Safety coefficient determination method based on full failure mode structure reliability

Abstract

The invention belongs to the field of aircraft structure safety calculation, and particularly relates to a safety coefficient determination method based on full failure mode structure reliability, an aircraft is divided into a plurality of sections, each section comprises a plurality of shell structures, and a safety coefficient of each shell structure and a performance function of each shell structure in each failure mode are constructed; taking the probability that the performance function of each shell structure in each failure mode is greater than 0 as the structural reliability of each shell structure in each failure mode; based on the structural reliability of all the shell structures in all the failure modes, constructing a relational expression between the structural reliability P of the aircraft and the safety coefficients of all the shell structures; the safety coefficient of each section is made to be the same as that of all shell structures of the section; constructing a relational expression between the structural reliability P of the aircraft and the safety coefficients of all the sections; and with the minimum total weight W of the aircraft as an optimization target and the structural reliability P of the aircraft meeting the design as a constraint, optimizing to obtain the safety coefficient of each section.

Description

Technical Field

[0001] The present application belongs to the field of aircraft structural safety calculation, and in particular relates to a method for determining a safety factor based on total failure mode structural reliability. Background Art

[0002] At present, the safety factor is mainly used in aircraft design to measure the uncertainty that affects structural safety. In fact, there are a lot of uncertainties that affect structural safety in the process of aircraft structure design, manufacturing and service. These uncertainties directly affect the probability of strength failure of the structure during the service of the aircraft. The safety factor is a rough representation of the uncertainty of the entire process of aircraft structure from design, manufacturing to service, and is determined based on long-term, large-scale test and actual flight test data combined with engineering experience.

[0003] Structural reliability theory uses probability theory and mathematical statistics to mathematically model structural uncertainty, and evaluates the safety and durability of aircraft structures through probability and statistical methods, with complete mathematical theoretical support. The structural reliability of various failure modes of various parts and components of the aircraft is calculated through uncertain statistical data such as aircraft load, material properties, and manufacturing tolerances, and the structural reliability of the entire aircraft is determined based on the reliability relationship between various parts and components. Finally, the safety factor of the aircraft can be calculated through the relationship between the safety factor and structural reliability and the aircraft strength design requirements. Summary of the invention

[0004] In order to solve the above problems, the present application provides a method for determining the safety factor based on the reliability of a full failure mode structure, which is characterized by comprising:

[0005] The aircraft is divided into multiple sections, each section includes multiple shell structures, and the safety factor of each shell structure and the functional function of each shell structure under each failure mode are constructed;

[0006] The probability that the function of each shell structure in each failure mode is greater than 0 is taken as the structural reliability of each shell structure in each failure mode;

[0007] Based on the structural reliability of all shell structures under all failure modes, the relationship between the structural reliability P of the aircraft and the safety factor of all shell structures is constructed;

[0008] Let the safety factor of each section be the same as the safety factor of all shell structures in that section;

[0009] Constructing a relationship between the structural reliability P of the aircraft and the safety factors of all sections;

[0010] Taking the minimum total weight W of the aircraft as the optimization goal and the structural reliability P of the aircraft satisfying the design as the constraint, the safety factor of each section is optimized.

[0011] Preferably, the safety factor of each shell structure and the function of each shell structure in each failure mode include:

[0012] F ij (u) = R ij -γ i S ij (u), (i=1,2,…,M; j=1,2,…,N)

[0013] In the formula, F ji (u) represents the functional function of the i-th shell structure in the j-th failure mode, R ij The ability of the i-th shell structure to withstand the j-th failure mode, M represents the number of shell structure blocks, N represents the number of shell structure failure modes, S ij The load of the i-th shell structure under the j-th failure mode, γ i represents the safety factor of the ith shell structure, R ij , S ij It is a function related to multiple random variables such as shell structure material, size, process conditions and external loads. M represents the total number of shell structures of the aircraft, and F ij (u)≥0 indicates that the shell structure is safe, F ij (u)<0 indicates shell structure failure.

