file. The preset indicators in step S500 include at least strength and stiffness indicators.

[0030] The beneficial effects of this invention are as follows: (1) Significant weight reduction effect: The present invention establishes a topology optimization mathematical model with minimum compliance as the target and volume fraction as the constraint through step S210, and obtains the converged topology optimization density field result through step S300, so that the material is redistributed along the main force transmission path, and the weight reduction of the connecting bridge structure is achieved under the premise of meeting the strength and stiffness requirements.

[0031] (2) Significantly reduce memory usage: In step S231, the present invention adopts a finite element solution process based on a matrix-free method. During the solution process, there is no need to explicitly assemble and store the global stiffness matrix, thereby avoiding the high storage overhead caused by large-scale sparse matrices and enabling desktop computers to perform high-resolution fine-grained topology optimization calculations.

[0032] (3) Significantly improve computational efficiency: This invention improves the solution efficiency of large-scale linear equation systems by using the multigrid conjugate gradient method in step S220, and accelerates key steps such as finite element analysis, sensitivity analysis and design variable update in parallel by using GPU in step S232, which significantly reduces the time consumption of a single iteration.

[0033] (4) Reduce the cost of manual reconstruction: In step S400, the present invention performs volume threshold truncation, boundary smoothing and entity reconstruction on the topology optimization density field results, thereby realizing the automatic conversion from density field to engineering entity model and reducing the reliance on manual interpretation, secondary modeling and repeated correction in traditional methods.

[0034] In summary, this invention combines topology optimization methods, matrix-free methods, multigrid conjugate gradient methods, and GPU parallel computing frameworks. It can not only achieve lightweight, high-efficiency, and low-memory design of trimaran connecting bridge structures, but also realize the automated reconstruction of topology optimization results into manufacturable engineering structures at low labor costs. Therefore, it has strong engineering practical value and promising prospects for widespread application. Attached Figure Description

[0035] Figure 1 This is a flowchart illustrating the implementation of a refined design method for a trimaran connecting bridge structure on a scale of hundreds of millions of units, based on topology optimization.

[0036] Figure 2The initial configuration of the three-dimensional connecting bridge semi-structure provided in the embodiment of the present invention.

[0037] Figure 3 This is a schematic diagram of a multi-grid V-loop provided in an embodiment of the present invention.

[0038] Figure 4 The flowchart of finite element solution based on matrix-free method and GPU is provided for embodiments of the present invention. Figure 4 (a) in the diagram is the KU calculation flowchart in the explicit matrix format; Figure 4 (b) in the diagram is a flowchart of the finite element solution based on the matrix-free method and GPU.

[0039] Figure 5 This invention provides a topology optimization configuration for a three-dimensional connecting bridge semi-structure with a 20% volume fraction, as provided in an embodiment of the invention. Figure 5 (a) in the diagram is the overall configuration diagram; Figure 5 (b) is a cross-sectional view.

[0040] Figure 6 This invention provides a topology optimization configuration for a three-dimensional connecting bridge semi-structure with a 10% volume fraction, as provided in an embodiment of the invention. Figure 6 (a) in the diagram is the overall configuration diagram; Figure 6 (b) is a cross-sectional view.

[0041] Figure 7 The diagram shows the boundary smoothing results of the three-dimensional connecting bridge topology optimization configuration with a 10% volume fraction provided in this embodiment of the invention.

[0042] Figure 8 This is a diagram of the reconstructed solid model of the three-dimensional connecting bridge provided in an embodiment of the present invention.

[0043] Figure 9 The displacement cloud diagram of the three-dimensional connecting bridge reconstruction model provided in the embodiment of the present invention.

[0044] Figure 10 Equivalent stress cloud diagram of the three-dimensional connecting bridge reconstruction model provided in the embodiments of the present invention. Detailed Implementation

[0045] The method of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention. Furthermore, it should be noted that, for ease of description, the accompanying drawings show only the parts relevant to the present invention and not all of them.

