Lightweight topological optimization design method for FPSO (floating production storage and offloading) deck grillage

Abstract

The invention relates to the technical field of ocean engineering, in particular to an FPSO (floating production storage and offloading) deck grillage lightweight topological optimization design method, which comprises the following steps of: constructing a parameterized model containing geometric topological information, material anisotropy parameters, a thermal stress field and dynamic load phase delay information; material density distribution is solved through frequency domain response analysis, a variable density method and an iterative optimization process, and an initial optimization structure containing phase compensation stress distribution is generated; a moving least square method is used for identifying a high stress gradient area, a smooth boundary is reconstructed through a cubic uniform B spline and an NURBS curved surface, an updated stress nephogram is formed, fiber trend optimization is executed based on principal stress direction data, an anisotropic material distribution model is generated, dynamic performance is analyzed and verified through phase matching, and final lightweight design is output. According to the invention, high-precision structure optimization oriented to multi-physics field coupling is realized, and the lightweight degree and the service reliability of the FPSO deck grillage are improved.

Description

Technical Field

[0001] This invention relates to the field of marine engineering technology, and in particular to a lightweight topology optimization design method for FPSO deck racks. Background Technology

[0002] With the expansion of deep-sea oil and gas development, the demand for long-term service of FPSOs (Floating Production Storage and Offloading) in complex marine environments is constantly increasing. As a key load-bearing system that supports production equipment and transmits wave loads and temperature differences, the lightweight design of FPSO deck structures has become an important direction for engineering optimization. The multi-physics characteristics of the marine environment subject FPSO deck structures to dynamic loads caused by wave excitation, thermo-mechanical coupling effects caused by environmental temperature differences, and the anisotropic characteristics of the materials themselves.

[0003] Current lightweight design methods for FPSO deck frames still face several key technical bottlenecks. First, most topology optimization methods construct input conditions based on a single physics field or static load model, making it difficult to simultaneously incorporate dynamic load phase delay information, thermal stress fields, and material anisotropy parameters into the same optimization framework, resulting in insufficient engineering realism of the initial input. Second, existing topology optimization results generally suffer from boundary discontinuities and concentrations of high stress gradient regions, leading to poor adaptability to subsequent manufacturing processes. Third, material allocation typically employs homogeneous materials or simplified layup strategies, failing to fully utilize principal stress direction data to optimize the fiber orientation of anisotropic materials, resulting in insufficient phase compatibility of the structure under dynamic loads. Finally, existing dynamic performance assessments are often disconnected from material distribution design, lacking a collaborative evaluation mechanism that spans the entire process of topology optimization, geometric smoothing, and material layup. Summary of the Invention

[0004] This invention provides a lightweight topology optimization design method for FPSO deck frames, which can uniformly couple multi-physics inputs, realize boundary continuity processing, perform intelligent allocation of anisotropic materials, and simultaneously verify dynamic performance, thereby improving the structural efficiency and service reliability of FPSO deck frames.

[0005] A lightweight topology optimization design method for FPSO deck racks includes the following steps: S1: Construct a parameterized model that includes dynamic load phase delay information and thermal stress field. The parameterized model includes geometric topology information, material anisotropy parameters and dynamic load phase delay information. S2: Based on the parameterized model, an initial optimized structure is generated by a phase-compensated topology optimization algorithm. The initial optimized structure includes a material density distribution and a phase-compensated stress cloud map. S3: Perform stress gradient smoothing on the initial optimized structure to generate a smooth topology, which includes smooth boundary curves and updated stress cloud maps; S4: Based on the smooth topology, perform anisotropic material optimization allocation and output the final lightweight design, which includes anisotropic material distribution model and dynamic performance index report.

[0006] Optionally, S1 includes: S11: Construct the geometric topology information of the FPSO deck frame using 3D modeling software. The geometric topology information includes the frame outline dimensions, support location distribution, and connection relationship data. S12: Based on the geometric topology information, define the material anisotropy parameters, which include the elastic modulus tensor, Poisson's ratio matrix, and thermal expansion coefficient tensor. S13: Combining the geometric topology information and the material anisotropy parameters, the thermal stress field is calculated through nonlinear thermo-mechanical coupling analysis. The thermal stress field includes a temperature distribution cloud map and a thermal stress contour map. S14: Based on the geometric topology information, the material anisotropic parameters, and the thermal stress field, dynamic load phase delay information is obtained through wave-structure coupled time history analysis. The dynamic load phase delay information includes wave load phase angle, structural response hysteresis angle, and phase difference matrix. S15: Integrate the geometric topology information, the material anisotropy parameters, the thermal stress field, and the dynamic load phase delay information to generate a complete parametric model, which includes all input parameters and boundary condition data.

[0007] Optionally, in S11, the 3D modeling software uses a parametric CAD platform to generate editable geometric topology information by inputting the outline dimensions of the frame, the distribution of support positions, and the connection relationship data.

