A dot matrix structure process uncertainty modeling method

Abstract

The application discloses a lattice structure process uncertainty modeling method, which comprises three parts of finite element model establishment, process uncertainty modeling and uncertainty response solving. The application establishes a lattice structure finite element model through a beam element, classifies the lattice structure according to the form of a rod piece, determines the covariance matrix of different types of rod pieces, carries out principal component analysis on the covariance matrix, determines the discrete model of different types of rod pieces, carries out truncation according to the required accuracy, determines the number of random variables, determines the polynomial chaos expansion order and corresponding calculation integral points, carries out finite element analysis on the integral points, and obtains the polynomial chaos coefficient and the mean value and standard deviation of the response. The application starts from the actual process of the lattice structure, considers the manufacturing process error of the lattice structure, and can improve the structure analysis accuracy.

Description

Technical Field

[0001] This invention relates to the field of uncertainty analysis in aerospace structural manufacturing processes, specifically a method for modeling uncertainty in the manufacturing processes of lattice structures. Background Technology

[0002] Lightweight structural design is a crucial topic in the aerospace field. Lattice structures, due to their high specific strength, high specific height, and ultralight weight, are increasingly being used in aerospace applications. However, the large number of internal structural members within lattice structures presents challenges to existing fabrication processes. Traditional fabrication methods include stretched mesh technology, overlapping splicing, and stamping. With the rapid development of 3D printing technology, the manufacture of highly complex lattice microstructures has become possible.

[0003] While 3D printing offers advantages in fabricating complex lattice structures, resulting in high precision and quality, it still presents significant manufacturing errors for smaller microstructures. Traditional lattice structure simulation methods generally do not consider process uncertainties and cannot measure their impact on structural strength, stiffness, and stability. Summary of the Invention

[0004] To address the uncertainty issues in the manufacturing process of lattice structures, this invention employs a random field model for discretization based on actually measured process uncertainty data, and then solves for the structural response using polynomial chaotic expansion, thereby improving the simulation accuracy of lattice structures. This invention is applicable to modeling process uncertainties in lattice structures in the aerospace field.

[0005] This invention is achieved through the following technical solution: a method for modeling process uncertainties in lattice structures, comprising three parts: establishing a finite element model, modeling process uncertainties, and solving for the uncertainty response. The specific steps are as follows:

[0006] Step 1: Establishing a finite element model

[0007] S100: Establish a deterministic finite element model of a lattice structure beam element, and parameterize the interface eccentricity and interface moment of inertia of the beam element in the finite element model.

[0008] Step 2: Model process uncertainties based on the parametric finite element model.

[0009] S200: By observing the connection form of the lattice structure members, the lattice structure members are divided into different types;

[0010] S201: For different types of lattice structure members, measurements are taken at different locations to obtain the model parameters of the beam element;

[0011] S202: Perform correlation analysis on the model parameters of beam elements at different measurement locations to obtain the covariance matrix of shape parameters at different locations;

[0012] S203: Perform principal component analysis on the covariance matrix to determine the discrete model for different types of bars, and truncate it according to the required accuracy ε1 to determine the number of random variables n;

[0013] Step 3: Solve for the structural response using the uncertain finite element model.

[0014] S300: Based on the number of random variables n obtained in step S203 and the required precision ε2, determine the order p of the polynomial chaotic expansion and the corresponding integration points.

[0015] S301: Perform finite element analysis on the integral points obtained from S300 to obtain the structural response at different integral points;

[0016] S302: Based on the structural responses at different integration points calculated in S301, solve for the polynomial chaotic expansion coefficients and obtain the mean and standard deviation of the responses.

[0017] In step S100, the beam element adopts the Beam188 type.

[0018] In step S200, the types of lattice structure members are divided into horizontal members, vertical members, and other members that are at different angles to the horizontal plane.

[0019] The number of measurement locations in step S201 is the same as the number of lattice structural rod elements in the finite element model.

[0020] The model parameters of the beam element in step S201 include cross-sectional eccentricity and cross-sectional moment of inertia.

[0021] In step S203, the required accuracy ε1 is greater than 95%.