[0046] Example 1: This embodiment provides a refined design method for a trimaran connecting bridge structure on a scale of hundreds of millions of units based on topology optimization. The graphics card used is an RTX 5090D (32GB). The implementation process is as follows: Figure 1 As shown, it includes the following steps: Step S100: Construct the design domain and finite element discrete model of the trimaran connecting bridge. Based on the geometric shape and stress characteristics of the connecting bridge, establish the design domain and complete the finite element discrete modeling. Specifically: Step S101: Establish the three-dimensional geometric model of the connecting bridge and the boundary of the design domain. In this embodiment, a three-dimensional semi-structural geometric model of the connecting bridge is established based on the geometric symmetry of the connecting bridge, and a cuboid envelope is used to define the design domain, the size of which is set to length. L = 7.5 m, width W = 1.5 m, height H = 2 m. Figure 2 A schematic diagram of the initial configuration used in this embodiment is shown.

[0047] Step S102: Divide the design domain and non-design domain. In this embodiment, a cuboid-shaped non-design domain is set at the lower right end of the connecting bridge to simulate structural areas that must be retained in the project, such as connection interfaces, equipment installation areas, or local reinforcement areas, to avoid the topology optimization results from damaging the assembly boundary; a fixed end area is set at the upper left end, corresponding to the connection constraint area between the connecting bridge and the main hull's strong deck; a stressed end area is set at the lower right end, corresponding to the connection area between the connecting bridge and the sheet body. The working load is applied to the corresponding position of the finite element model in the form of surface load, line load, or equivalent nodal force; for torsional loads, an equivalent force couple or a pair of oppositely distributed forces are used to form torque to ensure that the torsional effect is reflected in the structure.

[0048] Step S103: Establish a finite element discretization model. The design domain is discretized using eight-node hexahedral elements. To demonstrate the advantages of this invention in large-scale refined calculations, the domain is divided into 960×192×256 elements in the length, width, and height directions, resulting in a total of 47,185,920 elements. This forms a three-dimensional finite element discretization model with hundreds of millions of degrees of freedom, generating finite element metadata structures such as node information, element information, element volume information, and element-node connection relationships.

[0049] Step S104: Define material parameters. In this embodiment, the connecting bridge material is aluminum alloy, and the elastic modulus is set. Poisson's ratio .

[0050] Step S105: Define the initial configuration. The three-dimensional configuration formed by stretching two elliptical cross sections along the length of the connecting bridge is defined as the initial configuration, and the initial configuration is converted into an initial relative density field as the initial design variable distribution for topology optimization iteration.

[0051] Step S200: Based on the finite element discrete model obtained in Step S100, establish a topology optimization mathematical model and construct a multi-grid, matrix-free, and GPU parallel solution strategy. The specific steps are as follows: Step S210: Establish a topology optimization mathematical model based on the density method. This embodiment uses the SIMP topology optimization model, defining the design variable of each element as relative density. Minimum elastic modulus Punishment factor The interpolation relationship for the element elastic modulus is as follows: (1) For the Each element has an element stiffness matrix. Determined by both material parameters and element geometry information, it can be specifically expressed as: (2) After assembling all element stiffness matrices according to element-node connection relationships, the global stiffness matrix of the structure is obtained. Its expression is: (3) With minimum compliance as the optimization objective, the objective function expression is as follows: (4) The volume fraction constraint is used to control the structural materials usage. The constraint expression is as follows: (5) The mathematical formulation of this structural optimization problem is as follows: (6) Combined with the elastic modulus given in step S104 Compared to Poisson Determine the first according to formula (1) elastic modulus of each unit Calculate the element stiffness matrix according to equation (2) The global stiffness matrix of the assembled structure is calculated according to equation (3). Furthermore, based on equations (4) to (6), a topology optimization mathematical model is established with minimum compliance as the objective and volume fraction as the constraint. In this embodiment, the target volume fraction is taken respectively. = 20% and = 10% for comparative analysis.

[0052] Step S220: Solve the equilibrium equations obtained in step S210 using the multigrid conjugate gradient method (MGCG). Because the linear equation system corresponding to the billion-scale connecting bridge model is enormous, this embodiment coarsens the three-dimensional finite element discrete model obtained in step S103 by hierarchical coarsening, constructing a multi-layer mesh system including fine and coarse mesh layers, and employing a multi-mesh V-cycle strategy, such as... Figure 3 As shown, high-frequency errors are first eliminated on the fine grid layer, then the errors are restricted to the coarse grid layer for correction, and finally the correction results are interpolated and returned to the fine grid layer, thereby improving the solution efficiency of large-scale linear equation systems.

