A fatigue reliability analysis method for the curtain wall frame structure of a cruise ship under complex sea conditions

Abstract

The present invention relates to a fatigue reliability analysis method for the curtain wall frame structure of a cruise ship under complex sea conditions, comprising the following steps: establishing a simple finite element model of the cruise ship according to the structural form, structural characteristics, and load conditions of the cruise ship, and establishing a detailed finite element model of the curtain wall support frame structure of the cruise ship in combination with the structural form and dimensions of the glass curtain wall support structure model; selecting various combined wind and wave conditions in different sea areas within the ship's navigation area to perform dynamic calculations on the established whole-ship finite element model under the combined action of the wind load calculation condition and the wave load calculation condition; respectively inputting the wind and wave load data under several conditions into the finite element calculation software for simulation analysis to obtain the stress time history curves of different fatigue check points, and using the rain flow counting method to obtain the stress amplitude distribution; performing deterministic fatigue cumulative damage calculation by using the selected S-N curve and combining with the sea wind and wave data of the ship under different conditions; and reliability assessment.

Description

Technical Field

[0001] The present invention relates to the fields of fatigue damage and reliability analysis in the fields of ship and ocean engineering, and particularly relates to a method for fatigue reliability analysis of a cruise ship curtain wall frame structure under complex sea conditions. Background Art

[0002] The marine environment is complex and changeable. If the structural design strength of a cruise ship is insufficient to withstand extreme loads, once encountering sudden situations such as hurricanes, large waves or tsunamis, it is very likely to cause heavy casualties and economic losses.

[0003] At the same time, the large-scale and multi-functional nature of cruise ships means that their superstructures will become more and more special and delicate. Such superstructures require that the design and construction of the superstructures and the structural strength of the ships must reach a higher level. How to ensure that the superstructures are not damaged under various complex sea conditions during the normal operation of the ships has also become an important research topic. Due to the popularization of the application of glass curtain walls and the gradual increase in people's requirements for the external aesthetics of cruise ships, the application of glass curtain walls on cruise ship superstructures is becoming more and more extensive. As the peripheral protective structure of a building, the support structure of a glass curtain wall is mainly used to support the curtain wall, and on the premise of ensuring aesthetics, it is also required to have sufficient strength and fatigue resistance. Summary of the Invention

[0004] The object of the present invention is to provide a method for fatigue reliability analysis of a cruise ship curtain wall frame structure under complex sea conditions. The method is as follows:

[0005] A method for fatigue reliability analysis of a cruise ship curtain wall frame structure under complex sea conditions includes the following steps:

[0006] Step 1, establish a simple finite element model of the cruise ship according to the structural form, structural characteristics and load conditions of the cruise ship, and establish a detailed finite element model of the cruise ship curtain wall support frame structure in combination with the structural form and size of the glass curtain wall support structure model;

[0007] Step 2, select multiple combined wind and wave conditions in different sea areas within the ship's navigation area to perform dynamic calculations on the established whole-ship finite element model under the combined action of wind load calculation conditions and wave load calculation conditions. The method is as follows:

[0008] (1) Select the JONSWAP spectrum to describe the sea wave conditions;

[0009] (2) When calculating the wind load, the wind force is divided into three components: the wind force caused by the wind in the main wind direction, the wind force caused by gusts on the horizontal plane perpendicular to the main wind direction, and the wind force caused by gusts in the Z direction. Considering that the wind speed acting on each component of the curtain wall support structure above the still water level is independent of time and the horizontal coordinate axis, based on the measured wind load data, the angle θ between the wind direction and the positive X-axis, the average wind speed V at the reference position, the height Z0 of the waterplane in the still water state, the distance H0 from the waterplane to the average wind speed reference position, and the average period ratio T a / T a0 are obtained, and the wind speed v acting on the curtain wall support structure at different heights Z is calculated;

[0010] (3) For a cruise ship, through the wind speed v corresponding to each surface of the structure, its local wind pressure P0 is calculated, and its shape coefficient C s , height coefficient C h , and the vertical projected area C of each surface exposed to the wind h are obtained, and the calculation formula for the wind force F w is derived;

[0011] (4) The annual average value of the sea state is taken as the calculated sea state. The analysis time history should include at least 100 pairs of wave crests and wave troughs, and the corresponding calculation duration of 20 - 30 minutes; the fatigue calculation duration and calculation step size are selected;

[0012] Step 3: Input the wind and wave load data under several working conditions into the finite element calculation software for simulation analysis respectively to obtain the stress time history curves at different fatigue check points, and use the rain - flow counting method to obtain the stress amplitude distribution. The method is as follows:

[0013] (1) Through the established detailed finite element model of the cruise ship curtain wall support frame structure, the time - domain method is used to conduct fatigue analysis on the structure. Under the combined action of wind load and wave load, the interaction of hydrodynamic and aerodynamic forces is considered;

[0014] (2) Under the selected working conditions, the parts prone to fatigue damage are at the curtain wall support frame. Therefore, fatigue - dangerous nodes are selected on this structure. Several check positions including the connection between the end of the longitudinal support structure of the curtain wall and the upper deck, the large opening of the frame structure, and the longitudinal support members are selected. The meshes at these positions are refined respectively, and the average stress of the element to which the check point belongs is used as the calculated stress of the check point to obtain its stress time history curves under different working conditions;

[0015] Step 4: Use the selected S - N curve and, combined with the offshore wind and wave data of the ship under different working conditions, conduct deterministic fatigue cumulative damage calculation. The method is as follows:

[0016] (1) Calculate the amplitude σ of the stress at the fatigue check point by the rain - flow counting methodi and the number of cycles n of the stress within each range i , select the S-N curve;

[0017] (2) Select the Corten-Dolan cumulative damage criterion for calculation:

[0018]

[0019] Where: N represents the total number of cycles until failure under multi-level loads;

[0020] σ i represents the stress value at the i-th stress level;

[0021] σ1 represents the stress value at the highest stress level, that is, the maximum load in this load cycle;

[0022] γ i represents the proportion of the number of cycles at the i-th stress level in the total number of cycles;

[0023] N1 represents the number of cycles until failure under the action of σ1;

[0024] d represents the material constant;

[0025] Derive the expression of the damage variable D as:

[0026]

[0027] Obtain the stress σ i , 1 ≤ i ≤ k i , when acting Nγ i times, the damage accumulation is:

[0028]

[0029] Where: n i is the total number of times of the action of σ i ;

[0030] (3) Use the fatigue analysis method to calculate the fatigue cumulative damage of the check point under different short-term working conditions, and accumulate to obtain the total fatigue cumulative damage D0 within the said long time, and the structural fatigue life

[0031] Step 5, conduct fatigue reliability assessment on the glass curtain wall support frame structure, the method is as follows:

[0032] (1) Consider the following uncertain factors:

[0033] 1) The random variable considering the load uncertainty is represented by B;

[0034] 2) Δ is a random variable considering that the cumulative damage degree is not always 1 when the structure suffers fatigue damage;

[0035] 3) In the S-N curve, the change of parameter A is considered to be random, denoted by ΔA; parameter m is considered to be a constant;

[0036] (2) When the fatigue life is less than the design life, the structure undergoes fatigue failure, and the limit state equation of the structure is expressed as follows:

[0037]

[0038] The probability of structural fatigue failure is the calculated fatigue life T A less than the design life T D is:

[0039] P f = P(T D ≤ T A ) = P[g(Z) ≤ 0] = Φ(-β)

[0040] Then the reliability index of the glass curtain wall support frame structure is expressed as:

[0041]

[0042] The beneficial effects of the present invention include:

[0043] (1) This method establishes a detailed finite element model of the glass curtain wall support frame structure, filling the blank of fatigue damage analysis of the offshore glass curtain wall support frame structure.

[0044] (2) This evaluation method considers the situations of multiple sea areas, improving the integrity of the evaluation.

[0045] (3) Considering numerous uncertainties to conduct fatigue reliability assessment of the cruise ship glass curtain wall frame structure under complex sea conditions, improving the comprehensiveness and accuracy of the evaluation.

[0046] (4) It verifies the rationality of the application of the glass curtain wall on the cruise ship and provides new ideas for the full-coupling fatigue evaluation of the glass curtain wall support structure under complex sea conditions. Description of the Drawings

[0047] Figure 1 is the flowchart of the evaluation method according to an embodiment of the present invention;

[0048] Figure 2 is the finite element model diagram of the curtain wall support frame of the present invention;

[0049] Figure 3 is the finite element model diagram of the overall structure of the cruise ship of the present invention;

[0050] Figure 4 The stress history curve and the rain - flow counting result histogram of the checking point in an embodiment of the present invention. Detailed implementation manners

[0051] To make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be described in detail below with reference to the drawings and embodiments.

[0052] As Figure 1 shown, in an embodiment of the present invention, a fatigue reliability analysis method for the curtain wall frame structure of a cruise ship under complex sea conditions is disclosed, including the following steps:

[0053] Step 1: Establish a simple finite - element model of the cruise ship according to the common structural forms, structural characteristics, load conditions, etc. of the cruise ship, and perform detailed finite - element modeling on the curtain wall support structure model of the superstructure of the cruise ship in combination with the structural form and size characteristics of the actual glass curtain wall support structure model.

