Aeroelastic analysis method for variable stiffness composite wing with multi-source uncertainty

Abstract

The application discloses a variable stiffness composite wing aeroelastic analysis method containing multi-source uncertainty, comprising the following steps: dividing a probability space according to the conditions of random uncertainty factors, and determining the value of a random vector at each sampling point and the probability value of a subdomain where the random vector is located; regarding the random vector at each sampling point as a deterministic parameter, and calculating interval boundary values of aeroelastic response variables which need to be analyzed at each sample point through a loop; based on the interval boundary values, calculating the reliability of a structure at each sample point only under the influence of interval factors; discretizing initial conditions of a generalized probability density evolution equation to obtain the probability density of the reliability of the structure in each subdomain; superimposing the probability densities of each subdomain to obtain a probability density curve of the reliability of the structure considering multi-source uncertainty; and calculating the reliability of the structure based on the probability density curve. By adopting the technical scheme, the aeroelastic analysis of the variable stiffness composite wing containing multi-source uncertainty is realized.

Description

Technical Field

[0001] This invention belongs to the field of aeroelastic analysis technology, and particularly relates to an aeroelastic analysis method for variable stiffness composite material wings with multi-source uncertainties. Background Technology

[0002] For the aeroelastic analysis of variable stiffness composite materials with multi-source uncertainties, most existing engineering methods are based on the safety factor method. Aeroelastic analysis methods for variable stiffness composite materials mainly rely on engineering algorithms such as the low-order element method and the PK method.

[0003] Aeroelastic analysis plays a crucial role in modern aircraft development, primarily studying the interactions between aerodynamic forces, elastic forces, and inertial forces involved in aircraft operation. Some studies also consider the influence of factors such as temperature, thermal stress, and control systems on the aeroelastic system. Its applications are numerous, including preventing aircraft flutter under given conditions that could affect flight safety; and actively controlling the deformation of control surfaces such as ailerons to improve control efficiency. In engineering, aeroelastic analysis and theoretical verification are often based on theories such as the element method, piston theory, and PK method, as well as various experimental methods. Because the research object is affected by uncertainties from sources such as manufacturing processes and service environments, in addition to deterministic analysis, it is also necessary to analyze the reliability of the aircraft structure under the influence of these multi-source uncertainties, thereby improving the safety of aircraft design.

[0004] In variable stiffness composite layups, fiber bundles can be laid along designed curved paths, causing the laminate's stiffness to vary along the fiber angle direction. This designability of the layup angle not only expands the design space of variable stiffness composite structures but also improves buckling resistance and weight reduction. These characteristics make them promising candidates for application and have practical engineering value in aircraft structures such as high-aspect-ratio wings. However, existing processing technologies inevitably introduce angular deviations between the actual fiber layup path and the theoretical design path, creating gaps or overlaps within the layup and introducing uncertainties into the structure. Furthermore, in actual service environments, aircraft are affected by factors such as incoming flow velocity, causing the actual performance of variable stiffness composite structures to differ from theoretical calculations. Under the influence of these multi-source uncertainties, aircraft performance can sometimes decline, and in some cases, even serious safety issues may arise. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide an aeroelastic analysis method for variable stiffness composite airfoils with multi-source uncertainties, so as to realize aeroelastic analysis of variable stiffness composite airfoils with multi-source uncertainties.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] An aeroelastic analysis method for variable stiffness composite airfoils with multi-source uncertainties, comprising:

[0008] Step S1: Divide the probability space according to the actual random uncertainty factors, and determine the value of the random vector at each sampling point and the probability value of the subdomain it is in.

[0009] Step S2: Treat the random vector at each sampling point as a deterministic parameter, and calculate the interval boundary value of the aeroelastic response variable to be analyzed at each sampling point by iterative calculation;

[0010] Step S3: Based on the interval boundary value, calculate the reliability of the structure at each sample point under the influence of interval factors only, and use it as the sample point response value to quantify the reliability when considering the influence of random factors.

[0011] Step S4: Discretize the initial conditions of the generalized probability density evolution equation and solve the equation using the finite difference method of the TVD scheme to obtain the probability density of structural reliability in each subdomain.

[0012] Step S5: Superimpose the probability density of each subdomain to obtain the probability density curve of structural reliability considering multi-source uncertainties;

[0013] Step S6: Calculate the reliability of the structure based on the probability density curve of the structural reliability.

[0014] As a preferred embodiment, in step S1, the probability space is divided into subspaces with the same number of sample points based on number theory, and each subspace region is adjusted based on the GF minimum deviation principle to obtain the random uncertain vector value corresponding to the unique sample point in each subspace, as well as the probability value corresponding to each subspace.

[0015] Preferably, in step S2, the random vector values ​​at the sample points are treated as deterministic parameters, and the interval boundary values ​​of the aeroelastic response at each sample point, when the structure is only affected by interval uncertainties, are solved by iterative calculation and the Bernstein polynomial method.

