Topological optimization method for rudder system structure of high-anti-roughness marine engineering equipment

Abstract

The application belongs to the technical field of ocean engineering structure design, and discloses a high-wave-resistance ocean engineering equipment rudder system structure topology optimization method; firstly, ocean wave alternating load spectrum and rudder surface fluid dynamic load are acquired, and a multi-scale initial stress field of a design domain is solved through coupling mapping; in the topology iteration evolution process, a notch sensitive area is intelligently identified based on local geometric curvature change rate and stress gradient direction; a multi-scale fatigue damage factor evaluation model is established in combination with seawater corrosion environment parameters and micro material grain characteristics; a topology optimization objective function is constructed with minimization of structure flexibility as a basic target and the multi-scale fatigue damage factor as a dynamic penalty term, material is guided to flow to the notch sensitive area through dynamic adjustment of a weight coefficient; and finally, adaptive boundary smoothing processing is performed based on the geometric feature distribution of the notch sensitive area. The application realizes high reliability design of ocean engineering equipment structure under 100 million times of wave cyclic load.

Description

Technical Field

[0001] This invention relates to the field of marine engineering structure design technology, and more specifically, to a method for optimizing the topology of rudder systems for high wave-resistant marine engineering equipment. Background Technology

[0002] Existing technologies for topology optimization design of rudder systems in marine engineering equipment suffer from theoretical flaws and blind spots in engineering applications. Traditional topology optimization methods, with maximizing stiffness as their core objective, can achieve structural configurations with excellent load-bearing capacity, but they reveal fatal weaknesses when faced with the tens of millions of wave cycles in the marine environment. The key problem lies in the irreconcilable contradiction between the serrated and highly irregular boundary morphology naturally generated by topology optimization and the fatigue life requirements of marine engineering. In the harsh corrosive environment of seawater, even seemingly insignificant geometrical abrupt changes on the optimization boundary can rapidly evolve into stress concentration "hot spots" under the synergistic effects of chloride ion penetration, electrochemical corrosion, and alternating stress. These sensitive areas exhibit failure modes completely different from the macroscopic structural stiffness under multi-scale fatigue damage mechanisms: micromaterial grains undergo plastic deformation accumulation driven by local high stress gradients, corrosion pits and microcracks preferentially initiate and rapidly propagate at geometrical discontinuities, ultimately leading to fatigue failure of the overall structure far from reaching its static strength limit. Traditional optimization theory lacks a deep understanding of the multi-scale damage evolution process under such multi-physics coupling, and cannot predict and avoid the risk of shortened fatigue life caused by topology optimization in the design stage. This leads to the frequent occurrence of the abnormal phenomenon in engineering practice where "the optimized structure has excellent static performance, but its service life is significantly reduced", which restricts the reliable application of topology optimization technology in the field of marine engineering.

[0003] In view of this, the present invention proposes a topology optimization method for the rudder system structure of high wave resistance marine engineering equipment to solve the above problems. Summary of the Invention

[0004] To overcome the aforementioned deficiencies of the prior art and to achieve the above objectives, the present invention provides the following technical solution: a topology optimization method for the rudder system structure of high wave-resistant marine engineering equipment, comprising:

[0005] Obtain the design domain boundary conditions, material properties, ocean wave alternating load spectrum and rudder surface hydrodynamic load of the marine engineering equipment rudder system, couple and map the wave alternating load spectrum and rudder surface hydrodynamic load to the design domain, and solve to obtain the multi-scale initial stress field of the design domain under coupled alternating load.

[0006] Based on the multi-scale initial stress field and the preset material interpolation model, topological iterative evolution is performed. The topological boundary is extracted in the density field generated by each topological iterative evolution. The local geometric curvature change rate of each boundary node sequence on the topological boundary is calculated. Based on the local geometric curvature change rate and the stress gradient direction of the multi-scale initial stress field, the cut-sensitive region caused by geometric abrupt change is identified.

[0007] For the notch-sensitive area, a multi-scale fatigue damage factor is calculated by combining seawater corrosion environment parameters and micromaterial grain characteristics. The multi-scale fatigue damage factor is determined based on the cumulative difference between the local stress concentration factor, effective stress amplitude and corrosion fatigue crack initiation threshold in the notch-sensitive area.

[0008] A topology optimization objective function is constructed with minimizing the overall structural compliance as the basic objective and multi-scale fatigue damage factor as the dynamic penalty term. In the topology iterative evolution, the weight coefficient of the dynamic penalty term is dynamically adjusted based on the notch-sensitive evolution state of the current iteration step. The element sensitivity is modified based on the topology optimization objective function to promote the flow of topological material to the notch-sensitive region or smooth the topological boundary morphology to weaken stress concentration.

[0009] After the topology iteration converges, an adaptive boundary smoothing process is performed based on the distribution of the rate of change of local geometric curvature in the sensitive area of ​​the notch to generate a rudder system topology configuration that satisfies the multi-scale fatigue life constraint.

[0010] The technical effects and advantages of the topology optimization method for rudder system structure of high wave-resistant marine engineering equipment of this invention are as follows:

[0011] This invention eliminates the technical blind spots of traditional topology optimization in marine environment applications by establishing an intrinsic correlation mechanism between notch sensitivity and multi-scale fatigue damage, enabling the optimized rudder system structure to maintain fatigue resistance while withstanding tens of millions of wave cycles. This invention overcomes the technical bottleneck of the previous inability to simultaneously maximize stiffness and fatigue life in optimization design, achieving accurate prediction and active control of the entire process from microscopic grain damage to macroscopic structural failure in complex corrosive environments. This invention provides a new theoretical basis and implementation approach for the full life-cycle reliability design of marine engineering equipment, improving the environmental adaptability and service stability of structures in harsh marine environments, changing the passive situation of "qualified static strength but insufficient fatigue life" in traditional design, and laying a technical foundation for the expansion of marine engineering equipment to deeper sea areas and harsher environments. Attached Figure Description

[0012] Figure 1 This is a schematic diagram of the topology optimization method for the rudder system structure of high wave-resistant marine engineering equipment according to the present invention. Detailed Implementation

[0013] 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.

[0014] This application provides a topology optimization method for rudder systems of high wave-resistant marine engineering equipment. The method is applicable to improving fatigue resistance during the topology optimization design process of rudder systems in marine engineering equipment. The method enables accurate identification of sensitive areas and topology optimization under fatigue life constraints. The execution entities of the method include, but are not limited to: structural topology optimization platforms, marine engineering equipment design systems, rudder system design tools, and intelligent topology optimization units, which can be considered as general computing nodes in this application.

[0015] Please see Figure 1 In this embodiment of the invention, the specific implementation process of the topology optimization method for the rudder system structure of high wave-resistant marine engineering equipment includes:

[0016] This process involves acquiring the design domain boundary conditions, material properties, and alternating wave load spectrum and rudder surface hydrodynamic loads of the marine engineering equipment's rudder system. The alternating wave load spectrum and rudder surface hydrodynamic loads are then coupled and mapped to the design domain to obtain the multi-scale initial stress field under coupled alternating loads. Specifically, the spatial extent of the design domain is extracted from the three-dimensional geometric model of the rudder system structure, including the rudder blade shape, rudder stock connection points, and the geometric boundaries of the internal designable regions. Material databases are accessed to obtain key property parameters such as the elastic modulus, Poisson's ratio, density, and fatigue strength of the steel or composite materials used in the rudder system. Boundary conditions are set, including the fixed constraints between the rudder stock and the hull, and the contact boundaries between the rudder blade and the water medium. In the load acquisition phase, historical wave statistics from the marine engineering equipment's operating area are queried to extract significant wave height, average period, and other characteristic parameters. Combined with hydrodynamic simulation results, the rudder surface pressure distribution at different speeds and steering angles is obtained. This multi-source information provides comprehensive input data for subsequent analysis, ensuring the engineering applicability and safety reliability of the optimized design.

