Theoretical forecasting method for ultimate strength of multi-level composite structure

Abstract

The invention provides a theoretical forecasting method for ultimate strength of a multi-layer composite structure. The method comprises the following steps: inputting parameters of a multi-layer cylindrical shell structure; fiber layer equivalent calculation and sandwich plate equivalent calculation are carried out; a beam belt with a certain width is taken from the cylindrical shell, the interlayer beam belt is regarded as a laminated plate composed of three different materials to establish an equivalent mechanical model, and ultimate strength calculation is carried out; and outputting a theoretical strength calculation result. A calculation result obtained by the method is close to a structure obtained by a finite element, and compared with a finite element method, the method has the advantages that input parameters are fewer, a large amount of time cost for endowing material attributes does not need to be consumed, and the prediction efficiency is effectively improved.

Description

Technical Field

[0001] The invention relates to the technical field of ultimate strength prediction, and in particular to a theoretical prediction method for the ultimate strength of a multi-level composite structure. Background Art

[0002] As we all know, in the process of finite element analysis of composite materials, due to the complexity of composite material structures and the anisotropy of materials, it is often necessary to input tedious ply information when defining material properties. Especially when analyzing composite parts with more plies or more complex structures, a lot of time is required to assign material properties, and the prediction efficiency is low. Traditional multilayer plates (two layers of thin plates with a thicker core layer in between) are generally analyzed using multilayer plate theory. However, for multilayer composite cylindrical shells, unlike traditional sandwich plates (two layers of thin plates with a thicker core layer in between), it is a new type of composite structure and cannot be analyzed using sandwich plate theory. Summary of the invention

[0003] In view of this, the present invention proposes a theoretical prediction method for the ultimate strength of a multi-level composite structure to solve the technical problem that the multi-level composite cylindrical shell proposed in the above background technology cannot be analyzed using the sandwich plate theory.

[0004] The technical solution of the present invention is achieved in this way:

[0005] The present invention provides a method for theoretically predicting the ultimate strength of a multi-level composite structure, comprising the following steps:

[0006] Input the parameters of the multilayer cylindrical shell structure;

[0007] Carry out equivalent calculations of fiber layers and sandwich panels;

[0008] Take a beam strip of a certain width from the cylindrical shell, regard the sandwich beam strip as a laminate composed of three different materials, establish an equivalent mechanical model, and perform ultimate strength calculation;

[0009] Output theoretical strength calculation results.

[0010] On the basis of the above technical solution, preferably, the sandwich plate equivalent calculation comprises: treating the sandwich plate as a single-layer plate, obtaining an equivalent bending modulus according to the equivalent bending strength of the sandwich beam, and obtaining an equivalent bending strength D 11 Calculated according to the following formula;

[0011]

[0012] Where D 11 is the equivalent bending strength of the sandwich beam, D ij is the equivalent bending strength of the sandwich plate, i and j can be 1, 2, or 3; Qij is the two-dimensional stiffness matrix; z k With z k-1 is the coordinate value of the laminate along the thickness direction.

[0013] On the basis of the above technical solution, preferably, the fiber layer equivalent calculation comprises: based on the laminate equivalent theory, multiple layers of fibers are equivalent to a layer of anisotropic material, and the equivalent material parameters of the carbon fiber laminate are calculated.

[0014] On the basis of the above technical solution, preferably, a beam strip of a certain width is taken from the cylindrical shell, and the sandwich beam strip is regarded as a laminate composed of three different materials to establish an equivalent mechanical model, including: taking a pressure shell plate beam strip structure with rib supports at both ends as an equivalent mechanical model.

[0015] On the basis of the above technical solution, 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 mid-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 the Poisson's ratio; ε4 is the auxiliary function value four.

[0018] On the basis of the above technical solution, preferably, the input of multilayer cylindrical shell structure parameters includes: inputting the deflection ω of the midpoint at the mid-span x＝0 , cylindrical shell radius R, equivalent bending modulus E, equivalent wall thickness t, Poisson's ratio μ and auxiliary function value ε4.