[0053] Step S230: For the equilibrium equations in step S220 Based on the solution, the matrix-free finite element method (FEM) solution process is accelerated using GPU parallelism. A matrix-free GPU parallel finite element method (FEM) solution strategy is constructed to reduce memory usage and improve iteration efficiency. Specifically: Step S231: For the equilibrium equation in step S220 Explicitly assemble the global stiffness matrix Based on the mesh size estimation in this embodiment, if an explicit stiffness matrix is ​​used for storage, the storage size of the element stiffness matrix alone would be approximately 47,185,920 × 24 × 24 × 8 bytes, or about 202.5 GB. This does not include the overhead of the index matrix and solution cache, which is generally difficult for a desktop computer to handle. Therefore, this embodiment adopts a matrix-free method, performing matrix-vector multiplication operations node-by-node or element-by-element according to the element-node connection relationship during the iterative solution process, thereby avoiding the explicit storage and assembly of the global stiffness matrix.

[0054] Step S232: Based on the matrix-free finite element solution process in step S231, a GPU parallel computing framework is used to accelerate the solution process. Specifically, as follows... Figure 4 As shown: First, the global displacement vector is rearranged into an element displacement matrix according to the element-node connection relationship; then, in the GPU, the element is used as the basic parallel object, and the element stiffness matrix and element displacement vector are called to perform local matrix-vector multiplication to obtain the element local response; then, according to the element-node mapping relationship, the local responses of each element are accumulated in parallel to the global vector, thereby controlling the memory usage and improving memory access efficiency.

[0055] Step S300: Perform topology optimization iterative calculations and output the converged topology optimization density field results. This includes the following: Step S301: Use the initial relative density field obtained in step S105 as the initial design variable distribution, and set the iteration count. k = 0.

[0056] Step S302: In the first kIn this iteration, the MGCG matrix-free GPU parallel solution strategy established in steps S220 to S232 is used to complete the finite element analysis and obtain the global displacement vector. And calculate the compliance objective function value under the current design variable distribution according to equation (4). and its relation to the relative density of the unit x e The sensitivity. The sensitivity expression is as follows: (6) Step S303: Filter the relative density field or the sensitivity obtained in step S302 to suppress the checkerboard phenomenon and grid dependence; then, under the volume fraction constraint equation (5), update the design variables using the optimality criterion method (OC method) to obtain the relative density field for the next iteration.

[0057] Step S304: When the rate of change of the compliance objective function in two adjacent iterations satisfies And the maximum change in relative density among all elements satisfies If convergence is achieved, the topology optimization process is considered complete, and the final topology optimization density field result is output. Otherwise, the topology optimization process has not converged, and the updated relative density field is used as the design variable distribution for the next iteration, and the following is set... k = k +1, return to step S302 to continue iteration.

[0058] In this embodiment, the average time per iteration is approximately 1.5 minutes. For the two operating conditions of 20% volume fraction and 10% volume fraction, the following results were obtained: Figure 5 and Figure 6 The diagram shows an optimized topology configuration for a three-dimensional connecting bridge. (The diagram is derived from...) Figure 5 and Figure 6 As can be seen, the optimized result forms a relatively wide main load-bearing root near the fixed end, and a near-closed plate structure distributed along the principal stress transmission path between the free end and the fixed end. Compared with the simplified rod-shaped or open layouts commonly seen at conventional resolutions, this topological configuration can more fully reflect the complex force transmission relationships and local detailed features within the structure.

[0059] Step S400: Perform geometric post-processing and low-manual-cost automated reconstruction on the topology optimization density field results output in step S300. Specifically, this includes the following steps: Step S401: The topology optimization density field results are truncated using a volume-preserving threshold to extract candidate entity regions. In this embodiment, the threshold... λ The target volume is determined based on the target volume fraction and the target volume corresponding to the density field. Specifically, for topology optimization results with a target volume fraction of 20%, the threshold is... λ=0.02; For topology optimization results with a target volume fraction of 10%, the threshold is... λ =0.02. This ensures the truncated entity volume matches the target volume corresponding to the target volume fraction.

