Ultimate strength prediction method for multilevel composite structures

Abstract

The application provides a multilayer composite structure ultimate strength theory prediction method, including the following steps: inputting multilayer cylindrical shell structure parameters; performing fiber layer equivalent calculation and interlayer plate equivalent calculation; taking a certain width of a beam band from the cylindrical shell, regarding the interlayer beam band as a laminated plate composed of three different materials to establish an equivalent mechanical model, and performing ultimate strength calculation; and outputting the theoretical strength calculation result. The calculation result obtained by the method is close to the structure obtained by the finite element method, and compared with the finite element method, the method has fewer input parameters, does not need to consume a large amount of time cost for assigning material properties, and the prediction efficiency is effectively improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of ultimate strength prediction, in particular to a multilayer composite structure ultimate strength theoretical prediction method. BACKGROUND

[0002] It is known that in the process of composite finite element analysis, due to the complexity of the composite structure and the anisotropy of the material, it is often necessary to input the layer information when defining the material properties, especially when analyzing a composite part with more layers or a more complex structure, a large amount of time cost is required to assign material properties, and the prediction efficiency is low. Traditional multilayer plates (two thin plates with a thick core layer in between) are generally analyzed using multilayer plate theory. However, for multilayer composite cylindrical shells, unlike traditional sandwich plates (two thin plates with a thick core layer in between), which are a new type of composite structure, sandwich plate theory cannot be used for analysis. SUMMARY

[0003] Therefore, the present application provides a multilayer composite structure ultimate strength theoretical prediction method to solve the technical problem of the multilayer composite cylindrical shell being unable to use sandwich plate theory for analysis in the background art.

[0004] The technical scheme of the present application is as follows:

[0005] The present application provides a multilayer composite structure ultimate strength theoretical prediction method, comprising the following steps:

[0006] Inputting multilayer cylindrical shell structure parameters;

[0007] Performing fiber layer equivalent calculation and sandwich plate equivalent calculation;

[0008] Taking a certain width of beam strip from the cylindrical shell, regarding the sandwich beam strip as a laminated plate composed of three different materials to establish an equivalent mechanical model, and performing ultimate strength calculation;

[0009] Outputting the theoretical strength calculation results.

[0010] On the basis of the above technical scheme, preferably, the sandwich plate equivalent calculation comprises: equivalent to a single layer plate, according to the equivalent bending strength of the sandwich beam strip to obtain the equivalent bending modulus, the equivalent bending strength D 11 According to the following formula;

[0011] ;

[0012] In the formula, D 11 is the equivalent bending strength of the sandwich beam strip, D ij is the equivalent bending strength of the sandwich plate, i and j can be 1, 2, 3. is a two-dimensional stiffness matrix; and is a coordinate value along the thickness direction of the laminate.

[0013] On the basis of the above technical solutions, preferably, the fiber layer equivalent calculation comprises: equivalent of the multi-layer fiber to a layer of anisotropic material based on the laminate equivalent theory, and calculation of the material parameters after the equivalent of the carbon fiber laminate.

[0014] On the basis of the above technical solutions, preferably, the beam strip of a certain width taken from the cylindrical shell is considered as an equivalent mechanical model of a laminate composed of three different materials, comprising: taking the pressure-resistant shell plate beam strip structure with rib support at both ends as the equivalent mechanical model.

[0015] On the basis of the above technical solutions, preferably, the ultimate strength is calculated according to the following formula:

[0016] ;

[0017] In the formula, ω x=0 is the deflection of the midpoint at the midspan; P is the external pressure; R is the radius of the cylindrical shell; E is the equivalent bending modulus; t is the equivalent wall thickness; is the Poisson's ratio; and ε4 is the fourth auxiliary function value.

[0018] On the basis of the above technical solutions, preferably, the input of the multi-layer cylindrical shell structure parameters comprises: input of the deflection ω x=0 of the midpoint at the midspan, the radius R of the cylindrical shell, the equivalent bending modulus E, the equivalent wall thickness t, the Poisson's ratio and the fourth auxiliary function value ε4.

[0019] On the basis of the above technical solutions, preferably, before the output of the theoretical strength calculation result, further comprising: considering the influence of defects on the structure, introducing a defect influence parameter, combining the ultimate strength obtained by calculation with the defect influence parameter to obtain the final theoretical strength calculation result.

