A fastener modeling method and simulation analysis method thereof

Abstract

The present application belongs to the technical field of fastener modeling and simulation, and specifically relates to a fastener modeling method and a simulation analysis method thereof, wherein the fastener modeling method comprises: step 1, adding a reference point R between the nodes A and B at both ends of the fastener unit, regarding AR and BR as rigid rods, converting the displacement rigidity of points A and B to the position of point R, and regarding the displacement difference at the position of point R as the deformation of the fastener unit; step 2, calculating the stiffness values,,,,, of the fastener unit in six directions, corresponding to the stiffness values ​​of the spring element in six directions; step 3, writing the fastener unit equilibrium equation in the form of a block matrix, wherein the block matrix of the fastener unit stiffness matrix is ​​characterized by the stiffness values,,,,, of the fastener unit in six directions, and its components,, of AR and BR in the x-axis, y-axis and z-axis, and components,, of BR in the x-axis, y-axis and z-axis.

Description

Technical Field

[0001] The present application belongs to the technical field of fastener modeling and simulation, and specifically relates to a fastener modeling method and a simulation analysis method thereof. Background Art

[0002] There are a large number of fasteners such as rivets and bolts in the whole aircraft. In the past extensive simulation analysis, these fasteners were simplified by connecting the parts in a common node manner. However, as the simulation analysis of aviation structures develops towards refinement, the requirements for simulation accuracy and efficiency are getting higher and higher. The safety of fasteners has also become a key assessment in simulation analysis. Separate modeling and simulation of fasteners has become an indispensable part of aviation structure modeling and simulation.

[0003] There are many fasteners, which are large in size and distributed at the junctions between various components. Considering the workload of modeling and analysis, three-dimensional units are generally not used for modeling and simulation. Instead, one-dimensional units are often used for modeling and simulation of fasteners.

[0004] In one-dimensional units, rod units can only consider axial loads, which does not meet the load-bearing requirements of fasteners and cannot simulate the stiffness characteristics of fasteners in all directions; the unit definition and material parameter definition of beam units are relatively complex, the modeling method is complex, and the calculation amount is large, which is not suitable for large-scale fastener modeling and simulation; spring elements can more freely define the stiffness values ​​of fasteners in the axial and cross-sectional directions, and have the conditions for realizing large-scale rapid modeling and simulation. However, the spring element stiffness matrix has six stiffness values ​​on the main diagonal, and each stiffness value links the displacements of the two node degrees of freedom in the corresponding direction. There is no coupling term between the displacements in each direction, ignoring the geometric shape and rigid body displacement of the unit itself, and is only suitable for simulating the case of coincident nodes. If the two nodes do not coincide, the degree of freedom direction defining the stiffness is inconsistent with the direction of the line connecting the two nodes, which will generate internal constraints, and the deformation of the unit cannot correctly simulate the deformation of the actual structure. In the process of fastener modeling in aviation structures, the nodes connected are often not coincident, and spring elements cannot adapt well to these situations. Therefore, it is necessary to invent a unit construction method suitable for large-scale aviation fastener structure modeling and analysis.

[0005] This application is proposed in view of the above-mentioned technical defects. Summary of the invention

[0006] The purpose of the present application is to provide a fastener modeling method and a simulation analysis method thereof to overcome or alleviate at least one aspect of the known technical defects.

[0007] The technical solution of this application is:

[0008] On the one hand, a fastener modeling method is provided, comprising:

[0009] Step 1: Add a reference point R between the nodes A and B at both ends of the fastener unit. Point R is taken outside the AB line. AR and BR are regarded as rigid rods. The displacements of points A and B are rigidly converted to the position of point R. The displacement difference at the position of point R is regarded as the deformation of the fastener unit.

[0010] Step 2: Calculate the stiffness values ​​of the fastener unit in six directions , , , , , ,in,

[0011] is the stiffness value in the first direction, is the stiffness value along the x-axis, and is the axial stiffness along the x-axis;

[0012] is the stiffness value in the second direction, is the stiffness value along the y-axis, and is the tangential stiffness along the y-axis;

[0013] is the stiffness value in the third direction, is the stiffness value along the z-axis, and is the z-axis tangential stiffness;

[0014] is the stiffness value in the fourth direction, is the stiffness value around the x-axis, and is the x-axis rotation stiffness;

[0015] is the stiffness value in the fifth direction, is the stiffness value around the y-axis, and is the y-axis rotation stiffness;

[0016] is the stiffness value in the sixth direction, is the stiffness value around the z-axis, and is the z-axis rotation stiffness;

[0017] Step 3: Write the fastener unit equilibrium equation in the form of a block matrix:

[0018] ;

[0019] in:

[0020] , , is the block matrix of the fastener unit stiffness matrix, which consists of the stiffness values ​​of the fastener unit in six directions , , , , , and the components of AR and BR on the x-axis, y-axis, and z-axis , , and the components of BR on the x-axis, y-axis, and z-axis , , To characterize;

[0021] , is the displacement vector of point A and point B;

[0022] , are the internal force vectors acting on point A and point B respectively.

