A method for determining the spacing of long girders in composite reinforced wall panels

Abstract

The present invention relates to a method for determining the stringer spacing of a composite stiffened panel structure, belonging to the field of aircraft composite airframe structural strength design. The method comprises the following steps: S1: obtaining the expressions of the effective thickness t adj , effective width w eff and effective cross-sectional area A eff of the stringer cross-section; S2: calculating the equivalent elastic modulus E eqv of the stiffened panel cross-section; S3: establishing the constitutive equation of the load-bearing capacity of the composite stiffened panel structure; S4: modifying the constitutive equation by using the effective cross-sectional area and shear modulus; S5: determining the stringer spacing of the composite stiffened panel structure. The method of the present invention can design the optimal structural dimension configuration on the basis of meeting the structural strength requirements; helps to reduce unnecessary conservative design, greatly shortens the R & D time and reduces the R & D cost; reduces the time and economic costs brought by repeated tests, is conducive to optimizing the structural design and exploring the structural weight reduction ability, and reduces the transportation cost.

Description

Technical Field

[0001] The invention relates to a method for determining the spacing between long girders of a composite material reinforced wall panel structure, and belongs to the field of aircraft composite material fuselage structure strength design. Technical Background

[0002] Composite materials are a new type of material. Compared with traditional metal materials, they have the advantages of high specific strength, high specific stiffness, strong designability, and excellent fatigue resistance. They have been widely used in aerospace, vehicle and shipbuilding, mechanical engineering and other fields. Composite stiffened panels are a typical load-bearing structure in modern aircraft design. They have been widely used in aircraft wings, fuselages and tails. Their detailed design will play a positive role in reducing structural weight and improving structural bearing capacity. Accurate analysis methods for the spacing and cross-sectional dimensions of the long truss of composite stiffened panel structures will play a guiding role in the design of composite structural structures. Internationally, Antonio et al. used numerical analysis methods to study the influence of the geometric shape of the cross-section of the long truss on its bearing capacity, but they did not conduct experimental verification, did not further analyze how to design the reasonable cross-sectional dimensions, and did not give a method for determining the spacing of the long truss. In China, the application maturity of composite design technology in commercial aircraft is relatively low. At present, there is no standard method for determining the spacing and cross-sectional dimensions of composite stiffened panel structures. Most of them refer to the empirical data of Boeing and Airbus, which cannot truly reflect the stress and strain distribution during the service of the aircraft and may lead to overly conservative designs. According to the design and analysis experience of Boeing and Airbus, the spacing and cross-sectional dimensions of the long stringers are the key factors affecting the load-bearing capacity of composite materials. However, up to now, the design of long stringers at home and abroad still adopts the "trial and error method", that is, through the method of finite element simulation analysis + test verification, the parameters of the long stringers are repeatedly adjusted and the test is repeated to find the best spacing and cross-sectional dimensions of the long stringers. This method consumes a lot of manpower and material resources, and the development iteration efficiency is low and the cycle is long. Summary of the invention

[0003] The purpose of the present invention is to provide a method for determining the spacing of long girders for composite material reinforced wall panel structures of civil aircraft, so as to make up for the shortcomings of the methods for designing long girders for composite material reinforced wall panel structures. The method of the present invention can be applied to long girders of various shapes such as I-type, T-type, L-type and C-type.

[0004] The specific steps of the method of the present invention are as follows:

[0005] S1: The effective thickness t of the long stringer section is given by the long stringer section parameters adj 、Effective width w eff and effective cross-sectional area A eff The expression of is calculated as follows:

[0006] t adj =t skin +(2t sf1 E sf1 b sf1 +2t sf2 E sf2 b sf2 +t fb E fb b fb ) / (b st E skin ) (1)

[0007] w eff =0.95t adj / (ε c ) 1 / 2 (2)

[0008] A eff =w eff t adj +h web t web (3)

[0009] Among them, t skin : Skin thickness; t sf1 : Thickness of the top edge of the long stringer; E sf1 : elastic modulus of the upper edge of the long stringer; b sf1 : Width of the top edge of the long stringer; t sf2 : Thickness of the lower edge of the long stringer; E sf2 : elastic modulus of the lower edge of the long stringer; b sf2 : Width of the lower edge of the long stringer; t fb : Thickness of the lower edge strip pad; E fb : Elastic modulus of the lower edge strip pad; b fb : Width of lower edge strip pad; E skin : axial elastic modulus of the skin; ε c : Material compressive limit strain; h web : web height; t web : web thickness; b st : Spacing between long beams.