[0020] On the basis of the above technical solutions, preferably, the introduction of the defect influence parameter comprises: obtaining a first buckling load according to the buckling load curve of the structure after adding defects, obtaining a second buckling load according to the first-order overall buckling contour of the structure without adding defects, and the defect influence parameter is the ratio of the first buckling load to the second buckling load.

[0021] On the basis of the above technical solutions, preferably, the method further comprises: comparing the output theoretical strength calculation result with the finite element value obtained by finite element calculation, and judging whether the error of the two is within 15%.

[0022] Preferably, the method further comprises: verifying the universality of the method by inputting the structure parameters of a multilayer cylindrical shell of different sizes and different composite layer cyclic layups.

[0023] The multilayer composite structure ultimate strength theory prediction method has the following beneficial effects:

[0024] (1) The equivalent calculation of the fiber layer and the equivalent calculation of the sandwich plate are performed; a certain width of beam strip is taken from the cylindrical shell, the sandwich beam strip is regarded as a laminated plate composed of three different materials to establish an equivalent mechanical model, and the ultimate strength calculation is performed, the calculation result is close to the structure obtained by the finite element method, and compared with the finite element method, the method has fewer input parameters, does not need to consume a large amount of time cost for assigning material properties, and the prediction efficiency is effectively improved;

[0025] (2) The sandwich plate is equivalent to a single-layer plate, the equivalent bending modulus is obtained according to the equivalent bending strength of the sandwich beam strip, and the equivalent bending strength D 11 According to the formula, the calculated equivalent bending modulus is used for the following formula, and is prepared for the subsequent ultimate strength calculation;

[0026] (3) The ultimate strength is calculated by the formula, only the deflection ω x=0 , the radius of the cylindrical shell R, the equivalent bending modulus E, the equivalent wall thickness t, the Poisson's ratio , and the auxiliary function value four ε4 are substituted into the formula to calculate the ultimate strength P, compared with the finite element method, the method has fewer input parameters, and does not need to consume a large amount of time cost for assigning material properties;

[0027] (4) Before the output theoretical strength calculation result, it further comprises: considering the influence of defects on the structure, introducing a defect influence parameter, combining the calculated ultimate strength with the defect influence parameter to obtain the final theoretical strength calculation result, improving the accuracy of the output theoretical strength calculation result, and improving the reliability of the prediction;

[0028] (5) The universality of the method is verified by inputting the structure parameters of a multilayer cylindrical shell of different sizes and different composite layer cyclic layups, and a conclusion that the method has a certain universality for multilayer composite structures is obtained, and the reliability and accuracy of the method are improved. BRIEF DESCRIPTION OF DRAWINGS

[0029] In order to make the technical solutions in the embodiments of the present application or the prior art clearer, the accompanying drawings needed in the embodiments or prior art description will be briefly introduced. Obviously, the accompanying drawings in the following description only need to be some embodiments of the present application, and other drawings can be obtained by those of ordinary skill in the art without any creative work.

[0030] Figure 1 A flowchart of the ultimate strength prediction method for the multi-level composite structure in the embodiments of the present application is shown in the figure.

[0031] Figure 2 A schematic diagram of the principle of establishing an equivalent mechanical model for the cylindrical shell in the embodiments of the present application is shown in the figure.

[0032] Figure 3 A structural diagram of the equivalent mechanical model in the embodiments of the present application is shown in the figure.

[0033] Figure 4 A schematic diagram of the instability load curve of the structure after adding a defect in the embodiments of the present application is shown in the figure.

[0034] Figure 5 A schematic diagram of the first-order overall instability cloud chart of the structure without adding a defect in the embodiments of the present application is shown in the figure. DETAILED DESCRIPTION

[0035] The technical solutions in the embodiments of the present application will be described clearly and completely below in conjunction with the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments. Based on the embodiments of the present application, all other embodiments obtained by those of ordinary skill in the art without any creative work fall within the scope of the present application. EMBODIMENT

[0036] It should be noted that in the present embodiment, a long beam with a certain width (an arc of ) in the cylindrical shell is taken as the research object. The cross-sectional parameters of the long beam are as follows: : beam length, 1000 mm; : steel layer thickness, 2.9 mm; : panel width, 36 mm; : panel height, 7 mm; : web width, 6.4 mm; : web height, 40 mm; : elastic modulus of steel, 210000 MPa; : elastic modulus of damping material, 2362 MPa; : damping layer thickness, 2 mm; Equivalent elastic modulus of the post-carbon fiber in the length direction of the beam, 36511 MPa Thickness of the composite material layer, 24 mm.