[0019] On the basis of the above technical solution, preferably, before outputting the theoretical strength calculation result, it also 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.

[0020] On the basis of the above technical solution, preferably, the introduced defect influence parameter includes: obtaining a first instability load according to an instability load curve after the structure is defective, and obtaining a second instability load according to a first-order overall instability cloud diagram of the structure without defects, and the defect influence parameter is the ratio of the first instability load to the second instability load.

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

[0022] On the basis of the above technical solution, preferably, the method further comprises: verifying the universality of the method by inputting structural parameters of multilayer cylindrical shells of different sizes and cyclic lay-ups of different composite material layers.

[0023] Compared with the prior art, the theoretical prediction method for the ultimate strength of multi-layer composite structures of the present invention has the following advantages:

[0024] Beneficial effects:

[0025] (1) By performing equivalent calculations of the fiber layer and the sandwich plate, a beam strip of a certain width is taken from the cylindrical shell, and the sandwich beam strip is regarded as a laminate composed of three different materials to establish an equivalent mechanical model, and the ultimate strength calculation is performed. The calculation results are close to the structure obtained by the finite element method. Compared with the finite element method, this method has fewer input parameters and does not require a lot of time to assign material properties, so its prediction efficiency is effectively improved;

[0026] (2) By equating the sandwich plate to a single-layer plate, the equivalent bending modulus and equivalent bending strength D are obtained according to the equivalent bending strength of the sandwich beam. 11 According to the formula, the calculated equivalent bending modulus is used for the following formula to prepare for the subsequent ultimate strength calculation;

[0027] (3) The ultimate strength is calculated by the formula: x＝0 , cylindrical shell radius R, equivalent bending modulus E, equivalent wall thickness t, Poisson's ratio μ, and auxiliary function value ε4 are substituted into the formula to calculate the ultimate strength P. Compared with the finite element method, this method has fewer input parameters and does not require a lot of time to assign material properties.

[0028] (4) before outputting the theoretical strength calculation result, the method further includes: considering the influence of defects on the structure, introducing defect influence parameters, combining the calculated ultimate strength with the defect influence parameters to obtain the final theoretical strength calculation result, thereby improving the accuracy of the output theoretical strength calculation result and the reliability of the prediction;

[0029] (5) The universality of this method is verified by inputting the structural parameters of multilayer cylindrical shells with different sizes and cyclic lay-ups of different composite material layers. It is concluded that this method has a certain universality for multilayer composite structures, thereby improving the reliability and accuracy of the method. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0031] Figure 1 Schematic diagram of the process of the theoretical prediction method of the ultimate strength of a multi-level composite structure in an embodiment of the present invention;

[0032] Figure 2 A schematic diagram of the principle of establishing an equivalent mechanical model for a cylindrical shell in an embodiment of the present invention;

[0033] Figure 3 is a structural schematic diagram of an equivalent mechanical model in an embodiment of the present invention;

[0034] Figure 4 It is a schematic diagram of an instability load curve after a defect is added to the structure in an embodiment of the present invention;

[0035] Figure 5 It is a schematic diagram of the first-order overall instability cloud diagram of the structure without defects in an embodiment of the present invention. DETAILED DESCRIPTION

[0036] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0037] Example

[0038] It should be noted that in this embodiment, a certain width (radian is ) is taken as the research object. The cross-sectional parameters of the long beam are as follows: l: beam length, 1000mm; t1: steel layer thickness, 2.9mm; a1: panel width, 36mm; b1: panel height, 7mm; a2: web width, 6.4mm; b2: web height, 40mm; E s : Elastic modulus of steel, 210000MPa; E r : elastic modulus of damping material, 2362MPa; t r : Damping layer thickness, 2mm; E c : The elastic modulus of the carbon fiber along the length direction of the beam after equivalent, 36511MPa; t c : Composite material layer thickness, 24mm.

