Weibull shape parameter calculation method in ship fatigue strength checking

Abstract

The invention discloses a weibull shape parameter calculation method in ship fatigue strength checking, and relates to the technical field of ships, the method comprises the following steps: calculating a wave load of a ship under regular waves through hydrodynamic analysis, applying the wave load to a ship body structure finite element model, and obtaining a stress response transfer function through structure finite element calculation; stress response short-term distribution is calculated in combination with the sea wave statistical condition of a target navigation sea area of the ship, and stress response long-term distribution is obtained through further weighted combination, so that stress amplitude long-term forecast values under different exceeding probabilities are obtained and used for calculating weibull shape parameters at typical check nodes of the ship; the weibull shape parameters obtained through calculation have a good matching relation with the ship structure, the sea wave condition of the target navigation sea area and the checking position, accuracy and precision are high, a basis is provided for follow-up high-precision ship structure fatigue strength checking, and the ship structure fatigue life forecasting precision can be improved.

Description

Technical Field

[0001] This application relates to the field of shipbuilding technology, and in particular to a method for calculating the Weibull shape parameter in ship fatigue strength verification. Background Technology

[0002] Ships and marine engineering structures are subjected to complex random environmental loads throughout their entire life cycle, with wave loads being the dominant factor. Fatigue damage is one of the most common failure modes for these structures, and it is essentially a progressive damage caused by the long-term accumulation of alternating stress. Fatigue strength verification of these structures is the basis for assessing structural safety, predicting lifespan, and optimizing design.

[0003] Currently, fatigue cumulative damage theory (such as Miner's rule) based on spectral analysis and SN curves (stress-life curves) is the most commonly used method for fatigue strength verification of ship and marine engineering structures. One of the core steps of this method is to obtain the fatigue stress of the structure caused by wave loads. Due to the randomness of waves, the fatigue stress is usually fitted by a continuous probability distribution function. The two-parameter Weibull distribution is widely accepted as the standard model for describing fatigue stress caused by wave loads due to its flexibility and good characterization of tail data.

[0004] The Weibull distribution comprises scale and shape parameters, with the shape parameter directly determining the distribution morphology. The shape parameter has a decisive and highly nonlinear influence on the cumulative fatigue damage. Under the same scale parameter, minute changes in the shape parameter are significantly amplified by the gamma function, leading to orders of magnitude differences between the calculated cumulative fatigue damage and the predicted life, directly affecting the fatigue strength verification results. Currently, empirical values ​​or formulas for the shape parameter of the Weibull distribution given in various civil shipbuilding standards' fatigue specifications are generally used. However, the accuracy of the shape parameter determined by this method is not ideal, directly affecting the accuracy and precision of the fatigue strength verification results. Summary of the Invention

[0005] This application addresses the aforementioned problems and technical requirements by proposing a method for calculating Weibull shape parameters in ship fatigue strength verification. The technical solution of this application is as follows: A method for calculating Weibull shape parameters in ship fatigue strength verification, the method comprising: Hydrodynamic analysis was performed on the ship under the loading condition of fatigue strength verification. The wave load of the ship under regular waves was calculated and applied to the finite element model of the hull structure. The stress response transfer function was obtained through structural finite element calculation. Based on the wave statistics of the target navigation area of ​​the ship, determine multiple short-term sea states and the statistical probability of each short-term sea state. Select multiple wave direction angles evenly within the range of 0° to 360° and determine the statistical probability of each wave direction angle. Based on the stress response transfer function, the wave angle at typical check points of the ship is calculated. and short-term working conditions Short-term probability distribution of stress response; Based on the statistical probabilities of each wave direction angle and each short-term working condition, the short-term probability distributions of stress responses at typical ship check nodes under different wave direction angles and short-term working conditions are weighted and combined to obtain the long-term forecast values ​​of stress amplitude at typical ship check nodes under different exceedance probabilities. The Weibull shape parameters at typical check nodes of a ship are calculated using long-term predicted values ​​of stress amplitude under different exceedance probabilities. .

[0006] A further technical solution involves calculating the wave angle at typical check points of the ship based on the stress response transfer function. and short-term working conditions The short-term probability distribution of stress response includes: Calculation of wave direction angle based on stress response transfer function and short-term working conditions Variance of the stress response spectrum under ; Based on the narrow spectrum assumption, the wave direction angle is determined. and short-term working conditions Arbitrary stress amplitude at typical check points of the ship short-term probability density function .