[0008] Optionally, S2 includes: S21: Based on the dynamic load phase delay information in the parameterized model, the phase compensation factor is calculated through frequency domain response analysis. The phase compensation factor includes the amplitude modulation coefficient and the phase adjustment angle. S22: Input the phase compensation factor into the phase compensation topology optimization algorithm, and solve the intermediate material density distribution by the variable density method. The intermediate material density distribution includes the unit relative density matrix and sensitivity information. S23: Based on the intermediate material density distribution, the final material density distribution that satisfies the constraints is obtained through iterative optimization calculation. The final material density distribution includes the optimized unit density field and convergence criterion data. S24: Based on the final material density distribution, a phase-compensated stress cloud map is generated through post-processing calculation. The phase-compensated stress cloud map includes equivalent stress distribution and key area identification. S25: Integrate the final material density distribution and the phase-compensated stress cloud map to output a complete initial optimized structure, which includes material distribution data and stress analysis results.

[0009] Optionally, in S23, the iterative optimization calculation adopts the MMA optimization algorithm, which takes the intermediate material density distribution as the initial value, solves the element density field that satisfies the weight constraint and stress constraint through multiple iterations, and terminates the iteration when the convergence criterion data is met.

[0010] Optionally, S3 includes: S31: Based on the phase-compensated stress cloud map in the initial optimized structure, high stress gradient regions are identified by moving least squares method. The high stress gradient regions include a set of units with stress change rate exceeding a threshold and boundary line segment data. S32: Reconstruct the boundary curve of the high stress gradient region by fitting a Bezier curve to generate a smooth boundary curve, which includes a three-dimensional curve mesh with continuous curvature and a set of reconstruction parameters. S33: Update the geometric model of the initial optimized structure based on the smooth boundary curve, and generate a transition surface model through surface extension and Boolean operations. The transition surface model includes a smoothly connected geometric surface and updated boundary data. S34: Perform finite element analysis on the transition surface model, and obtain an updated stress cloud map by solving the updated stress distribution. The updated stress cloud map includes the optimized equivalent stress distribution and smoothing effect index. S35: Integrate the smooth boundary curve, the transition surface model, and the updated stress cloud map to generate a complete smooth topology, which includes geometric model data, boundary information, and stress analysis results.

[0011] Optionally, in S34, the finite element analysis uses high-order element meshing to perform static stress analysis on the transition surface model, and obtains an updated stress cloud map containing equivalent stress distribution and smoothing effect indicators by solving.

[0012] Optionally, in S35, the generation of the smooth topology structure adopts parametric association technology, which associates the smooth boundary curve, the transition surface model and the updated stress cloud map to form complete structural data containing geometric model data, boundary information and stress analysis results.

[0013] Optionally, S4 includes: S41: Based on the updated stress cloud map in the smooth topology, calculate the principal stress direction data using the finite element method. The principal stress direction data includes the principal stress direction vector and principal stress magnitude sorting information for each element. S42: Based on the principal stress direction data and material anisotropy parameters, an anisotropic material distribution model is generated using a fiber orientation optimization algorithm. The anisotropic material distribution model includes a fiber orientation distribution map and a laminate layup scheme. S43: Perform dynamic performance verification on the anisotropic material distribution model, and calculate the dynamic performance index report through phase matching analysis. The dynamic performance index report includes the natural frequency spectrum, dynamic response amplitude, and phase matching degree. S44: Integrate the anisotropic material distribution model and the dynamic performance index report to generate a complete final lightweight design, which includes manufacturing drawings, material specifications and performance certification documents.

[0014] Optionally, in S41, the finite element method uses eight-node hexahedral elements for mesh generation, and obtains the principal stress direction vector and principal stress magnitude sorting information of each element by solving the stress tensor eigenvalue problem.

[0015] The beneficial effects of this invention are: This invention constructs a parametric model incorporating geometric topology information, material anisotropy parameters, thermal stress field, and dynamic load phase delay information. By integrating wave load time history response, thermo-mechanical coupling effects, and material anisotropy characteristics into the initial conditions of topology optimization, it achieves a realistic reconstruction of the actual service environment of FPSO deck structures. Nonlinear thermo-mechanical coupling analysis and wave-structure time history analysis jointly provide temperature distribution contour maps, thermal stress contour maps, wave load phase angles, structural response hysteresis angles, and phase difference matrices, ensuring high fidelity and engineering interpretability of the initial input. The parametric model is stored in a structured data format and can be directly accessed in subsequent optimizations, significantly improving the accuracy, completeness, and traceability of the basic data for topology optimization, laying a highly reliable input foundation for the final lightweight design.

[0016] This invention employs a phase-compensated topology optimization algorithm, incorporating the amplitude modulation coefficient and phase adjustment angle obtained from frequency domain response analysis into an improved variable density method. This allows material distribution optimization to be directly influenced by the phase delay information of dynamic loads, achieving compensation for the actual mechanical behavior of the structure under dynamic conditions. Simultaneously, a SIMP interpolation model and MMA iterative strategy are used to solve the material density field, ensuring robust convergence of the optimization process under weight and stress constraints. High-stress gradient regions are identified using the moving least squares method, and smooth boundary curves and transition surface models are constructed using cubic uniform B-splines and NURBS surface techniques, enabling curvature and boundary continuity in the geometric model within high-stress regions. Updated stress contour maps reflect the true stress state after smoothing, and the effectiveness of the geometric update is verified using smoothing performance indicators. This process achieves closed-loop optimization of "material density—stress response—geometric boundary—finite element feedback," significantly alleviating localized high-stress regions, effectively controlling stress concentration, and improving the manufacturability and overall stability of the lightweight structural topology.