[0037] Referring to Figures 1-5 The embodiment of the present application proposes a multilayer composite structure ultimate strength theoretical prediction method, including the following steps:

[0038] Step S1: input the multilayer cylindrical shell structure parameters;

[0039] Step S2: perform fiber layer equivalent calculation and sandwich plate equivalent calculation;

[0040] Step S3: take a certain width of beam strip from the cylindrical shell, and consider the sandwich beam strip as a laminated plate composed of three different materials to establish an equivalent mechanical model and perform ultimate strength calculation;

[0041] Specifically, as shown in Figure 2 A certain width of beam strip is taken from the cylindrical shell, and the sandwich beam strip is considered as a laminated plate composed of three different materials, namely rigid, polyurethane and composite material;

[0042] Step S4: output the theoretical strength calculation result.

[0043] In some embodiments, in step S2, the fiber layer equivalent calculation includes: based on the equivalent theory of laminated plates, the multilayer fiber is equivalent to a layer of anisotropic material, and the material parameters of the equivalent carbon fiber laminated plate are calculated.[( 20°) (90°) 3] cyclically layered carbon fiber laminated plate equivalent material parameters are shown in Table 1.

[0044] Table 1

[0045]

[0046] In Table 1, E1 is the tensile modulus in the 1 direction; E2 is the tensile modulus in the 2 direction; E3 is the tensile modulus in the 3 direction; u12 is the Poisson's ratio in the 12 direction; u13 is the Poisson's ratio in the 13 direction; u23 is the Poisson's ratio in the 23 direction; G12 is the shear modulus in the 12 direction; G13 is the shear modulus in the 13 direction; G23 is the shear modulus in the 23 direction.

[0047] In some embodiments, in step S2, the sandwich plate equivalent calculation includes: equivalent to a single layer plate, and according to the equivalent bending strength of the sandwich beam strip, the equivalent bending modulus is obtained, and the equivalent bending strength D 11 According to formula (1);

[0048] (1);

[0049] In formula (1), D11 D is the equivalent bending strength of the sandwich beam strip ij i, j can be 1, 2, 3 is a two-dimensional stiffness matrix and is the coordinate value of the laminate along the thickness direction.

[0050] The specific calculation method is described in the record of Composite Mechanics, which will not be repeated here. Substituting the parameters into formula (1), the calculated .

[0051] According to formula (2), the equivalent bending modulus E is calculated as

[0052] M / E=D 11 (2);

[0053] In formula (2), M is the bending moment, E is the equivalent bending modulus, and D 11 is the equivalent bending strength of the sandwich beam strip.

[0054] Substituting the bending moment M and the equivalent bending strength D 11 into formula (2), the equivalent bending modulus E=80407MPa is calculated.

[0055] In some embodiments, the beam strip taken from the cylindrical shell is considered as a sandwich beam strip, and an equivalent mechanical model is established for a laminate composed of three different materials, including: taking the beam strip structure with two end rib supports as the equivalent mechanical model. Specifically, as shown in Figure 3 the intercostal beam strip mechanical calculation model is obtained, which is taken as the equivalent mechanical model. The beam strip taken from the cylindrical shell satisfies the following deflection differential equation:

[0056] (3);

[0057] In formula (3), D 11 is the equivalent bending strength of the sandwich beam strip; ω is the deflection; P is the external pressure; R is the radius of the cylindrical shell; E is the equivalent bending modulus; t is the equivalent wall thickness; is the Poisson's ratio.

[0058] In some embodiments, the ultimate strength is calculated according to formula (4);

[0059] (4);

[0060] In formula (4), D 11 is the equivalent bending strength of the sandwich beam strip; ω x=0δ is the deflection at the mid-point of the span; P is the external pressure; R is the radius of the cylindrical shell; E is the equivalent bending modulus; t is the equivalent wall thickness; ν is the Poisson's ratio; ε4 is the auxiliary function value four.