[0010] Figure 1 The cross-sectional diagram of the I-type long stringer is shown in FIG. Taking the I-type long stringer as an example, the specific meaning of each parameter related to size (width, height, thickness, etc.) in the above parameters can be seen. The purpose of the present invention is to determine the appropriate long stringer spacing value applied to the shape and material when the shape and material of the long stringer and the skin are determined. Therefore, in addition to the long stringer spacing b st All other dimension-related parameters can be considered as known parameters.

[0011] In the composite material reinforced wall panel for civil aircraft targeted by the present invention, the long stringer and the skin are made of the same composite material, ε c It refers to the compressive limit strain of the material in the load-bearing direction.

[0012] S2: Calculate the equivalent elastic modulus E of the stiffened panel section eqv .

[0013] The equivalent elastic modulus can be calculated using the following formula:

[0014] E eqv ×(A stringer +A skin )=E stringer ×A stringer +E skin ×A skin (4)

[0015] Elastic modulus E of the upper and lower edge bars of the long stringer sf1 、E sf2 All are in the load direction (also called axial direction, i.e. vertical Figure 1 Elastic modulus (in the paper direction), E stringer and E skin is the axial equivalent elastic modulus of the stringer and skin, A stringer and A skin is the cross-sectional area of ​​the long stringer and the skin. The axial equivalent elastic modulus of the upper edge bar, lower edge bar, long stringer and skin can be calculated by the stiffness matrix according to the specific laying method and the method in the prior art. It can be seen from formula (4) that the equivalent elastic modulus E of the stiffened wall section is eqv The axial equivalent elastic modulus E of the long stringer and skin is stringer 、E skin , and the cross-sectional area ratio A of the stringer and the skin stringer / A skin Related.

[0016] The cross-sectional area ratio of the stringer to the skin is A stringer / A skin A selection can be made within the range of 3:7 to 4:6 based on empirical values, and the optimal value can be determined in advance by finite element method and other methods.

[0017] S3: Establish the constitutive equation of the bearing capacity of the composite reinforced wall panel structure:

[0018] P cr,E =cπ 2 D min / b st 2 (5)

[0019] in:

[0020] c: fixed coefficient; b: fixed coefficient st : Spacing between long girders; minimum bending stiffness D min =E eqv t adj w 3 eff / 12.

[0021] The fixing coefficient c is determined according to the specific fixing form at both ends of the stiffened wall panel. The specific corresponding relationship can be referred to in Table 1 below:

[0022] Table 1 Fixed form and fixed coefficient c

[0023] Fixed form Fixed coefficient c Simply supported at both ends 1 Fixed support at both ends 4 One end is simply supported, the other end is fixed 2.05 One end fixed, one end free 0.25

[0024] S4: Modified constitutive equation using effective cross-sectional area and shear modulus:

[0025] P cr,Ec =P cr,E / (1+P cr,E / A eff G)

[0026] Where P cr,E is the buckling load before correction obtained in step S3, P cr,Ec is the corrected buckling load, and G is the transverse shear elastic modulus of the material used for the stringer and skin.

[0027] S5: Determine the spacing of the long girders in the composite stiffened panel structure:

[0028] According to the constitutive equation modified in step S4, plot b st -P cr,Ec The curve diagram is used to determine the spacing b of the long girders according to the required bearing capacity of the composite reinforced wall panel structure. st The value of .

