A method for determining buckling loads of stiffened panels in aircraft structures

Abstract

The present application belongs to the technical field of determining the buckling load of composite material reinforced wall panels in aircraft structures, and specifically relates to a method for determining the buckling load of reinforced wall panels in aircraft structures, comprising: calculating the equivalent width of the wall panels between adjacent ribs based on the stiffness relationship between the wall panels and the ribs; constructing a structural potential energy formula for the reinforced wall panels based on the equivalent width of the wall panels between adjacent ribs; based on the potential energy formula for the reinforced wall panels, using the Ritz method according to the minimum potential energy principle to obtain the buckling stress of the reinforced wall panels; and calculating the axial compression buckling load per unit length of the reinforced wall panels based on the buckling stress of the reinforced wall panels.

Description

Technical Field

[0001] The present application belongs to the technical field of determining the buckling load of a composite material stiffened wall panel in an aircraft structure, and specifically relates to a method for determining the buckling load of a stiffened wall panel in an aircraft structure. Background Art

[0002] In order to reduce the overall weight of the aircraft, composite stiffened panel structures are widely used in aircraft structures. Accurately determining the buckling load of composite stiffened panel is of great significance for the design and improvement of composite stiffened panel and ensuring the safety of aircraft structure.

[0003] At present, the buckling load of composite reinforced panels is mainly determined by the following two methods:

[0004] 1) Engineering experience method, using empirical formulas for estimation, the calculation formula is too simplified, there are many restrictions on the use of conditions, the solution accuracy is poor, and it is difficult to ensure accurate results;

[0005] 2) Finite element analysis method has high precision and can obtain reliable and accurate results, but the modeling process is complicated, time-consuming, labor-intensive and inefficient.

[0006] This application is proposed in view of the above-mentioned technical defects.

[0007] It should be noted that the disclosure of the above background technology content is only used to assist in understanding the inventive concept and technical solution of the present invention, and it does not necessarily belong to the prior art of this patent application. In the absence of clear evidence that the above content has been disclosed on the filing date of this application, the above background technology should not be used to evaluate the novelty and creativity of the present application. Summary of the invention

[0008] The purpose of the present application is to provide a method for determining the buckling load of a stiffened panel in an aircraft structure, so as to overcome or alleviate at least one aspect of the known technical deficiencies.

[0009] The technical solution of this application is:

[0010] A method for determining buckling load of a stiffened panel in an aircraft structure, comprising:

[0011] According to the stiffness relationship between the wall plate and the ribs, the equivalent width of the wall plate between adjacent ribs is calculated;

[0012] Based on the equivalent width of the wall panel between adjacent ribs, the potential energy formula of the stiffened wall panel structure is constructed;

[0013] Based on the potential energy formula of the stiffened wall panel and the principle of minimum potential energy, the buckling stress of the stiffened wall panel is obtained by using the Ritz method.

[0014] Based on the buckling stress of the stiffened panel, the axial compression buckling load per unit width of the stiffened panel is calculated.

[0015] According to at least one embodiment of the present application, in the above-mentioned method for determining the buckling load of a stiffened panel in an aircraft structure, the equivalent width of the panel between adjacent ribs is obtained based on the stiffness relationship between the panel and the ribs, specifically:

[0016] For closed section bars:

[0017]

[0018] Split section ribs:

[0019]

[0020] in,

[0021] b is the equivalent width of the wall plate between adjacent ribs;

[0022] b1 is the width of the plate element where the rib is connected to the wall panel;

[0023] b f is the distance between the edges of adjacent ribs;

[0024] W′ is the bending stiffness ratio of the ribs to the wall panels;

[0025] N′ is the torsional stiffness ratio of the ribs to the wall panel.

[0026] According to at least one embodiment of the present application, in the above-mentioned method for determining the buckling load of a stiffened panel in an aircraft structure, the formula for constructing the potential energy of the stiffened panel is specifically:

[0027] Π=U sk +U st -W;

[0028]

[0029]

[0030]

[0031] in,

[0032] Π is the potential energy of the reinforced wall panel;

[0033] U sk is the elastic strain energy of the panel;

[0034] U st is the torsional strain energy of the tendon;

[0035] W is the work done by the external force;

[0036] a is the length of the wall panel;

[0037] x is the coordinate in the length direction of the wall panel;

[0038] y is the coordinate in the width direction of the wall panel;

[0039] D 11 , D 22 , D 12 D 66 D 16 D 26 is the bending stiffness matrix component of the stiffened panel;

[0040] w is the off-plane displacement function of the wall panel;

[0041] k L is the elastic constraint stiffness of the left side of the panel;

[0042] k R is the elastic constraint stiffness of the right side of the panel;

[0043] σ x is the stress of the wall panel along the x direction;

[0044] t is the wall thickness.