[0022] In step S300, the order of the polynomial chaotic expansion is p = 3.

[0023] In step S300, the integration points for the polynomial chaotic expansion calculation are determined using sparse mesh technology.

[0024] The step S302, which involves solving for the polynomial chaotic expansion coefficients, includes:

[0025]

[0026] Where, N i To calculate the number of integration points, g j Let ζ be the coefficient of the j-th term in polynomial chaos. i For the i-th integration point, Ψ jLet j be the basis function of the polynomial chaos. Let ω be the mean of the squares of the j-th basis functions. i Let f(ζ) be the weight of the i-th integration point. i ) represents the response value corresponding to the i-th integration point.

[0027] The expressions for the mean and standard deviation of the response in step S302 are as follows:

[0028] μ=g0

[0029]

[0030] Where P is the total number of terms in the polynomial chaotic expansion, μ is the mean, and σ is the standard deviation.

[0031] The beneficial effects of this invention are as follows:

[0032] (1) The method of the present invention takes into account the uncertainty of the process of the lattice structure, improves the simulation accuracy of the lattice structure, and at the same time, the method can also avoid structural failure caused by process error to a certain extent.

[0033] (2) The method of the present invention is based on actual measurement results, and the model has high realism;

[0034] (3) The method of the present invention takes into account different forms of rods and rod eccentricity, which is more in line with the process uncertainty in engineering practice;

[0035] (4) The method of the present invention is easy to integrate with existing commercial finite element software, has low engineering application difficulty, and can provide future simulation personnel with a new means of simulating the uncertainty of lattice structures. Attached Figure Description

[0036] Figure 1 This is a schematic diagram of the deterministic modeling results in an embodiment of the present invention;

[0037] Figure 2 This is a schematic diagram of an integral point modeling result for calculating the process uncertainty response in an embodiment of the present invention; Detailed Implementation

[0038] The present invention will now be described in detail with reference to the embodiments.

[0039] like Figure 1 The deterministic modeling results of this invention are presented. Figure 2 The modeling results at one integration point considering the process uncertainty response calculation are presented. This invention provides a method for modeling process uncertainties in lattice structures, mainly comprising three parts: establishing a finite element model, modeling process uncertainties, and solving for the uncertainty response. The specific steps are as follows:

[0040] Step 1: Establishing a finite element model

[0041] S100: Establish a deterministic finite element model of a lattice structure beam element, and parameterize the interface eccentricity and interface moment of inertia of the beam elements in the finite element model. The beam elements are of type Beam188. In this example, the deterministic modeling results are as follows: Figure 1 As shown.

[0042] Step 2: Model process uncertainties based on the parametric finite element model.

[0043] S200: By observing the connection form of the lattice structure members, such as... Figure 1 The members are divided into horizontal members, vertical members, and members at a 45° angle to the horizontal plane. 0 There are three types of rods;

[0044] S201: For different types of rods, measurements are taken at different locations to obtain the model parameters of the beam element; in this embodiment, there are 8 rod beam elements in the finite element model, so the measurement positions are divided into eight equal positions to measure the eccentricity and moment of inertia of the beam element section.

[0045] S202: Perform correlation analysis on the model parameters at different measurement locations to obtain the covariance matrix of the shape parameters at different locations;

[0046] S203: Perform principal component analysis on the covariance matrix to determine the discrete model for different types of members, and truncate the model according to the required accuracy ε1 to determine the number of random variables n; in this example, the truncation accuracy ε1 = 98%, and the number of random variables n = 4;

[0047] Step 3: Solve for the structural response using the uncertain finite element model.