[0029] Substituting equations (1) to (4) into equation (5), equation (5) can be written as follows:

[0030]

[0031] In the formula

[0032]

[0033] From formula (6), it can be seen that the buckling load value is related to t adj and b st The other parameters are known, and according to formula (1), t adj And only the distance between the long stringer and st Therefore, formula (6) is only related to the long stringer spacing b stRelated functions, so we can plot b st -P cr,Ec The curve shows that the load value that the reinforced wall panel needs to bear can be used to select a reasonable spacing b between the long girders. st The value range of .

[0034] When determining the spacing of the long girders, if the spacing of the long girders is designed to be too large, the skin is prone to buckling as a whole, and if the spacing is too small, the web of the long girders may buckle. Finite element analysis, test and other methods or empirical values ​​can be used to determine in advance the spacing of the long girders that can cause the skin of the stiffened panel to buckle as a whole and the web of the long girders to buckle when the set length of the long girders, skin size and material are applied. st Remove the range of values ​​from the curve graph and use the remaining curve area to determine the long stringer spacing b according to the required bearing capacity of the composite reinforced wall panel structure. st The value of the stringer spacing b can also be selected according to the load value and the curve graph, and the stringer spacing value close to the middle of the curve can be selected. After determining the stringer spacing value range, some stringer spacing values ​​that will cause overall buckling of the skin or buckling of the stringer web can be eliminated according to the test results. In short, when determining the stringer spacing b st When selecting the value of , ensure that the selected stringer spacing will not cause the overall skin buckling of the stiffened wall panel and the stringer web buckling.

[0035] The present invention has the following advantages and beneficial effects:

[0036] 1) The content of the present invention has a wide range of applications in composite material structure design in aviation, aerospace, automobiles, etc.;

[0037] 2) It can improve the utilization efficiency of composite material structures, design the optimal size and configuration of the structure on the basis of meeting the structural strength requirements; give full play to the bearing capacity of the composite material reinforced wall panel structure and achieve the lightweight design purpose;

[0038] 3) The method of the present invention helps to reduce unnecessary conservative design, greatly shortens the R&D time and reduces R&D costs; reduces the time and economic costs caused by repeated experiments, is conducive to optimizing structural design and tapping the weight reduction capacity of the structure, and reduces transportation costs;

[0039] 4) The present invention has been applied to the design of the CR929 aircraft, and its analysis accuracy and reliability have been verified, and it has broad prospects for practical engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 This is a schematic diagram of the cross-section parameters of the reinforced wall panel. 1-upper edge of the long stringer; 2-web; 3-lower edge of the long stringer; 4-pad of the lower edge; 5-skin.

[0041] Figure 2is the delta-P of the embodiment of the present invention cr,Ec Graph.

[0042] Figure 3 is t of the embodiment of the present invention adj -P cr,Ec and b st -P cr,Ec Graph.

[0043] Figure 4 and Figure 5 These are some of the finite element analysis results of the finite element test pieces in Table 3 and the corresponding constitutive equation calculation results.

[0044] Figure 6 is the b of the finite element test pieces of groups A1 and B1 in Table 3 st -P cr,Ec Relationship diagram and t of finite element test pieces of groups A2 and B2 adj -P cr,Ec Relationship diagram.

[0045] Figure 7 is A2(t adj =1.8mm)(left) and B2(t adj =1.8mm) (right) Load-displacement curves obtained by finite element (FEM) and experimental (Test) analysis of the two test pieces. DETAILED DESCRIPTION

[0046] The following is a detailed description of the specific implementation process of the present invention in conjunction with a specific design example of a composite material reinforced wall panel for a CR929 aircraft. The composite material specification used is CMS_CP_306 unidirectional tape material, and both the skin and the long stringer are made of this medium-mode high-strength carbon fiber toughened epoxy resin prepreg, with a single layer thickness of 0.13mm, a Poisson's ratio of 0.31, and a compressive limit strain of 4500με. The material mechanical properties data are shown in Table 2.

[0047] Table 2 Material parameters of carbon fiber unidirectional tape CMS-CP-306

[0048]

[0049] A stiffness matrix is ​​established based on the properties of the material itself. Based on the stiffness matrix and the laying method of the stringer and skin, the elastic modulus of the upper and lower edge strips of the stringer and the axial equivalent elastic modulus of the stringer and skin can be calculated.