[0039] Reference Figure 1-5 As shown, the embodiment of the present invention proposes a theoretical prediction method for the ultimate strength of a multi-level composite structure, comprising the following steps:

[0040] Step S1: input multilayer cylindrical shell structure parameters;

[0041] Step S2: Perform fiber layer equivalent calculation and sandwich plate equivalent calculation;

[0042] Step S3: Take a beam strip of a certain width from the cylindrical shell, regard the sandwich beam strip as a laminate composed of three different materials to establish an equivalent mechanical model, and perform ultimate strength calculation;

[0043] Specifically, Figure 2 As shown, a beam strip of a certain width is taken from the cylindrical shell, and the sandwich beam strip is regarded as a laminate composed of three different materials, namely steel, polyurethane and composite material;

[0044] Step S4: Output theoretical strength calculation results.

[0045] In some embodiments, in step S2, the fiber layer equivalent calculation includes: based on the laminate equivalent theory, the multiple layers of fibers are equivalent to a layer of anisotropic material, and the material parameters of the carbon fiber laminate equivalent are calculated. The material parameters of the cyclically laid carbon fiber laminate equivalent are shown in Table 1.

[0046] Table 1

[0047] parameter E1 E2 E3 u12 u13 u23 G12 G13 G23 original 100000 8000 8000 0.21 0.21 0.3 4000 4000 3000 Equivalence 36511 63286 8602 0.0835 0.2692 0.2407 7678 3290 3578

[0048] In Table 1, E1 is the tensile modulus in direction 1; E2 is the tensile modulus in direction 2; E3 is the tensile modulus in direction 3; u12 is the Poisson's ratio in direction 12; u13 is the Poisson's ratio in direction 13; u23 is the Poisson's ratio in direction 23; G12 is the shear modulus in direction 12; G13 is the shear modulus in direction 13; G23 is the shear modulus in direction 23.

[0049] In some embodiments, in step S2, the sandwich plate equivalent calculation includes: treating the sandwich plate as a single-layer plate, obtaining an equivalent bending modulus according to the equivalent bending strength of the sandwich beam, and obtaining an equivalent bending strength D 11 Calculated according to formula (1);

[0050]

[0051] In formula (1), D 11 is the equivalent bending strength of the sandwich beam, D ij is the equivalent bending strength of the sandwich plate, i and j can be 1, 2, or 3; Q ij is the two-dimensional stiffness matrix; zk With z k-1 is the coordinate value of the laminate along the thickness direction.

[0052] Q ij The specific calculation method of is described in the "Composite Materials Mechanics" and will not be repeated here. Substituting the parameters into formula (1), the calculated D is 11 =161735271N*mm 2 .

[0053] The equivalent bending modulus E is calculated according to formula (2):

[0054] M / E=D 11 (2);

[0055] 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.

[0056] The bending moment M and the equivalent bending strength D 11 Substituting into formula (2), the equivalent bending modulus E=80407MPa is calculated.

[0057] In some embodiments, the method of taking a beam strip of a certain width from a cylindrical shell and treating the sandwich beam strip as a laminate composed of three different materials to establish an equivalent mechanical model includes: taking a pressure shell plate beam strip structure with rib supports at both ends as an equivalent mechanical model. Specifically, the following is obtained: Figure 3 The intercostal beam belt mechanical calculation model shown is used as an equivalent mechanical model. The beam belt taken out of the cylindrical shell satisfies the following deflection differential equation:

[0058]

[0059] In formula (3), D 11 is the equivalent bending strength of the sandwich beam; 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; μ is the Poisson's ratio.

[0060] In some embodiments, the ultimate strength is calculated according to formula (4);

[0061]

[0062] In formula (4), D 11 is the equivalent bending strength of the sandwich beam; ω x＝0 is the deflection of the midpoint at the mid-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 the Poisson's ratio; ε4 is the auxiliary function value four.