[0060] Step S402: Smooth the boundaries of the candidate solid regions obtained in step S401 to reduce the jagged boundaries caused by the hexahedral mesh. Figure 7 The boundary smoothing results for the topology optimization configuration with a 10% volume fraction are shown.

[0061] Step S403: Export the smoothed entity candidate region as an STL file and import it into Rhino software for feature processing and solidification, constructing a smooth NURBS surface model and converting it into a solid model, such as... Figure 8 As shown. During the reconstruction process, the geometric continuity between the constrained region and the load application region is maintained, and local transition regions are rounded or thickened to reduce the risk of stress concentration.

[0062] Step S500: Perform finite element analysis on the 3D connecting bridge solid model obtained in step S400, and complete the closed-loop design based on the analysis results. Specifically, this includes the following steps: Step S501: Import the reconstructed 3D connecting bridge solid model into the finite element analysis software, and perform static analysis under the same boundary conditions and load conditions as in the topology optimization stage to obtain the maximum equivalent stress. σ max and maximum displacement δ max .

[0063] Step S502: In this embodiment, the connecting bridge material is aluminum alloy, and the material yield strength is... σ y =220 MPa, the allowable stress of the material σ allow Take 220 MPa; the allowable displacement δ allow The stiffness design requirement for the connecting bridge is set at 0.20m. Taking a 10% volume fraction reconstruction model as an example, its displacement contour plot is as follows. Figure 9 As shown, the equivalent stress contour map is as follows: Figure 10 As shown. The calculation results show that the maximum equivalent stress σ max = 189 MPa, less than the allowable stress of the material σ allow = 220 MPa; Maximum displacement δ max =0.169 m, less than the allowable displacement δ allow= 0.20 m, meeting the preset strength and stiffness indicators. If the verification result does not meet the preset indicators, adjust the target volume fraction, non-design domain range, or threshold. λ Then return to steps S200 to S400 and re-execute.

[0064] As can be seen from the above embodiments, the method provided by this invention can effectively solve the problem of lightweight and refined design of trimaran connecting bridge structures on a desktop computing platform with scales of hundreds of millions. This invention combines topology optimization, multi-grid conjugate gradient method, matrix-free methods, and GPU parallel acceleration to construct a computational framework. Without requiring explicit assembly of the global stiffness matrix, it significantly reduces the storage overhead of large-scale three-dimensional topology optimization calculations and effectively improves iterative solution efficiency. Furthermore, by performing volume-preserving threshold truncation, boundary smoothing, and solid reconstruction on the topology optimization density field results, it can further achieve automated reconstruction with low manual costs, providing an feasible technical path for the innovative design of complex engineering structures.

[0065] The embodiments described above are merely illustrative of implementation methods of the present invention and should not be construed as limiting the scope of the invention. It should be noted that any modifications or improvements made based on the inventive concept should be included within the scope of protection of the present invention.

Claims

1. A refined design method for trimaran connecting bridges based on topology optimization, characterized in that, The refined design method for the trimaran connecting bridge includes the following steps: Step S100: Construct the design domain and three-dimensional finite element discrete model of the trimaran connecting bridge; Based on the geometry, boundary constraints, and stress conditions of the trimaran connecting bridge, a design domain is established. The design domain is then finely meshed to form a three-dimensional finite element discrete model. Material parameters, non-design domain, load application area, and initial configuration are defined, and the initial configuration is converted into an initial relative density field. Step S200: Based on the three-dimensional finite element discrete model obtained in step S100, establish a topology optimization mathematical model, and further construct the multigrid, matrix-free method and GPU parallel solution strategy corresponding to the topology optimization mathematical model to obtain the matrix-free GPU parallel solution strategy of the multigrid conjugate gradient method (MGCG). Step S300: Based on the initial relative density field obtained in step S100 and the topology optimization mathematical model and parallel solution strategy established in step S200, perform topology optimization iterative calculation and output the converged topology optimization density field result. Step S400: Automated reconstruction of the topology optimization density field results output in step S300 to obtain a three-dimensional solid structure of the engineering-manufacturable connecting bridge; Step S500: Perform finite element verification on the three-dimensional connecting bridge solid model obtained in step S400; when the verification result meets the preset index, output the final design scheme; otherwise, return to steps S200 to S400 to adjust the optimization parameters and iterate again.