[0007] A further technical solution involves obtaining long-term predicted values ​​of stress amplitude at typical ship check nodes under different exceedance probabilities, including: Based on the statistical probabilities of various wave angles and various short-term operating conditions, the stress amplitudes of typical ship check nodes under different wave angles and short-term operating conditions are calculated. short-term probability density function By performing weighted combinations, the stress amplitude at typical check points of the ship was obtained. Exceeding probability The expression; Based on transcendence probability expression calculation The stress amplitude under the condition of being exceeded is used as the probability of exceeding the limit. Long-term forecast value of stress amplitude under ,calculate The stress amplitude under the condition of being exceeded is used as the probability of exceeding the limit. Long-term forecast value of stress amplitude under .

[0008] A further technical solution involves setting the stress amplitude at typical ship verification nodes. Exceeding probability The expression is:

[0009] in, It is a short-term working condition The statistical probability, Is the wave angle The statistical probability.

[0010] A further technical solution involves calculating the wave direction angle based on the stress response transfer function. and short-term working conditions Variance of the stress response spectrum under include: According to short-term working conditions Wave spectrum and wave angle Stress response transfer function The wave angle was calculated. and short-term working conditions Stress response spectral density And obtain the variance of the stress response spectrum. ;in, This indicates the angular frequency of the wave.

[0011] Its further technical solution is that the Weibull shape parameter calculation method also includes: Based on the Bretschneider two-parameter spectrum, according to short-term conditions Meaningful Wave High and average zero-crossing period Short-term working conditions were calculated. Wave spectrum .

[0012] A further technical solution involves calculating the Weibull shape parameters at typical ship check nodes using long-term predicted values ​​of stress amplitude under different exceedance probabilities. Including calculations according to the following formula:

[0013] in, It is beyond probability Long-term forecast value of stress amplitude under the following conditions It is beyond probability Long-term forecast value of stress amplitude under [condition].

[0014] A further technical solution involves obtaining the stress response transfer function through structural finite element analysis, including: Mass points are set on the finite element model of the hull structure to make the mass characteristics of the finite element model consistent with the actual mass distribution of the ship. Wave loads are applied to the finite element model of the hull structure, and rigid displacement constraints are set on the finite element model of the hull structure. The stress response transfer function is obtained through structural finite element calculation.

[0015] A further technical solution involves applying wave loads to the finite element model of the ship's hull structure, including: Wave dynamic pressure is applied to the wetted surface of the hull in the form of pressure, while inertial force is applied to the finite element model of the hull structure through acceleration field and mass distribution.

[0016] Its further technical solution is that the Weibull shape parameter calculation method also includes: When performing hydrodynamic analysis on a ship under the loading condition for fatigue strength verification, the ship's speed is taken as 0 m / s. Multiple wave direction angles are uniformly selected within the range of 0° to 360° at wave direction intervals not exceeding 30°. Multiple wave circular frequencies are selected within the range of 0.2 rad / s to 1.8 rad / s at frequency intervals of 0.1 rad / s. Hydrodynamic analysis of the ship is performed under different combinations of wave direction angles and wave circular frequencies.

[0017] The beneficial technical effects of this application are: This application discloses a method for calculating the weibull shape parameter in ship fatigue strength verification. This method calculates the stress response transfer function through hydrodynamic analysis and structural finite element analysis, and then calculates the short-term distribution of stress response by combining the wave statistics of the target navigation area of ​​the ship. The stress response is further weighted and combined to obtain the long-term distribution of stress response, thereby obtaining the long-term predicted value of stress amplitude under different exceedance probabilities. This value is used to calculate the weibull shape parameter at typical verification nodes of the ship. The calculated weibull shape parameter has a good matching relationship with the ship structure, the wave conditions of the target navigation area, and the verification location, with high accuracy and precision. This provides a foundation for subsequent high-precision ship structure fatigue strength verification and can improve the accuracy of ship structure fatigue life prediction. Attached Figure Description

[0018] Figure 1 This is a flowchart of a method for calculating the shape parameters of Weibull according to an embodiment of this application. Detailed Implementation

[0019] The specific embodiments of this application will be further described below with reference to the accompanying drawings.