[0045] According to at least one embodiment of the present application, in the above-mentioned method for determining the buckling load of a stiffened panel in an aircraft structure,

[0046] in,

[0047] q is the correlation coefficient;

[0048] m is the axial buckling half-wave number;

[0049] GJ is the free torsional stiffness of the reinforcement.

[0050] According to at least one embodiment of the present application, in the above-mentioned method for determining the buckling load of the stiffened panel in the aircraft structure, the buckling stress of the stiffened panel is obtained by using the Ritz method based on the potential energy formula of the stiffened panel and the principle of minimum potential energy, which is specifically:

[0051]

[0052]

[0053]

[0054]

[0055] in,

[0056] σ buck is the buckling stress of the stiffened panel.

[0057] According to at least one embodiment of the present application, in the above-mentioned method for determining the buckling load of a stiffened panel in an aircraft structure, the axial compression buckling load per unit width of the stiffened panel is calculated based on the buckling stress of the stiffened panel, specifically:

[0058]

[0059] in,

[0060] N buck is the axial compression buckling load per unit width of the stiffened panel;

[0061] B is the width of the wall panel;

[0062] N is the number of tendons;

[0063] n is the number of plate elements of the ribs;

[0064] (E x ) k is the axial equivalent elastic modulus of the kth plate element of the reinforcement;

[0065] (E x ) skin is the axial equivalent elastic modulus of the wall panel;

[0066] b k is the width of the kth plate element of the rib, where b1 is the width of the plate element where the rib is connected to the wall panel;

[0067] t k is the thickness of the kth plate element of the rib. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 is a flow chart of a method for determining buckling load of a stiffened panel in an aircraft structure provided by an embodiment of the present application;

[0069] Figure 2 is a partial top view of adjacent ribs of a reinforced wall panel provided in an embodiment of the present application;

[0070] Figure 3 is a schematic diagram of a hat-shaped reinforced wall panel provided in an embodiment of the present application;

[0071] Figure 4 is a schematic diagram of a Z-shaped reinforced wall panel provided in an embodiment of the present application;

[0072] Figure 5 It is a schematic diagram of a T-shaped reinforced wall panel provided in an embodiment of the present application.

[0073] In order to better illustrate this embodiment, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of the actual product; in addition, the drawings are used for illustrative purposes, and their positional relationships are limited to illustrative purposes and cannot be understood as limitations on this patent. DETAILED DESCRIPTION

[0074] In order to make the technical solution and advantages of the present application clearer, the technical solution of the present application will be further described in detail in detail and in detail in conjunction with the accompanying drawings. It can be understood that the specific embodiments described here are only partial embodiments of the present application, which are only used to explain the present application, not to limit the present application. It should be noted that, for the convenience of description, only the parts related to the present application are shown in the accompanying drawings, and other related parts can refer to the general design. In the absence of conflict, the embodiments in the present application and the technical features in the embodiments can be combined with each other to obtain new embodiments.

[0075] In addition, unless otherwise defined, the technical terms or scientific terms used in the description of this application shall be the common meanings understood by the general technicians in the field to which this application belongs. The words "upper", "lower", "left", "right", "center", "vertical", "horizontal", "inside", "outside" and other words indicating orientation used in the description of this application are only used to indicate the relative direction or positional relationship, and do not imply that the device or element must have a specific orientation, be constructed and operated in a specific orientation. When the absolute position of the described object changes, its relative positional relationship may also change accordingly, so it cannot be understood as a limitation on this application. The "first", "second", "third" and similar terms used in the description of this application are only used for descriptive purposes to distinguish different components, and cannot be understood as indicating or implying relative importance. The similar words "one", "one" or "the" used in the description of this application should not be understood as an absolute limitation on quantity, but should be understood as the existence of at least one. The similar words "including" or "comprising" used in the description of this application mean that the elements or objects appearing in front of the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects.

[0076] In addition, it should be noted that, unless otherwise clearly specified and limited, the words "installed", "connected", "connected" and similar terms used in the description of this application should be understood in a broad sense. For example, the connection can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, an indirect connection through an intermediate medium, or the internal connection of two components. Technical personnel in the field can understand their specific meanings in this application according to the specific circumstances.

[0077] The following is combined with Figures 1 to 5This application is described in further detail.