[0017] Topological iterative evolution is performed based on a multi-scale initial stress field and a pre-defined material interpolation model. In each iteration, the topological boundary is extracted from the density field generated. The rate of change of local geometric curvature of each boundary node sequence is calculated. Based on the rate of change of local geometric curvature and the stress gradient direction of the multi-scale initial stress field, sensitive regions for cuts caused by geometric abrupt changes are identified. This identification process is performed in real-time at each step of the topological iteration. First, the material-void topological boundary is extracted based on the relative density field of the current element. Isosurface extraction is used, identifying isolines or isosurfaces with relative densities between 0.3 and 0.7 as the current topological boundary. Discrete node sequences are extracted along the boundary. A local curvature analysis window is constructed for each node. By fitting the coordinates of the node and its multiple neighboring nodes, the second derivative of the local fitted curve is calculated to obtain the geometric curvature value at that point. The rate of change of curvature is obtained by the difference in curvature values ​​between adjacent nodes. When the rate of change of curvature of a node increases abnormally and the stress gradient direction at that location points outward from the boundary, it is marked as a potential sensitive point for cuts.

[0018] For the notch-sensitive area, a multi-scale fatigue damage factor is calculated by combining seawater corrosion environment parameters and microstructure grain characteristics. The multi-scale fatigue damage factor is determined based on the cumulative difference between the local stress concentration factor, effective stress amplitude, and corrosion fatigue crack initiation threshold in the notch-sensitive area. The calculation process first extracts the stress amplitude time history of the notch-sensitive area under coupled alternating loads, and uses the rainflow counting method to count the number of cycles for each stress amplitude level. Combining local geometric features (such as minimum radius of curvature and thickness gradient) and microstructure grain size, the theoretical stress concentration factor is calculated, and corrosion reduction corrections are applied based on the cathodic protection potential and dissolved oxygen concentration of the seawater corrosion environment to obtain the multi-scale effective stress amplitude. The effective stress amplitude is compared with the corrosion fatigue crack initiation threshold of the material to extract the stress cycle parameters exceeding the limit, and the fatigue damage factor is calculated based on the proportion of exceeding the limit cycles to the total number of cycles. By fully considering the coupled effects of geometric factors, material microstructure, and the marine environment, the accuracy and engineering applicability of fatigue life prediction are significantly improved.

[0019] A topology optimization objective function is constructed with minimizing the overall structural compliance as the basic goal and multi-scale fatigue damage factors as the dynamic penalty term. During topology iterative evolution, the weight coefficients of the dynamic penalty term are dynamically adjusted based on the notch-sensitive evolution state of the current iteration step. Element sensitivity is modified based on the topology optimization objective function to encourage material flow towards notch-sensitive regions or smooth topological boundary morphology to reduce stress concentration. First, a traditional compliance minimization objective term is established, which characterizes the overall stiffness performance of the structure through global displacement energy. Then, a fatigue penalty term is added, which is a weighted sum of fatigue damage factors in all notch-sensitive regions, initially assigned a small weight coefficient to prioritize the overall load-bearing efficiency of the topology configuration. In the mid-to-late stages of iterative evolution, the maximum fatigue damage factor in the notch-sensitive regions is monitored in real time. When this value exceeds a preset safety threshold, an exponential growth mechanism of the weight coefficients is triggered, significantly increasing the influence of the fatigue penalty term on the optimization direction. The sensitivity modification stage calculates the sensitivity of each element to the objective function using the adjoint method, applying an additional density maintenance or increase tendency to the elements corresponding to the notch-sensitive regions, guiding the material distribution towards reducing geometric abrupt changes and increasing transition fillets.

[0020] After topological iteration convergence, adaptive boundary smoothing is performed based on the local geometric curvature change rate distribution of the sensitive area to generate a rudder system topology that satisfies multi-scale fatigue life constraints. Specifically, after determining topological iteration convergence (objective function change rate is less than a set threshold and constraint conditions are met), the density field distribution and topological boundary geometry of the final iteration step are first obtained, and all identified sensitive areas and their local geometric curvature change rate distribution features are extracted. Adaptive smoothing kernel scales are assigned to different nodes on the boundary. Nodes in the sensitive area are assigned larger smoothing kernels (usually 3 to 5 times the element size) to achieve stronger geometric smoothing effects; nodes in non-sensitive areas are assigned smaller smoothing kernels (1 to 2 times the element size) to maintain the overall characteristics of the topology. The smoothing process uses a kernel function-based local convolution method to perform weighted averaging of the position coordinates of the boundary nodes, eliminating sharp angle abrupt changes and jagged shapes. After processing, local mesh reconstruction is performed to generate a high-quality finite element mesh on the smoothed boundary, and multi-scale stress verification is performed to confirm that the stress concentration factor and fatigue damage factor of the sensitive area have both decreased to a safe range. After successful verification, the final rudder system topology is output as the input model for the detailed design phase.

[0021] In this embodiment of the invention, the detailed implementation steps for obtaining the design domain boundary conditions, material properties, ocean wave alternating load spectrum, and rudder surface hydrodynamic load of the marine engineering equipment rudder system, coupling and mapping the wave alternating load spectrum and rudder surface hydrodynamic load to the design domain, and solving for the multi-scale initial stress field of the design domain under coupled alternating loads include:

[0022] Wave statistics for the rudder system's operating area are obtained, and a wave alternating load spectrum containing tens of millions of cycles is generated. This spectrum is then decomposed into multi-order harmonic loads. First, multi-year wave observation data for the target area is extracted from operational records of marine engineering equipment and marine environmental databases, including key parameters such as significant wave height, peak period, and wave direction. A Weibull distribution or log-normal distribution is used to statistically fit the wave height, and a joint probability density function is used to describe the correlation between wave height and period. Based on the fitted statistical model, a wave time history covering the rudder system's design life (typically 20 to 30 years) is generated, typically containing tens of millions of wave cycles. To facilitate subsequent calculations, the time-domain wave load spectrum is decomposed into multi-order harmonic components using a fast Fourier transform. Each harmonic corresponds to a specific frequency and amplitude; typically, the first 10 to 20 major harmonics are retained to ensure a balance between accuracy and computational efficiency. The harmonic decomposition method transforms complex random loads into controllable combinations of periodic loads, providing a convenient mathematical expression for subsequent frequency domain analysis and stress superposition.

[0023] Multi-order harmonic loads and rudder surface hydrodynamic loads are superimposed on the fluid-structure interaction boundary of the design domain, and transient dynamic analysis is performed to extract the stress response under each order of coupled loads. The application process begins by defining the load application region on the fluid-structure interaction boundary (outer surface of the rudder blade) of the rudder system design domain. This region is determined based on the hydrodynamic geometry of the rudder blade and the flow field distribution. The rudder surface hydrodynamic loads (including lift, drag, and torque distribution) are used as the basic load field. These loads are pre-calculated through computational fluid dynamics simulations at different speeds and rudder angles. Harmonic loads of each order are superimposed on the basic load field. Each harmonic load is expanded in the time domain according to its frequency and phase relationship, forming a time-varying composite load history. An implicit time integration method is used to perform transient dynamic analysis. The time step is determined based on the highest-order harmonic frequency to satisfy the sampling theorem, and the calculation period covers a sufficiently long time to capture the complete influence of low-frequency harmonics. The analysis process extracts the stress tensor components of all elements within the design domain at each time step, paying particular attention to fatigue-related stress indices such as maximum principal stress and Von Mises equivalent stress. This stress response extraction method accurately reflects the dynamic characteristics of the load and the dynamic effects of the structure.