[0020] This application discloses a method for calculating Weibull shape parameters in ship fatigue strength verification. This method is used to calculate high-precision Weibull shape parameters for application in ship structural fatigue strength verification based on spectral analysis. Please refer to [reference needed]. Figure 1 The flowchart shown illustrates the following steps in the Weibull shape parameter calculation method: Step 110: Perform hydrodynamic analysis on the ship under the loading condition of fatigue strength verification to calculate the wave load of the ship under regular waves.

[0021] According to relevant specifications / standards, the loading conditions for fatigue strength verification of the ship are determined, and hydrodynamic analysis is performed using three-dimensional hydrodynamic analysis software / programs to obtain the wave loads of the ship under regular waves under the current loading conditions and weight distribution. When performing hydrodynamic analysis on the ship under the loading conditions for fatigue strength verification, the ship's speed is taken as 0 m / s, and sufficient wave direction angles and frequency ranges should be considered. One approach is to uniformly select multiple wave direction angles at intervals not exceeding 30° within the range of 0° to 360°, and select multiple wave circular frequencies at intervals of 0.1 rad / s within the range of 0.2 rad / s to 1.8 rad / s. Hydrodynamic analysis is then performed on the ship under different combinations of wave direction angles and wave circular frequencies to obtain the ship's performance under different wave direction angles. and wave circular frequency Wave load under regular waves.

[0022] Step 120: Apply the calculated wave load to the finite element model of the hull structure, and obtain the stress response transfer function through structural finite element calculation.

[0023] To accurately simulate ship characteristics, mass points were added to the finite element model of the hull structure to ensure that the mass characteristics of the finite element model were consistent with the actual mass distribution of the ship. The finite element mesh was set to 50mm*50mm. Then, the ship's wave angle calculated in step 110 was used... and wave circular frequency Wave loads under regular wave conditions are applied to the finite element model of the ship structure, and rigid displacement constraints are set on the finite element model of the ship structure. The current wave direction angle is obtained through structural finite element calculation. and wave circular frequency Stress response transfer function .

[0024] The wave load calculated in step 110 above includes the wave dynamic pressure on the wetted surface of the hull and the motion (acceleration) at the center of mass. Therefore, when applying the wave load to the finite element model of the hull structure, the wave dynamic pressure is applied to the wetted surface of the hull in the form of pressure, and the inertial force is applied to the finite element model of the hull structure through the acceleration field and mass distribution.

[0025] Step 130: Based on the wave statistics of the target navigation area of ​​the ship, determine multiple short-term sea states and the statistical probability of each short-term sea state, and uniformly select multiple wave direction angles within the range of 0°~360° and determine the statistical probability of each wave direction angle.

[0026] Each short-term sea state includes two overall parameters describing the sea state: significant wave height. and average zero-crossing period The meaningful wave height and mean zero-crossing period differ among different short-term sea states. Wave scatter plots can be used to statistically determine the frequency of each short-term sea state in the target navigation area, and then the frequency of each short-term sea state can be calculated as its statistical probability. This application refers to any short-term sea state. The meaningful wave height is The average zero-crossing period is The statistical probability is Wave statistics for the target navigation area can be obtained from actual statistical data, or North Atlantic wave data can be used directly. For example, in one instance, the wave scattering diagram for the target navigation area is shown in the table below, where the horizontal axis represents the average zero-crossing period. (Unit: seconds), the vertical axis represents the meaningful wave height. (Unit: m), each cell represents a short-term sea state corresponding to the mean cross-zero period and significant wave height, and the data in the cell represents the number of times the short-term sea state occurs.

[0027]

[0028] When selecting wave directions, they are also selected evenly at intervals not exceeding 30°. The statistical probability of each wave direction is its frequency of occurrence, which can be predetermined based on wave statistics. This application arbitrarily... The statistical probability is For example, in one instance, if the wave direction interval is 15°, then a total of 24 different wave direction angles are selected. The statistical probabilities of the 13 wave direction angles within the range of 0° to 180° are shown in the table below:

[0029] Step 140: Calculate the wave angle at typical check nodes of the ship based on the stress response transfer function. and short-term working conditions The short-term probability distribution of stress response under the given conditions.