[0017] This invention, based on principal stress direction data calculated from updated stress cloud maps, obtains principal stress direction vectors and principal stress magnitude ranking information through eigenvalue solving, enabling the fiber orientation optimization algorithm to accurately match the main stress direction of the structure under the maximum stress criterion. By combining material anisotropy parameters to construct fiber orientation distribution maps and laminate layup schemes, the consistency between fiber orientation and principal stress direction is maximized, improving the structure's load-bearing capacity in the main stress direction and reducing stress peaks. Subsequently, phase matching analysis and frequency domain decomposition are used to calculate the natural frequency spectrum, dynamic response amplitude, and phase matching degree, allowing the selection of anisotropic materials and dynamic performance to mutually verify each other, ensuring the structure possesses higher phase compatibility and vibration stability under wave excitation. Finally, a digital integration platform outputs manufacturing drawings, material specifications, and performance certification documents, achieving end-to-end collaborative optimization from geometry to materials to dynamic performance, ensuring the final lightweight design is manufacturable, verifiable, and adaptable to marine environments. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only for this invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the S2 process in an embodiment of the present invention. Detailed Implementation

[0020] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. It should also be noted that, to make the embodiments more comprehensive, the following embodiments are the best and preferred embodiments, and those skilled in the art can use other alternative methods to implement some well-known technologies; moreover, the accompanying drawings are only for more specific description of the embodiments and are not intended to specifically limit the present invention.

[0021] It should be noted that the use of terms such as "an embodiment," "an embodiment," "an exemplary embodiment," and "some embodiments" in the specification indicates that the described embodiment may include a specific feature, structure, or characteristic, but not every embodiment necessarily includes that specific feature, structure, or characteristic. Furthermore, when a specific feature, structure, or characteristic is described in connection with an embodiment, implementing such a feature, structure, or characteristic in conjunction with other embodiments (whether explicitly described or not) should be within the knowledge of those skilled in the art.

[0022] Generally, terms can be understood at least partly from their use in context. For example, depending at least partly on the context, the term "one or more" as used herein can be used to describe any feature, structure, or characteristic in a singular sense, or a combination of features, structures, or characteristics in a plural sense. Additionally, the term "based on" can be understood not necessarily to convey an exclusive set of factors, but rather, alternatively, depending at least partly on the context, to allow for the presence of other factors that are not necessarily explicitly described.

[0023] like Figures 1-2 As shown, a lightweight topology optimization design method for FPSO deck racks includes the following steps: S1: Construct a parametric model that includes dynamic load phase delay information and thermal stress field. The parametric model includes geometric topology information, material anisotropy parameters, and dynamic load phase delay information, specifically: S11: Establish a 3D model of the FPSO deck frame using a parametric CAD platform. First, input the frame outline dimensions, entering the dimensional parameters of the deck frame in the length, width, and height directions into the parametric CAD platform to generate the baseline geometric boundary for modeling. Then, according to the structural design requirements, input the support location distribution in coordinate form into the parametric CAD platform, specifying a specific spatial coordinate point for each support location and assigning a support category identifier to each support location to distinguish support areas with different stress characteristics. Next, import the connection relationship data, completely entering the connection sequence, connection node numbers, and connection types between plate members, beam members, and reinforcing members into the parametric CAD platform, associating each component unit as the overall frame structure through node numbers. The parametric CAD platform automatically generates editable geometric topology information based on the frame outline dimensions, support location distribution, and connection relationship data, allowing subsequent parametric modifications to the frame outline dimensions, support location distribution, and connection relationship data to obtain geometric topology information versions that meet the requirements of different working conditions.

[0024] S12: After obtaining the geometric topological information, the anisotropic parameters of the material are defined based on the composite laminate theory. First, according to the type of composite material used in the FPSO deck frame, material test data for this composite material are collected. The material test data includes stress-strain curves obtained under tensile conditions in different principal directions, lateral deformation data obtained under different loading directions, and thermal expansion data obtained under different temperature loads. The elastic modulus in each principal direction is calculated based on the material test data, and the elastic modulus in each principal direction is assembled into an elastic modulus tensor according to the laminate theory, so that the elastic modulus tensor can reflect the stiffness difference of the material in each principal direction. Then, based on the lateral deformation test results, Poisson's ratio between each principal direction is calculated, and the Poisson's ratio data between each direction is organized into a Poisson's ratio matrix, so that the Poisson's ratio matrix can describe the deformation coupling relationship between different principal directions. Furthermore, based on the thermal expansion test results, the coefficient of thermal expansion of the material in each principal direction is calculated, and the coefficient of thermal expansion is arranged according to the principal direction to form a coefficient of thermal expansion tensor, which is used to characterize the directional expansion characteristics of the material under temperature changes. Finally, based on the geometric topology information, the elastic modulus tensor, Poisson's ratio matrix, and thermal expansion coefficient tensor are assigned to different plate structure component elements, and the corresponding material anisotropy parameters are bound to each component element, forming a material anisotropy parameter dataset that corresponds one-to-one with the geometric topology information.

