Integrated lightweight method for floating body structure based on SIMP model

Abstract

The invention relates to a comprehensive lightweight method for a floating body structure based on an SIMP model. The method comprises the following steps: designing a preliminary scheme of the floating body structure; local parameters are selected as optimization variables through global sensitivity analysis; taking the relative density of the unit as a design variable, and introducing a weight coefficient of each working condition; converting the structural strength and fatigue evaluation result into a weighted penalty term and taking the weighted penalty term as a constraint condition; taking the lightest weight of the floating body structure as a target optimization function, establishing a topological optimization model, and carrying out iterative optimization on the floating body structure; determining the optimal density and the structural volume; fatigue life constraint is introduced into floating body structure topological optimization, and the design requirement of a floating body platform in a long-term marine environment is met. According to the method, corresponding working condition coefficients and working condition weights are distributed for different working conditions, and a topological optimization model considering multiple working conditions is constructed, so that the quality requirements under all working conditions can be met while comprehensive light weight of the floating body structure is achieved.

Description

Technical Field

[0001] The present invention relates to the field of marine engineering technology, and in particular to a comprehensive lightweight method for floating structures based on a SIMP model. Background Art

[0002] Over 80% of the world's high-quality wind energy resources are located in deepwater areas exceeding 60 meters. Traditional fixed foundations (such as monopiles and jackets) are technically limited and cannot be economically developed in these areas. Floating offshore wind power, which uses floating structures to support wind turbines, overcomes these water depth limitations and has become a core technology for developing deepwater wind energy.

[0003] Early floating buoy designs relied heavily on steel and concrete, resulting in excessive weight and high material, manufacturing, and installation costs. Therefore, lightweighting floating offshore wind turbine buoys is imperative. This not only reduces material usage and manufacturing energy consumption, lowering the cost of each buoy, but also allows for transport using smaller vessels, reducing reliance on heavy lifting equipment and shortening offshore operations. Simplified structures also reduce maintenance complexity. Lightweight design, combined with optimized dynamic stability, makes buoys more reliable in harsh environments such as deep seas, high waves, and strong winds.

[0004] In the prior art, the lightweighting of structures is usually achieved by the following methods: taking the lightest weight as the objective function and density as the design variable, solving the problem under single working conditions and various design constraints;

[0005] For example, the patent announcement number CN108875125B announces "a method for topological optimization of continuum dual-material structures under mixed constraints of displacement and global stress". It constructs design variables through the variable density method, takes volume minimization as the goal, combines displacement and global stress constraints to establish an optimization model, and uses density filtering, ε stress relaxation method and moving progressive algorithm to achieve convergence.

[0006] However, floating bodies need to withstand multi-source dynamic loads such as waves, ocean currents, and wind loads in open waters. Their stress state changes in real time with sea conditions (such as wave height, period, and wind direction), forming time-varying multi-working conditions. Existing optimization models are mostly designed based on a single working condition, which may lead to risks such as local stress concentration, insufficient fatigue life, or dynamic instability in the structure under other working conditions. Summary of the Invention

[0007] In view of the deficiencies of the prior art, the present invention provides a comprehensive lightweight method for floating structures based on the SIMP model to solve the above problems.

[0008] The present invention provides the following technical solutions:

[0009] A comprehensive lightweighting method for floating structures based on a SIMP model includes the following steps:

[0010] Design a preliminary plan for the floating structure;

[0011] Dynamically calculate the weight coefficients of different working conditions according to the load constraints under different working conditions;

[0012] Through global sensitivity analysis, the influence of each local parameter on the strength and fatigue performance of the floating structure is quantified, and local parameters are selected as optimization variables according to the influence degree;

[0013] The floating structure is discretized, and each unit is assigned a material density variable. The solid isotropic material penalty material function model is used as the interpolation model of the optimization variable. The unit elastic modulus is associated with the relative density, and a penalty factor p is introduced to penalize the intermediate density material, so that the unit density gradually approaches the two ends.

[0014] The relative density of the unit is used as the design variable, and the weight coefficient of each working condition is introduced. The structural strength and fatigue assessment results are converted into weighted penalty terms and used as constraints. The lightest weight of the floating structure is used as the target optimization function, and a topology optimization model is established.

[0015] Iteratively optimize the floating structure based on the topology optimization model;

[0016] The optimal density of the materials in all parts of the floating structure is solved to determine the optimal density and structural volume, thus achieving comprehensive lightweight optimization of the floating structure.