[0030] First, the wave angle is calculated based on the stress response transfer function. and short-term working conditions Variance of the stress response spectrum under Specifically: According to short-term working conditions Meaningful Wave High and average zero-crossing period Short-term operating conditions were calculated. Wave spectrum In one embodiment, the wave spectrum is calculated based on the Bretschneider two-parameter spectrum, then the short-term condition... Wave spectrum for:

[0031] Further based on short-term working conditions The Waves Below and wave angle Stress response transfer function The wave angle was calculated. and short-term working conditions Stress response spectral density :

[0032] According to the wave angle and short-term working conditions Stress response spectral density Further calculations yielded the variance of the stress response spectrum. :

[0033] Get the current wave angle and short-term working conditions Variance of the stress response spectrum under Subsequently, based on the narrow spectrum assumption, the wave direction angle was determined. and short-term working conditions Arbitrary stress amplitude at typical check points of the ship short-term probability density function This yields the short-term probability distribution of the stress response:

[0034] Step 150: Based on the statistical probabilities of each wave direction angle and each short-term working condition, the short-term probability distributions of stress responses at the typical check node of the ship under different wave direction angles and short-term working conditions are weighted and combined to obtain the long-term forecast values ​​of stress amplitude at the typical check node of the ship under different exceedance probabilities.

[0035] Based on step 140, the stress amplitude under different wave angles and short-term working conditions can be obtained respectively. short-term probability density function Then, based on the statistical probabilities of each wave direction angle and each short-term working condition, the stress amplitude of the typical check node of the ship under different wave direction angles and short-term working conditions is calculated. short-term probability density function By performing weighted combinations, we can obtain the stress amplitude at typical check nodes of the ship that is greater than a certain value. Exceeding probability The expression is:

[0036] Based on the above exceedance probability The expression is used to calculate the long-term forecast values ​​of stress amplitude under different exceedance probabilities. In one embodiment, calculating the long-term forecast values ​​of stress amplitude under two different exceedance probabilities includes: calculating... The stress amplitude under the condition of being exceeded is used as the probability of exceeding the limit. Long-term forecast value of stress amplitude under ,calculate The stress amplitude under the condition of being exceeded is used as the probability of exceeding the limit. Long-term forecast value of stress amplitude under .

[0037] Step 160: Calculate the Weibull shape parameters at typical check nodes of the ship using long-term predicted values ​​of stress amplitude under different exceedance probabilities. .

[0038] Obtaining the transcendence probability Long-term forecast value of stress amplitude under and the probability of exceeding Long-term forecast value of stress amplitude under The Weibull shape parameters at typical ship verification nodes can be calculated using the following formula. :

[0039] and The value can be customized, according to standard applications. and The value range of is 1-10. The calculation results for different combinations of values ​​show little deviation and all meet the accuracy requirements. A typical combination of values ​​is... , .

[0040] The Weibull shape parameters obtained from this calculation It can accurately match characteristics such as ship type, ship structure, sea area features, and verification location, and has high accuracy and precision, providing a foundation for achieving high-precision fatigue strength verification of ship structures.

[0041] The above descriptions are merely preferred embodiments of this application, and this application is not limited to the above embodiments. It is understood that other improvements and variations that can be directly derived or conceived by those skilled in the art without departing from the spirit and concept of this application should be considered to be included within the protection scope of this application.

Claims

1. A method for calculating Weibull shape parameters in ship fatigue strength verification, characterized in that, The method for calculating the shape parameters of Weibull includes: Hydrodynamic analysis was performed on the ship under the loading condition of fatigue strength verification. The wave load of the ship under regular waves was calculated and applied to the finite element model of the hull structure. The stress response transfer function was obtained through structural finite element calculation. Based on the wave statistics of the target navigation area of ​​the ship, determine multiple short-term sea states and the statistical probability of each short-term sea state. Select multiple wave direction angles evenly within the range of 0° to 360° and determine the statistical probability of each wave direction angle. Based on the stress response transfer function, the wave angle at typical check points of the ship is calculated. and short-term working conditions Short-term probability distribution of stress response; Based on the statistical probabilities of each wave direction angle and each short-term working condition, the short-term probability distributions of stress responses at typical ship check nodes under different wave direction angles and short-term working conditions are weighted and combined to obtain the long-term forecast values ​​of stress amplitude at typical ship check nodes under different exceedance probabilities. The Weibull shape parameters at typical check nodes of a ship are calculated using long-term predicted values ​​of stress amplitude under different exceedance probabilities. .