[0016] Preferably, in step S4, the initial conditions of the generalized probability density evolution equation are discretized, and the sample points previously divided and their corresponding upper and lower boundary values ​​of structural reliability are used to solve the generalized probability density evolution equation based on the finite difference method of the TVD scheme to obtain the probability density of reliability at each sample point.

[0017] This invention performs aeroelastic analysis on variable stiffness composite material wings based on the generalized probability density evolution equation and Bernstein polynomials. It uses the generalized probability density evolution equation to quantify the influence of random uncertainties in the aeroelastic analysis process, and uses Bernstein polynomials to quantify the influence of interval uncertainties in the aeroelastic analysis process. The quantification results of the uncertainties are used for reliability analysis to consider the rationality and safety of the aeroelastic analysis results, thereby improving the reliability of the structural design and reducing the impact of redundant design. Attached Figure Description

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

[0019] Figure 1 This is a flowchart of the aeroelastic analysis method for variable stiffness composite airfoils with multi-source uncertainties according to an embodiment of the present invention. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0022] Example 1:

[0023] like Figure 1 As shown, this embodiment of the invention provides an aeroelastic analysis method for variable stiffness composite airfoils with multi-source uncertainties, including:

[0024] Step S0: Determine the number of random uncertain parameters involved in the specific problem, the distribution of each parameter, the number of interval uncertain parameters, and the interval center value and interval radius of each parameter. In the aeroelastic analysis of variable stiffness composite airfoils with multi-source uncertainties, the possible random uncertain parameters mainly include: incoming flow velocity, incoming flow density, geometric parameters of the airfoil structure, and physical properties of the airfoil structure material. The specific types and number of uncertain parameters in the analysis process are determined by the actual analysis object and working environment. The interval uncertain parameters considered in the analysis mainly come from the deviation between the actual processing path and the theoretical design path of the reinforcing fibers in the variable stiffness composite layup. Their number depends on the specific processing method and the number of layups of the variable stiffness composite. Determine the number of sample points required for the generalized probability density conservation method and the order of the Bernstein polynomial based on the number of random / interval uncertain parameters.

[0025] Step S1: Divide the probability space into multiple subdomains based on the actual random uncertainties. Each subdomain contains a sample point, and the information of each sample point includes three parts: coordinate value, function value, and probability value. The coordinate value and probability value of the sample point are only related to the distribution of the random uncertainties and the total number of sample points. The function value of the sample point is related to the specific physical model (flutter model, wingtip deformation model, etc.). The coordinate value of the sample point is the value of all random uncertainties involved in the random problem (flow velocity, flow density, geometric parameters of the wing structure, physical properties of the wing structure material). The function value corresponding to the sample point is the value of the variables of interest in the aeroelastic analysis of the variable stiffness composite wing with multi-source uncertainties (eigenvalues ​​of the aeroelastic characteristic equation, maximum wingtip displacement or twist angle, reliability of interval uncertainties, etc.). The probability value of the sample point is the probability value of its subdomain within the entire sample space.

[0026] Step S2: Treat the random vector at each sampling point as a deterministic parameter, and calculate the interval boundary values ​​of the aeroelastic response variables (e.g., the maximum real root of the characteristic equation, flutter damping) to be analyzed at each sampling point by iterative calculation.

[0027] Step S3: Based on the interval boundary value, calculate the reliability of the structure at each sample point under the influence of interval factors only, and use it as the sample point response value to quantify the reliability when considering the influence of random factors.

[0028] Step S4: Discretize the initial conditions of the generalized probability density evolution equation and solve the equation using the finite difference method of the TVD scheme to obtain the probability density of structural reliability in each subdomain.

[0029] Step S5: Superimpose the probability density of each subdomain to obtain the probability density curve of structural reliability considering multi-source uncertainties;

[0030] Step S6: Calculate the reliability of the structure based on the probability density curve of the structural reliability.

[0031] As one embodiment of the present invention, in step S1, the probability space is divided into subspaces with the same number of sample points based on number theory, and each subspace region is adjusted based on the GF minimum deviation principle to obtain the random uncertain vector value corresponding to the unique sample point in each subspace, and the probability value corresponding to each subspace.

[0032] The process of subspace partitioning is as follows:

[0033] In geometric space [0,1] s Select a uniform point set P basic Where s is the number of random uncertainties; the spherical screening-scaling transformation method is used to reduce the point set P. basic The number of elements in the set is determined, and the positions of each point are adjusted; based on the inverse function transformation corresponding to the probability distribution of each random uncertainty factor, the adjusted point set P is obtained. basic Obtain the point set P n Point set P n The coordinates of the elements in the set P are the values ​​of the random uncertainties in the problem (flow velocity, flow density, geometric parameters of the wing structure, and physical properties of the wing structure material); n After two mathematical renormalizations to reduce the GF bias, the final point set P is obtained, where the coordinates of each element in point set P are the values ​​of each random uncertainty factor. After subspace partitioning, the coordinates of each sample point and the probability value of its subspace are obtained.