[0014] Preferably, the expression of the structural reliability of each shell structure in each failure mode is:

[0015] P ij =Prob(γ i R ij -S ij (u)>0).

[0016] Preferably, the relationship between the structural reliability P of the aircraft and the safety factor of all shell structures is:

[0017]

[0018] Preferably, the optimization format of the safety factor of each section is:

[0019]

[0020] Among them, β represents the vector composed of the safety factors of each section of the aircraft, W represents the total weight of the aircraft, P represents the overall reliability of the aircraft, and P cf represents the maximum structural failure probability that meets the design requirements, is the safety factor of each section of the aircraft, N c The total number of machine sections.

[0021] Preferably, the calculation formula of the performance function of the shell structure in a failure mode is:

[0022]

[0023] Among them, K i Indicates the stability coefficient of each plate and shell structure, D i represents the stiffness of each plate and shell structure, a i Indicates the length of each plate and shell structure, D i Related to material stiffness, Poisson's ratio and structural design size, N represents the load value.

[0024] The advantages of the present application include: (1) In the present invention, long-term, large-scale experimental tests and actual flight test data are not required, but the safety factor of the aircraft is calculated by inputting statistical data that affects the failure probability of the aircraft through structural reliability calculation and structural optimization;

[0025] (2) The reliability calculation of the present invention has strong universality. It combines the first-order second moment method, reliability confidence check and Monte Carlo method to improve the application scope of the structural reliability algorithm. It is suitable for reliability calculation of different functional functions under various random parameters. The calculation accuracy of the first-order second moment reliability calculation part is tested by Monte Carlo sampling, and the reliability calculation accuracy is high.

[0026] (3) The present invention has passed the actual aircraft optimization design test, and the calculated safety factor, failure probability of each aircraft plate and shell structure failure mode, and the relationship between the aircraft safety factor and reliability are consistent with the conventional aircraft safety factor engineering design experience. The safety factor value is basically consistent with the actual aircraft model design value;

[0027] (4) The aircraft safety factor calculation efficiency of the present invention is high, and the reliability and safety factor calculation of the entire aircraft composed of 4,000 plate and shell block structures can be completed within 1 hour. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is a logic diagram for calculating the aircraft structural safety factor in a preferred embodiment of the present application. DETAILED DESCRIPTION

[0029] In order to make the technical solution and advantages of the present application clearer, the technical solution of the present application will be further described in detail in detail and in detail in conjunction with the accompanying drawings. It can be understood that the specific embodiments described here are only partial embodiments of the present application, which are only used to explain the present application, not to limit the present application. It should be noted that, for the convenience of description, only the parts related to the present application are shown in the accompanying drawings, and other related parts can refer to the general design. In the absence of conflict, the embodiments in the present application and the technical features in the embodiments can be combined with each other to obtain new embodiments.

[0030] In addition, it should be noted that, unless otherwise clearly specified and limited, the words "installed", "connected", "connected" and similar terms used in the description of this application should be understood in a broad sense. For example, the connection can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, an indirect connection through an intermediate medium, or the internal connection of two components. Technical personnel in the field can understand their specific meanings in this application according to the specific circumstances.

[0031] like Figure 1 As shown, the purpose of the present invention is achieved through the following technical solutions.

[0032] 1. Structural reliability calculation of aircraft under full strength failure mode:

[0033] a) Constructing structural functional functions: Carry out 2D finite element strength simulation calculations for the entire aircraft, split the entire aircraft structure into thousands of shell structures according to failure modes, materials, and structural characteristics, optimize and calculate the design dimensions of each block shell structure under various allowable safety factors considering all aircraft working conditions and all failure modes, extract the stiffness, load, optimized size, material properties, etc. under the dominant working conditions of each shell structure, and construct the functional function under the full strength failure mode of the aircraft:

[0034] F ij (u) = R ij -γ i S ij (u), (i=1,2,…,M; j=1,2,…,N)