[0061] The ε4 in equation (4) is calculated by the following equation:

[0062] (5);

[0063] In equation (5), ε1 is the auxiliary function value one; F2(u1, u2) is function two;

[0064] (6);

[0065] In equation (6), l L is the beam length; t is the equivalent wall thickness; A is the sectional area of the profile; F1(u1, u2) is function one;

[0066] (7);

[0067] In equation (7), γ is the ratio of the axial mid-surface stress to the buckling Euler stress of the axial compression; u 1 is the intermediate parameter one; u 2 is the intermediate parameter two; F5(u1, u2) is function five;

[0068] (8);

[0069] (9);

[0070] (10);

[0071] In equation (10), u is the conversion parameter;

[0072] (11);

[0073] (12);

[0074] In equation (12), l l is the rib spacing;

[0075] (13);

[0076] In equation (13), γ is the ratio of the axial mid-surface stress to the buckling Euler stress of the axial compression; is the axial mid-surface stress; is the buckling Euler stress of the axial compression.

[0077] Substitute equation (4) into equation (13), E = 80407 MPa, t = 28.9 mm, = 1000 mm, R = 435.5 mm, = 0.3, = 120, ω x=0 = 7 into the above equation, the equation is solved to get P = 102 MPa. At this time, the calculation result does not consider the influence of defects.

[0078] In some embodiments, the input multi-layer cylindrical shell structure parameters include: inputting the deflection ω x=0 of the midpoint at the midspan, the radius R of the cylindrical shell, the equivalent bending modulus E, the equivalent wall thickness t, the Poisson's ratio and the auxiliary function value four ε4. The ultimate strength is calculated by the formula. Only the deflection ω x=0 of the midpoint at the midspan, the radius R of the cylindrical shell, the equivalent bending modulus E, the equivalent wall thickness t, the Poisson's ratio and the auxiliary function value four ε4 are substituted into the formula, the ultimate strength P can be calculated. Compared with the finite element method, the input parameters are less, and a large amount of time cost is not needed to assign material properties.

[0079] In some embodiments, before the output theoretical strength calculation result, it further includes: considering the influence of defects on the structure, introducing a defect influence parameter, combining the ultimate strength calculated with the defect influence parameter to obtain the final theoretical strength calculation result. By introducing the defect influence parameter, combining the ultimate strength calculated with the defect influence parameter to obtain the final theoretical strength calculation result, the accuracy of the output theoretical strength calculation result can be improved, and the reliability of the prediction can be improved.

[0080] In some embodiments, the introduction of the defect influence parameter includes: obtaining a first buckling load according to the buckling load curve of the structure after adding defects (strength failure has occurred before buckling), obtaining a second buckling load according to the first-order overall buckling cloud atlas of the structure without adding defects, and the defect influence parameter is the ratio of the first buckling load to the second buckling load. Figure 4 The buckling load curve of the structure after adding defects (strength failure has occurred before buckling) is given, and the first buckling load is 28.5 MPa; Figure 5 The first-order overall buckling cloud atlas of the structure without adding defects is given, and the second buckling load is 135 MPa.

[0081] In some embodiments, the method further includes: comparing the output theoretical strength calculation result with the finite element value calculated by the finite element method, and judging whether the error of the two is within 15%. According to the finite element method, the influence of defects on the structure is (the ratio of the first buckling load to the second buckling load), so the ultimate bearing of the structure after adding defects is actually: The limit bearing P * As the theoretical strength calculation structure output, the error is 11.0%, and the error between the theoretical solution and the finite element result is within 15%.

[0082] In some embodiments, the method further comprises: by inputting the multi-layer cylindrical shell structure parameters of different sizes and different composite material layer cycle lay-up, the method is verified for universality.

[0083] The universality is explained as follows in combination with Comparative Example 1 and Comparative Example 2:

[0084] Comparative Example 1

[0085] Different from the embodiment: the composite material layer [(70° / -70°)2(35° / -35°)3] cycle lay-up, and other parameters are the same.

[0086] The running result is P=97.4MPa, and the influence of the defect on the structure is The theoretical limit bearing P of the structure after adding the defect is * 21.6MPa, and the error compared with the finite element value (23.7MPa) is 9.7%.