[0025] S13: Based on the obtained geometric topology information and material anisotropy parameters, the thermal stress field is calculated through nonlinear thermo-mechanical coupling analysis. First, temperature boundary conditions are defined according to the environmental temperature distribution characteristics of the FPSO under long-term service conditions in the target sea area. These include temperature boundary conditions for the seawater contact area on the outer surface, the exposed area of ​​the upper deck, and the internal compartment area. These temperature boundary conditions are applied to the plate surface corresponding to the geometric topology information. Then, transient thermal analysis is used to solve the temperature field that changes over time, obtaining the temperature distribution results of the FPSO deck plate at different time points. The temperature distribution results at each time point are output graphically, forming a temperature distribution cloud map, where each element corresponds to a specific temperature value. Next, the temperature distribution cloud map is used as a load input to the static structural analysis module. In the static structural analysis, the elastic modulus tensor, Poisson's ratio matrix, and thermal expansion coefficient tensor bound to each element are called to calculate the element thermal strain and thermal stress distribution caused by temperature changes, thus obtaining the thermal stress field of the complete plate structure. The calculation results are displayed in stages according to stress amplitude, and a thermal stress contour map is generated. The thermal stress contour map identifies areas of concentrated thermal stress, areas of varying thermal stress gradients, and low-stress areas, providing basic data of the thermal stress field for subsequent topology optimization.

[0026] S14: After completing the thermal stress field calculation, dynamic load phase delay information is obtained through wave-structure coupled time history analysis based on geometric topology information and material anisotropic parameters. First, target sea state parameters are selected according to the FPSO design conditions, clarifying the wave height, wave period, and wave direction of the representative design wave. Wave time history signals describing wave characteristics in the time domain are generated according to the design wave method. The wave time history signals are converted into wave load time histories acting on relevant parts of the FPSO deck frame using the Morison equation, obtaining a wave load time history sequence that varies with time. The wave load time history sequence is applied to the surface of the frame element corresponding to the geometric topology information. Wave-structure coupled time history analysis is performed in the structural dynamics solution environment, combined with material anisotropic parameters, to solve for the displacement response, velocity response, and acceleration response of the structure under wave load. Phase analysis is performed on the wave load time history and structural response time history using Fourier analysis or other deterministic phase extraction methods to calculate the wave load phase angle and structural response hysteresis angle at a given frequency component. Based on the difference between the wave load phase angle and the structural response hysteresis angle, phase difference arrays are established for different frequencies, locations, and response types, and then assembled into a phase difference matrix. The dynamic load phase delay information obtained through the above process includes the wave load phase angle, the structural response hysteresis angle, and the phase difference matrix, providing complete phase input data for subsequent phase compensation topology optimization.

[0027] S15: After obtaining the geometric topology information, material anisotropic parameters, thermal stress field, and dynamic load phase delay information, the above data are integrated to generate a complete parametric model. First, a unified data indexing system is established based on the plate frame element number, binding the plate frame outline dimensions, support location distribution, and connection relationship data in the geometric topology information to the corresponding element number. Then, the elastic modulus tensor, Poisson's ratio matrix, and thermal expansion coefficient tensor in the material anisotropic parameters are written into the material parameter data block according to the element number, ensuring that each element has a unique corresponding anisotropic material description. Next, the temperature values ​​and stress values ​​in the temperature distribution cloud map and thermal stress contour map are mapped to the corresponding elements and written into the thermal stress field data block. Then, the wave load phase angle, structural response hysteresis angle, and phase difference matrix in the dynamic load phase delay information are written into the phase information data block according to the frequency, location, and response type index. After completing the above data mapping, the geometric topology information, material anisotropic parameters, thermal stress field, and dynamic load phase delay information are combined into a unified input file using a structured data format. The input file records all input parameters and boundary condition data, forming a complete parametric model. The parameterized model can be directly read by the topology optimization analysis module and used to generate the initial optimized structure in the subsequent phase compensation topology optimization algorithm. It also supports parameterized adjustment and sensitivity analysis of geometric topology information, material anisotropy parameters, thermal stress field and dynamic load phase delay information.

[0028] S2: Based on the parametric model, an initial optimized structure is generated using a phase-compensated topology optimization algorithm. The initial optimized structure includes material density distribution and phase-compensated stress cloud map, specifically: S21: Read the dynamic load phase delay information from the parametric model, and organize the wave load phase angle and structural response hysteresis angle in time order into time history data of load excitation and time history data of structural response, respectively.

[0029] The load time history data is converted into frequency domain using the Fast Fourier Transform method to obtain a set of load spectrum data corresponding to discrete frequency points. The load spectrum data includes the load amplitude and load phase at each discrete frequency point.

[0030] The same frequency domain transformation is performed on the structural response time history data using the Fast Fourier Transform method to obtain structural response spectrum data that corresponds one-to-one with the load frequency. The structural response spectrum data contains the response amplitude and response phase at each discrete frequency point.