2. The refined design method for trimaran connecting bridges based on topology optimization as described in claim 1, characterized in that, The specific steps of S100 are as follows: Step S101: Establish the three-dimensional geometric model of the connecting bridge and the design domain boundary; establish the three-dimensional geometric model of the connecting bridge according to the connection relationship between the main hull and the sheet hull of the trimaran, and define the design domain boundary using a cuboid envelope or an envelope body that matches the shape of the connecting bridge. Step S102: Divide the design domain and non-design domain; Based on the assembly interface, constraint area, load application area, and engineering structural area that must be retained, divide the entire connecting bridge into an optimizable design domain and a non-optimizable non-design domain; Among them, the non-design domain is used to retain the connection boundary, installation area, or local reinforcement area; Step S103: Establish a three-dimensional finite element discretization model; use eight-node hexahedral elements to finely discretize the design domain to obtain a three-dimensional finite element discretization model containing node information, element information, element volume information, and element node connection relationships; Step S104: Set material parameters; set the elastic modulus of the connecting bridge material. Poisson's ratio ; Step S105: Define the initial configuration; construct the initial configuration formed by stretching two elliptical sections along the length of the connecting bridge, and convert the initial configuration into an initial relative density field as the initial design variable distribution for subsequent topology optimization iterations.

3. The refined design method for trimaran connecting bridges based on topology optimization as described in claim 2, characterized in that, The specific steps of S200 are as follows: Step S210: Establish a topology optimization mathematical model based on the density method; [The remaining text appears to be incomplete and requires further context.] e The design variable for each unit is defined as relative density. The SIMP interpolation method is used to establish the first e The elastic modulus of each element is: (1) In the formula, For the first The elastic modulus of each unit; It is the minimum elastic modulus, used to avoid singularity problems; The elastic modulus of a solid material, and ; For the first with punishment Relative density of each unit As a penalty factor; For the Each element has an element stiffness matrix. Determined by both material parameters and element geometry information, specifically expressed as: (2) In the formula, For the first The volume region of each unit; For the first The strain-displacement matrix of each element; For the first The material elasticity matrix of each unit; When the connecting bridge material is an isotropic linear elastic material, the material elasticity matrix From the elastic modulus of the material Compared to Poisson Determined; during the topology optimization process, the first Material elasticity matrix of each unit By the elastic modulus of each unit Compared to Poisson The global stiffness matrix of the structure is obtained by assembling all element stiffness matrices according to the element-node connection relationships. Its expression is: (3) in, The design variable vector is composed of the relative densities of all elements; Total number of design variables; For the first Assembly matrix from unit to global degrees of freedom; With minimum compliance as the optimization objective, the objective function is established as follows: (4) In the formula, Let compliance be the objective function; This is the global load vector; This is the global displacement vector; Material usage is controlled using volume fraction constraints: (5) in, and These represent the volume of each unit and the total volume of the structure, respectively. The target volume fraction; Relative density; This yields the mathematical model for topology optimization, whose mathematical expression is as follows: (6) Step S220: Equilibrium equations in the topology optimization mathematical model established in step S210 Using the global stiffness matrix Due to the sparsity property, MGCG is used to solve the global displacement vector. ; Step S230: Based on the solution of the equilibrium equation in step S220, the matrix-free finite element solution process is accelerated by GPU parallelism. A matrix-free GPU parallel finite element solution strategy is constructed to reduce memory usage and improve iteration efficiency.

4. The refined design method for trimaran connecting bridges based on topology optimization as described in claim 3, characterized in that, In step S210, the penalty factor It is 3; relative density The value range is from 0 to 1.

5. The refined design method for trimaran connecting bridges based on topology optimization as described in claim 4, characterized in that, In step S220, the multi-mesh system is constructed by hierarchically coarsening the three-dimensional finite element discrete model to form a multi-layer mesh system from fine mesh to coarse mesh. The V-cycle strategy is preferably adopted to eliminate high-frequency errors on the fine mesh layer and correct low-frequency errors on the coarse mesh layer.

