Equivalent method of static force in three-dimensional space on the node of finite element model of aircraft structure

Abstract

The application belongs to the technical field of aircraft structure strength design, and particularly relates to a three-dimensional space static force equivalent method of loading on an aircraft structure finite element model node, which is based on a multi-point array method and combined with an inverse distance weight method to give a three-dimensional space static force equivalent method of loading, under the premise of meeting a static force balance equation, the distribution of the loading of an active loading point on a passive loading point can be controlled by adjusting a weight index, a relatively reasonable loading distribution can be obtained, and the three-dimensional space structure aerodynamic load and inertial load can be well converted into the node load of the structure finite element model, thereby providing support for accurately analyzing the aircraft structure strength.

Description

Technical Field

[0001] This application belongs to the field of aircraft structural strength design technology, specifically involving a three-dimensional spatial static equivalent method for loads on nodes of an aircraft structural finite element model. Background Technology

[0002] In aircraft structural strength design, aerodynamic and inertial loads are often converted into nodal loads in the structural finite element model for analysis.

[0003] Currently, when converting aerodynamic and inertial loads into nodal loads in a structural finite element model, a multi-point arrangement method based on the principle of minimum energy is used. This method can obtain a relatively satisfactory load distribution in a two-dimensional plane, but it is difficult to apply well to three-dimensional space. It cannot effectively convert aerodynamic and inertial loads of three-dimensional structures into nodal loads in a structural finite element model, making it difficult to accurately analyze the structural strength of aircraft.

[0004] This application is made in view of the aforementioned technical deficiencies. Summary of the Invention

[0005] The purpose of this application is to provide a three-dimensional spatial static equivalent method for loads on nodes of a finite element model of an aircraft structure, in order to overcome or mitigate at least one of the known technical defects.

[0006] The technical solution of this application is:

[0007] A three-dimensional spatial static equivalent method for loads on nodes of an aircraft structural finite element model includes:

[0008] Step 1: Construct a rectangular coordinate system oxyz;

[0009] Step 2: Use aerodynamic load points and inertial load points as active load points, and use the nodes of the aircraft structure finite element model as passive load points.

[0010] Step 3: Along the x-axis, project each passive load point onto the oyz plane where the i-th active load point is located, connect the i-th active load point, and construct the oyz plane cantilever beam structure; along the y-axis, project each passive load point onto the oxz plane where the i-th active load point is located, connect the i-th active load point, and construct the oxz plane cantilever beam structure; along the z-axis, project each passive load point onto the oxy plane where the i-th active load point is located, connect the i-th active load point, and construct the oxy plane cantilever beam structure.

[0011] Step 4: Calculate the strain energy generated by the oyz plane cantilever beam structure, the oxz plane cantilever beam structure, and the oxy plane cantilever beam structure;

[0012] Step 5: Construct the static equilibrium constraint equations for the oyz-plane cantilever beam structure, the oxz-plane cantilever beam structure, and the oxy-plane cantilever beam structure;

[0013] Step 6: Combine the strain energy and static equilibrium constraint equations generated by the oyz plane cantilever beam structure, oxz plane cantilever beam structure, and oxy plane cantilever beam structure to construct the Lagrangian function. Substitute the necessary condition for the existence of the extremum of the Lagrangian function into the static equilibrium constraint equation to obtain the Lagrange multipliers, and then obtain the loads along the x-axis, y-axis, and z-axis directions of the i-th active load point at each passive load point.

[0014] Step 7: Combine the loads distributed at each passive load point along the x, y, and z axes to obtain the loads distributed at each passive load point.

[0015] Optionally, in the above-mentioned three-dimensional spatial static equivalent method for loads on the nodes of the finite element model of the aircraft structure, step four involves calculating the strain energy generated by the oxy-plane cantilever beam structure, specifically as follows:

[0016]

[0017]

[0018]

[0019]

[0020]

[0021] in,

[0022] U z,i The strain energy generated by the oxy-plane cantilever beam structure;

[0023] F z,i,j The load along the z-axis is obtained from the j-th passive load point at the i-th active load point.

[0024] L z,i,j The distance between the j-th passive load point and the ith active load point is on the oxy plane where the ith active load point is located.