[0031] At each discrete frequency point, the amplitude modulation coefficient is calculated based on the ratio of the load amplitude to the response amplitude, so that the amplitude modulation coefficient can quantitatively characterize the amplification effect or attenuation effect of the structure on the load excitation at that frequency point.

[0032] The phase adjustment angle is further calculated based on the phase difference between the load phase and the response phase, so that the phase adjustment angle can be used to counteract the response hysteresis effect of the structure at that frequency point.

[0033] A data table is generated based on the frequency index of the amplitude modulation coefficients and phase adjustment angles corresponding to all discrete frequency points, forming a phase compensation factor that includes the amplitude modulation coefficients and phase adjustment angles, providing complete frequency domain input parameters for subsequent phase compensation topology optimization.

[0034] S22: Input the amplitude modulation coefficient and phase adjustment angle from the phase compensation factor obtained in S21 into the phase compensation topology optimization algorithm as input parameters.

[0035] The phase-compensated topology optimization algorithm uses the variable density method as the core method for solving material density optimization. The variable density method uses the SIMP interpolation model as the material interpolation model. A phase compensation factor is introduced into the material interpolation function of the SIMP interpolation model, so that the material interpolation function considers the influence of dynamic load phase delay information on structural dynamic performance when calculating the equivalent stiffness based on the relative density of the elements.

[0036] Based on the geometric topology information in the parametric model, a material density design variable is defined for each element in the structural mesh, and an element relative density matrix is ​​generated under a given initial design state. Each element in the element relative density matrix corresponds to the initial relative density value of an element.

[0037] The relative density matrix of the elements is input into the variable density method using the SIMP interpolation model. The response of the structure under the current density distribution is calculated by the material interpolation function that incorporates the phase compensation factor. Based on this, the sensitivity information of the optimization target to the relative density of each element is obtained.

[0038] The relative density matrix of the unit cells and the sensitivity information are combined to form an intermediate material density distribution, which provides the initial material density field and sensitivity data for subsequent iterative optimization calculations.

[0039] S23: After obtaining the intermediate material density distribution, the relative density matrix of the unit cells in the intermediate material density distribution is used as the initial input for iterative optimization calculation, and the density field is updated using the MMA optimization algorithm.

[0040] Weight constraints and stress constraints are set as constraints for topology optimization to control the overall weight of the structure within the target range, while ensuring that the stress level of the structure under thermal stress field and dynamic load does not exceed the predetermined safety limit.

[0041] In each iteration, the current relative density matrix of the elements, sensitivity information, and phase compensation factor are input into the MMA optimization algorithm. Based on the update rules of the MMA optimization algorithm, a new relative density matrix of the elements is calculated, forming a new round of material density distribution. After one iteration, the relative change between the new round of element density field and the previous round of element density field is calculated, and this relative change is compared with the relative change threshold in the convergence criterion data. When the relative change is less than the relative change threshold, the material density distribution is determined to have reached a convergence state during the iteration process.

[0042] The number of iterations is accumulated during the iteration process. When the number of iterations reaches the maximum number of iterations in the convergence criterion data, the update of the unit relative density matrix is ​​stopped.

[0043] The iterative optimization calculation shall terminate if any of the following conditions are met: 1. The relative change in the unit density field is less than the threshold of relative change in the convergence criterion data; 2. The number of iterations reaches the maximum number of iterations in the convergence criterion data.

[0044] After the iteration is terminated, the relative density matrix of the unit obtained in the last iteration is used as the output of the optimized unit density field, and the relative change threshold and the maximum number of iterations are used to form the convergence criterion data, thus forming the final material density distribution containing the optimized unit density field and the convergence criterion data.

[0045] S24: Based on the final material density distribution, reconstruct the structural geometric model in the finite element analysis software according to the optimized element relative density, so that the equivalent stiffness of each element in the geometric model corresponds to the final material density distribution.

[0046] The load conditions corresponding to the thermal stress field and dynamic load phase delay information in the parameterized model are applied to the reconstructed geometric model, including thermal loads applied based on temperature distribution cloud maps and thermal stress contour maps, and wave loads applied based on dynamic load phase delay information.

[0047] The finite element analysis software is used to perform structural analysis, solving for the equivalent stress value of each element in the optimized structure under load conditions, thus forming the equivalent stress distribution. Based on a pre-set stress threshold, element regions with stress levels exceeding the threshold are selected and marked as maximum stress regions. Furthermore, based on the gradient variation characteristics of the equivalent stress in spatial distribution, element regions with abrupt changes in stress gradient are identified and marked as stress concentration regions. The maximum stress regions and stress concentration regions are combined to form key region identifiers, which are then overlaid onto the equivalent stress distribution map to generate a phase-compensated stress cloud map containing the equivalent stress distribution and key region identifiers. This provides intuitive stress distribution information for subsequent structural smoothing and material distribution steps.

[0048] S25: After obtaining the final material density distribution and phase-compensated stress contour map, the two types of data are integrated based on a unified element number indexing system. The optimized element density field and convergence criterion data from the final material density distribution are organized into material distribution data, and a material distribution data structure is constructed using the element number as the index field. The equivalent stress distribution and key region markers from the phase-compensated stress contour map are organized into stress analysis results, and a stress analysis result data structure is constructed using the element number as the index field.