[0024] Based on the principle of stress superposition, the stress responses under various coupled loads are combined, and multi-scale interpolation mapping is performed on the combined stress field to separate the macroscopic overall stress distribution and microscopic local stress fluctuation characteristics, thereby obtaining a multi-scale initial stress field. The construction process first applies the principle of linear superposition to vector synthesize the stress responses under individual harmonic loads according to their amplitude and phase relationships, obtaining the comprehensive stress field under global coupled loads. Superposition employs frequency domain complex number operations to improve computational efficiency, and the stress value at each spatial point is obtained through complex vector addition. The combined stress field contains multi-level information from the overall structural scale to the local unit scale, which is decomposed into macroscopic and microscopic scale components using multi-scale interpolation mapping technology. The separation process uses wavelet transform or Gaussian filtering methods, setting a characteristic length threshold (usually one-tenth of the structural feature size) to identify slowly changing spatial stress distributions as macroscopic overall stress and drastically changing spatial stress fluctuations as microscopic local stress. Macroscopic stress reflects the overall stress state and main force transmission paths of the structure, while microscopic stress captures the stress concentration effects caused by local geometric features (such as holes, transitions, etc.). The separated multi-scale initial stress field provides rich mechanical information for subsequent identification of sensitive areas of the cut. Macroscopic stress is used to determine the main force direction, while microscopic stress is used to identify local peaks and gradient anomalies. The combination of the two significantly improves the accuracy and comprehensiveness of dangerous part identification.

[0025] In this embodiment of the invention, topological iterative evolution is performed based on a multi-scale initial stress field and a preset material interpolation model. Topological boundaries are extracted from the density field generated in each topological iterative evolution. The local geometric curvature change rate of each boundary node sequence on the topological boundary is calculated. Based on the local geometric curvature change rate and the stress gradient direction of the multi-scale initial stress field, the detailed implementation steps for identifying the cut-sensitive region caused by geometric abrupt changes include:

[0026] During the topological iterative evolution process, relative density isosurfaces are extracted based on the relative density field of the cells in the current iteration step as the current topological boundary, and an ordered sequence of boundary nodes is extracted along the current topological boundary. The extraction process is executed immediately after the density update in each iteration step. First, the relative density values ​​of all cells are read (ranging from 0 to 1, where 0 represents voids and 1 represents solid material). Using a moving cube algorithm or isosurface tracing algorithm, a spatial surface with a relative density equal to a preset threshold (usually 0.5) is identified in the 3D density field; this surface is the current topological boundary. Boundary extraction employs adaptive mesh refinement technology, increasing the sampling point density in areas with large density gradients to improve the accuracy of boundary localization. The extracted boundary is expressed as triangular patches or curve segments. All vertices are geometrically traversed along the boundary, and ordered according to spatial continuity to form an ordered sequence of nodes. The ordered nature of the node sequence ensures the correctness of adjacency relationships in subsequent curvature calculations, providing a structured data foundation for local geometric analysis.

[0027] For any node in an ordered boundary node sequence, a local fitting curve is constructed based on that node and its neighboring nodes. The curvature value of the local fitting curve at that node is calculated as the local geometric curvature change rate. Specifically, for each node in the node sequence, several neighboring nodes (usually 3 to 5 each) are selected to form a local analysis window. Least square fitting is performed on the node coordinates within the window, fitting a quadratic curve in two dimensions and a parametric equation of a space curve in three dimensions. After fitting, the curvature value at the target node is obtained by solving the first and second derivatives of the fitted curve and applying the curvature calculation formula. The sign of the curvature value reflects the concavity / convexity direction of the curve, and the absolute value reflects the degree of curvature. To obtain the curvature change rate, the difference in curvature values ​​between adjacent nodes is calculated and normalized by dividing by the node spacing to obtain the curvature change per unit length. The curvature change rate intuitively reflects the degree of abrupt change in the boundary geometry; regions with high curvature change rates correspond to geometric features prone to stress concentration, such as sharp corners and abrupt turns. This curvature calculation method based on local fitting has good noise resistance and robustness, and can accurately extract geometric features even when there are certain discrete errors in the topological boundary.

[0028] If the difference in the rate of change of local geometric curvature between adjacent nodes exceeds a preset curvature abrupt change threshold, and the equivalent stress gradient resulting from the superposition of the macroscopic principal stress direction and the peak value of microscopic stress fluctuation at that node points outward from the boundary, then that node is marked as a notch-sensitive node. First, a threshold detection is performed on the rate of change of curvature of all boundary nodes. The set curvature abrupt change threshold is usually determined based on the notch sensitivity of the material and the stress concentration tolerance of the structure. For high-strength steel, the threshold can be set to a curvature change of 0.1 to 0.5 per millimeter. When the rate of change of curvature of a node exceeds the threshold, the second layer of judgment is initiated, extracting detailed information about the multi-scale stress field at that node. The macroscopic principal stress direction is obtained by calculating the eigenvector of the stress tensor, reflecting the main force direction at that location; the peak value of microscopic stress fluctuation is obtained through extreme value search of the local stress field, reflecting the stress concentration caused by small-scale geometric features. By vector superimposing macroscopic principal stresses and microscopic stress fluctuations, the direction of the equivalent stress gradient is calculated. When this gradient direction points outward from the boundary (i.e., from the material interior to the void), it indicates that the location exhibits the dual unfavorable conditions of outward stress diffusion and abrupt boundary curvature change, making it highly susceptible to fatigue crack initiation. Nodes satisfying these dual conditions are marked as notch-sensitive nodes, and their spatial coordinates, curvature information, and stress state are recorded to provide precise location for subsequent damage assessment.

[0029] Clustering of spatially continuous, cut-sensitive nodes is performed, and the regions containing the node sets formed by these clusters are defined as cut-sensitive regions. A density-based spatial clustering algorithm is used, setting a spatial neighborhood radius (typically 2 to 3 times the element feature size) and a minimum node count threshold (typically 3 to 5 nodes). The algorithm traverses all cut-sensitive nodes, grouping nodes whose spatial distance is less than the neighborhood radius into the same cluster. When a cluster contains more nodes than the minimum threshold, that cluster is identified as a valid cut-sensitive region. The clustering results form several spatially continuous node sets, each representing an independent cut-sensitive region. Statistical characteristics such as the geometric center, spatial extent, and total number of nodes are calculated for each region, and the maximum rate of curvature change and maximum stress concentration factor within the region are extracted as indicators of its hazard level. The regionalized identification results provide clear spatial targets for subsequent fatigue damage assessment and topology optimization adjustments. Compared to discrete node labels, region identification facilitates the implementation of local geometric optimization and material reinforcement measures. The clustering method also effectively eliminates isolated noise points, improving the reliability and engineering applicability of the identification results.

[0030] In this embodiment of the invention, the detailed implementation steps for calculating multi-scale fatigue damage factors by combining seawater corrosion environment parameters and microscopic material grain characteristics for the cut-sensitive area include:

[0031] The local stress concentration factor is determined by reading the local stress amplitude in the notch-sensitive region and combining it with the micromaterial grain size and the rate of change of local geometric curvature. The determination process first extracts the stress time history of each node in the notch-sensitive region under alternating loads from the transient dynamic analysis results. The stress amplitude spectrum of each node is then statistically analyzed using the rainflow counting method to obtain the cycle number distribution for different amplitude levels. The calculation of the local stress concentration factor comprehensively considers the influence of both macroscopic geometry and micromaterials. The macroscopic geometric influence is characterized by the minimum radius of curvature and thickness variation gradient of the notch-sensitive region, while the micromaterial influence is characterized by the average grain size obtained through metallographic testing. A correlation model between the stress concentration factor and geometric and material parameters is established using the notch stress concentration theory based on fracture mechanics.

[0032] ;

[0033] in, This is the local stress concentration factor. The minimum radius of curvature at the cut is... The average grain size of the material. For thickness variation gradient, and These are material-related empirical coefficients. The model reflects the influence of the relative relationship between geometric and microscopic dimensions on stress concentration. When the notch radius of curvature approaches the grain size, microscopic inhomogeneity significantly enhances the stress concentration effect. The calculated local stress concentration coefficients are used for subsequent stress amplitude amplification correction, laying the foundation for accurate fatigue damage assessment.