[0025] Let n be the distance between the j-th passive load point and the ith active load point along the z-axis, and let n be the number of passive load points.

[0026] z j Let be the coordinate of the j-th passive load point on the z-axis;

[0027] z i Let be the coordinate of the i-th active load point on the z-axis;

[0028] EI is an arbitrary constant;

[0029] k is the weighting index;

[0030] The distance between the j-th passive load point and the i-th active load point in the x-axis direction;

[0031] x j Let be the coordinate of the j-th passive load point on the x-axis;

[0032] x i Let be the coordinate of the i-th active load point on the x-axis;

[0033] The distance between the j-th passive load point and the i-th active load point in the y-axis direction;

[0034] y j Let be the coordinate of the j-th passive load point on the y-axis;

[0035] y i Let be the coordinates of the i-th active load point on the y-axis.

[0036] Optionally, in the above-mentioned three-dimensional spatial static equivalent method of load on the nodes of the finite element model of the aircraft structure, k can be -0.2, -0.1, 0, 0.1 or 0.2.

[0037] Optionally, in the above-mentioned three-dimensional spatial static equivalent method for loads on nodes of the finite element model of aircraft structure, a distance threshold ε is set;

[0038] when When the absolute value is less than ε, take ε.

[0039] Optionally, in the above-mentioned three-dimensional spatial static equivalent method of load on the nodes of the finite element model of the aircraft structure, ε is taken as 0.01.

[0040] Optionally, in the above-mentioned three-dimensional spatial static equivalent method for loads on nodal points of the finite element model of an aircraft structure, step five involves constructing the static equilibrium constraint equations for the oxy-plane cantilever beam structure, specifically as follows:

[0041]

[0042]

[0043]

[0044] in,

[0045] F z,i Let be the load component along the z-axis at the i-th active load point.

[0046] Optionally, in the above-mentioned three-dimensional spatial static equivalent method for loads on nodal points of the finite element model of an aircraft structure, in step six, the strain energy and static equilibrium constraint equations generated by the oxy-plane cantilever beam structure are combined to construct a Lagrangian function. The necessary condition for the existence of the extremum of the Lagrangian function is substituted into the static equilibrium constraint equation to obtain the Lagrange multipliers, and then the load along the z-axis direction of the i-th active load point at each passive load point is obtained, where:

[0047] Construct the Lagrange function as follows:

[0048]

[0049]

[0050] The necessary condition for the existence of an extreme point of the Lagrange function is:

[0051]

[0052] Substituting the necessary condition for the existence of the extremum of the Lagrange function into the static equilibrium constraint equations, we get:

[0053]

[0054] in,

[0055] λ、λ x , λ y It is a Lagrange multiplier.

[0056] This application has at least the following beneficial technical effects:

[0057] This paper presents a three-dimensional static equivalent method for loads on nodal points in an aircraft structural finite element model. Based on the multi-point arrangement method, it combines the inverse distance weighting method to provide a static equivalent method for loads in three-dimensional space. Under the premise of satisfying the static equilibrium equation, the method can control the load distribution of active load points on passive load points by adjusting the weight index, thus obtaining a more reasonable load distribution. This method effectively converts the aerodynamic and inertial loads of the three-dimensional structure into nodal loads in the structural finite element model, providing support for accurate analysis of aircraft structural strength. In addition, compared with the constrained least squares method, this method has a certain mechanical background, strong theoretical basis, and the calculation results are deterministic under given conditions, without uncertainty issues. Attached Figure Description

[0058] Figure 1 This is a schematic diagram of the three-dimensional spatial static equivalent method for loads on nodes of an aircraft structural finite element model provided in this application embodiment;

[0059] Figure 2This is a schematic diagram showing the distribution of active load points and passive load points in the Cartesian coordinate system oxyz, as provided in the embodiments of this application.

[0060] Figure 3 This is a schematic diagram of the finite element model of the wing box segment provided in the embodiments of this application.