[0063] ε4 in formula (4) is calculated by the following formula:

[0064] ε4=ε1F2(u1,u2) (5);

[0065] In formula (5), ε1 is the auxiliary function value 1; F2(u1,u2) is function 2;

[0066]

[0067] In formula (6), l is the beam length; t is the equivalent wall thickness; A is the cross-sectional area of ​​the profile; F1(u1,u2) is function 1;

[0068]

[0069] In formula (7), γ is the ratio of the axial mid-plane stress to the axial compression instability Euler stress; u1 is the intermediate parameter one; u2 is the intermediate parameter two; F5(u1,u2) is function five;

[0070]

[0071] F5(u1,u2)=u2sh2u1+u1sin2u2 (9);

[0072]

[0073] In formula (10), u is the conversion parameter;

[0074]

[0075] In formula (12), l l is the rib spacing;

[0076]

[0077] In formula (13), γ is the ratio of the axial mid-plane stress to the axial compression instability Euler stress; is the axial mid-plane stress; is the axial compression instability Euler stress.

[0078] Combining equations (4) to (13), we can obtain E = 80407 MPa, t = 28.9 mm, l = 1000 mm, R = 435.5 mm, μ = 0.3, l l =120,ω x＝0 Substitute =7 into the above formula and solve the equation to get P=102MPa. At this time, the calculation result does not take into account the influence of defects.

[0079] In some embodiments, the input of multilayer cylindrical shell structure parameters includes: inputting the deflection ω of the midpoint at the mid-span x＝0, cylindrical shell radius R, equivalent bending modulus E, equivalent wall thickness t, Poisson's ratio μ and auxiliary function value ε4. The ultimate strength is obtained by calculating the formula, and only the deflection ω at the midpoint of the span is required. x＝0 , cylindrical shell radius R, equivalent bending modulus E, equivalent wall thickness t, Poisson's ratio μ, and auxiliary function value ε4 are substituted into the formula to calculate the ultimate strength P. Compared with the finite element method, this method has fewer input parameters and does not require a lot of time to assign material properties.

[0080] In some embodiments, 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. By introducing defect influence parameters, combining the calculated ultimate strength with the defect influence parameters 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.

[0081] In some embodiments, the introducing defect influence parameter includes: obtaining a first instability load according to an instability load curve after adding defects to the structure, and obtaining a second instability load according to a first-order overall instability cloud diagram of the structure without adding defects, and the defect influence parameter is the ratio of the first instability load to the second instability load. Figure 4 The instability load curve after the structure is defective is given (strength damage has occurred before instability), and the first instability load is 28.5MPa; Figure 5 The first-order overall instability cloud diagram of the structure without defects is given, and the second instability load is obtained to be 135MPa.

[0082] In some embodiments, the method further includes: comparing the output theoretical strength calculation result with the finite element value obtained by finite element calculation to determine whether the error between the two is within 15%. The finite element method is used to determine the influence of the defect on the structure. (the ratio of the first buckling load to the second buckling load), so the ultimate load of the structure after adding defects is actually: This limit load P * As the output of the theoretical strength calculation structure, the error is 11.0%, which satisfies that the error between the theoretical solution and the finite element result is within 15%.

[0083] In some embodiments, the method further includes: verifying the universality of the method by inputting structural parameters of a multilayer cylindrical shell with different sizes and cyclic lay-ups of different composite material layers.

[0084] The universality is described below in conjunction with Comparative Examples 1 and 2:

[0085] Comparative Example 1

[0086] The difference from the embodiment is that the composite material layers [(70° / -70°)2(35° / -35°)3] are cyclically laid, and the other parameters are the same.

[0087] The operating result is P = 97.4MPa, and the influence of the defect on the structure is Theoretical limit load of the structure after adding defects P * It is 21.6MPa, and the error of the finite element value (23.7MPa) compared with it is 9.7%.