[0034] The local stress amplitude is amplified and corrected based on the local stress concentration factor, and then the corrected stress amplitude is reduced by corrosion based on the cathodic protection potential and dissolved oxygen content in the seawater corrosion environment parameters to obtain the multi-scale effective stress amplitude. First, the statistically obtained local stress amplitude is multiplied by the local stress concentration factor to obtain the amplified stress amplitude considering geometric and material effects. Then, key information such as seawater temperature, salinity, pH, dissolved oxygen concentration, and the protection potential of the cathodic protection system is read. Based on electrochemical corrosion kinetics theory, a reduction model of the corrosion environment on fatigue strength is established. This model considers the beneficial effect of the cathodic protection potential on crack tip passivation and the promoting effect of dissolved oxygen on stress corrosion cracking. The corrosion reduction factor is obtained by querying a corrosion fatigue test database. Different combinations of protection potential and dissolved oxygen concentration correspond to different reduction factors, with a typical reduction range of 0.6 to 0.9. Multiplying the amplified stress amplitude by the corrosion reduction factor yields the multi-scale effective stress amplitude. This value comprehensively reflects the triple coupling effect of geometric stress concentration, material microstructure, and marine environmental corrosion, and is the core input parameter for subsequent fatigue life assessment.

[0035] This method compares the multi-scale effective stress amplitude with a preset corrosion fatigue crack initiation threshold to extract over-limit stress cycle parameters where the multi-scale effective stress amplitude exceeds the threshold. First, the crack initiation stress threshold under current seawater environmental parameters is retrieved from a material corrosion fatigue performance database. This threshold is typically determined through small crack propagation tests or corrosion fatigue limit tests. The multi-scale effective stress amplitude at each node in the sensitive area of ​​the notch is compared with this threshold. When the effective stress amplitude exceeds the threshold, the stress cycle is identified as an over-limit cycle with a risk of crack initiation. For all over-limit cycles, detailed parameters such as stress amplitude, number of cycles, and average stress are recorded to form an over-limit stress cycle parameter set. Specifically, the over-limit amplitude of each over-limit cycle, i.e., the difference between the effective stress amplitude and the threshold, is calculated. This difference directly reflects the severity of damage; a larger difference indicates a stronger tendency for crack initiation. The extraction of over-limit cycle parameters enables a refined assessment of fatigue damage, refining the total number of cycles (in the millions) into effective cycles that truly affect fatigue life, providing high-quality data support for the accurate calculation of damage factors.

[0036] Based on the ratio of the over-limit stress cycle parameters to the total characteristic parameters of tens of millions of cycles, the multi-scale fatigue damage factor of the notch-sensitive area is calculated. Damage factor calculation is a crucial step in the quantification of fatigue risk, comprehensively assessing the degree of damage accumulation through ratio analysis. The calculation process first involves statistically analyzing the total number of over-limit stress cycles and the over-limit amplitude of each cycle. Then, linear damage accumulation theory (Miner's rule) or a nonlinear damage accumulation model is applied to calculate the cumulative damage caused by the over-limit cycles. This damage is then compared with the allowable damage corresponding to the total number of cycles (tens of millions) within the design life; the ratio of these two values ​​is the multi-scale fatigue damage factor. The formula is expressed as:

[0037] ;

[0038] in, It is a multi-scale fatigue damage factor. Let be the number of the i-th out-of-bounds loop. This is the effective stress amplitude of the cycle. The threshold for corrosion fatigue crack initiation. This is a material-related damage index (usually taken as 3 to 5). The total number of cycles over the design life. This is the fatigue strength coefficient of the material. The damage factor typically ranges from 0 to 1, with values ​​close to 0 indicating extremely low fatigue risk, close to 1 indicating near fatigue failure, and values ​​exceeding 1 indicating failure to meet design life requirements. This factor integrates the influence of multiple scales and factors, including notch geometry, material microstructure, marine environment, and cyclic characteristics, and is a comprehensive indicator for evaluating the fatigue safety of notch-sensitive areas.

[0039] In this embodiment of the invention, a topology optimization objective function is constructed with minimizing the overall structural compliance as the basic objective and using a multi-scale fatigue damage factor as the dynamic penalty term. The detailed implementation steps for dynamically adjusting the weight coefficients of the dynamic penalty term based on the cut-sensitive evolution state of the current iteration step during topology iterative evolution, and modifying the element sensitivity based on the topology optimization objective function, include:

[0040] A topology optimization objective function is constructed, comprising a structural compliance minimization term and a fatigue penalty term. The fatigue penalty term is the product of multi-scale fatigue damage factors and dynamic weighting coefficients. First, the structural compliance minimization term is defined. Compliance is defined as the work done by external loads, mathematically equal to the structural displacement energy, and calculated as the sum of the strain energies of all elements. Compliance minimization is essentially equivalent to structural stiffness maximization, a classic objective of traditional topology optimization. A fatigue penalty term is then added, which is the weighted sum of multi-scale fatigue damage factors in all notch-sensitive regions. The weighting coefficients are initially set to small values ​​(e.g., 0.01 to 0.1) to ensure that stiffness is the primary factor in the initial optimization phase, avoiding premature entrapment in local optima. The complete objective function is expressed as follows:

[0041] ;

[0042] in, Let be the overall objective function. The relative density vector of the elements. Let w(k) be the structural compliance, and w(k) be the first... The dynamic weight coefficients of the next iteration This represents the total number of sensitive areas at the incision site. For the first The objective function achieves an adaptive balance between stiffness optimization and fatigue optimization through dynamic weights, emphasizing different performance indicators at different stages of the optimization process, thus avoiding the limitation of fixed weights that cannot take multiple objectives into account.

[0043] In the early stages of topology iterative evolution, the dynamic weight coefficient is set to a low initial value to guide the iterative evolution to prioritize minimizing the overall structural compliance. Specifically, at the beginning of the iteration (usually within the first 20% to 30% of iterations), the dynamic weight coefficient w(k) is set to a preset low initial value, typically 0.01 to 0.05. The low weight ensures that the contribution of the fatigue penalty term to the objective function is much smaller than that of the compliance term, allowing the optimization algorithm to primarily respond to the needs of stiffness optimization, quickly forming efficient load-bearing paths and a reasonable topological configuration. This initial stiffness-dominated strategy helps establish a stable overall structural framework, avoiding insufficient structural load-bearing capacity or low material utilization that may result from prematurely introducing fatigue constraints. The initial stage focuses primarily on the macroscopic distribution of materials and the formation of the main force transmission paths, laying a good overall foundation for subsequent local optimization. This phased optimization strategy conforms to the general principles of engineering design, prioritizing the overall before the local, and the primary before the secondary, significantly improving the convergence and quality of the optimization results.

[0044] In the mid-to-late stages of topological iterative evolution, the maximum multi-scale fatigue damage factor of the sensitive area at the current iteration step is extracted. If the maximum multi-scale fatigue damage factor exceeds a preset safety threshold, the dynamic weight coefficient is increased according to an exponential function rule. Specifically, after completing density update and stress analysis in each iteration step, the fatigue damage factor of all sensitive areas at the incision step is traversed, and the maximum value is extracted as the fatigue risk index of the current state. This maximum value is compared with a preset safety threshold (usually set to 0.3 to 0.5, representing 30% to 50% fatigue life consumption). If it exceeds the threshold, the weight increase mechanism is triggered. The weight increase adopts an exponential function rule to ensure rapid weight growth and smooth transition.

[0045] ;

[0046] in, For the first The dynamic weight coefficients of the next iteration As the initial weights, This is the growth rate parameter (usually taken as 3 to 5). The current maximum fatigue damage factor, A preset safety threshold is established. The exponential growth rule causes the weights to increase slowly when the damage factor just exceeds the threshold, and rapidly when it is severely exceeded, achieving a sensitive response to fatigue risk. After the weights are increased, the impact of the fatigue penalty term on the objective function is significantly enhanced, guiding the optimization algorithm to prioritize reducing fatigue damage, even at the cost of sacrificing some stiffness.