[0023] Optionally, in the above-mentioned fastener modeling method, in step 1, the offset of point R outside the AB straight line is taken to be consistent with the offset of the fastener on the model.

[0024] Optionally, in the above fastener modeling method, in step 2:

[0025] ;

[0026] ;

[0027] ;

[0028] ;

[0029] in:

[0030] is the modulus of the fastener; , is the thickness of the two connected plates; is the diameter of the fastener; The flexibility of the fastener.

[0031] Optionally, in the above fastener modeling method, in step 2:

[0032] ;

[0033] in:

[0034] It is the characterization value of the shear form of the fastener, which is 1 in single shear and 2 in double shear;

[0035] , is the modulus of the two connected plates;

[0036] , It is the characterization value of fasteners and their connection types. When bolts are used to connect metals, the values ​​are 2 / 3 and 3.0; when rivets are used to connect metals, the values ​​are 2 / 5 and 2.2; when bolts are used to connect composite materials, the values ​​are 2 / 3 and 4.2.

[0037] Optionally, in the above fastener modeling method, in step 3:

[0038] ;

[0039] ;

[0040] .

[0041] On the other hand, a fastener simulation analysis method is provided, which is implemented based on the above fastener modeling method, and includes:

[0042] Calculate the stiffness values ​​of the fastener element in six directions , , , , , ;

[0043] Process the nodes connected by the fastener units and convert the node numbers into internal node numbers;

[0044] Calculate the block matrix of the fastener element stiffness matrix , , , and then assemble the fastener unit stiffness matrix into the overall stiffness matrix of the structure according to the internal node number;

[0045] Combined with the working conditions of structural analysis, the node load vector is calculated, the stiffness matrix and the load vector are condensed, the related terms are eliminated, the linear equations are solved, the stress and strain results are restored and the results are post-processed.

[0046] This application has at least the following beneficial technical effects:

[0047] A fastener modeling method and a simulation analysis method thereof are provided, which can realize rapid modeling and accurate analysis of fasteners at any position and simulate fasteners between any two positions in space. The unit definition and stiffness property definition are simple, which can effectively shorten the modeling and analysis time of aviation structures and improve the design and optimization efficiency of aviation aircraft structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is a schematic diagram of adding a reference point R between the nodes A and B at both ends of the fastener unit provided by the embodiment of the present application;

[0049] Figure 2It is a schematic diagram of establishing a rigid relationship between a node and a reference point R provided in an embodiment of the present application;

[0050] Figure 3 It is a schematic diagram of the displacement change position of point A and point B rotating at point R provided in an embodiment of the present application;

[0051] Figure 4 It is a schematic diagram of the fastener simulation analysis method provided in an embodiment of the present application.

[0052] In order to better illustrate the present embodiment, some contents of the drawings may be omitted, enlarged or reduced, which is only used for illustrative purposes and should not be construed as limiting the present application. DETAILED DESCRIPTION

[0053] In order to make the technical solution and advantages of the present application clearer, the technical solution of the present application will be described in further detail in detail and in detail with reference to 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.

[0054] In addition, unless otherwise defined, the technical terms or scientific terms used in the description of this application should be the common meanings understood by those skilled in the art in the field to which this application belongs. The term "include" used in the description of this application means that the concepts appearing before the term include the concepts listed after the term and their equivalents, without excluding other related concepts.

[0055] In addition, the words indicating orientation used in the description of this application are only used to indicate relative directions or positional relationships. When the absolute position of the object being described changes, its relative positional relationship may also change accordingly. It should also be noted that, unless otherwise clearly specified and limited, the words "installation", "connection" and other similar words used in the description of this application should be understood in a broad sense. For example, the connection can be a fixed connection or a detachable connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium. Technical personnel in the field can understand its specific meaning in this application according to the specific circumstances.

[0056] A fastener modeling method includes the following steps.