[0050] Firstly, a finite element simulation model of the composite material reinforced wall panel structure is established, and after loading the axial compression load, the experimental strain data and the strain data obtained by the finite element model are compared to verify the rationality of the finite element simulation model.

[0051] This embodiment uses SAC (strain judgment criterion) to test the rationality and feasibility of the simulation model: extract the strain values ​​of the experimental analysis and the finite element analysis respectively, and calculate the SAC values ​​of the two. The calculation formula is:

[0052]

[0053] in:

[0054] ε fi T Sε fi ≠0ε fi T Sε fj =0(i≠j)

[0055] ε fi : i-th order finite element analysis strain vector;

[0056] ε ti : strain vector of the i-th order test analysis;

[0057] When SAC≥0.7, it means that the two vibration mode vectors have good consistency, that is, the simulated finite element model can better approximate its actual situation; when SAC≤0.2, it is considered that the two vibration mode vectors are orthogonal and there is no linear relationship.

[0058] In this embodiment, multiple cross-sectional shapes of the long stringers, skin thickness, long stringer spacing, and the cross-sectional area ratio of the long stringers to the skin (i.e., A stringer / A skin , abbreviated as δ), the strain value, buckling load and buckling form of the reinforced wall panel after loading. It has been verified that under multiple groups of loads, the strain vectors of finite element analysis and experimental analysis meet the above judgment criteria. It can be determined that the finite element model used in this embodiment is suitable for the simulation of the reinforced wall panel in this embodiment.

[0059] In this embodiment, the above finite element simulation and test results are mainly used to verify the results obtained by the constitutive equation proposed in the present invention and to select the initial values ​​of some parameters, but are not necessary steps of the core method of the present invention.

[0060] Use the following method to determine the appropriate range of stringer spacing that should be selected:

[0061] S1: The effective thickness t of the long stringer section is given by the long stringer section parameters adj 、Effective width w eff and effective cross-sectional area A eff The expression of is calculated as follows:

[0062] t adj =t skin +(2t sf1 Esf1 b sf1 +2t sf2 E sf2 b sf2 +t fb E fb b fb ) / (b st E skin )

[0063] w eff =0.95t adj / (ε c ) 1 / 2

[0064] A eff =w eff t adj +h web t web

[0065] The meaning of each parameter has been introduced in detail in the content of the invention.

[0066] S2: Calculate the equivalent elastic modulus E of the stiffened panel section eqv :

[0067] E eqv ×(A stringer +A skin )=E stringer ×A stringer +E skin ×A skin

[0068] In this embodiment, the axial elastic modulus E of the long stringer and the skin is stringer E skin is the inherent property of the material and can be obtained through stiffness matrix calculation.

[0069] The value that needs to be determined is the cross-sectional area ratio of the stringer to the skin (i.e. A stringer / A skin , abbreviated as δ). According to the finite element simulation model of this embodiment, it can be obtained that when other conditions are fixed, the buckling load P cr,Ec The relationship between the cross-sectional area ratio δ is as follows: Figure 2 As shown. Figure 2 It can be seen from the figure that when the cross-sectional area ratio δ is 3.5:6.5, the buckling load reaches the maximum value. Therefore, this embodiment uses this cross-sectional area ratio to calculate the equivalent elastic modulus of the stiffened wall panel section.

[0070] S3: Establish the constitutive equation of the bearing capacity of the composite reinforced wall panel structure:

[0071] P cr,E =cπ 2 Dmin / b st 2

[0072] in:

[0073] c: fixed coefficient; b: fixed coefficient st : Spacing between long girders; minimum bending stiffness D min =E eqv t adj w 3 eff / 12;

[0074] S4: Modified constitutive equation using effective cross-sectional area and shear modulus:

[0075] P cr,Ec =P cr,E / (1+P cr,E / A eff G)

[0076] Where P cr,Ec is the corrected buckling load, G is the transverse elastic shear modulus;

[0077] S5: Determine the spacing of the long girders in the composite stiffened panel structure:

[0078] According to the constitutive equation modified in step S4, plot b st -P cr,Ec In this embodiment, the t is plotted based on a known long stringer and skin shape. adj -P cr,Ec 、b st -P cr,Ec The curve diagram is as follows Figure 3 As shown (t adj and b st There is a relationship as shown in formula (1).