[0061] To better illustrate this embodiment, some parts in the accompanying drawings may be omitted, enlarged, or reduced, and do not represent the actual size of the product. Furthermore, the accompanying drawings are for illustrative purposes only and should not be construed as limiting this patent. Detailed Implementation

[0062] To make the technical solution and advantages of this application clearer, the technical solution of this application will be described in a clearer and more complete manner below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are only some embodiments of this application, and are only used to explain this application, not to limit this application. It should be noted that, for ease of description, only the parts related to this application are shown in the accompanying drawings, and other related parts can be referred to the general design.

[0063] Furthermore, unless otherwise defined, the technical or scientific terms used in this application description shall have the ordinary meaning understood by one of ordinary skill in the art to which this application pertains. The terms indicating direction used in this application description are used only to indicate relative direction or positional relationship; when the absolute position of the described object changes, its relative positional relationship may also change accordingly. The word "comprising" as used in this application description indicates that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, but does not exclude other elements or objects.

[0064] Furthermore, it should be noted that, unless otherwise explicitly specified and limited, terms such as "installation" and "connection" used in the description of this application should be interpreted broadly. For example, a 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. Those skilled in the art can understand its specific meaning in this application according to the specific circumstances.

[0065] This application provides a three-dimensional spatial static equivalent method for loads on nodes of an aircraft structural finite element model, such as... Figure 1 As shown.

[0066] Step 1: Construct a rectangular coordinate system oxyz.

[0067] Step 2: Use aerodynamic load points and inertial load points as active load points, numbered sequentially as 1, 2, ..., m, and use the nodes of the aircraft structural finite element model as passive load points, numbered sequentially as 1, 2, ..., n.

[0068] Step 3: Project each passive load point along the z-axis onto the oxy plane where the i-th active load point is located, and connect it with the i-th active load point to construct a cantilever beam structure.

[0069] Using the inverse distance weighting method, the bending stiffness of each cantilever beam in the oxy plane where the i-th active load point is located is calculated as follows:

[0070]

[0071]

[0072] in,

[0073] (EI) z,i,j Let be the bending stiffness of the cantilever beam corresponding to the j-th passive load point;

[0074] The distance between the j-th passive load point and the ith active load point along the z-axis;

[0075] z j Let be the coordinate of the j-th passive load point on the z-axis;

[0076] z i Let be the coordinate of the i-th active load point on the z-axis;

[0077] EI is an arbitrary constant and is not needed in actual calculations;

[0078] k is the weighting index. When k = 0, the influence of distance in the z-axis direction is not considered, which is equivalent to the multi-point arrangement method. When k > 0, the passive load points that are closer to the active load point in the z-axis direction have relatively more load distribution. When k < 0, the passive load points that are closer to the active load point in the z-axis direction have relatively less load distribution.

[0079] Step 4: Calculate the strain energy of the cantilever beam structure in the oxy plane where the i-th active load point is located.

[0080]

[0081]

[0082]

[0083]

[0084] in,

[0085] U z,i The strain energy generated by the cantilever beam structure in the oxy plane where the i-th active load point is located;

[0086] F z,i,jThe load along the z-axis is obtained from the j-th passive load point at the i-th active load point.

[0087] L z,i,j The distance between the j-th passive load point and the ith active load point is on the oxy plane where the ith active load point is located.

[0088] The distance between the j-th passive load point and the i-th active load point in the x-axis direction;

[0089] x j Let be the coordinate of the j-th passive load point on the x-axis;

[0090] x i Let be the coordinate of the i-th active load point on the x-axis;

[0091] The distance between the j-th passive load point and the i-th active load point in the y-axis direction;

[0092] y j Let be the coordinate of the j-th passive load point on the y-axis;

[0093] y i Let be the coordinates of the i-th active load point on the y-axis.

[0094] To avoid numerical singularities, when When the absolute value is less than the distance threshold ε, take ε.

[0095] Step 5: Construct the static equilibrium constraint equations for the cantilever beam structure in the oxy plane where the i-th active load point is located.

[0096]

[0097]

[0098]

[0099] in,

[0100] F z,i Let be the load component along the z-axis at the i-th active load point.

[0101] Step 6: Combine the strain energy and static equilibrium constraint equations generated by the cantilever beam structure in the oxy plane where the i-th active load point is located to construct the Lagrangian function. Substitute the necessary condition for the existence of the extremum of the Lagrangian function into the static equilibrium constraint equation to obtain the Lagrange multipliers, and then obtain the load along the z-axis of the i-th active load point at each passive load point.