2. The method for calculating Weibull shape parameters according to claim 1, characterized in that, Based on the stress response transfer function, the wave angle at typical check points of the ship is calculated. and short-term working conditions The short-term probability distribution of stress response includes: Calculation of wave direction angle based on stress response transfer function and short-term working conditions Variance of the stress response spectrum under ; Based on the narrow spectrum assumption, the wave direction angle is determined. and short-term working conditions Arbitrary stress amplitude at typical check points of the ship short-term probability density function .

3. The method for calculating Weibull shape parameters according to claim 2, characterized in that, The long-term forecast values ​​of stress amplitude at typical ship check nodes under different exceedance probabilities are obtained, including: Based on the statistical probabilities of various wave angles and various short-term operating conditions, the stress amplitudes of typical ship check nodes under different wave angles and short-term operating conditions are calculated. short-term probability density function By performing weighted combinations, the stress amplitude at typical check points of the ship was obtained. Exceeding probability The expression; Based on transcendence probability expression calculation The stress amplitude under the condition of being exceeded is used as the probability of exceeding the limit. Long-term forecast value of stress amplitude under ,calculate The stress amplitude under the condition of being exceeded is used as the probability of exceeding the limit. Long-term forecast value of stress amplitude under .

4. The method for calculating Weibull shape parameters according to claim 3, characterized in that, The stress amplitude is greater than that at typical check points of ships. Exceeding probability The expression is: in, It is a short-term working condition The statistical probability, Is the wave angle The statistical probability.

5. The method for calculating Weibull shape parameters according to claim 2, characterized in that, Calculation of wave direction angle based on stress response transfer function and short-term working conditions Variance of the stress response spectrum under include: According to short-term working conditions Wave spectrum and wave angle Stress response transfer function The wave angle was calculated. and short-term working conditions Stress response spectral density And obtain the variance of the stress response spectrum. ;in, This indicates the angular frequency of the wave.

6. The method for calculating Weibull shape parameters according to claim 5, characterized in that, The method for calculating the shape parameters of Weibull also includes: Based on the Bretschneider two-parameter spectrum, according to short-term conditions Meaningful Wave High and average zero-crossing period Short-term working conditions were calculated. Wave spectrum .

7. The method for calculating Weibull shape parameters according to claim 1, characterized in that, The Weibull shape parameters at typical check nodes of a ship are calculated using long-term predicted values ​​of stress amplitude under different exceedance probabilities. Including calculations according to the following formula: in, It is beyond probability Long-term forecast value of stress amplitude under the following conditions It is beyond probability Long-term forecast value of stress amplitude under [condition].

8. The method for calculating Weibull shape parameters according to claim 1, characterized in that, The stress response transfer function obtained through structural finite element analysis includes: Mass points are set on the finite element model of the hull structure to make the mass characteristics of the finite element model consistent with the actual mass distribution of the ship. Wave loads are applied to the finite element model of the hull structure, and rigid displacement constraints are set on the finite element model of the hull structure. The stress response transfer function is obtained through structural finite element calculation.

9. The method for calculating Weibull shape parameters according to claim 1, characterized in that, Applying wave loads to the finite element model of the ship structure includes: Wave dynamic pressure is applied to the wetted surface of the hull in the form of pressure, while inertial force is applied to the finite element model of the hull structure through acceleration field and mass distribution.

10. The method for calculating Weibull shape parameters according to claim 1, characterized in that, The method for calculating the shape parameters of Weibull also includes: When performing hydrodynamic analysis on a ship under the loading condition for fatigue strength verification, the ship's speed is taken as 0 m / s. Multiple wave direction angles are uniformly selected within the range of 0° to 360° at wave direction intervals not exceeding 30°. Multiple wave circular frequencies are selected within the range of 0.2 rad / s to 1.8 rad / s at frequency intervals of 0.1 rad / s. Hydrodynamic analysis of the ship is performed under different combinations of wave direction angles and wave circular frequencies.

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