[0079] exist Figure 3 In the curve diagram, in region I, due to the large spacing between the long girders and the relatively small skin thickness, the stiffened panel structure is the overall buckling of the skin; in region III, due to the small spacing between the long girders and the relatively large skin thickness, the stiffened panel structure is the buckling of the long girders' webs. In aircraft design, overall buckling of the skin and buckling of the long girders' webs are generally not allowed, so it is recommended to select the long girders' spacing from region II where the above two types of buckling never occur.

[0080] According to the materials and cross-sectional dimensions of the long stringer and skin to be studied, the above-mentioned areas I and III, i.e., the specific areas where the overall buckling of the skin or the buckling of the web of the long stringer occurs, are stThe values ​​are obtained by the finite element simulation model in this embodiment. They can also be obtained by some test methods, or by using empirical values. When selecting the long-string spacing according to the load value and the curve graph, the long-string spacing value close to the middle of the curve can also be selected.

[0081] According to the required bearing capacity (buckling load) of the composite reinforced wall panel structure, the long stringer spacing b is determined by using a curve diagram st The value of makes the buckling load corresponding to the long stringer spacing in the curve diagram greater than the actual required bearing capacity.

[0082] The above content explains the specific implementation of the present invention. In order to verify the accuracy of the constitutive equation of the present invention, a series of T-shaped and I-shaped long stringer test pieces were designed based on finite element software. The key parameters of all 54 test pieces of reinforced composite panels are shown in Table 3. In order to make the results easier to compare, the test pieces do not use long stringers and skins of fixed shapes, but introduce three variables: long stringer spacing, effective thickness, and web height. The relationship between them is shown in equations (1) and (2). In each set of data, only one variable changes.

[0083] Table 3 Parameters of different long stringer sections

[0084]

[0085]

[0086] Finite element analysis of 54 test specimen models will yield a large number of analysis results. Figure 4 and Figure 5 Only a few representative groups are shown. The force cloud diagram is the force mode obtained by finite element analysis. cr,Ec is the buckling load value calculated according to the constitutive equation (6) of the present invention. The buckling load result obtained according to the finite element result is as follows Figure 6 As shown, it corresponds well with the calculation results of the constitutive equation.

[0087] In order to further verify the accuracy of the calculation results of the constitutive equation, A2(t adj =1.8mm) and B2(t adj =1.8mm) as an example, Figure 7 The load-displacement curves of two test pieces obtained according to finite element analysis and actual experimental analysis are shown, and the buckling load and failure load can be seen from the curves. As shown in Table 4, the buckling load results of the experimental (Test) analysis, finite element (FEM) analysis and the engineering algorithm of the constitutive equation proposed in the present invention are compared. From the comparison results, it can be seen that the maximum error of the buckling load calculated by the constitutive equation of the present invention is 4.5%, which is within the range allowed by engineering applications and is in good agreement with the experimental value and the finite element analysis value.

[0088] Table 4 Comparison of analysis results

[0089]

[0090] The above results show that the constitutive equation (Equation (6)) proposed in the present invention for calculating the buckling load based on the spacing between long girders corresponds well to the finite element results and the results of actual engineering experiments. By applying the constitutive equation to engineering design according to the method of the present invention, the appropriate spacing between long girders can be directly obtained according to the required bearing capacity of the stiffened wall panel, which greatly reduces the test cost.