[0049] A structured database format is used to merge material distribution data and stress analysis results into a unified design file, ensuring a one-to-one correspondence between the material distribution data and the corresponding stress analysis results for each element. This design file serves as the complete initial optimized structure output, containing both material distribution data and stress analysis results. This provides a complete and directly accessible input data foundation for subsequent steps, including generating smooth topologies and optimizing anisotropic material allocation.

[0050] S3: Perform stress gradient smoothing on the initial optimized structure to generate a smooth topology. The smooth topology includes smoothing the boundary curves and updating the stress contour plot, specifically: S31: Based on the phase-compensated stress cloud map in the initial optimized structure, the high stress gradient region is identified by the moving least squares method.

[0051] The equivalent stress values ​​of each element in the phase-compensated stress cloud map are sorted according to spatial coordinates to establish a stress gradient calculation region for each element. The moving least squares method is used to calculate the stress gradient of each element in the local region, where a Gaussian kernel function is used to apply weights to each sampling point in the region, so that the sampling point closer to the current position has a higher weight.

[0052] The stress change rate of each element is calculated and compared with a stress change rate threshold automatically set based on the material's fatigue limit. The set of elements whose stress change rates exceed the threshold is defined as a high stress gradient region, and boundary segment data is extracted based on the spatial arrangement of these elements. The output is the high stress gradient region identification result composed of the element set and boundary segment data, providing a data foundation for boundary curve reconstruction.

[0053] S32: Reconstruct the boundary curves from the boundary segment data of the high-stress gradient region obtained in S31. A Bézier curve fitting method is used, with a cubic uniform B-spline algorithm as the curve fitting technique. By inputting the boundary segment data of the high-stress gradient region, the coordinates of control points, node vectors, and weighting coefficients are calculated to ensure that the fitted curve meets the continuity requirements of a cubic uniform B-spline curve.

[0054] During the fitting process, the distance between the boundary line segment data and the fitted curve is minimized to ensure the curvature continuity of the generated 3D curve mesh, thus guaranteeing the smoothness of the boundary shape. The control point coordinates, node vectors, and weight coefficients form a reconstruction parameter set to describe the geometric characteristics of the cubic uniform B-spline curve. The final output is a smooth boundary curve containing the curvature-continuous 3D curve mesh and the reconstruction parameter set.

[0055] S33: Based on the smooth boundary curve obtained in S32, the geometric model of the initial optimized structure is updated. NURBS surface modeling technology is used to extend the smooth boundary curve. By establishing a continuous array of surface control points in the curve normal direction, surface segments that maintain geometric continuity with the smooth boundary curve are generated.

[0056] The surface fragments generated by the extension are geometrically combined with the original geometric model of the initial optimized structure through Boolean operations. These Boolean operations include analyzing the intersection relationships of the models, removing the overlapping portions between the original model and the extended surface, and fully incorporating the extended surface into the model, generating a transition surface model with a smooth transition of structural boundaries. This transition surface model contains smoothly connected geometric surfaces and boundary data automatically updated according to Boolean operations, ensuring that the model has a smooth and continuous shape characteristic in high-stress gradient regions.

[0057] S34: After generating the transition surface model, finite element analysis is performed based on the updated geometric model. First, a high-order element meshing method is used to construct a finite element mesh for the transition surface model, ensuring that the mesh accurately describes the geometry after the surface extension. Then, load boundary conditions consistent with the initial optimized structure are applied, including load conditions corresponding to the thermal stress field and dynamic load phase delay information.

[0058] Static stress analysis was performed using finite element analysis software to solve for the equivalent stress distribution of the optimized geometric model under load conditions. The obtained equivalent stress distribution data was then organized into an updated stress contour map according to the element number, and smoothing effect indices were calculated. These indices included the stress gradient reduction magnitude in high stress gradient regions and the boundary continuity evaluation value.

[0059] The final output is an updated stress cloud map that includes the optimized equivalent stress distribution and smoothing effect indicators.

[0060] S35: Integrate the smooth boundary curve obtained in S32, the transition surface model obtained in S33, and the updated stress cloud map obtained in step S34. Using parametric association technology, with element number and geometric control information as index fields, associate the reconstructed parameter set of the smooth boundary curve with the geometric surface data of the transition surface model and the stress analysis results in the updated stress cloud map.

[0061] The associated data is then used to generate a complete smooth topology according to the structural topology representation format. The smooth topology contains geometric model data, boundary information, and stress analysis results, providing a continuous and usable geometric and mechanical input basis for the next step of anisotropic material optimization allocation.

[0062] S4: Based on a smooth topology, perform anisotropic material optimization allocation and output the final lightweight design. The final lightweight design includes anisotropic material distribution model and dynamic performance index report, specifically: S41: Based on the updated stress contour map in the smooth topology, a finite element analysis model is constructed for each element, and eight-node hexahedral elements are used for mesh generation. An adaptive meshing technique is employed during mesh generation, automatically refining the mesh in high-stress gradient regions identified in the updated stress contour map. This results in a higher element density in these regions and ensures the accuracy of the principal stress direction data calculation.