[0087] Comparative Example 2

[0088] Different from Comparative Example 1: l l =800, t=17.8, and other parameters are the same as those in Comparative Example 1.

[0089] The running result is 85.4MPa, and the influence of the defect is The theoretical limit bearing P of the structure after adding the defect is * 17.2MPa, and the error compared with the finite element value (16.1MPa) is 6.9%.

[0090] It can be seen from Comparative Example 1, Comparative Example 2 and the embodiment that the theoretical calculation method has certain universality for multi-layer composite structures.

[0091] The above only describes the preferred embodiments of the present application and is not used to limit the present application, and any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the protection scope of the present application.

Claims

1. A theoretical prediction method for the ultimate strength of multi-level composite structures, characterized in that, Includes the following steps: Input the parameters for the multi-layer cylindrical shell structure; Perform equivalent calculations for the fiber layer and the sandwich panel; The equivalent calculation of the sandwich panel includes: treating the sandwich panel as a single-layer plate, obtaining the equivalent bending modulus based on the equivalent bending strength of the sandwich beam strip, and the equivalent bending strength D. 11 It is calculated using the following formula; In the formula, D 11 D represents the equivalent bending strength of the sandwich beam strip. ij For the equivalent bending strength of the sandwich panel, i and j can both be 1, 2, or 3; Q ij The stiffness matrix is ​​two-dimensional; z k With z k-1 These are the coordinate values ​​of the laminate along its thickness direction. The equivalent calculation of the fiber layer includes: based on the equivalent theory of laminates, the multi-layer fiber is equivalent to a single layer of anisotropic material, and the material parameters of the carbon fiber laminate after the equivalent calculation are calculated. A beam strip of a certain width is taken from the cylindrical shell. The sandwich beam strip is regarded as a laminated plate composed of three different materials to establish an equivalent mechanical model and perform ultimate strength calculation. Output the theoretical strength calculation results.

2. The method for theoretically predicting the ultimate strength of multi-level composite structures as described in claim 1, characterized in that, The method of taking a beam strip of a certain width from the cylindrical shell and establishing an equivalent mechanical model by treating the sandwich beam strip as a laminate composed of three different materials includes: taking the pressure-resistant shell plate beam strip structure with ribs at both ends as the equivalent mechanical model.

3. The method for theoretically predicting the ultimate strength of multi-level composite structures as described in claim 2, characterized in that, The ultimate strength is calculated according to the following formula; In the formula, ω x＝0 denoted as , where is the deflection at the midpoint of the span; P is the external pressure; R is the radius of the cylindrical shell; E is the equivalent bending modulus; t is the equivalent wall thickness; μ is Poisson's ratio; and ε4 is the auxiliary function value.

4. The method for theoretically predicting the ultimate strength of multi-level composite structures as described in claim 3, characterized in that, The input parameters for the multi-layer cylindrical shell structure include: the deflection ω at the midpoint of the span. x＝0 The cylindrical shell radius R, equivalent bending modulus E, equivalent wall thickness t, Poisson's ratio μ, and auxiliary function value ε4.

5. The method for theoretically predicting the ultimate strength of multi-level composite structures as described in claim 1, characterized in that, Before outputting the theoretical strength calculation result, the method further includes: considering the influence of defects on the structure, introducing defect influence parameters, and combining the calculated ultimate strength with the defect influence parameters to obtain the final theoretical strength calculation result.

6. The method for theoretically predicting the ultimate strength of multi-level composite structures as described in claim 5, characterized in that, The introduced defect influence parameter includes: obtaining a first instability load based on the instability load curve after adding defects to the structure, and obtaining a second instability load based on the first-order overall instability cloud diagram of the structure without defects. The defect influence parameter is the ratio of the first instability load to the second instability load.

7. The method for theoretically predicting the ultimate strength of multi-level composite structures as described in any one of claims 1-6, characterized in that, The method also includes comparing the output theoretical strength calculation results with the finite element values ​​obtained by finite element calculation, and determining whether the error between the two is within 15%.

8. The method for theoretically predicting the ultimate strength of multi-level composite structures as described in any one of claims 1-6, characterized in that, The method also includes: verifying the universality of the method by inputting parameters of multi-layer cylindrical shell structures with different sizes and different composite material layer cyclic layups.

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