[0088] Comparative Example 2

[0089] The difference from Comparative Example 1 is: l =800, t=17.8, other parameters are the same as those of Comparative Example 1.

[0090] The operating result is 85.4MPa, and the influence of defects calculated by finite element is Theoretical limit load of the structure after adding defects P * It is 17.2MPa, and the error of the finite element value (16.1MPa) compared with it is 6.9%.

[0091] It can be seen from the comparative examples 1 and 2 and the embodiment that the theoretical calculation method has a certain universality for multi-level composite structures.

[0092] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A theoretical prediction method for the ultimate strength of a multi-layer composite structure, characterized in that: The following steps are involved: Input the structural parameters of multilayer cylindrical shell; Carry out equivalent calculations of fiber layers and sandwich panels; Take a beam strip of a certain width from the cylindrical shell, regard the sandwich beam strip as a laminate composed of three different materials, establish an equivalent mechanical model, and perform ultimate strength calculation; Output theoretical strength calculation results.

2. The method for theoretical prediction of ultimate strength of multi-layer composite structure according to claim 1, characterized in that: The sandwich plate equivalent calculation includes: treating the sandwich plate as a single-layer plate, obtaining an equivalent bending modulus according to the equivalent bending strength of the sandwich beam, and obtaining an equivalent bending strength D 11 Calculated according to the following formula; Where D 11 is the equivalent bending strength of the sandwich beam, D ij is the equivalent bending strength of the sandwich plate, i and j can be 1, 2, or 3; Q ij is the two-dimensional stiffness matrix; z k With z k-1 is the coordinate value of the laminate along the thickness direction.

3. The method for theoretical prediction of ultimate strength of multi-layer composite structure according to claim 1, characterized in that: The fiber layer equivalent calculation comprises: based on the laminate equivalent theory, the multiple layers of fibers are equivalent to a layer of anisotropic material, and the equivalent material parameters of the carbon fiber laminate are calculated.

4. The method for theoretical prediction of ultimate strength of multi-layer composite structure according to claim 1, characterized in that: The method comprises taking a beam strip of a certain width from the cylindrical shell and treating the sandwich beam strip as a laminated plate composed of three different materials to establish an equivalent mechanical model, including taking a pressure shell plate beam strip structure with rib supports at both ends as an equivalent mechanical model.

5. The method for theoretical prediction of ultimate strength of multi-layer composite structure according to claim 4, characterized in that: The ultimate strength is calculated according to the following formula: In the formula, ω x＝0 is the deflection of the midpoint at the mid-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 the Poisson's ratio; ε4 is the auxiliary function value four.

6. The method for theoretical prediction of ultimate strength of multi-layer composite structure according to claim 5, characterized in that: The input multilayer cylindrical shell structure parameters include: inputting the deflection ω of the midpoint at the mid-span x＝0 , cylindrical shell radius R, equivalent bending modulus E, equivalent wall thickness t, Poisson's ratio μ and auxiliary function value ε4.

7. The method for theoretical prediction of ultimate strength of multi-layer composite structure according to 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.

8. The method for theoretically predicting the ultimate strength of a multi-layer composite structure according to claim 7, characterized in that: The introducing defect influence parameter comprises: obtaining a first instability load according to an instability load curve after the structure is defected, and obtaining a second instability load according to a first-order overall instability cloud diagram of the structure without defects, and the defect influence parameter is a ratio of the first instability load to the second instability load.

9. The method for theoretically predicting the ultimate strength of a multi-layer composite structure according to any one of claims 1 to 8, characterized in that: The method further includes: comparing the output theoretical strength calculation result with the finite element value obtained by finite element calculation to determine whether the error between the two is within 15%.

10. The method for theoretically predicting the ultimate strength of a multi-layer composite structure according to any one of claims 1 to 8, characterized in that: The method also includes: verifying the universality of the method by inputting structural parameters of multilayer cylindrical shells with different sizes and cyclic lay-ups of different composite material layers.

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