[0054] Among them: In the design of the ship's skeleton, the important support skeletons such as the transverse bulkheads, longitudinal middle bulkheads, middle inner keels, and multi - layer decks of the ship are key - arranged. In order to make the subsequent operations and calculations simpler and more convenient, some strengthening structures of the hull plates will be equivalently replaced in the form of increasing the panel stiffness;

[0055] The curtain wall support structure established in the present invention mainly adopts a framed curtain wall structure, with beams and brackets as strengthening members. The support structure is built on the main deck of the cruise ship, that is, the fourth deck. The main window part starts from the fifth deck, crosses the sixth deck, and finally connects to the seventh deck. The design uses bulb flats and T - sections as the main support members of the deck, and the overall structure is mainly supported by grillages.

[0056] Table 1 Dimensions of main support members

[0057] Component type Dimension parameter T-section steel T300×150×8 Longitudinal girder FB100×15 Bulb flat steel HP100×6

[0058] Step 2: Select a variety of combined wind - wave conditions in different sea areas within the ship's navigation area to perform dynamic calculations on the established whole - ship finite - element model under the combined action of wind - load calculation conditions and wave - load calculation conditions:

[0059] 1. In the actual ocean, waves are composed of a series of waves with different wave heights and different periods. The present invention selects the JONSWAP spectrum with relatively more accurate numerical values to describe the sea - wave conditions, and its formula is:

[0060]

[0061] In the formula: H 1 / 3 is the significant wave height of 1 / 3, T pis the spectral peak period, ω is the wave circular frequency, γ is the spectral peak elevation coefficient with a value of 3.3, σ is the peak coefficient, when ω ≤ ω p , take 0.07, when ω > ω p , take 0.09.

[0062] 2. When calculating wind loads, the wind force is usually divided into three components: the wind force caused by the wind in the main wind direction, the wind force caused by gusts on the horizontal plane perpendicular to the main wind direction, and the wind force caused by Z-direction gusts. And according to the content in API RP 2A, 21st Edition, the wind speed acting on each component of the curtain wall support structure above the still water level has nothing to do with time and the horizontal coordinate axis. According to the measured wind load data, the included angle θ between the wind direction and the positive X-axis, the average wind speed V at the reference position, the height Z0 of the waterplane in the still water state, the distance H0 from the waterplane to the average wind speed reference position, and the average period ratio T a / T a0 , the wind speed acting on the curtain wall support structure at different heights can be calculated as follows:

[0063]

[0064] 3. For ships and platforms, the local wind pressure can be calculated through the wind speed v corresponding to each surface of the structure, and its shape coefficient C s , height coefficient C h , the vertical projected area C of each surface exposed to the wind h , and the wind force F w can be calculated by the following formula:

[0065] P0 = 0.613v 2

[0066] F w = C w ∑(C s C h A)v 2

[0067] 3. In this example, the cruise ship is planned to sail in the polar region. Since the time-domain analysis calculation is time-consuming, the sea conditions in the central and western waters, northeastern waters, and southeastern waters of the Barents Sea are selected as examples, and the annual average value of the sea conditions is taken as the calculated sea conditions.

[0068] 4. During the analysis process, the time history of the analysis must include at least 100 pairs of wave crests and wave troughs, corresponding to a calculation duration of 20 - 30 minutes. To meet the time-domain fatigue calculation requirements of each working condition, the calculation duration of this example is 2000 s. Therefore, 1000 s after removing the unstable time at the beginning and end is selected as the fatigue calculation duration. To ensure the calculation convergence, the calculation step size is set to 0.5 s.

[0069] Step 3: Input the wind and wave load data under several working conditions into the finite element calculation software for simulation analysis respectively to obtain the stress time history curves of different fatigue check points, and use the rain flow counting method to obtain the stress amplitude distribution;

[0070] 1. Through the established detailed finite element model of the cruise ship curtain wall support frame structure, the time domain method is applied to conduct fatigue analysis on the structure. Under the combined action of wind load and wave load, the interaction of hydrodynamic and aerodynamic forces is considered.

[0071] 2. Under the selected working conditions, the parts prone to fatigue damage are all at the curtain wall support frame. Therefore, fatigue dangerous nodes are selected on this structure. In this example, several check positions are selected, including the connection between the end of the longitudinal support structure of the curtain wall and the upper deck, the large opening of the frame structure, and the longitudinal support members. The meshes of these positions are refined respectively, and the average stress of the element to which the check point belongs is used as the calculated stress of the check point. The stress time history curves under different working conditions are obtained.