[0035] In the formula, F ji (u) represents the functional function of the i-th shell structure in the j-th failure mode, R ij The ability of the i-th shell structure to withstand the j-th failure mode, M represents the number of shell structure blocks, N represents the number of shell structure failure modes, S ij The load of the i-th shell structure under the j-th failure mode, γ i Represents the safety factor of the i-th shell structure. R ij , S ijIt is a function related to multiple random variables such as shell structure material, size, process conditions and external loads. M represents the total number of shell structures of the aircraft. ij (u)≥0 indicates that the shell structure is safe, F ij (u) < 0 indicates shell structure failure;

[0036] b) Calculation method for each strength failure mode: Calculating the overall / local shear stability and compression-shear coupling stability of the block shell structure in the reinforced state is very complicated, and there is currently no analytical formula applicable to various parameters. Considering the dimensionless K value and small coefficient of variation of each stability failure mode, the structural stability formula is simplified to Where K can be calculated by commercial optimization software. The stability function is written as Where K i , D i 、a i Respectively represent the stability coefficient, stiffness and length of each plate and shell structure. i It is related to the material stiffness, Poisson's ratio and the structural design size. The strength failure theory formula is simple and direct and can be directly substituted into the functional function;

[0037] c) Structural reliability calculation: The structural reliability of each block shell structure under each failure mode is calculated according to the structural function using the first-order second-moment reliability algorithm in a mixed mean format. Since there is no absolutely universal first-order second-moment reliability algorithm, Monte Carlo testing and correction of singular structures are required after reliability calculation.

[0038] 2. Build the relationship between structural reliability and safety factor:

[0039] The safety factor is a rough measure of structural uncertainty, while the structural reliability is a strict description of the mathematical probability and statistical theory of structural uncertainty. Therefore, there is no one-to-one correspondence between the safety factor and the structural reliability. But in fact, there is no need to establish a one-to-one correspondence between them, because we only focus on the reliability under the design value of the safety factor, and do not need to focus on the safety factor under each reliability. Therefore, the reliability value of the optimized design result of all allowable safety factor values ​​can be calculated to construct the relationship between the structural reliability and safety factor required for aircraft design: (i=1,2,…,M,j=1,2,…,N).

[0040] Where M represents the number of plates and shells, N represents the number of failure modes of each plate and shell, and P ij It represents the structural reliability of the i-th shell structure in the j-th failure mode, expressed as P ij =Prob(γ i R ij -S ij(u)>0), indicating the functional function F ij (u) = γ i R ij -S ij The probability that (u)>0. P represents the structural reliability of all the blocks that make up the aircraft structure.

[0041] 3. Optimization calculation of safety factor based on structural reliability:

[0042] In order to more accurately measure the uncertainty of the aircraft structure through the safety factor method and tap the potential of aircraft structure weight reduction design, each block shell structure can take a different safety factor. Limited by the static test of the whole aircraft, the shell structure of each section of the aircraft needs to take the same safety factor and the same safety factor as the section to ensure the feasibility of the test and the verifiability of the design. Therefore, a safety factor γ is taken for each section of the aircraft. s ,(s=1,2,…,N c ). γ s represents the safety factor of the sth section, N c The total number of sections of the whole machine. The safety factor of each section of the whole machine is determined by the following optimization format:

[0043]

[0044] Among them, γ represents the vector composed of the safety factors of each section of the aircraft, W represents the total weight of the aircraft, P represents the overall reliability of the aircraft, and P cf Represents the maximum probability of structural failure that meets design requirements.