[0078] A method for determining buckling load of a stiffened panel in an aircraft structure, comprising:

[0079] According to the stiffness relationship between the wall plate and the ribs, the equivalent width of the wall plate between adjacent ribs is calculated;

[0080] Based on the equivalent width of the wall panel between adjacent ribs, the potential energy formula of the stiffened wall panel structure is constructed;

[0081] Based on the potential energy formula of the stiffened wall panel and the principle of minimum potential energy, the buckling stress of the stiffened wall panel is obtained by using the Ritz method.

[0082] Based on the buckling stress of the stiffened panel, the axial compression buckling load per unit width of the stiffened panel is calculated.

[0083] As for the method for determining the buckling load of the stiffened wall panel in the aircraft structure disclosed in the above-mentioned embodiment, it can be understood by those skilled in the art that, based on the stiffness relationship between the wall panel and the ribs, the equivalent width of the wall panel between adjacent ribs is obtained, and then the structural potential energy formula of the stiffened wall panel is constructed. Based on the principle of minimum potential energy, the buckling stress of the stiffened wall panel is obtained by using the Ritz method, and the axial compression buckling load per unit length of the stiffened wall panel is calculated, which can realize the rapid determination of the buckling load of the stiffened wall panel and has a high solution efficiency.

[0084] In some optional embodiments, in the above-mentioned method for determining the buckling load of the stiffened panel in the aircraft structure, the relationship between the bending stiffness and torsional stiffness of the ribs and the panel is combined, and a large number of finite element analysis results are used to fit a reasonable equivalent width of the panel between adjacent ribs as follows:

[0085] For closed section reinforcement, Figure 3 As shown:

[0086]

[0087] Split section reinforcement, such as Figure 4-5 As shown:

[0088]

[0089] in,

[0090] b is the equivalent width of the wall plate between adjacent ribs;

[0091] b1 is the width of the plate element where the rib is connected to the wall panel;

[0092] b f is the distance between the edges of adjacent ribs;

[0093] W′ is the bending stiffness ratio of the ribs to the wall panels;

[0094] N′ is the torsional stiffness ratio of the ribs to the wall panel.

[0095] In some optional embodiments, in the above-mentioned method for determining the buckling load of a stiffened panel in an aircraft structure, the formula for constructing the potential energy of the stiffened panel is specifically:

[0096] Π=U sk +U st -W;

[0097]

[0098]

[0099]

[0100] in,

[0101] Π is the potential energy of the reinforced wall panel;

[0102] U sk is the elastic strain energy of the panel;

[0103] U st is the torsional strain energy of the tendon;

[0104] W is the work done by the external force;

[0105] a is the length of the wall panel;

[0106] x is the coordinate in the length direction of the wall panel;

[0107] y is the coordinate in the width direction of the wall panel;

[0108] D 11 , D 22 , D 12 D 66 D 16 D 26 is the bending stiffness matrix component of the stiffened panel;

[0109] w is the off-plane displacement function of the wall panel;

[0110] k L is the elastic constraint stiffness of the left side of the panel;

[0111] k R is the elastic constraint stiffness of the right side of the panel;

[0112] σ x is the stress of the wall panel along the x direction;

[0113] t is the wall thickness.

[0114] In some optional embodiments, in the above-mentioned method for determining the buckling load of the stiffened panel in the aircraft structure, the panel off-surface displacement function w that satisfies the boundary conditions of simply supported loading side and elastic non-loading side is selected, which is specifically as follows:

[0115]

[0116] in,

[0117] q is the correlation coefficient;

[0118] m is the axial buckling half-wave number;

[0119] GJ is the free torsional stiffness of the reinforcement.

[0120] In some optional embodiments, in the above-mentioned method for determining the buckling load of the stiffened panel in the aircraft structure, the buckling stress of the stiffened panel is obtained by using the Ritz method based on the potential energy formula of the stiffened panel and the principle of minimum potential energy, which is specifically:

[0121]

[0122]

[0123]

[0124]

[0125] in,

[0126] σ buck is the buckling stress of the stiffened panel.

[0127] In some optional embodiments, in the above-mentioned method for determining the buckling load of a stiffened panel in an aircraft structure, the axial compression buckling load per unit width of the stiffened panel is calculated based on the buckling stress of the stiffened panel, specifically:

[0128]

[0129] in,

[0130] N buck is the axial compression buckling load per unit width of the stiffened panel;

[0131] B is the width of the wall panel;

[0132] N is the number of tendons;

[0133] n is the number of plate elements of the ribs;

[0134] (E x ) k is the axial equivalent elastic modulus of the kth plate element of the reinforcement;

[0135] (E x ) skin is the axial equivalent elastic modulus of the wall panel;

[0136] b k is the width of the kth plate element of the rib, where b1 is the width of the plate element where the rib is connected to the wall panel;

[0137] t k is the thickness of the kth plate element of the rib.