[0091] The above is only an implementation method of the present invention. It should be pointed out that for technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for determining the spacing of long girders in a composite material reinforced wall panel structure, characterized in that: The following steps are involved: S1: The effective thickness t of the long stringer section is obtained through the long stringer section parameters adj 、Effective width w eff and effective cross-sectional area A eff The expression of is calculated as: t adj =t skin +(2t sf1 E sf1 b sf1 +2t sf2 E sf2 b sf2 +t fb E fb b fb ) / (b st E skin ) w eff =0.95t adj / (e c ) 1 / 2 A eff =w eff t adj +h web t web Among them, t skin : Skin thickness; t sf1 : Thickness of the top edge of the long stringer; E sf1 : elastic modulus of the upper edge of the long stringer; b sf1 : Width of the top edge of the long stringer; t sf2 : Thickness of the lower edge of the long stringer; E sf2 : elastic modulus of the lower edge of the long stringer; b sf2 : Width of the lower edge of the long stringer; t fb : Thickness of the lower edge strip pad; E fb : Elastic modulus of the lower edge strip pad; b fb : Width of lower edge strip pad; E skin : axial elastic modulus of the skin; ε c : Material compressive limit strain; h web : web height; t web : web thickness; b st : Spacing of long beams; S2: Calculate the equivalent elastic modulus E of the stiffened panel section eqv ; S3: Establish the constitutive equation of the bearing capacity of composite reinforced wall panels; P cr,E =cπ 2 D min / b st 2 in: c: fixed coefficient; b: fixed coefficient st : Spacing between long girders; minimum bending stiffness D min =E eqv t adj w 3 eff / 12; S4: Modification of constitutive equation using effective cross-sectional area and shear modulus; P cr,Ec =P cr,E / (1+P cr,E / A eff G) Where P cr,Ec is the corrected buckling load, G is the transverse shear modulus of the material; S5: Determine the spacing of long girders in composite stiffened panel structures; According to the constitutive equation modified in step S4, plot b st -P cr,Ec The curve diagram is used to determine the spacing b of the long girders according to the required bearing capacity of the composite reinforced wall panel structure. st The value of .

2. The method for determining the spacing between long girders of a composite material reinforced wall panel structure according to claim 1, characterized in that: The ratio of the cross-sectional area of ​​the stringer to the skin is A stringer / A skin The value range is 3:7~4:

6.

3. The method for determining the spacing between long girders of a composite material reinforced wall panel structure according to claim 1, characterized in that: In the step S3, the fixing coefficient c is determined according to the fixing form of the two ends of the composite material reinforced wall panel under the concentrated axial load.

4. The method for determining the spacing between long girders of a composite material reinforced wall panel structure according to claim 3, characterized in that: When the two ends of the reinforced wall panel are fixed by simply supporting at both ends, the fixing coefficient c is 1; when it is fixed by fixed supports at both ends, the fixing coefficient c is 4; when it is fixed by simply supporting at one end and fixed at the other end, the fixing coefficient c is 2.05; when it is fixed by fixed support at one end and free at the other end, the fixing coefficient c is 0.

25.

5. The method for determining the spacing between long girders of a composite material reinforced wall panel structure according to claim 1, characterized in that: In step S5, after determining the long stringer spacing b st When selecting the value of , ensure that the selected stringer spacing will not cause the overall skin buckling of the stiffened wall panel and the stringer web buckling.

6. The method for determining the spacing between long girders of a composite material reinforced wall panel structure according to claim 5, characterized in that: In step S5, the spacing b between the long girders that can cause the stiffened panel to buckle as a whole and the web of the long girders to buckle is determined. st The value range of b st -P cr,Ec Remove this value range from the curve graph and use the remaining curve area to determine the long stringer spacing b according to the required bearing capacity of the composite reinforced wall panel structure. st The value of .

7. The method for determining the spacing between long girders of a composite material reinforced wall panel structure according to claim 1, characterized in that: In step S2, the equivalent elastic modulus E of the reinforced wall panel section eqv The calculation method is: AND eqv ×(A stringer +A skin )=And stringer ×A stringer +E skin ×A skin Among them, E stringer and E skin is the axial equivalent elastic modulus of the stringer and skin, A stringer and A skin is the cross-sectional area of ​​the stringer and skin.

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