[0057] Step 1: Add a reference point R between the nodes A and B at both ends of the fastener unit. Usually, point R can be located on the AB line. However, considering the modeling offset, the actual position of the fastener is often inconsistent with the modeling position. In order to ensure the accuracy of the solution, point R is offset and located outside the AB line. The offset of point R outside the AB line is consistent with the offset of the fastener on the model. Figure 1 As shown, AR and BR are regarded as rigid rods, the displacements of points A and B are rigidly converted to the position of point R, and the displacement difference at point R is regarded as the deformation of the fastener unit.

[0058] Step 2: Calculate the stiffness values ​​of the fastener unit in six directions , , , , , .

[0059] The stiffness values ​​of the fastener element in six directions correspond to the stiffness values ​​of the spring element in six directions, where:

[0060] is the stiffness value in the first direction, is the stiffness value along the x-axis, and is the axial stiffness along the x-axis;

[0061] is the stiffness value in the second direction, is the stiffness value along the y-axis, and is the tangential stiffness along the y-axis;

[0062] is the stiffness value in the third direction, is the stiffness value along the z-axis, and is the z-axis tangential stiffness;

[0063] is the stiffness value in the fourth direction, is the stiffness value around the x-axis, and is the x-axis rotation stiffness;

[0064] is the stiffness value in the fifth direction, is the stiffness value around the y-axis, and is the y-axis rotation stiffness;

[0065] is the stiffness value in the sixth direction, is the stiffness value around the z-axis, and is the z-axis rotational stiffness.

[0066] ;

[0067] ;

[0068] ;

[0069] ;

[0070] in:

[0071] is the modulus of the fastener; , is the thickness of the two connected plates; is the diameter of the fastener; The flexibility of the fastener.

[0072] By comparing various test results, the tangential stiffness value of the fastener calculated using the HUTH formula has a higher accuracy.

[0073] ;

[0074] in:

[0075] It is the characterization value of the shear form of the fastener, which is 1 in single shear and 2 in double shear;

[0076] , is the modulus of the two connected plates;

[0077] , is the characterization value of the fastener and its connection type. When bolts are used to connect metals, 2 / 3 and 3.0 are used; when rivets are used to connect metals, 2 / 5 and 2.2 are used; when bolts are used to connect composite materials, 2 / 3 and 4.2 are used. The specific values ​​are shown in the following table:

[0078]

[0079] Step 3: Write the fastener unit equilibrium equation in the form of a block matrix:

[0080] ;

[0081] in:

[0082] , , is the block matrix of the fastener unit stiffness matrix, which can be obtained by the stiffness values ​​of the fastener unit in six directions , , , , , and the components of AR and BR on the x-axis, y-axis, and z-axis , , and the components of BR on the x-axis, y-axis, and z-axis , , To characterize;

[0083] , is the displacement vector of point A and point B;

[0084] , are the internal force vectors acting on point A and point B respectively.

[0085] , It can be written as:

[0086] ;

[0087] ;

[0088] in,

[0089] , , , , , is the displacement of point A in the first, second, third, fourth, fifth and sixth directions;

[0090] , , , , , is the displacement of point B in the first, second, third, fourth, fifth and sixth directions.

[0091] , It can be written as:

[0092] ;

[0093] ;

[0094] in,

[0095] , , , , , It is the internal force acting on the fastener in the first, second, third, fourth, fifth and sixth directions.

[0096] Establish a node, which can be point A or point B, with a rigid relationship to the reference point R. The distance between the node and point R is ,like Figure 2 As shown, when the node occurs in the plane When the rotation of will drive point R to also happen The rotation of point R causes the change of translation displacement at the same time. Assuming that the fastener does not have a large bending deformation, the rotation can be regarded as a small rotation. At this time, we have:

[0097] , that is, the displacement change of point R along the y-axis , based on this, the deformation of the fastener unit is calculated.

[0098] Take the deformation calculation in the second direction as an example. Figure 3 As shown, point A rotates along the x-axis, that is, , the rotation along the z-axis, that is , point B rotates along the x-axis, that is , the rotation along the z-axis, that is , at this time, the displacement difference along the y-axis at the reference point R for:

[0099] .

[0100] According to the equilibrium equation relationship in the second direction, we have:

[0101] .

[0102] Similarly, the equilibrium equations in other directions can be written, and considering the symmetry of the matrix, the explicit expression of the fastener element stiffness matrix can be obtained:

[0103] ;

[0104] ;

[0105] .

[0106] The fastener modeling method disclosed in the above embodiment introduces a reference point between the nodes at both ends of the fastener unit to divide the one-dimensional unit into two rigid rods. The displacements of the two nodes are rigidly converted to the reference point position, and the difference in the reference point displacement reflects the deformation of the unit. This method can well solve the problem that traditional spring elements cannot reflect the size of the unit itself and generate internal constraints. In addition, its definition and construction method are simple, and it can be applied to large-scale aviation structure modeling and analysis, effectively improving the modeling and analysis efficiency of fastener structures, and providing support for aviation structure design and optimization.