[0063] A stress tensor is established on each eight-node hexahedral element, and the eigenvalue problem of the stress tensor is solved. During the solution process, three eigenvalues ​​and their corresponding three eigenvectors of the stress tensor are calculated. The three eigenvalues ​​are sorted according to their numerical values ​​to form the principal stress magnitude sorting information, and the three eigenvectors are used as the principal stress direction vectors according to their eigenvalue sorting order. The principal stress direction vectors and the principal stress magnitude sorting information are organized according to the element number to generate complete principal stress direction data, providing the directional input basis for subsequent fiber orientation optimization algorithms.

[0064] S42: After obtaining the principal stress direction data from S41, a fiber orientation optimization algorithm is executed based on the material anisotropy parameters. The fiber orientation optimization algorithm uses the maximum stress criterion, determining the optimal fiber orientation direction for each element by comparing the principal stress magnitude ranking information in the principal stress direction data with the allowable stress in the material anisotropy parameters. The principal stress direction vector is used as the directional reference for fiber orientation adjustment. By rotating the fiber direction to align with the principal stress direction, the tensile and compressive strength of the element in the principal stress directions is improved.

[0065] Based on the optimization results, a fiber orientation distribution map is generated, and the fiber orientation angle parameters are recorded for each element. A laminate layup scheme is established according to the fiber orientation distribution map and the laminate structure requirements in the material anisotropy parameters. By calculating the angle, thickness sequence, and layup order of each layer, a complete laminate layup scheme is formed. The fiber orientation distribution map and the laminate layup scheme are organized by element index to generate an anisotropic material distribution model containing both the fiber orientation distribution map and the laminate layup scheme.

[0066] S43: After generating the anisotropic material distribution model, phase matching analysis is performed based on the smooth topology to verify the dynamic performance of the structure. The phase matching analysis uses the frequency domain decomposition method, which obtains the frequency domain response characteristics of the structure under dynamic load by solving the coherence function between the phase delay information of the dynamic load and the vibration characteristics of the structure.

[0067] First, a dynamic finite element model is established using an anisotropic material distribution model that includes fiber orientation distribution and laminate layup scheme. The natural frequency spectrum of the structure is obtained by solving the dynamic equilibrium equations. Then, the dynamic response amplitude is calculated based on the natural frequency spectrum and dynamic load phase delay information. The structural response amplitude corresponding to the loading frequency is recorded as dynamic performance output data.

[0068] Finally, the dynamic load phase delay information is compared with the dynamic response phase, and the phase matching degree is calculated using the coherence function. The phase matching degree is used as an important indicator to measure the dynamic compatibility of the structure. A complete dynamic performance index report is formed using three dimensions: natural frequency spectrum, dynamic response amplitude, and phase matching degree.

[0069] S44: Integrate the anisotropic material distribution model generated in S42 with the dynamic performance index report generated in S43, and generate the final lightweight design through a digital integration platform. The digital integration platform adopts model-based definition technology, using 3D model data as the core carrier, and automatically converts the fiber orientation distribution diagram and laminate layup scheme into manufacturing-executable drawings.

[0070] Based on the material parameters required by the manufacturing drawings, material performance data, material thickness, and laminate composition sequence are extracted from the material anisotropy parameters to generate the corresponding material specifications. The manufacturing drawings, material specifications, and dynamic performance reports are then integrated into a performance certification document, providing a complete description of the structural strength, safety, and dynamic performance of the final lightweight design.

[0071] The final output of the lightweight design documents includes manufacturing drawings, material specifications, and performance certification documents, enabling the design results to be directly used for production and engineering verification, and serving as the final output of the entire topology optimization process.

[0072] This invention encompasses any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of this invention. To provide the public with a thorough understanding of this invention, specific details are described in detail in the following preferred embodiments; however, those skilled in the art will fully understand the invention even without these details. Furthermore, to avoid unnecessary misunderstanding of the essence of this invention, well-known methods, processes, procedures, components, and circuits are not described in detail.

[0073] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A lightweight topology optimization design method for FPSO deck racks, characterized in that, Includes the following steps: S1: Construct a parameterized model that includes dynamic load phase delay information and thermal stress field. The parameterized model includes geometric topology information, material anisotropy parameters and dynamic load phase delay information. S2: Based on the parameterized model, an initial optimized structure is generated by a phase-compensated topology optimization algorithm. The initial optimized structure includes a material density distribution and a phase-compensated stress cloud map. S3: Perform stress gradient smoothing on the initial optimized structure to generate a smooth topology, which includes smooth boundary curves and updated stress cloud maps; S4: Based on the smooth topology, perform anisotropic material optimization allocation and output the final lightweight design, which includes anisotropic material distribution model and dynamic performance index report.