[0017] Preferably, the preliminary scheme of the floating structure adopts a uniform material density distribution.

[0018] Preferably, the degree of influence is: retaining local parameters whose relevance to the optimization target is greater than a set threshold but whose influence on structural performance is lower than a set threshold as optimization variables.

[0019] Preferably, the correlation includes mass, stress and fatigue life contribution; and the structural performance includes strength and fatigue life.

[0020] Preferably, the weight coefficient is calculated dynamically:

[0021]

[0022] Where, E i is the wave energy corresponding to the i-th working condition;

[0023] ω i is the weight coefficient corresponding to the i-th working condition;

[0024] Q is the total number of working conditions;

[0025] is the sum of wave energy for all conditions.

[0026] Preferably, the wave energy is estimated using the potential energy of seawater fluctuation:

[0027]

[0028] Where T is the wave period;

[0029] H is the significant wave height.

[0030] Preferably, each unit is assigned a material density variable, that is, each unit is assigned a relative density x n ∈[0,1];

[0031] The unit density gradually approaches the two ends: E n =E0·x n p , where E0 is the initial elastic modulus of the material, and p is the penalty factor, which ranges from 2≤p≤5.

[0032] Preferably, the topology optimization model is:

[0033]

[0034]

[0035] Where:

[0036] X: Matrix, which is the vector of relative density of each unit;

[0037] x n : represents the relative density of the nth unit;

[0038] M: comprehensive optimization goal;

[0039] M x : the overall weight of the floating structure;

[0040] The operating condition coefficient corresponding to the i-th operating condition;

[0041] ω i : The weight coefficient corresponding to the i-th working condition;

[0042] Positive penalty term, when σ i >[σ] or y i <y min The penalty item takes effect when , otherwise it is 0;

[0043] V n : the volume of the nth unit;

[0044] σ i : maximum stress under the i-th working condition;

[0045] [σ]: allowable stress corresponding to the working condition;

[0046] σ u : ultimate stress;

[0047] m: safety factor;

[0048] y i : fatigue life under the i-th working condition;

[0049] y min : Minimum required life span corresponding to the working conditions;

[0050] f n is the nth optimization variable.

[0051] Preferably, when iteratively optimizing the floating structure, the finite element analysis software is called by MATLAB software for batch processing, stress and fatigue life calculations are performed for different working conditions, and the weight coefficients are updated in real time.

[0052] Preferably, the density variable is updated in combination with the optimization criterion method to accelerate convergence and reduce the number of iterations.

[0053] The present invention has the following beneficial technical effects:

[0054] The present invention introduces fatigue life constraints in the topology optimization of the floating structure, which meets the design requirements of the floating platform in a long-term marine environment.

[0055] Different operating conditions are assigned corresponding operating coefficients, prioritizing the performance requirements of key operating conditions. Based on the statistical characteristics of different operating conditions, operating condition weights are introduced; the larger the weight, the stricter the load constraints corresponding to multiple operating conditions. A topology optimization model that considers multiple operating conditions is constructed to achieve comprehensive lightweighting of the floating structure while meeting quality requirements under all operating conditions. This avoids the situation where the optimal density and structural volume calculated based on only a single operating condition is only suitable for that condition and not for other conditions.

[0056] The constraints are converted into positive weighted penalty terms of the target conditions to avoid the problem of algorithm convergence difficulties caused by direct constraints, and improve the robustness and convergence efficiency of the optimization algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0058] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0059] Example:

[0060] Comprehensive lightweighting method of floating structure based on SIMP model, such as Figure 1 As shown:

[0061] Step S1: Based on the design requirements of the floating structure (such as wave loads, structural deadweight and other loads and basic design data of the floating platform), combined with design experience and relevant technical standards and guidelines, a preliminary scheme of the floating structure is designed. The initial structure adopts a uniform material density distribution.

[0062] Step S2: dynamically calculate the weight coefficient ω of different working conditions according to the load constraints under different working conditions. i For example, after inputting the environmental load parameters of a floating structure, the weight coefficient is dynamically calculated:

[0063]

[0064] Where, E i is the wave energy corresponding to the i-th working condition;

[0065] ω i is the weight coefficient corresponding to the i-th working condition;

[0066] Q is the total number of working conditions;

[0067] is the sum of wave energy for all conditions.