[0048] S300: Based on the number of random variables n=4 obtained in step S203 and the required precision ε2=99%, determine the polynomial chaotic expansion order p=3 and the corresponding integration points; wherein, the polynomial chaotic expansion integration points are determined using sparse grid technology; such as Figure 2 The result of modeling the uncertainty at one of the integration points;

[0049] S301: Perform finite element analysis on the calculation integration points obtained from S300 to obtain the structural response at different integration points;

[0050] S302: Based on the structural responses at different integration points calculated in S301, solve for the polynomial chaos coefficients and obtain the mean and standard deviation of the responses;

[0051] The polynomial chaos solution expression is as follows:

[0052]

[0053] Where, N i To calculate the number of integration points, g j Let ζ be the coefficient of the j-th term in polynomial chaos. i For the i-th integration point, Ψ j Let j be the basis function of the polynomial chaos. Let ω be the mean of the squares of the j-th basis functions. i Let f(ζ) be the weight of the i-th integration point. i ) represents the response value corresponding to the i-th integration point.

[0054] The expressions for the mean and standard deviation of the response are:

[0055] μ=g0

[0056]

[0057] Where P is the total number of terms in the polynomial chaotic expansion, μ is the mean, and σ is the standard deviation.

[0058] This invention establishes a process uncertainty model for lattice structures using a random field model, which can improve the accuracy of simulation solutions for lattice structures. The above embodiments are merely one application example of this invention and should not be construed as limiting the scope of application of this invention.

Claims

1. A method for modeling uncertainties in the manufacturing process of lattice structures, characterized in that, include: Establish a finite element model: A deterministic finite element model of a lattice structure beam element is established, and the interface eccentricity and interface moment of inertia of the beam element in the finite element model are parameterized. Modeling process uncertainties based on parametric finite element model: By observing the connection form of the lattice structure members, the lattice structure members can be divided into different types; For different types of lattice structure members, measurements are taken at different locations to obtain the model parameters of the beam element; Correlation analysis was performed on the model parameters of beam elements at different measurement locations to obtain the covariance matrix of shape parameters at different locations; Principal component analysis is performed on the covariance matrix to determine the discrete model for different types of bars, and the model is truncated according to the required accuracy ε1 to determine the number of random variables n. Solve for the structural response using the uncertain finite element model: Based on the number of random variables n and the required precision ε2, determine the order p of the polynomial chaotic expansion and the corresponding integration points. Finite element analysis was performed on the calculated integration points to obtain the structural response at different integration points; Based on the structural responses at different integration points obtained from the calculations, the polynomial chaotic expansion coefficients are solved, and the mean and standard deviation of the responses are obtained.

2. The method for modeling process uncertainties of a lattice structure according to claim 1, characterized in that, The beam element is of type Beam188.

3. The method for modeling process uncertainties of a lattice structure according to claim 1, characterized in that, The types of rods in the lattice structure are divided into horizontal rods, vertical rods, and other rods at different angles to the horizontal plane.

4. The method for modeling process uncertainties of lattice structures according to claim 1, Its features are, The number of measurement locations is the same as the number of lattice structural rod elements in the finite element model.

5. The method for modeling process uncertainties of a lattice structure according to claim 1, characterized in that, The model parameters of the beam element include cross-sectional eccentricity and cross-sectional moment of inertia.

6. The method for modeling process uncertainties of a lattice structure according to claim 1, characterized in that, The required accuracy ε1 is greater than 95%.

7. The method for modeling process uncertainties of a lattice structure according to claim 1, characterized in that, The order of the polynomial chaotic expansion is p = 3.

8. The method for modeling process uncertainties of a lattice structure according to claim 1, characterized in that, The integration points for the polynomial chaotic expansion calculation are determined using sparse mesh technology.

9. The method for modeling process uncertainties of a lattice structure according to claim 1, characterized in that, The solution to the polynomial chaotic expansion coefficients includes: Where, N i To calculate the number of integration points, g j Let ζ be the coefficient of the j-th term in polynomial chaos. i For the i-th integration point, Ψ j Let j be the basis function of the polynomial chaos. Let ω be the mean of the squares of the j-th basis functions. i Let f(ζ) be the weight of the i-th integration point. i ) represents the response value corresponding to the i-th integration point.

10. The method for modeling process uncertainties of a lattice structure according to claim 9, characterized in that, The expressions for the mean and standard deviation of the response are: μ=g0 Where P is the total number of terms in the polynomial chaotic expansion, μ is the mean, and σ is the standard deviation.

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