[0072] Table 2 Coordinates of the check positions

[0073]

[0074] Step 4: Use the selected S-N curve and the Corten-Dolan cumulative damage criterion, combined with the sea wind and wave data of the ship under certain working conditions, to conduct deterministic fatigue cumulative damage calculation;

[0075] 1. Calculate the amplitude σ of the stress at the fatigue check point by the rain flow counting method i and the number of cycles n of the stress within each range i . The relevant parameters of the ABS code are used in the calculation. Since the curtain wall support structure is exposed to the air and the curtain wall support structure is not a tubular joint, the ABS-D-A curve in the following table is selected for the S-N curve. The main parameters of the curve are as follows in the table, where m2 = m1 and A2 = A1:

[0076] Table 3 Main parameters of the S-N curve

[0077] name <![CDATA[m0]]> <![CDATA[m1]]> <![CDATA[log N0]]> <![CDATA[log N1]]> <![CDATA[S0 / MPa]]> <![CDATA[S1 / MPa]]> <![CDATA[log A0]]> <![CDATA[log A1]]> ABS-D-A 3 5 7 8 53.4 33.67 30.183 45.636

[0078] 2. In the calculation theory of engineering cumulative damage, the Miner linear criterion is more commonly used. However, more and more studies have shown that the results obtained by simply applying linear accumulation to calculate the action of loads may deviate greatly from the actual situation. Therefore, the present invention does not use the Miner linear cumulative damage criterion, but selects the Corten Dolan criterion with higher calculation accuracy and better application prospects. The expression is as follows:

[0079]

[0080] Where: N represents the total number of cycles up to failure under multi-level loads;

[0081] σ i represents the stress value at the i-th stress level;

[0082] σ1 represents the stress value at the highest stress level, i.e., the maximum load in this load cycle;

[0083] γ i represents the proportion of the number of stress cycles at the i-th level in the total number of cycles;

[0084] N1 represents the number of cycles up to failure under the action of σ1;

[0085] d represents a material constant.

[0086] The expression for the damage variable D can be deduced as:

[0087]

[0088] Therefore, the stress σ i (1 ≤ i ≤ k i ) under the action of Nγ i times, the damage accumulation is:

[0089]

[0090] Where: n i is the total number of times of the action of σ i .

[0091] 3. Calculate the fatigue cumulative damage of the check point under different short-term working conditions by using the fatigue analysis method. Finally, accumulate to obtain the total fatigue cumulative damage D0 within the said long time, and the structural fatigue life

[0092] Step 5. Considering the actual situation, due to various uncertain factors such as various assumptions, idealized numerical models, and errors in the applied methods, when conducting the fatigue reliability assessment of the glass curtain wall support frame structure, the following uncertain factors should be considered:

[0093] 1) Due to reasons such as experimental data acquisition and processing methods, the random variable considering load uncertainty is represented by B;

[0094] 2) The cumulative damage theory believes that the structure fails when the fatigue cumulative damage degree is equal to 1. However, in fact, due to the approximation of the theory itself, the true structure does not always equal 1 when it fails. Δ is a random variable considering that the cumulative damage degree is not always 1 when the structure suffers fatigue damage;

[0095] 3) The S-N curve is an empirical formula commonly used in engineering. Its parameters A and m are often determined through experiments. However, due to the differences between experimental conditions and application conditions, as well as the uncertainty of material structures, the parameter A varies greatly and can be considered random, represented by ΔA. The change in m is relatively small and can be considered a constant.

[0096] Table 4 Uncertainty parameters

[0097]

[0098]

[0099] When the fatigue life is less than the design life, fatigue failure of the structure occurs. Therefore, the limit state equation is expressed as follows:

[0100]

[0101] The probability of structural fatigue failure is the probability that the calculated fatigue life T A is less than the design life T D :

[0102] P f = P(T D ≤ T A ) = P[g(Z) ≤ 0] = Φ(-β)

[0103] Among them, for ship and ocean engineering structures, the design life T D usually takes 20 years or 25 years (corresponding to a total of about 10 8 stress cycles)

[0104] The reliability index is:

[0105]

[0106] Table 5

[0107]

[0108] Table 5 gives the fatigue reliability calculation results of the checking position HS1 under different working conditions.