[0047] Based on the updated topology optimization objective function, the associated load and element sensitivity are calculated. An additional penalty is applied to suppress the sensitivity of elements corresponding to the notch-sensitive region, guiding the material density update towards a boundary morphology that weakens local geometrical abrupt changes. First, based on the updated objective function, the adjoint method is used to calculate the sensitivity of each element to the objective function. Sensitivity represents the rate of change of the objective function caused by a small change in element density, and is key information for the optimization algorithm to determine the direction of density update. For elements within and adjacent to the notch-sensitive region, an additional correction term is applied to the original sensitivity. This correction term is positively correlated with the rate of curvature change and fatigue damage factor at the element's location; the larger the curvature abrupt change and the more severe the fatigue damage, the larger the correction magnitude. The corrected sensitivity tends to increase the material density or smooth the boundary morphology in this region. Specifically, for elements inside the boundary, the tendency to retain material is increased; for elements on the boundary, their density gradient is adjusted to form a smoother transition. Density update uses the optimization criterion method or the moving asymptote method, calculating the new density value of each element based on the corrected sensitivity. Through multiple iterations, the geometry of the sensitive area gradually evolves from a sharp abrupt change to a smooth transition, the rate of curvature change and stress concentration factor gradually decrease, and the fatigue damage factor tends to a safe range. This local guidance mechanism based on sensitivity modification achieves precise control of fatigue performance through topology optimization, transforming abstract fatigue constraints into specific material distribution adjustments, and is an effective way to realize multi-objective topology optimization.

[0048] In this embodiment of the invention, after the topology iteration converges, adaptive boundary smoothing is performed based on the local geometric curvature change rate distribution of the sensitive area of ​​the notch to generate a rudder system structure topology configuration that satisfies multi-scale fatigue life constraints. The detailed implementation steps include:

[0049] After determining that the topology iteration has converged, the distribution of the local geometric curvature change rate of the current topology boundary and the sensitive area of ​​the cut is obtained in the final iteration step. Specifically, after each iteration step, the relative change rate of the objective function is calculated. When the change rate of several consecutive steps (usually 5 to 10 steps) is less than a preset threshold (e.g., 0.1% to 0.5%), the iteration is considered converged. After convergence, all calculation results of the final iteration step are locked, including the element relative density field, stress field, fatigue damage distribution, etc. The boundary extraction process is consistent with the method in the iteration process. Isosurface technology is used to identify the topology boundary in the final density field and extract the geometric representation of the boundary (node ​​coordinates, patch connection relationships, etc.). For all identified sensitive areas of the cut, the local geometric curvature change rate of its boundary nodes is statistically analyzed to generate a spatial distribution map of the curvature change rate. This distribution map intuitively shows the location and severity of geometric abrupt changes on the boundary, providing accurate spatial guidance for subsequent adaptive smoothing. The completeness and accuracy of data acquisition ensure that post-processing can specifically solve the geometric defects left over from topology optimization and achieve effective transformation from optimized configuration to engineering-usable configuration.

[0050] An adaptive smoothing kernel scale is assigned to each node on the current topological boundary based on the distribution of local geometric curvature change rate. Nodes within the cut-sensitive region are assigned a first smoothing kernel scale, while nodes outside the cut-sensitive region are assigned a second smoothing kernel scale, with the first smoothing kernel scale being larger than the second. The assignment process traverses all nodes on the topological boundary, assigning different smoothing kernel scales based on whether they belong to the cut-sensitive region and the magnitude of their curvature change rate. For nodes within the cut-sensitive region, a larger first smoothing kernel scale is assigned, typically 3 to 5 times the element feature size. This large-scale smoothing kernel can perform weighted averaging of boundary node positions over a larger range, effectively eliminating sharp geometric abrupt changes and jagged boundaries. For nodes outside the cut-sensitive region, a smaller second smoothing kernel scale is assigned, typically 1 to 2 times the element feature size. This smaller scale preserves the overall morphological characteristics of the boundary and only eliminates small-scale discrete errors. For transitional regions with curvature change rates at intermediate levels, an interpolation method is used to assign a smoothing kernel scale between the two scales, achieving continuous variation in smoothing intensity. The adaptive scale allocation strategy enables "localized" smoothing processing. Large-scale smoothing is applied to dangerous areas that require enhanced processing, while small-scale smoothing is applied to safe areas that need to maintain features. This avoids the problems of over-smoothing or under-smoothing that may be caused by global uniform smoothing, and significantly improves the targeting and effectiveness of post-processing.

[0051] Local convolutional smoothing is performed on the current topological boundary based on an adaptive smoothing kernel scale to eliminate jagged geometric abrupt changes in cut-sensitive regions. For each node on the boundary, the smoothing process searches for all neighboring nodes within its assigned smoothing kernel scale, constructing a local node set. A Gaussian kernel function or a uniform kernel function is used to perform a weighted average of the coordinates of the local nodes; the weights are negatively correlated with the distance between nodes, with closer nodes receiving larger weights. The weighted average yields the new coordinate position of the node, achieving local smoothing of the boundary. The Gaussian kernel function is expressed as:

[0052] ;

[0053] ;

[0054] in, For nodes New coordinates For nodes The set of neighboring nodes within the smoothing kernel range. For nodes For nodes The weight, For nodes The original coordinates, For nodes The smoothing kernel scale is used. Convolutional smoothing is performed in parallel on all boundary nodes, iterating multiple times (usually 3 to 5 times) until the boundary shape is stable. The smoothed boundary eliminates the jagged and stepped geometric defects inherent in topology optimization, transforms sharp abrupt changes in the cut-sensitive region into a smooth transition, and significantly reduces the rate of curvature change, laying a good geometric foundation for subsequent stress verification and engineering applications.

[0055] Local mesh reconstruction and multi-scale stress verification are performed on the smoothed topological boundary. If the verification passes, the reconstructed boundary is output as the rudder system topology configuration that satisfies multi-scale fatigue life constraints. Specifically, based on the smoothed boundary, a high-quality mesh generation algorithm is used to re-mesh the finite element mesh, ensuring that the shape quality of the mesh elements (such as aspect ratio, interior angles, etc.) meets the numerical calculation requirements. The reconstructed mesh is locally refined near the boundary to improve the accuracy of stress calculation. During the verification process, the original coupled alternating loads are reapplied to the reconstructed model, and static or transient dynamic analysis is performed to extract the stress field distribution in all notch-sensitive areas. The local stress concentration factor, multi-scale effective stress amplitude, and multi-scale fatigue damage factor of each region are recalculated and compared with preset safety thresholds. If the fatigue damage factor of all notch-sensitive areas is lower than the threshold and the overall structural stiffness meets the design requirements, the verification is considered successful, and the final rudder system topology configuration, including complete information such as the three-dimensional geometric model, material distribution, and performance indicators, is output as input for the detailed design stage. If the verification fails, areas that still exceed the limits are identified and fed back to the topology optimization process as new sensitive areas for cutting, triggering local shape optimization or material enhancement until all constraints are met.

[0056] In this embodiment of the invention, after performing local convolutional smoothing on the current topological boundary based on an adaptive smoothing kernel scale, and before performing local mesh reconstruction and multi-scale stress verification on the smoothed topological boundary, the method further includes:

[0057] The updated curvature change rate of the smoothed boundary node sequence is re-extracted. The extraction process is consistent with the initial curvature calculation method. For the smoothed boundary node sequence, a local fitting curve is constructed and the curvature value is calculated based on the new coordinate positions of each node and its neighboring nodes. Then, the updated curvature change rate is obtained by the difference between the curvature values ​​of neighboring nodes. The updated curvature change rate reflects the degree of residual geometric abruptness of the boundary after smoothing. Ideally, it should be significantly lower than the curvature change rate before smoothing, indicating that the smoothing process effectively eliminates geometric defects. The distribution of curvature change rates before and after smoothing is compared, and the average reduction magnitude and maximum residual value are calculated as quantitative indicators of the smoothing effect. This step provides the latest geometric feature data for subsequent identification of residual sensitive nodes, ensuring that subsequent processing is based on the actual boundary state rather than a hypothetical state.