[0138] When the buckling load determination method of the stiffened panel in the aircraft structure disclosed in the present application is specifically applied, the equivalent width b of the panel between adjacent ribs and the buckling stress N of the stiffened panel can be directly calculated based on the basic structure and physical parameters of the stiffened panel using the above explicit formula. buck , and then the axial compression buckling load per unit length of the stiffened wall panel can be quickly obtained to ensure higher efficiency.

[0139] In a verification test, the buckling load of the stiffened wall panel obtained by the test, the buckling load of the stiffened wall panel obtained by the finite element analysis method, and the buckling load of the stiffened wall panel obtained by the method disclosed in this application are compared as shown in the following table:

[0140]

[0141] It can be seen from the above table that the buckling load of the stiffened wall panel obtained by the method disclosed in this application is closer to the experimental value than the buckling load of the stiffened wall panel obtained by the finite element analysis method, has a smaller relative error with the experimental value, and has a higher calculation accuracy.

[0142] The various embodiments in the specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0143] So far, the technical solution of the present application has been described in conjunction with the preferred embodiments shown in the accompanying drawings. Those skilled in the art should understand that the scope of protection of the present application is obviously not limited to these specific embodiments. Without departing from the principles of the present application, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will fall within the scope of protection of the present application.

Claims

1. A method for determining the buckling load of stiffened panels in aircraft structures. It is characterized in that include: According to the stiffness relationship between the wall plate and the ribs, the equivalent width of the wall plate between adjacent ribs is calculated; Based on the equivalent width of the wall panel between adjacent ribs, the potential energy formula of the stiffened wall panel structure is constructed; Based on the potential energy formula of the stiffened wall panel and the principle of minimum potential energy, the buckling stress of the stiffened wall panel is obtained by using the Ritz method. Based on the buckling stress of the stiffened panel, the axial compression buckling load per unit width of the stiffened panel is calculated; According to the stiffness relationship between the wall panel and the ribs, the equivalent width of the wall panel between adjacent ribs is obtained, which is specifically: For closed section bars: Split section ribs: in, b is the equivalent width of the wall plate between adjacent ribs; b 1 is the width of the plate element where the rib is connected to the wall panel; b f is the distance between the edges of adjacent ribs; W′ is the bending stiffness ratio of the ribs to the wall panels; N′ is the torsional stiffness ratio of the ribs to the wall panel; The potential energy formula for constructing the reinforced wall panel is specifically: Π=U sk +U st -IN; in, Π is the potential energy of the reinforced wall panel; U sk is the elastic strain energy of the wall panel; U st is the torsional strain energy of the tendon; W is the work done by the external force; a is the length of the wall panel; x is the coordinate in the length direction of the wall panel; y is the coordinate in the width direction of the wall panel; D 11 , D 22 , D 12 D 66 D 16 D 26 is the bending stiffness matrix component of the stiffened panel; w is the off-plane displacement function of the wall panel; k L is the elastic constraint stiffness of the left side of the panel; k R is the elastic constraint stiffness of the right side of the panel; σ x is the stress of the wall panel along the x direction; t is the wall thickness.

2. The method for determining the buckling load of a stiffened panel in an aircraft structure according to claim 1, It is characterized in that in, q is the correlation coefficient; m is the axial buckling half-wave number; GJ is the free torsional stiffness of the reinforcement.

3. The method for determining the buckling load of a stiffened panel in an aircraft structure according to claim 2, It is characterized in that Based on the potential energy formula of the stiffened wall panel and the principle of minimum potential energy, the buckling stress of the stiffened wall panel is obtained by using the Ritz method, which is specifically: in, σ buck is the buckling stress of the stiffened panel.

4. The method for determining the buckling load of a stiffened panel in an aircraft structure according to claim 3, It is characterized in that Based on the buckling stress of the stiffened wall panel, the axial compression buckling load per unit width of the stiffened wall panel is calculated, which is specifically: in, N buck is the axial compression buckling load per unit width of the stiffened panel; B is the width of the wall panel; is the thickness of the wall panel and N is the number of ribs; n is the number of plate elements of the ribs; (E x ) k is the axial equivalent elastic modulus of the kth plate element of the reinforcement; (E x ) skin is the axial equivalent elastic modulus of the wall panel; b k is the width of the kth plate element of the rib, where b 1 is the width of the plate element where the rib is connected to the wall panel; t k is the thickness of the kth plate element of the rib.

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