[0102] To minimize the sum of strain energies generated by the cantilever beam structure in the oxy plane where the i-th active load point is located, the following Lagrangian function is constructed:

[0103]

[0104]

[0105] The necessary condition for the existence of an extreme point of the Lagrange function is:

[0106] Right now:

[0107]

[0108] Substituting the three static equilibrium constraint equations, we obtain the following system of equations:

[0109]

[0110] Solving the above system of equations will yield the Lagrange multipliers λ and λ'. x , λ y This allows us to calculate the load along the z-axis at each passive load point that is assigned to the i-th active load point, where the load along the z-axis at the j-th passive load point that is assigned to the i-th active load point is F. z,i,j , .

[0111] Referring to steps three through six, the load along the x-axis of the i-th active load point allocated to each passive load point is calculated, where the load along the x-axis of the i-th active load point allocated to the j-th passive load point is F. x,i,j ;

[0112] The load along the x-axis of the i-th active load point at each passive load point is calculated, where the load along the y-axis of the i-th active load point at the j-th passive load point is F. y,i,j .

[0113] The torque M at the j-th passive load point, distributed along the x, y, and z axes, can be calculated by referring to the above process. x,i,j M y,i,j M z,i,j .

[0114] Step 7: Combine the loads distributed at each passive load point along the x, y, and z axes to obtain the loads distributed at each passive load point. The three-dimensional static equivalent method for loads on the nodes of the finite element model of the aircraft structure disclosed in the above embodiment, based on the multi-point arrangement method and combined with the inverse distance weighting method, provides a static equivalent method for loads in three-dimensional space. Under the premise of satisfying the static equilibrium equation, the distribution of loads from active load points to passive load points can be controlled by adjusting the weight index, resulting in a more reasonable load distribution. This method effectively converts the aerodynamic and inertial loads of the three-dimensional structure into nodal loads of the structural finite element model, providing support for accurate analysis of the strength of the aircraft structure. In addition, compared with the constrained least squares method, this method has a certain mechanical background, strong principle, and the calculation results are deterministic under given conditions, without uncertainty issues.

[0115] In a specific example, there is 1 active load point and 8 passive load points, distributed in a Cartesian coordinate system oxyz, as follows: Figure 2 As shown, the load component F along the z-axis at the active load point z =1000, distance threshold ε is 0.01, and the weighting index k is -0.2, -0.1, 0, 0.1, 0.2. The loads along the z-axis of the i-th active load point at the 8 passive load points are shown in the table below:

[0116] As shown in the table above, in the oxy plane, the distances from the 8 passive load points to the active load point are equal. When k = 0, the load distributed along the z-axis is uniform among the 8 passive load points. When k > 0, the 4 passive load points with the same z-coordinate as the active load point receive a larger load along the z-axis, and this trend becomes more pronounced as the value of k increases. When k < 0, the 4 passive load points with the same z-coordinate as the active load point receive a smaller load along the z-axis, and this trend becomes more pronounced as the value of k decreases. This aligns with mechanical principles. Therefore, by adjusting k according to requirements, the load distribution of the active load point on the passive load point can be controlled, and the expected load distribution can be obtained for finite element analysis.

[0117] In another specific example, the finite element model of the wing box segment is constructed as follows: Figure 3 As shown, the finite element mesh has a total of 479 nodes, which are passive load points, 16 inertial load points, and active load points at the dots between adjacent ribs. There are 10 load conditions. Based on the three-dimensional spatial static equivalent method of load on the nodes of the finite element model of the aircraft structure disclosed in the above embodiment, the loads along the x, y, and z axes of the 16 active load points are obtained from the 479 passive load points under the 10 load conditions, and the loads obtained from the 479 passive load points are obtained.

[0118] The technical solution of this 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 this application is obviously not limited to these specific embodiments. Without departing from the principles of this 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 all fall within the scope of protection of this application.