6. The refined design method for trimaran connecting bridges based on topology optimization as described in claim 5, characterized in that, Step S230 specifically includes: Step S231: For the equilibrium equations in the topology optimization mathematical model in step S220... Based on the element-node connection relationship, matrix-vector multiplication is directly completed during the iterative solution process, forming a finite element solution process based on the matrix-free method; Step S232: The local matrix-vector multiplication operation and multigrid conjugate gradient method calculation in the finite element solution process based on the matrix-free method formed in step S231 are accelerated in parallel using GPU, and a GPU parallel accelerated finite element solution process is constructed, which is used as the parallel solution strategy for topology optimization iterative calculation in step S300.

7. A refined design method for trimaran connecting bridges based on topology optimization, as described in claim 6, is characterized in that... Specifically, step S300 includes: Step S301: Use the initial relative density field as the initial design variable distribution and set the iteration count. k ; Step S302: In the first k In this iteration, the MGCG matrix-free GPU parallel solution strategy established in steps S220 to S232 is used to complete the finite element analysis and obtain the global displacement vector under the current design variable distribution. And calculate the compliance objective function value under the current design variable distribution according to equation (4). and its relation to the relative density of the unit Sensitivity: (7) In the formula, and The first The element displacement vector and element stiffness matrix corresponding to each element; Step S303: Filter the relative density field or the sensitivity obtained in step S302 to suppress the checkerboard phenomenon and grid dependence. Subsequently, under the volume fraction constraint, the design variables are updated using the optimal criterion method to obtain the relative density field for the next iteration; Step S304: Determine if the convergence criterion is met; when the rate of change of the compliance objective function value between two adjacent iterations meets the convergence criterion... And the maximum change in relative density among all elements satisfies When the topology optimization process is considered converged, the final topology optimization density field result is output; where, The compliance convergence threshold, Design a convergence threshold for the variable; Otherwise, if the topology optimization process does not converge, the updated relative density field is used as the design variable distribution for the next iteration, and then... k = k +1, return to step S302 to continue iteration.

8. The refined design method for trimaran connecting bridges based on topology optimization as described in claim 7, characterized in that, Specifically, step S400 includes: Step S401: Perform volume-preserving threshold truncation on the topology optimization density field results, according to the threshold. λ Extract entity candidate regions; the threshold λ Determined based on the target volume fraction, so that the truncated solid volume matches the target volume fraction. f Maintain consistency or be largely consistent; Step S402: Smooth the boundaries of the candidate entity regions obtained in step S401 to eliminate the jagged boundaries caused by the discretization of the hexahedral mesh; Step S403: Output the smoothed candidate solid region as an intermediate geometry format file, and perform surface-sculpting and solidification reconstruction to obtain a manufacturable 3D connecting bridge solid model.

9. A refined design method for trimaran connecting bridges based on topology optimization, as described in claim 8, is characterized in that... Specifically, step S500 includes: Step S501: Import the three-dimensional connecting bridge solid model obtained in step S400 into the finite element analysis software, and perform strength and stiffness checks under the same boundary conditions and load conditions as in step S100 to obtain the maximum equivalent stress. σ max and maximum displacement δ max ; Step S502: Apply the maximum equivalent stress σ max With the allowable stress of the material σ allow Compare and determine the maximum displacement. δ max With allowable displacement δ allow Compare; when σ max ≤ σ allow and δ max ≤ δ allow If the three-dimensional connecting bridge solid model meets the preset indicators, the final design scheme is output; if it does not meet the indicators, the target volume fraction, non-design domain range, and threshold are adjusted. λ Alternatively, iterate the control parameters and return to steps S200 to S400 to re-execute; the allowable stress of the material σ allow The allowable stress value is determined based on the mechanical properties of the connecting bridge material, and the allowable displacement is... δ allow This is the upper limit of allowable deformation pre-set based on the stiffness requirements and service conditions of the connecting bridge.

10. A refined design method for trimaran connecting bridges based on topology optimization, as described in claim 9, characterized in that... In the refined design method for the trimaran connecting bridge: In step S102, the fixed end area corresponds to the connection area between the connecting bridge and the main hull strong deck, and the force-bearing end area corresponds to the connection area between the connecting bridge and the sheet body. The filtration process in step S303 uses density filtration or sensitivity filtration. The intermediate geometry format file in step S403 is an STL file; The preset indicators in step S500 include at least strength indicators and stiffness indicators; In step S500, the allowable stress of the material σ allow Not greater than the material's yield strength σ y .

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