[0058] The process determines whether the rate of change of updated curvature is lower than a preset safe curvature threshold. If the rate of change of updated curvature of residual sensitive nodes is not lower than the preset safe curvature threshold, a local material transition region is generated at the residual sensitive nodes. First, a preset safe curvature threshold is set, which is typically determined based on the material's notch sensitivity and fatigue design specifications, representing the maximum acceptable rate of change of curvature. All nodes on the smoothed boundary are traversed, and their rate of change of updated curvature is compared with the safe threshold. If the rate of change of curvature of a node is still not lower than the threshold, it is marked as a residual sensitive node, indicating that the geometric abrupt change at that location has not been completely eliminated by the smoothing process. For the identified residual sensitive nodes, a local material transition region is generated around them. The spatial extent of this region is adaptively determined according to the spatial distribution of curvature changes, typically encompassing several units before and after the node. The generation of the transition region defines the operational scope for subsequent local shape optimization, avoiding the high cost of global adjustments and achieving precise problem localization and efficient solution.

[0059] Local shape optimization based on fatigue life constraints is performed within the local material transition region. This is achieved by increasing the transition fillet radius to reduce the rate of change of curvature at residual sensitive nodes to below a preset safe curvature threshold. Within the local material transition region, a local shape optimization model is established using geometric parameters such as the transition fillet radius or thickness gradient as design variables, the rate of change of curvature and fatigue damage factor as constraints, and minimizing material usage or maximizing local stiffness as the objective function. Sequential quadratic programming or gradient descent optimization algorithms are used to iteratively adjust the geometric parameters, gradually reducing the rate of change of curvature at residual sensitive nodes. The optimization focus is on increasing the transition fillet radius to transform sharp transitions into smooth transitions with large fillets, or adjusting the thickness variation to make it more gradual. After each geometric adjustment, the rate of change of curvature and stress distribution are recalculated to assess whether the safety threshold requirement is met. The iterative process continues until the rate of change of curvature at all residual sensitive nodes drops below the safety threshold, or the upper limit of the material usage constraint is reached. The introduction of local shape optimization enables an effective connection between topology optimization and shape optimization. Topology optimization determines the overall material layout, while shape optimization finely adjusts local geometric details. The combination of the two ensures that the final structure has both efficient material utilization and excellent fatigue performance, meeting the stringent requirements of marine engineering equipment.

[0060] In this embodiment of the invention, the detailed process of determining the local stress concentration factor by combining the grain size of the micromaterial with the rate of change of local geometric curvature includes:

[0061] This process extracts the minimum radius of curvature of the cut-sensitive region at the current topological boundary depression and the material thickness variation gradient of the cut-sensitive region at the current topological boundary transition. The extraction process begins with a detailed analysis of the boundary geometry of the cut-sensitive region, identifying the location with the maximum curvature on the boundary, i.e., the depression with the smallest radius of curvature. This location typically corresponds to the point of most severe geometric stress concentration. The minimum radius of curvature for this region is obtained through curvature calculation and extremum search. Simultaneously, the spatial distribution of material thickness is extracted along the boundary normal direction, and the thickness variation gradient is calculated, i.e., the change in thickness per unit distance. The thickness variation gradient reflects the degree of abrupt change in the structural cross-section; a larger gradient indicates a more drastic thickness change and a stronger corresponding stress concentration effect. The minimum radius of curvature and the thickness variation gradient are two key parameters for quantitatively describing geometric stress concentration, characterizing the curvature effect and thickness effect of the boundary, respectively, providing sufficient geometric information for subsequent stress concentration factor modeling.

[0062] Based on the relative proportions of minimum radius of curvature, material thickness gradient, and micromaterial grain size, the local stress concentration factor is calculated. The calculation process comprehensively considers the relative relationships between macroscopic geometry (radius of curvature, thickness gradient) and microscopic materials (grain size). When geometric feature dimensions (such as radius of curvature) are close to microscopic material feature dimensions (grain size), the influence of microscopic inhomogeneities on macroscopic stress concentration is significantly enhanced. Using the aforementioned stress concentration factor calculation model, the extracted geometric and material parameters are substituted to calculate the local stress concentration factor. The physical meaning of this factor is the ratio of the maximum stress at the notch to the nominal stress, reflecting the amplification effect of geometric discontinuities on the stress level. The calculation model is based on extensive finite element simulations and experimental verification, ensuring the calculation accuracy under different combinations of geometric and material parameters. The obtained local stress concentration factor is directly used for amplification correction of local stress amplitude and is a key input parameter for subsequent fatigue damage assessment.

[0063] The ratio of grain size to minimum radius of curvature is used to characterize the sensitivity of a material to geometric notches at the microscale. When the grain size is large relative to the radius of curvature (ratio close to or greater than 1), the stress field distribution at the notch tip is significantly affected by the material's microstructure. The orientation, shape, and grain boundary characteristics of individual grains can alter the local stress state, leading to an actual stress concentration factor higher than the predicted value of traditional continuous medium theory. Conversely, when the grain size is much smaller than the radius of curvature (ratio much less than 1), the material can be considered a continuous homogeneous medium, and stress concentration is mainly controlled by macroscopic geometry, with microscopic effects negligible. The introduction of this ratio extends the calculation of the stress concentration factor from a simple geometric model to a geometry-material multi-scale coupled model, significantly improving the accuracy of notch sensitivity assessment. This is particularly important for coarse-grained materials or small-sized geometric features, where traditional methods may significantly underestimate fatigue risk, while multi-scale methods can accurately capture this scale effect.

[0064] In this embodiment of the invention, the process of calculating the multi-scale fatigue damage factor of the notch-sensitive region based on the ratio of the over-limit stress cyclic parameters to the total characteristic parameters of tens of millions of cycles further includes:

[0065] Identifying the load-stress ratio acting on the notch-sensitive region after coupling the wave alternating load spectrum with the hydrodynamic load on the control surface. Load-stress ratio identification is a crucial step in load characteristic analysis, distinguishing the differentiated effects of different cycle types on fatigue through the stress ratio parameter. The identification process extracts the maximum and minimum stress values ​​for each stress cycle from the stress time history of the notch-sensitive region and calculates the stress ratio. The stress ratio reflects the asymmetry of the stress cycle, when... Time indicates a tension-compression alternating cycle, when Time indicates a pull-pull pulsation cycle, when The stress ratio represents a symmetrical alternating cycle. Statistical analysis of the cycle number distribution across different stress ratio ranges identifies the dominant cycle type, providing a basis for subsequent damage weighting. Accurate identification of the stress ratio is particularly important for marine engineering equipment because the coupling effect of wave and fluid loads can generate complex asymmetric cycles, and a simple assumption of symmetrical cycles may lead to serious misjudgments of fatigue life.

[0066] When the load-stress ratio is primarily characterized by tensile load, the stress corrosion cracking threshold from seawater corrosion environment parameters is incorporated to apply a first-weight amplification to the fatigue damage during the half-cycle of the tensile load. This amplification reflects the synergistic effect of tensile stress and corrosion accelerating crack initiation. First, the tensile portion of the stress cycle is identified, i.e., the half-cycle where the stress is positive. During this half-cycle, tensile stress induces tensile strain on the material surface, promoting the opening of corrosion cracks and the penetration of electrolytes to the crack tip, significantly accelerating the initiation and propagation of corrosion fatigue cracks. The stress corrosion cracking threshold from seawater corrosion environment parameters is consulted. When the tensile stress exceeds this threshold, the synergistic effect of corrosion and mechanics is dramatically enhanced. The first-weight amplification factor is determined based on the ratio of the tensile stress amplitude to the threshold; the greater the amplitude exceeding the threshold, the larger the amplification factor, typically ranging from 1.5 to 3.0. Applying this amplification factor to the fatigue damage during the tensile half-cycle, the corrected damage value more accurately reflects the actual severity of tensile stress in the marine environment. This damage amplification method based on physical mechanisms overcomes the limitation of traditional fatigue analysis that neglects the environmental-mechanical coupling.