Claims

1. A three-dimensional spatial static equivalent method for loads on nodes of an aircraft structural finite element model, characterized in that, include: Step 1: Construct a rectangular coordinate system oxyz; Step 2: Use aerodynamic load points and inertial load points as active load points, and use the nodes of the aircraft structure finite element model as passive load points. Step 3: Along the x-axis, project each passive load point onto the oyz plane where the i-th active load point is located, connect the i-th active load point, and construct the oyz plane cantilever beam structure. Along the y-axis, project each passive load point onto the oxz plane where the i-th active load point is located, connect the i-th active load point, and construct the oxz plane cantilever beam structure. Along the z-axis, project each passive load point onto the oxy plane where the i-th active load point is located, connect the i-th active load point, and construct the oxy plane cantilever beam structure. Step 4: Calculate the strain energy generated by the oyz plane cantilever beam structure, the oxz plane cantilever beam structure, and the oxy plane cantilever beam structure; Step 5: Construct the static equilibrium constraint equations for the oyz-plane cantilever beam structure, the oxz-plane cantilever beam structure, and the oxy-plane cantilever beam structure; Step 6: Combine the strain energy and static equilibrium constraint equations generated by the oyz plane cantilever beam structure, oxz plane cantilever beam structure, and oxy plane cantilever beam structure to construct the Lagrangian function. Substitute the necessary condition for the existence of the extremum of the Lagrangian function into the static equilibrium constraint equation to obtain the Lagrange multipliers, and then obtain the loads along the x-axis, y-axis, and z-axis directions of the i-th active load point at each passive load point. Step 7: Combine the loads distributed at each passive load point along the x, y, and z axes to obtain the loads distributed at each passive load point; In step four, the strain energy generated by the oxy-plane cantilever beam structure is calculated, specifically as follows: ； ； ； ； ； in, The strain energy generated by the oxy-plane cantilever beam structure; The load along the z-axis is obtained from the j-th passive load point at the i-th active load point. The distance between the j-th passive load point and the ith active load point is on the oxy plane where the ith active load point is located. Let n be the distance between the j-th passive load point and the ith active load point along the z-axis, and let n be the number of passive load points. Let be the coordinate of the j-th passive load point on the z-axis; Let be the coordinate of the i-th active load point on the z-axis; It is an arbitrary constant; Weighted index; The distance between the j-th passive load point and the i-th active load point in the x-axis direction; Let be the coordinate of the j-th passive load point on the x-axis; Let be the coordinate of the i-th active load point on the x-axis; The distance between the j-th passive load point and the i-th active load point in the y-axis direction; Let be the coordinate of the j-th passive load point on the y-axis; Let be the coordinates of the i-th active load point on the y-axis.

2. The method for three-dimensional spatial static equivalent load on nodes of an aircraft structural finite element model according to claim 1, characterized in that, Take -0.2, -0.1, 0, 0.1 or 0.

2.

3. The method for three-dimensional spatial static equivalent load on nodes of an aircraft structural finite element model according to claim 2, characterized in that, Set distance threshold ; when , , The absolute value is less than At that time, take .

4. The method for three-dimensional spatial static equivalent load on nodes of an aircraft structural finite element model according to claim 3, characterized in that, Take 0.

01.

5. The method for three-dimensional spatial static equivalent load on nodes of an aircraft structural finite element model according to claim 4, characterized in that, In step five, the static equilibrium constraint equations for the oxy-plane cantilever beam structure are constructed, specifically as follows: ； ； ； in, Let be the load component along the z-axis at the i-th active load point.

6. The method for three-dimensional spatial static equivalent load on nodes of an aircraft structural finite element model according to claim 5, characterized in that, In step six, the strain energy and static equilibrium constraint equations generated by the oxy-plane cantilever beam structure are combined to construct the Lagrangian function. The necessary condition for the existence of the extremum of the Lagrangian function is substituted into the static equilibrium constraint equations to obtain the Lagrange multipliers. Then, the load along the z-axis at each passive load point, which is allocated to the i-th active load point, is obtained. Where: Construct the Lagrange function as follows: ； The necessary condition for the existence of an extreme point of the Lagrange function is: ， ； Substituting the necessary condition for the existence of the extremum of the Lagrange function into the static equilibrium constraint equations, we get: ； in, It is a Lagrange multiplier.

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