[0068] The wave energy can be estimated using the potential energy of seawater, namely:

[0069]

[0070] Where:

[0071] T: wave period;

[0072] H: Significant wave height.

[0073] In step S3, the influence of each local parameter on the strength and fatigue performance of the floating structure is quantified through global sensitivity analysis, and parameters with high relevance to the optimization target (contribution to mass, stress and fatigue life is greater than the set threshold, and the specific threshold can be set according to demand) but low influence on structural performance (strength, stiffness, fatigue life and stability are less than the set threshold, and the specific threshold can be set according to demand) are retained as optimization variables to reduce redundant variables.

[0074] Step S4: discretize the floating structure and assign a material density variable to each unit, that is, assign a relative density x to each unit. n ∈[0,1]. The solid isotropic material penalty material function model is used as the interpolation model of the optimization variable (SIMP model), which associates the element elastic modulus with the relative density, and introduces a penalty factor p to penalize the intermediate density material, so that the element density gradually approaches the two ends:

[0075] E n =E0·x n p

[0076] E0 is the initial elastic modulus of the material, p is the penalty factor, and its value range is 2≤p≤5.

[0077] In step S5, the relative density of the unit is used as the design variable, the working condition weight coefficient is introduced, and the structural strength and fatigue assessment results are converted into weighted penalty terms and constraints of the final solution to form a comprehensive optimization goal, thereby obtaining a floating structure solution that meets the lightweight goal. Specifically, its mathematical model is:

[0078]

[0079] Where,

[0080] X: Matrix, which is the vector of relative density of each unit;

[0081] x n : relative density of the nth unit;

[0082] M: comprehensive optimization objective, requiring the minimum value of the function;

[0083] M x : the overall weight of the floating structure;

[0084] Working condition coefficient, which is adjusted in real time under different working conditions to ensure the reliability of the structure under extreme working conditions; Positive penalty term, when σ i >[σ] or y i <y min The penalty item takes effect when , otherwise it is 0;

[0085] ω i : The weight coefficient corresponding to the i-th working condition;

[0086] V n : the volume of the nth unit;

[0087] σ i : maximum stress under the i-th working condition;

[0088] [σ]: allowable stress corresponding to the working condition;

[0089] σ u : ultimate stress;

[0090] m: safety factor;

[0091] y i : fatigue life under the i-th working condition, in years;

[0092] y min : The minimum required life span corresponding to the working conditions should be no less than 20;

[0093] f n is the nth optimization variable.

[0094] Step S6: Based on the lightweight topology optimization model for the floating structure, the floating structure is iteratively optimized. Finite element analysis software is called via MATLAB for batch processing. Stress and fatigue life calculations are performed for different operating conditions, and weight coefficients are updated in real time. Strength and fatigue performance are used as the final constraints of the mathematical model. If the constraints are not met, the optimization variable is updated again until convergence.

[0095] Step S7: update the density variable in combination with the optimization criterion method to accelerate convergence and reduce the number of iterations.

[0096] Step S8: Optimize the material density of all parts of the floating structure to determine the optimal density and structural volume, achieving comprehensive lightweight optimization of the structure. The topology-optimized model is smoothed, and the final model is verified for stress and fatigue life using the finite element method to ensure that the constraints are met.

[0097] Step S3, performing global sensitivity analysis, is a conventional technique and is briefly described below:

[0098] 1. Based on the plate thickness distribution and static strength analysis of various parts of the wind turbine foundation (floating structure), 10 groups of plate thickness variables were preliminarily screened out.

[0099] 2. Set the initial value and upper and lower limits of the plate thickness variable, and generate 200 sets of plate thickness combinations using the Latin hypercube design method to form a 10*200 variable matrix. The plate thickness variable information is shown in the following table:

[0100] variable Part Initial / mm Lower limit / mm Upper limit / mm X1 Column housing 1 10 7 13 … … … … … X10 Buoy shell and inner plate 13 10 16

[0101] 3. Use MATLAB to call finite element software for batch analysis to generate 200 sets of fan foundation structure quality, maximum stress and fatigue life tables for different plate thickness variable combinations.

[0102] 4. By comparing the contribution of each group of mass, stress and fatigue life, 6 groups of plate thickness combinations were finally selected.