[0067] When the load-stress ratio characterization is dominated by compressive load, a second weighting reduction is applied to the fatigue damage during the compressive load half-cycle to reflect the delaying effect of compressive stress on crack initiation. First, the compressive portion of the stress cycle is identified, i.e., the half-cycle with negative stress. During this half-cycle, compressive stress induces compressive strain on the material surface, promoting crack closure, hindering the diffusion of corrosive media into the crack interior, and simultaneously inhibiting the opening displacement of the crack tip, thus slowing the crack propagation rate. The second weighting reduction factor is determined based on the ratio of the compressive stress amplitude to the material's yield strength. When the compressive stress is large, the crack closure effect is more significant, and the reduction factor is smaller, typically ranging from 0.5 to 0.8. Applying this reduction factor to the fatigue damage during the compressive half-cycle reflects the beneficial contribution of compressive stress to fatigue life. It is important to note that the beneficial effect of compressive stress is mainly manifested in the crack propagation stage; for the crack initiation stage, the influence of compressive stress is relatively small. Therefore, the setting of the reduction factor needs to be calibrated in conjunction with the specific fatigue stage and failure mode.

[0068] A multi-scale fatigue damage factor is obtained by jointly calculating the tensile half-cycle fatigue damage amplified by the first weight and the compressive half-cycle fatigue damage reduced by the second weight. Specifically, each stress cycle is decomposed into a tensile half-cycle and a compressive half-cycle, and the fatigue damage is corrected by applying the corresponding weight coefficients to each. Then, the corrected tensile and compressive damages are added together to obtain the total damage for that cycle. The total damage for all out-of-limit cycles is accumulated and compared with the allowable damage for the design life to obtain the multi-scale fatigue damage factor. This damage factor comprehensively reflects multiple factors such as load asymmetry, the corrosive effects of the marine environment, the stress concentration effect of geometry, and the microscopic properties of the material, and is the most comprehensive indicator for evaluating the fatigue safety of the notch-sensitive area. Based on topology optimization and shape optimization using this damage factor, structural configurations that truly meet the long-term service requirements of marine engineering equipment can be generated, significantly improving the reliability and durability of the rudder system.

[0069] In this embodiment of the invention, after generating the rudder system topology configuration that satisfies multi-scale fatigue life constraints, the method further includes:

[0070] A three-dimensional solid model was reconstructed based on the topological configuration of the rudder system, and wave alternating load spectrum and rudder surface hydrodynamic load were applied to the 3D solid model. Specifically, the geometric boundary and material distribution information output from the topology optimization were read, and a complete 3D solid model was built in CAD software using parametric modeling or direct geometric reconstruction techniques. The model includes all geometric details such as the rudder blade outline, internal stiffener arrangement, and rudder stock connection structure, and defines material properties and assembly relationships. The load application process is consistent with the initial analysis, mapping the wave alternating load spectrum and rudder surface hydrodynamic load to the corresponding boundaries and regions of the model according to actual working conditions, providing accurate input conditions for full-cycle fatigue simulation. The establishment of the solid model enables the optimization results to be verified and further designed in a standard engineering software environment, ensuring the engineering usability of the optimization results.

[0071] A full-cycle corrosion fatigue simulation analysis was performed on a 3D solid model, extracting fatigue life distribution cloud maps under tens of millions of cycles. The simulation process employed professional fatigue analysis software, performing multi-axis fatigue analysis based on the finite element mesh and load time history of the 3D solid model. Key factors such as the material's SN curve, mean stress correction, and the influence of the seawater corrosion environment were considered to calculate the cumulative fatigue damage and fatigue life of various structural components under tens of millions of cycles. The fatigue life distribution across the entire domain was extracted and visualized as a cloud map. This cloud map intuitively presents the fatigue-prone areas and safety margin distribution of the structure, providing a clear basis for design evaluation. The high fidelity of the full-cycle simulation ensures the reliability of fatigue life prediction and is a key means of engineering verification of optimization results.

[0072] If the lowest fatigue life value in the fatigue life distribution cloud map is lower than the preset design life threshold, the local danger region corresponding to the lowest fatigue life is extracted. This local danger region is then fed back into the topology optimization objective function as a new sensitive area, triggering a new round of topology iteration evolution and adaptive boundary smoothing until the lowest fatigue life value meets the preset design life threshold. First, it is determined whether the lowest life value in the fatigue life cloud map meets the design requirements (usually a safety factor of 1.5 to 2 times the design life of the rudder system). If not, the spatial location and area corresponding to the lowest life are identified and defined as a new sensitive area. The geometric features, stress state, and fatigue damage information of this area are fed back into the topology optimization model. The constraint weight of this area is increased in the fatigue penalty term of the objective function, or a stricter upper limit for the fatigue damage factor is directly applied to this area. Then, a new round of topology iteration evolution is triggered. Under the new constraints, the optimization algorithm readjusts the material distribution and topology configuration to specifically enhance the fatigue performance of the danger region. After the iteration evolution is completed, adaptive boundary smoothing and full-cycle fatigue verification are performed again, forming a complete design-analysis-verification-feedback closed loop. This process continues until the fatigue life at all locations in the fatigue life cloud map meets the design threshold requirements, outputting the final rudder system topology. This iterative closed-loop mechanism ensures the convergence and reliability of the optimized design, organically combining theoretical optimization with engineering verification to generate a high-wave-resistant rudder system structure that truly meets the stringent requirements of marine engineering equipment, providing technical support for the safe operation of ships and offshore platforms.

[0073] The above description is merely 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.

[0074] It should be noted that all formulas in this manual are calculated by removing dimensions and taking their numerical values. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters and thresholds in the formulas are set by those skilled in the art according to the actual situation.

[0075] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. A method for optimizing the topology of the rudder system structure of high wave-resistant marine engineering equipment, characterized in that, include: Obtain the design domain boundary conditions, material properties, ocean wave alternating load spectrum and rudder surface hydrodynamic load of the marine engineering equipment rudder system, couple and map the wave alternating load spectrum and the rudder surface hydrodynamic load to the design domain, and solve to obtain the multi-scale initial stress field of the design domain under coupled alternating load; Based on the multi-scale initial stress field and the preset material interpolation model, topological iterative evolution is performed. In the density field generated by each topological iterative evolution, the topological boundary is extracted, the local geometric curvature change rate of each boundary node sequence on the topological boundary is calculated, and based on the local geometric curvature change rate and the stress gradient direction of the multi-scale initial stress field, the cut-sensitive region caused by geometric abrupt change is identified. For the notch-sensitive area, a multi-scale fatigue damage factor is calculated by combining seawater corrosion environment parameters and micromaterial grain characteristics. The multi-scale fatigue damage factor is determined based on the cumulative difference between the local stress concentration factor, effective stress amplitude and corrosion fatigue crack initiation threshold of the notch-sensitive area. A topology optimization objective function is constructed with minimizing the overall structural compliance as the basic objective and the multi-scale fatigue damage factor as the dynamic penalty term. In the topology iterative evolution, the weight coefficient of the dynamic penalty term is dynamically adjusted based on the cut-sensitive evolution state of the current iteration step, and the unit sensitivity is modified based on the topology optimization objective function. After the topology iteration converges, an adaptive boundary smoothing process is performed based on the local geometric curvature change rate distribution of the sensitive area of ​​the notch to generate a rudder system structure topology configuration that satisfies the multi-scale fatigue life constraint.

2. The method according to claim 1, characterized in that, The process involves acquiring the design domain boundary conditions and material properties of the marine engineering equipment's rudder system, as well as the alternating wave load spectrum and rudder surface hydrodynamic loads. This is followed by coupling and mapping the alternating wave load spectrum and the rudder surface hydrodynamic loads to the design domain, and solving for the multi-scale initial stress field of the design domain under the coupled alternating loads. The wave statistics of the working sea area of ​​the rudder system are obtained, and a wave alternating load spectrum containing tens of millions of cycles is generated by fitting. The wave alternating load spectrum is then decomposed into multi-order harmonic loads. The multi-order harmonic loads and the rudder surface hydrodynamic loads are superimposed and applied on the fluid-structure interaction boundary of the design domain, and transient dynamic analysis is performed to extract the stress response under each order of coupled loads. Based on the principle of stress superposition, the stress responses under each order of coupled loads are combined, and multi-scale interpolation mapping is performed on the combined stress field to separate the macroscopic overall stress distribution and microscopic local stress fluctuation characteristics, thereby obtaining the multi-scale initial stress field.