[0045] One implementation includes:

[0046] (1) Establish a finite element model of the entire aircraft and perform finite element simulation calculations on all operating conditions of the entire aircraft to obtain finite element simulation calculation results for all operating conditions under the initial design state;

[0047] (2) Input all the calculation results and simulation models of the working conditions into the commercial optimization software Hypersizer to obtain the margin, stiffness, design parameters, allowable strength value, and load value of each block plate and shell structure of the aircraft under the most risky load condition of each failure mode. According to the structural stability calculation formula, the total stability failure coefficient value K of each block plate and shell structure is obtained;

[0048] (3) Based on all the parameters obtained by Hypersizer, the structural function of each block structure of the aircraft under each failure mode is constructed, and the reliability calculation of each block under each failure mode is completed by the first-order second-moment reliability algorithm in the mixed mean format combined with the Monte Carlo method correction. The overall reliability of the aircraft is calculated based on the reliability results of each block under each failure mode and the failure relationship of each block area of ​​the aircraft;

[0049] (4) Construct the relationship between the reliability and safety factor of the aircraft structure based on the reliability results calculated under different safety factors of the whole aircraft;

[0050] (5) According to the number of aircraft segments N c Set N for the aircraft c The safety factor of each section of the aircraft is optimized based on the lightweight design principle, the reliability index requirements of the aircraft manual, and the relationship between the aircraft structure reliability and safety factor.

[0051] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application shall be based on the protection scope of the claims.

Claims

1. A method for determining safety factor based on total failure mode structural reliability, characterized in that: include: The aircraft is divided into multiple sections, each section includes multiple shell structures, and the safety factor of each shell structure and the functional function of each shell structure under each failure mode are constructed; The probability that the function of each shell structure in each failure mode is greater than 0 is taken as the structural reliability of each shell structure in each failure mode; Based on the structural reliability of all shell structures under all failure modes, the relationship between the structural reliability P of the aircraft and the safety factor of all shell structures is constructed; Let the safety factor of each section be the same as the safety factor of all shell structures in that section; Constructing a relationship between the structural reliability P of the aircraft and the safety factors of all sections; Taking the minimum total weight W of the aircraft as the optimization goal and the structural reliability P of the aircraft satisfying the design as the constraint, the safety factor of each section is optimized.

2. The method for determining the safety factor based on the total failure mode structural reliability according to claim 1, characterized in that: The safety factors of the individual shell structures and the functional functions of each shell structure under each failure mode include: F ij (u)=R ij -γ j S ij (u),(i=1,2,…,M;j=1,2,…,N) In the formula, F ji (u) represents the functional function of the i-th shell structure in the j-th failure mode, R ij The ability of the i-th shell structure to withstand the j-th failure mode, M represents the number of shell structure blocks, N represents the number of shell structure failure modes, S ij The load of the i-th shell structure under the j-th failure mode, γ i represents the safety factor of the ith shell structure, R ij , S ij It is a function related to multiple random variables such as shell structure material, size, process conditions and external loads. M represents the total number of shell structures of the aircraft, and F ij (u)≥0 indicates that the shell structure is safe, F ij (u)<0 indicates shell structure failure.

3. The method for determining the safety factor based on the total failure mode structural reliability according to claim 2, characterized in that: The expression of structural reliability of each shell structure in each failure mode is: P ij =Prob(γ i R ij -S ij (u)>0)。 4. The method for determining the safety factor based on the total failure mode structural reliability according to claim 3, characterized in that: The relationship between the structural reliability P of the aircraft and the safety factor of all shell structures is:

5. The method for determining the safety factor based on the reliability of the structure in all failure modes according to claim 3, characterized in that: The optimization format of the safety factor of each section obtained by optimization is: Among them, γ represents the vector composed of the safety factors of each section of the aircraft, W represents the total weight of the aircraft, P represents the overall reliability of the aircraft, and P cf represents the maximum structural failure probability that meets the design requirements, is the safety factor of each section of the aircraft, N c The total number of machine sections.

6. The method for determining the safety factor based on the total failure mode structural reliability according to claim 3, characterized in that: The calculation formula of the performance function of the shell structure under a failure mode is: Among them, K i Indicates the stability coefficient of each plate and shell structure, D i represents the stiffness of each plate and shell structure, a i Indicates the length of each plate and shell structure, D i Related to material stiffness, Poisson's ratio and structural design size, N represents the load value.

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