[0107] Based on the fastener modeling method disclosed in the above embodiment, a fastener simulation analysis method is further provided. Figure 4 As shown, including:

[0108] Calculate the stiffness values ​​of the fastener element in six directions , , , , , ;

[0109] Process the nodes connected by the fastener units and convert the node numbers into internal node numbers;

[0110] Calculate the block matrix of the fastener element stiffness matrix , , , and then assemble the fastener unit stiffness matrix into the overall stiffness matrix of the structure according to the internal node number;

[0111] Combined with the working conditions of structural analysis, the node load vector is calculated, the stiffness matrix and the load vector are condensed, the related terms are eliminated, the linear equations are solved, the stress and strain results are restored and the results are post-processed.

[0112] The fastener simulation and analysis method disclosed in the above embodiment can realize the rapid modeling and accurate analysis of fasteners at any position, simulate the fasteners between any two positions in space, and has simple unit definition and stiffness property definition, which can effectively shorten the modeling and analysis time of aviation structures and improve the efficiency of aviation aircraft structure design and optimization.

[0113] 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 fastener modeling method, characterized in that: include: Step 1: Add a reference point R between the nodes A and B at both ends of the fastener unit. Point R is taken outside the AB line. AR and BR are regarded as rigid rods. The displacements of points A and B are rigidly converted to the position of point R. The displacement difference at the position of point R is regarded as the deformation of the fastener unit. Step 2: Calculate the stiffness values ​​K1, K2, K3, K4, K5, and K6 of the fastener unit in six directions, where: K1 is the stiffness value in the first direction, which is the stiffness value along the x-axis and is the axial stiffness of the x-axis; K2 is the stiffness value in the second direction, which is the stiffness value along the y-axis direction and is the tangential stiffness of the y-axis; K3 is the stiffness value in the third direction, which is the stiffness value along the z-axis direction and is the z-axis tangential stiffness; K4 is the stiffness value in the fourth direction, which is the stiffness value around the x-axis and is the x-axis rotation stiffness; K5 is the stiffness value in the fifth direction, which is the stiffness value around the y-axis and is the y-axis rotation stiffness; K6 is the stiffness value in the sixth direction, which is the stiffness value around the z-axis and is the z-axis rotation stiffness; Step 3: Write the fastener unit equilibrium equation in the form of a block matrix: in: K 11 , K 12 , K 22 is the block matrix of the fastener unit stiffness matrix, which consists of the stiffness values ​​K1, K2, K3, K4, K5, K6 in six directions of the fastener unit and the components X of AR and BR in the x-axis, y-axis and z-axis. A , Y A , Z A and BR's components X on the x-axis, y-axis, and z-axis B , Y B , Z B To characterize; U A , U B is the displacement vector of point A and point B; F A 、F B are the internal force vectors acting on point A and point B respectively; In step 2: K4=1×10 2 N / mm; K5=K6=1×10 8 N / mm; in: E f is the modulus of the fastener; t1 and t2 are the thicknesses of the two connected plates; d is the diameter of the fastener; h is the flexibility of the fastener; In step three:

2. The fastener modeling method according to claim 1, characterized in that: In step 1, the offset of point R outside the AB line is taken to be consistent with the offset of the fastener on the model.

3. The fastener modeling method according to claim 2, characterized in that: In step 2: in: n is the shear form characterization value of the fastener, which is 1 in single shear and 2 in double shear; E1 and E2 are the moduli of the two connected plates; a and b are the characterization values ​​of fasteners and their connection types. When bolts are used to connect metals, they are 2 / 3 and 3.0; when rivets are used to connect metals, they are 2 / 5 and 2.2; when bolts are used to connect composite materials, they are 2 / 3 and 4.

2.

4. A fastener simulation analysis method, characterized in that: The fastener modeling method according to claim 3 is implemented, comprising: Calculate the stiffness values ​​K1, K2, K3, K4, K5, and K6 of the fastener unit in six directions; Process the nodes connected by the fastener units and convert the node numbers into internal node numbers; Calculate the block matrix K of the fastener element stiffness matrix 11 , K 12 , K 22 , and then assemble the fastener unit stiffness matrix into the overall stiffness matrix of the structure according to the internal node number; Combined with the working conditions of structural analysis, the node load vector is calculated, the stiffness matrix and the load vector are condensed, the related terms are eliminated, the linear equations are solved, the stress and strain results are restored and the results are post-processed.

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