2. The lightweight topology optimization design method for FPSO deck frame according to claim 1, characterized in that, S1 includes: S11: Construct the geometric topology information of the FPSO deck frame using 3D modeling software. The geometric topology information includes the frame outline dimensions, support location distribution, and connection relationship data. S12: Based on the geometric topology information, define the material anisotropy parameters, which include the elastic modulus tensor, Poisson's ratio matrix, and thermal expansion coefficient tensor. S13: Combining the geometric topology information and the material anisotropy parameters, the thermal stress field is calculated through nonlinear thermo-mechanical coupling analysis. The thermal stress field includes a temperature distribution cloud map and a thermal stress contour map. S14: Based on the geometric topology information, the material anisotropic parameters, and the thermal stress field, dynamic load phase delay information is obtained through wave-structure coupled time history analysis. The dynamic load phase delay information includes wave load phase angle, structural response hysteresis angle, and phase difference matrix. S15: Integrate the geometric topology information, the material anisotropy parameters, the thermal stress field, and the dynamic load phase delay information to generate a complete parametric model, which includes all input parameters and boundary condition data.

3. The lightweight topology optimization design method for FPSO deck frame according to claim 2, characterized in that, In S11, the 3D modeling software uses a parametric CAD platform to generate editable geometric topology information by inputting the outline dimensions of the frame, the distribution of support positions, and the connection relationship data.

4. The lightweight topology optimization design method for FPSO deck frame according to claim 2, characterized in that, S2 includes: S21: Based on the dynamic load phase delay information in the parameterized model, the phase compensation factor is calculated through frequency domain response analysis. The phase compensation factor includes the amplitude modulation coefficient and the phase adjustment angle. S22: Input the phase compensation factor into the phase compensation topology optimization algorithm, and solve the intermediate material density distribution by the variable density method. The intermediate material density distribution includes the unit relative density matrix and sensitivity information. S23: Based on the intermediate material density distribution, the final material density distribution that satisfies the constraints is obtained through iterative optimization calculation. The final material density distribution includes the optimized unit density field and convergence criterion data. S24: Based on the final material density distribution, a phase-compensated stress cloud map is generated through post-processing calculation. The phase-compensated stress cloud map includes equivalent stress distribution and key area identification. S25: Integrate the final material density distribution and the phase-compensated stress cloud map to output a complete initial optimized structure, which includes material distribution data and stress analysis results.

5. The lightweight topology optimization design method for FPSO deck racks according to claim 4, characterized in that, In S23, the iterative optimization calculation adopts the MMA optimization algorithm, which takes the intermediate material density distribution as the initial value, solves the element density field that satisfies the weight constraint and stress constraint through multiple iterations, and terminates the iteration when the convergence criterion data is met.

6. The lightweight topology optimization design method for FPSO deck frame according to claim 4, characterized in that, S3 includes: S31: Based on the phase-compensated stress cloud map in the initial optimized structure, high stress gradient regions are identified by moving least squares method. The high stress gradient regions include a set of units with stress change rate exceeding a threshold and boundary line segment data. S32: Reconstruct the boundary curve of the high stress gradient region by fitting a Bezier curve to generate a smooth boundary curve, which includes a three-dimensional curve mesh with continuous curvature and a set of reconstruction parameters. S33: Update the geometric model of the initial optimized structure based on the smooth boundary curve, and generate a transition surface model through surface extension and Boolean operations. The transition surface model includes a smoothly connected geometric surface and updated boundary data. S34: Perform finite element analysis on the transition surface model, and obtain an updated stress cloud map by solving the updated stress distribution. The updated stress cloud map includes the optimized equivalent stress distribution and smoothing effect index. S35: Integrate the smooth boundary curve, the transition surface model, and the updated stress cloud map to generate a complete smooth topology, which includes geometric model data, boundary information, and stress analysis results.

7. The lightweight topology optimization design method for FPSO deck racks according to claim 6, characterized in that, In S34, the finite element analysis uses high-order element meshing to perform static stress analysis on the transition surface model, and obtains an updated stress cloud map containing equivalent stress distribution and smoothing effect indicators by solving.

8. The lightweight topology optimization design method for FPSO deck racks according to claim 6, characterized in that, In step S35, the generation of the smooth topology structure adopts parametric association technology, which associates the smooth boundary curve, the transition surface model and the updated stress cloud map to form complete structural data containing geometric model data, boundary information and stress analysis results.

9. A lightweight topology optimization design method for FPSO deck racks according to claim 6, characterized in that, S4 includes: S41: Based on the updated stress cloud map in the smooth topology, calculate the principal stress direction data using the finite element method. The principal stress direction data includes the principal stress direction vector and principal stress magnitude sorting information of each element. S42: Based on the principal stress direction data and material anisotropy parameters, an anisotropic material distribution model is generated using a fiber orientation optimization algorithm. The anisotropic material distribution model includes a fiber orientation distribution map and a laminate layup scheme. S43: Perform dynamic performance verification on the anisotropic material distribution model, and calculate the dynamic performance index report through phase matching analysis. The dynamic performance index report includes the natural frequency spectrum, dynamic response amplitude, and phase matching degree. S44: Integrate the anisotropic material distribution model and the dynamic performance index report to generate a complete final lightweight design, which includes manufacturing drawings, material specifications and performance certification documents.

10. A lightweight topology optimization design method for FPSO deck racks according to claim 9, characterized in that, In S41, the finite element method uses eight-node hexahedral elements for mesh generation, and obtains the principal stress direction vector and principal stress magnitude sorting information of each element by solving the stress tensor eigenvalue problem.

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