[0034] As one embodiment of the present invention, in step S2, the random vector values ​​at the sample points are regarded as deterministic parameters, and the interval boundary values ​​of the aeroelastic response at each sample point, when the structure is only affected by interval uncertainties, are solved by iterative calculation and the Bernstein polynomial method.

[0035] The calculation process for the interval response boundary value corresponding to each sample point in the random problem is as follows:

[0036] The coordinates of random sample points in a problem with mixed uncertainty are used as deterministic parameters. This is for problems with only one interval parameter. To address the issue of (errors in the placement angle of reinforcing fibers within a single layer of composite materials), we first extend the independent variable interval of the Bernstein polynomial from [0,1] to [-1,1] through coordinate transformation:

[0037]

[0038] Among them, P s (t) represents the response variable; m is the order of the Bernstein polynomial; ωs Let be the coefficients to be determined. Define the following sub-function terms:

[0039]

[0040] b mk The extreme point t of (t) k for:

[0041]

[0042] t k The corresponding interval uncertainty parameter α sk for:

[0043]

[0044] In the formula, This represents the upper boundary of the interval parameter; α s This represents the lower boundary of the interval parameter. (By...) The response variable value λ corresponding to the sample points in the interval can be calculated. ri,s .

[0045] The coefficients ω to be determined are calculated using the least squares method and the Bernstein-Vandermonde determinant B by the following formula. s :

[0046]

[0047] The coefficients to be determined, ω, are obtained. s Then, P can be obtained by differentiation. s The maximum point t of (t) s，max and the minimum point t s，min In aeroelastic analysis, the interval response variable P of the physical quantities of interest (the maximum real part of the eigenvalues ​​of the aeroelastic characteristic equation, the maximum displacement or twist angle of the wingtip, etc.) is... s (α s Maximum point α s,max and the minimum point α s,min Then it is calculated by the following formula:

[0048]

[0049] From α s,max and α s,min The upper boundary value P of the interval response can then be calculated. s (α s,max ) and lower boundary value P s (α s,min ).

[0050] For the l interval uncertainty parameters involved in the l-layer layup (the angle error of the reinforcing fiber placement between each layup needs to be considered separately), then the uncertainty parameter of each interval is considered separately. Calculate the parameter of the j-th interval. When determining the response boundary, taking the remaining l-1 interval parameters as the interval center values ​​yields the following results: Corresponding maximum point and minimum point The obtained extreme value point vector α s,max and α s,min Substituting these parameters into the actual physical model, we can obtain the upper boundary value P of the interval response of the physical quantities of interest (the maximum real part of the eigenvalues ​​of the aeroelastic characteristic equation, the maximum displacement or twist angle of the wingtip, etc.) under the simultaneous influence of l interval uncertainty parameters in the aeroelastic analysis. s (α s,max ) and lower boundary value P s (α s,min ).

[0051] As one embodiment of the present invention, in step S3, the structural reliability under the influence of interval factors is calculated based on the interval boundary values ​​and the index requirements of aeroelastic response (for example, for flutter problems, the structure is considered safe when the maximum real root of the aeroelastic characteristic equation is greater than 0, otherwise the structure is considered unsafe).

[0052] The calculation process for interval reliability is as follows:

[0053] Determine the critical value P of the response variable for the physical quantities of interest in the aeroelastic analysis (such as the maximum real part of the eigenvalues ​​of the aeroelastic characteristic equation, the maximum displacement or twist angle at the wingtip, etc.). cr Different failure ranges and safe ranges can be defined for different physical quantities of interest. For example, for the flutter problem, P is considered to be... cr ~P s (α s,max ) represents the failure interval, P s (α s,min )~P cr This is a safe interval. According to P... s (α s,max ), P s (α s,min ) and P cr The limit state function L is calculated using the following formula.

[0054] L(α s )=L(P cr ,P(α s ))=P cr -P(α s )

[0055] For flutter problems, the structure is considered reliable when L>0 and unreliable when L<0. The interval reliability R for this type of problem can be calculated by the following formula:

[0056]

[0057] In one embodiment of the present invention, in step S4, the initial conditions of the generalized probability density evolution equation are discretized, and the generalized probability density evolution equation is solved using the previously divided sample points and their corresponding upper and lower boundary values ​​of structural reliability based on the finite difference method of the TVD scheme, so as to obtain the probability density of reliability at each sample point.