Claims

1. A method for fatigue reliability analysis of the curtain wall frame structure of a cruise ship under complex sea conditions, comprising the following steps: Step 1: Establish a simple finite element model of the cruise ship according to the structural form, structural characteristics, and load conditions of the cruise ship, and establish a detailed finite element model of the curtain wall support frame structure of the cruise ship in combination with the structural form and dimensions of the glass curtain wall support structure model; Step 2: Select a variety of combined wind and wave conditions in different sea areas within the ship's navigation area to perform dynamic calculations on the established whole-ship finite element model under the combined action of the wind load calculation condition and the wave load calculation condition. The method is as follows: (1) Select the JONSWAP spectrum to describe the sea wave conditions; (2) When calculating the wind load, the wind force is divided into three components: the wind force caused by the wind in the main wind direction, the wind force caused by gusts on the horizontal plane perpendicular to the main wind direction, and the wind force caused by gusts in the Z direction. Considering that the wind speed acting on each component of the curtain wall support structure above the still water level is independent of time and the horizontal coordinate axis, based on the measured wind load data, the angle θ between the wind direction and the positive X-axis, the average wind speed V at the reference position, the height Z0 of the waterplane in the still water state, the distance H0 from the waterplane to the average wind speed reference position, and the average period ratio T a / T a0 are obtained. The wind speed v acting on the curtain wall support structure at different heights Z is calculated; (3) For a cruise ship, based on the wind speed v corresponding to each surface of the structure, calculate its local wind pressure P0, and define its shape coefficient C s , height coefficient C h , vertical projected area C of each surface exposed to the wind h , and obtain the calculation formula for the wind force F w ; (4) Take the annual average of the sea conditions as the calculated sea conditions. The time history analyzed should include at least 100 pairs of wave crests and wave troughs, and the corresponding calculation duration of 20 - 30 minutes; Select the fatigue calculation duration and calculation step size; Step 3: Input the wind and wave load data under several conditions into the finite element calculation software for simulation analysis respectively to obtain the stress time history curves of different fatigue check points, and use the rain flow counting method to obtain the stress amplitude distribution. The method is as follows: (1) Through the established detailed finite element model of the curtain wall support frame structure of the cruise ship, apply the time domain method to perform fatigue analysis on the structure. Under the combined action of wind load and wave load, consider the interaction of hydrodynamic and aerodynamic forces; (2) Under the selected conditions, the part prone to fatigue damage is the curtain wall support frame. Therefore, select fatigue dangerous nodes on this structure, select several check positions including the connection between the end of the longitudinal support structure of the curtain wall and the upper deck, the large opening of the frame structure, and the longitudinal support members. Refine the mesh for these positions respectively, and use the average stress of the element to which the check point belongs as the calculated stress of the check point to obtain its stress time history curve under different conditions; Step 4: Use the selected S-N curve and, combined with the sea wind and wave data of the ship under different conditions, perform deterministic fatigue cumulative damage calculation. The method is as follows: (1) Calculate the amplitude σ of the stress at the fatigue check point by the rainflow counting method i and the number of stress cycles n within each range i , and select the S-N curve; (2) Select the Corten-Dolan cumulative damage criterion for calculation: Where: N represents the total number of cycles until failure under multi-level loads; σ i represents the stress value at the i-th stress level; σ1 represents the stress value at the highest stress level, that is, the maximum load in this load cycle; γ i represents the proportion of the stress cycle number at the i-th level in the total cycle number; N1 represents the number of cycles until failure under the action of σ1; d represents the material constant; Derive the expression of the damage variable D as: Obtain the stress σ i where 1 ≤ i ≤ k i and the downward acting force is Nγ i The damage accumulation when it acts n times is as follows: where: n i is the total number of times of the action of σ i ; (3) Calculate the fatigue cumulative damage of the check point under different short-term working conditions by using the fatigue analysis method, and accumulate to obtain the total fatigue cumulative damage D0 within the said time, and the structural fatigue life Step 5: Conduct fatigue reliability assessment of the glass curtain wall support frame structure. The method is as follows: (1) Consider the following uncertain factors: 1) The random variable considering load uncertainty is represented by B; 2) Δ is a random variable considering that the cumulative damage degree is not always 1 when the structure suffers fatigue damage; 3) In the S-N curve, the change of the parameter A is considered to be random and is represented by ΔA; the parameter m is considered to be a constant; (2) When the fatigue life is less than the design life, the structure suffers fatigue failure. The limit state equation of the structure is expressed as follows: The probability of structural fatigue failure is the calculated fatigue life T A less than the design life T D and the probability is: P f = P(T D ≤ T A ) = P[g(Z) ≤ 0] = Φ(-β) Then the reliability index of the glass curtain wall support frame structure is expressed as:

Images