[0103] 5. For the 6 sets of plate thickness combinations screened out, the plate thickness contribution analysis of 10 sets of plate thickness variables was carried out, and finally 6 plate thickness variables were retained, namely X1, X4, X5, X8, X9, and X10, which were used as optimization variables for subsequent lightweight calculations.

[0104] The above-described embodiments merely represent specific implementations of the present invention. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art would be able to make numerous variations and improvements without departing from the spirit of the present invention, and all such variations and improvements fall within the scope of protection of the present invention.

Claims

1. A comprehensive lightweight method for floating structures based on the SIMP model, characterized in that: The following steps are involved: Design a preliminary plan for the floating structure; Dynamically calculate the weight coefficients of different working conditions according to the load constraints under different working conditions; Through global sensitivity analysis, the influence of each local parameter on the strength and fatigue performance of the floating structure is quantified, and local parameters are selected as optimization variables according to the influence degree; The floating structure is discretized, and each unit is assigned a material density variable. The solid isotropic material penalty material function model is used as the interpolation model of the optimization variable. The unit elastic modulus is associated with the relative density, and a penalty factor p is introduced to penalize the intermediate density material, so that the unit density gradually approaches the two ends. The relative density of the unit is used as the design variable, and the weight coefficient of each working condition is introduced. The structural strength and fatigue assessment results are converted into weighted penalty terms and used as constraints. The lightest weight of the floating structure is used as the target optimization function, and a topology optimization model is established. Iteratively optimize the floating structure based on the topology optimization model; The optimal density of the material in all parts of the floating structure is solved to determine its optimal density and structural volume.

2. The comprehensive lightweight method for floating structures based on the SIMP model according to claim 1 is characterized in that: The preliminary design of the floating structure adopts uniform material density distribution.

3. The comprehensive lightweight method for floating structures based on the SIMP model according to claim 1 is characterized in that: The degree of influence is: retaining local parameters whose relevance to the optimization target is greater than a set threshold but whose influence on structural performance is lower than a set threshold as optimization variables.

4. The comprehensive lightweight method for floating structures based on the SIMP model according to claim 3 is characterized in that: The correlation includes mass, stress and fatigue life contribution; the structural performance includes strength and fatigue life.

5. The comprehensive lightweight method for floating structures based on the SIMP model according to claim 1 is characterized in that: Dynamically calculate weight coefficient: Where, E i is the wave energy corresponding to the i-th working condition; ω i is the weight coefficient corresponding to the i-th working condition; Q is the total number of working conditions; is the sum of wave energy for all conditions.

6. The comprehensive lightweight method for floating structures based on the SIMP model according to claim 5 is characterized in that: The wave energy is estimated using the potential energy of seawater fluctuation: Where T is the wave period; H is the significant wave height.

7. The comprehensive lightweight method for floating structures based on the SIMP model according to claim 1 is characterized in that: Each unit is assigned a material density variable, that is, each unit is assigned a relative density x n ∈[0,1]; The unit density gradually approaches the two ends: E n =E0·x n p , where E0 is the initial elastic modulus of the material, and p is the penalty factor, which ranges from 2≤p≤5.

8. The comprehensive lightweight method for floating structures based on the SIMP model according to claim 1 is characterized in that: The topology optimization model is: Where: X: Matrix, which is the vector of relative density of each unit; x n : represents the relative density of the nth unit; M: comprehensive optimization goal; M x : the overall weight of the floating structure; The operating condition coefficient corresponding to the i-th operating condition; ω i : The weight coefficient corresponding to the i-th working condition; Positive penalty term, when σ i >[σ] or y i <y min The penalty item takes effect when , otherwise it is 0; V n : the volume of the nth unit; σ i : maximum stress under the i-th working condition; [σ]: allowable stress corresponding to the working condition; σ u : ultimate stress; m: safety factor; y i : fatigue life under the i-th working condition; y min : Minimum required life span corresponding to the working conditions; f n is the nth optimization variable.

9. The comprehensive lightweight method for floating structures based on the SIMP model according to claim 1, characterized in that: When iteratively optimizing the floating structure, the finite element analysis software is called through MATLAB software for batch processing, stress and fatigue life calculations are performed for different working conditions, and the weight coefficients are updated in real time.

10. The comprehensive lightweight method for floating structures based on the SIMP model according to claim 9, characterized in that: The density variable is updated in combination with the optimization criterion method to accelerate convergence and reduce the number of iterations.

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