[0058] The process of calculating the probability density of reliability at each sample point is as follows:

[0059] The generalized probability density evolution equation for the reliability R of the physical quantities of interest (the maximum real part of the eigenvalues ​​of the aeroelastic characteristic equation, the maximum displacement or twist angle of the wingtip, etc.) under the influence of interval factors only is:

[0060]

[0061] Based on the subspace partitioning results in step S1, the initial conditions for the generalized probability density evolution equation can be obtained as follows:

[0062] p RΘ (R,α s ,α in ,t)| t＝0 =δ(R-R0)p Θ (α s ,α in )

[0063] Substitute the reliability R at each sample point of the stochastic uncertainty problem calculated in step S3 into the generalized probability density evolution equation of reliability R, and solve the discrete generalized probability density evolution equation using the finite difference method of the TVD scheme to obtain the joint probability density p. RΘ (R j ,α s ,α in ,t k ), where R j =R0+jΔR, where ΔR is the distance step of the system state variable; j is the distance step number; The time step is used to solve the generalized probability density evolution equation; k is the time step number. Typically,

[0064] As one embodiment of the present invention, in step S5, the probability density of the reliability R of the physical quantity of interest (the maximum real part of the eigenvalues ​​of the aeroelastic characteristic equation, the maximum displacement or twist angle of the wingtip, etc.) at each random problem sample point under the influence of interval factors is accumulated using the following formula:

[0065]

[0066] In the formula, n is the number of random problem sample points; q is the random problem sample point number; P q The probability value at each sample point. Time t... k Setting it to 1 yields the probability density function p(R) of structural reliability under the influence of interval factors.

[0067] As one embodiment of the present invention, in step S6, the reliability of the structure under the influence of mixed uncertainty factors is calculated by the following formula based on the probability density function p(R) of the structural reliability.

[0068]

[0069] The advantages of the embodiments of the present invention are as follows:

[0070] (1) The quantitative results of the effects of interval uncertainty and random uncertainty, as well as the calculation results of structural reliability, are consistent with the results of the traditional Monte Carlo method, which proves the correctness and effectiveness of the aeroelastic analysis method with multi-source uncertainty.

[0071] (2) The results of the uncertainty quantification analysis and reliability calculation method adopted are more efficient and require fewer samples compared with the classic Monte Carlo method, which proves the efficiency and simplicity of the reliability calculation method.

[0072] (3) The uncertainty quantification analysis and reliability calculation methods adopted are more accurate than the safety factor method commonly used in engineering. They can reduce the impact of redundant factors on structural performance and are more in line with actual engineering needs.

[0073] (4) By quantitatively analyzing the uncertainties in the processing and service environment, the reliability of aircraft analysis results and structural safety can be improved on the basis of deterministic analysis.

[0074] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for aeroelastic analysis of variable stiffness composite airfoils containing multi-source uncertainties, characterized in that, include: Step S1: Divide the probability space according to the actual random uncertainty factors, and determine the value of the random vector at each sampling point and the probability value of the subdomain it is in. Step S2: Treat the random vector at each sampling point as a deterministic parameter, and calculate the interval boundary value of the aeroelastic response variable to be analyzed at each sampling point by iterative calculation; Step S3: Based on the interval boundary value, calculate the reliability of the structure at each sample point under the influence of interval factors only, and use it as the sample point response value to quantify the reliability when considering the influence of random factors. Step S4: Discretize the initial conditions of the generalized probability density evolution equation and solve the equation using the finite difference method of the TVD scheme to obtain the probability density of structural reliability in each subdomain. Step S5: Superimpose the probability density of each subdomain to obtain the probability density curve of structural reliability considering multi-source uncertainties; Step S6: Calculate the reliability of the structure based on the probability density curve of the structural reliability.

2. The aeroelastic analysis method for variable stiffness composite airfoils with multi-source uncertainties as described in claim 1, characterized in that, In step S1, the probability space is divided into subspaces with the same number of sample points based on number theory, and each subspace region is adjusted based on the GF minimum deviation principle to obtain the random uncertain vector value corresponding to the unique sample point in each subspace, as well as the probability value corresponding to each subspace.

3. The aeroelastic analysis method for variable stiffness composite airfoils with multi-source uncertainties as described in claim 2, characterized in that, In step S2, the random vector values ​​at the sample points are treated as deterministic parameters. The interval boundary values ​​of the aeroelastic response at each sample point, when the structure is only affected by interval uncertainties, are solved by iterative calculation and the Bernstein polynomial method.

4. The aeroelastic analysis method for variable stiffness composite airfoils with multi-source uncertainties as described in claim 3, characterized in that, In step S4, the initial conditions of the generalized probability density evolution equation are discretized. Using the previously divided sample points and their corresponding upper and lower boundary values ​​of structural reliability, the generalized probability density evolution equation is solved based on the finite difference method of the TVD scheme to obtain the probability density of reliability at each sample point.

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