3. The method according to claim 1, characterized in that, The topological iterative evolution is performed based on the multi-scale initial stress field and a preset material interpolation model. In each iteration, topological boundaries are extracted from the density field generated by the topological evolution. The local geometric curvature change rate of each boundary node sequence on the topological boundary is calculated. Based on the local geometric curvature change rate and the stress gradient direction of the multi-scale initial stress field, the cut-sensitive region caused by geometric abrupt changes is identified, including: During the topological iterative evolution process, relative density isosurfaces are extracted based on the unit relative density field of the current iteration step as the current topological boundary, and an ordered boundary node sequence is extracted along the current topological boundary; For any node in the ordered boundary node sequence, a local fitting curve is constructed based on the node and its neighboring nodes, and the curvature value of the local fitting curve at the node is calculated as the local geometric curvature change rate. If the difference in the rate of change of local geometric curvature of adjacent nodes exceeds the preset curvature mutation threshold, and the equivalent stress gradient after the superposition of the macroscopic principal stress direction and the microscopic stress fluctuation peak at the node points to the outside of the boundary, then the node is marked as a cut-sensitive node. Cluster the spatially continuous cut-sensitive nodes and determine the region where the clustered node set is located as the cut-sensitive region.

4. The method according to claim 1, characterized in that, The calculation of multi-scale fatigue damage factors for the sensitive area of ​​the cut, combining seawater corrosion environment parameters and microscopic material grain characteristics, includes: The local stress amplitude of the sensitive area of ​​the cut is read, and the local stress concentration factor is determined by combining the micromaterial grain size and the local geometric curvature change rate. The local stress amplitude is amplified and corrected based on the local stress concentration factor, and the corrected stress amplitude is reduced by corrosion based on the cathodic protection potential and dissolved oxygen content in the seawater corrosion environment parameters to obtain the multi-scale effective stress amplitude. The multi-scale effective stress amplitude is compared with a preset corrosion fatigue crack initiation threshold, and the over-limit stress cycle parameters of the multi-scale effective stress amplitude exceeding the corrosion fatigue crack initiation threshold are extracted. Based on the ratio of the over-limit stress cycle parameters to the total characteristic parameters of the tens of millions of cycles, the multi-scale fatigue damage factor of the incision sensitive area is calculated.

5. The method according to claim 1, characterized in that, The construction of a topology optimization objective function with minimizing the overall structural compliance as the basic objective and the multi-scale fatigue damage factor as the dynamic penalty term, dynamically adjusts the weight coefficients of the dynamic penalty term based on the cut-sensitive evolution state of the current iteration step during the topology iterative evolution, and modifies the element sensitivity based on the topology optimization objective function, including: Construct the topology optimization objective function, which includes a structural compliance minimization term and a fatigue penalty term, wherein the fatigue penalty term is the product of the multi-scale fatigue damage factor and the dynamic weight coefficient; In the early stage of the topology iterative evolution, the dynamic weight coefficient is set to a low initial value to guide the topology iterative evolution to prioritize minimizing the overall structural compliance. In the middle and late stages of the topological iterative evolution, the maximum multi-scale fatigue damage factor of the sensitive area of ​​the cut in the current iteration step is extracted. If the maximum multi-scale fatigue damage factor exceeds the preset safety threshold, the dynamic weight coefficient is increased according to the exponential function rule. The associated load and element sensitivity are calculated based on the updated topology optimization objective function, and additional penalty suppression is applied to the sensitivity of the elements corresponding to the sensitive area of ​​the notch.

6. The method according to claim 1, characterized in that, After the topology iteration converges, adaptive boundary smoothing is performed based on the local geometric curvature change rate distribution of the sensitive area of ​​the notch to generate a rudder system topology configuration that satisfies multi-scale fatigue life constraints, including: After determining that the topology iteration has converged, the current topology boundary and the local geometric curvature change rate distribution of the sensitive area of ​​the cut are obtained in the final iteration step; Based on the distribution of the rate of change of local geometric curvature, an adaptive smoothing kernel scale is assigned to each node on the current topological boundary, wherein nodes in the cut-sensitive region are assigned a first smoothing kernel scale, nodes in the non-cut-sensitive region are assigned a second smoothing kernel scale, and the first smoothing kernel scale is greater than the second smoothing kernel scale. Based on the adaptive smoothing kernel scale, local convolution smoothing is performed on the current topological boundary to eliminate jagged geometric abrupt changes in the cut-sensitive region; Local mesh reconstruction and multi-scale stress verification are performed on the smoothed topological boundary. If the verification passes, the reconstructed boundary is output as the rudder system topology configuration that satisfies the multi-scale fatigue life constraint.

7. The method according to claim 6, characterized in that, After performing local convolution smoothing on the current topological boundary based on the adaptive smoothing kernel scale, and before performing local mesh reconstruction and multi-scale stress verification on the smoothed topological boundary, the method further includes: Re-extract the rate of change of curvature of the smoothed boundary node sequence; Determine whether the rate of change of the updated curvature is lower than a preset safe curvature threshold. If the rate of change of the updated curvature of a residual sensitive node is not lower than the preset safe curvature threshold, then a local material transition region is generated at the residual sensitive node. Local shape optimization based on fatigue life constraints is performed in the local material transition region. By increasing the transition fillet radius, the rate of change of the update curvature of the residual sensitive node is reduced to below the preset safe curvature threshold.

8. The method according to claim 4, characterized in that, The determination of the local stress concentration factor by combining the micromaterial grain size with the rate of change of local geometric curvature includes: Extract the minimum radius of curvature of the cut-sensitive region at the current topological boundary depression, and extract the material thickness change gradient of the cut-sensitive region at the current topological boundary transition. Based on the minimum radius of curvature, the gradient of material thickness variation, and the relative proportions of micromaterial grain size, the local stress concentration factor is calculated.

9. The method according to claim 4, characterized in that, The process of calculating the multi-scale fatigue damage factor of the incision-sensitive region based on the ratio of the over-stress cyclic parameters to the total characteristic parameters of tens of millions of cycles also includes: Identify the load stress ratio acting on the sensitive area of ​​the notch after the coupling of the wave alternating load spectrum and the rudder surface hydrodynamic load; When the load-stress ratio characterization is dominated by tensile load, the fatigue damage of the tensile load half-cycle is amplified by first weighting in combination with the stress corrosion cracking threshold in the seawater corrosion environment parameters. When the load-stress ratio characterization is dominated by compressive load, a second weighting is applied to reduce the fatigue damage during the half-cycle of the compressive load. The multi-scale fatigue damage factor is obtained by jointly calculating the tensile half-cycle fatigue damage after the first weight amplification and the compressive half-cycle fatigue damage after the second weight reduction.

10. The method according to claim 1, characterized in that, After generating the rudder system topology configuration that satisfies multi-scale fatigue life constraints, the method further includes: A three-dimensional solid model is reconstructed based on the topological configuration of the rudder system, and the wave alternating load spectrum and the rudder surface hydrodynamic load are applied to the three-dimensional solid model. A full-cycle corrosion fatigue simulation analysis was performed on the three-dimensional solid model, and the fatigue life distribution cloud map of the three-dimensional solid model under tens of millions of cycles was extracted. If the lowest fatigue life value in the fatigue life distribution cloud map is lower than the preset design life threshold, the local danger area corresponding to the lowest fatigue life is extracted, and the local danger area is fed back to the topology optimization objective function as a new cutting-sensitive area, triggering a new round of topology iteration evolution and adaptive boundary smoothing processing until the lowest fatigue life value meets the preset design life threshold.

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