CN112711812B - Method for calculating torsional deformation of large-opening structure of rectangular thin-wall machine body - Google Patents

Method for calculating torsional deformation of large-opening structure of rectangular thin-wall machine body Download PDF

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CN112711812B
CN112711812B CN202011613170.9A CN202011613170A CN112711812B CN 112711812 B CN112711812 B CN 112711812B CN 202011613170 A CN202011613170 A CN 202011613170A CN 112711812 B CN112711812 B CN 112711812B
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苏雁飞
高小青
冯雅君
赵占文
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AVIC First Aircraft Institute
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Abstract

The invention discloses a method for calculating torsional deformation of a large opening structure of a rectangular thin-wall machine body, which comprises the following steps: establishing a torsion model of the large opening of the machine body according to the shape and the size of the actual large opening structure of the machine body; calculating relevant parameters of the section characteristics of the torsion model of the large-opening structure of the fuselage, including the fanning area and the main fanning moment of inertia; determining a torsion angle control equation at different section positions under the action of an external load; determining an expression of displacement components of any point on the section of the large-opening structure torsion model along the y axis and the z axis after torsion deformation; and determining torsional deformation key points, and obtaining the displacement components of the y axis and the z axis at each torsional deformation key point based on the expression of the displacement components, thereby obtaining the torsional deformation of the whole large-opening structure of the fuselage. The method effectively solves the problems that when the parameters change, the traditional finite element method needs to reestablish a finite element model, re-divide the grids and load the optimization calculation, and has a longer calculation iteration process and larger workload.

Description

Method for calculating torsional deformation of large-opening structure of rectangular thin-wall machine body
Technical Field
The invention relates to the field of aviation structure design, and particularly provides a method for calculating structural torsional deformation under a torsional load of a large-opening structure of a rectangular thin-wall fuselage, which can obtain sensitive parameters influencing the torsional deformation and provide support for controlling the torsional deformation.
Background
The large opening structure is generally a throwing opening at the lower part of the airplane body, a cargo compartment door mounting opening, a missile compartment door mounting opening and the like; compared with the traditional circular fuselage structure of the airplane, the rectangular fuselage section is a special airplane structure form, the rectangular fuselage with the large opening is the difficult point of special airplane structure design, the problems of discontinuous load transmission, uncoordinated deformation and the like caused by the large opening are urgently solved, and the control of the torsional deformation under the torsional load is one of the important problems which must be solved.
During strength design, the torsional deformation of the structure can be solved by using a finite element method, and during finite element calculation, the type selection, scale, boundary conditions and the like of model elements influence the calculation result. The correctness of the obtained finite element structure cannot be judged, the theoretical support of an analytic solution is lacked, key factors influencing the torsional deformation cannot be obtained, and the method lacks powerful data support for controlling the torsional deformation.
Disclosure of Invention
The invention aims to provide a method for calculating torsional deformation of a large-opening structure of a rectangular thin-wall machine body, which is used for solving the problem of low efficiency of the existing finite element calculation method in repeated iterative calculation of a re-established model when size parameters change.
In order to realize the task, the invention adopts the following technical scheme:
a method for calculating torsional deformation of a large opening structure of a rectangular thin-wall machine body comprises the following steps:
according to the shape and the size of an actual large opening structure of the machine body, a structural model of the large opening of the machine body is established, and in the structural model, reinforcing frames at two ends of the actual large opening structure are simplified into a model structure connected with the large opening through one of the reinforcing frames; setting a restraint end face to simulate a reinforcing frame at the end part of a large-opening structure of an actual structure, wherein the end face of a large-opening structure model is superposed with the restraint end face, the end face is used as a fixed end, and the other end face is used as a loading end; determining an origin of a coordinate axis in the structural model, and then establishing a coordinate system; applying a torsional load around an x axis to the large-opening structure model at the loading end so as to establish a torsional model;
calculating relevant parameters of the section characteristics of the torsion model of the large-opening structure of the fuselage, including the fanning area and the main fanning moment of inertia;
determining a torsion angle control equation at different section positions under the action of an external load;
determining an expression of displacement components of any point on the section of the large-opening structure torsion model along the y axis and the z axis after torsion deformation;
and determining torsional deformation key points in the large-opening structure torsional model, and obtaining the displacement components of the y axis and the z axis at each torsional deformation key point based on the expression of the displacement components, thereby obtaining the torsional deformation of the whole large-opening structure of the fuselage.
Further, determining an origin of a coordinate axis in the structural model, and then establishing a coordinate system, including:
taking a symmetrical surface of the large opening structure as a reference, wherein the symmetrical surface vertically divides the end surface of the large opening structure; taking the top z of the large-distance opening structure on the intersection line of the symmetrical surface and the end surface h Point (c) is regarded as point O, z h The calculation formula of (c) is:
Figure BDA0002868653230000021
wherein h represents the height of the large opening structure, and b represents the width of the large opening structure;
and based on the origin O, determining that the length direction of the large opening structure is an x axis, the height direction is a z axis and the direction is upward, and the y axis is determined according to a right-hand coordinate system rule.
Further, the calculation process of the fanning area and the main fanning moment of inertia is as follows:
torsional load M borne by large-opening structure torsional model t Then torsional deformation occurs; determining a torsional center position P of torsion on a z-axis, taking the torsional center P as a main pole point, taking an intersection point D of the z-axis and the upper part of the large-opening structure model as a main zero point, taking a vertical distance from any point Q to P on a section as r, and defining the integral of the vertical distance r from the main zero point D to the point Q along the arc length of the profile of the section as a fanning area A w
Based on the fanning area A w Calculating the main fan-shaped moment of inertia I of the section of the large-opening model w (ii) a Principal fan moment of inertia I w Is: - Ω A w 2 dA, wherein dA represents the integral infinitesimal area, and Ω represents the cross-sectional area of the large opening of the fuselage; a is to be w After substituting the foregoing equation, the following equation is used:
Figure BDA0002868653230000031
where t represents the wall thickness of the large opening model.
Further, the torsion angle control equation at the different cross-sectional positions is expressed as:
Figure BDA0002868653230000032
in the above formula, x represents the distance between the position of the calculated profile and the constraint end face, and the calculated profile is a profile perpendicular to the x axis; l represents the length of the fuselage large opening model and E is the modulus of elasticity of the structural material.
Further, the expression for determining the displacement components of any point on the large-opening structure torsion model section along the y and z axes after the torsion deformation is generated comprises:
any point on the large-opening structure torsion model section is marked as S, the position of the S point after torsion deformation is S', and the distance from the S point to the torsion center P point is r; the component of the S distance P along the z-axis is r z (ii) a The component of the S distance P point along the y axis is r y (ii) a θ is the angle between PS and y-axis, then:
the deformation amount of the S point is:
Figure BDA0002868653230000033
the displacement components of the S point torsional deformation along the y axis and the z axis are respectively as follows:
Figure BDA0002868653230000034
will I w Substitution of expressions into the above formula
Figure BDA0002868653230000036
The displacement components of the S point torsional deformation along the y axis and the z axis are respectively as follows:
Figure BDA0002868653230000035
further, in the large-opening structure torsion model, determining a torsion deformation key point includes:
and taking four corner points of the cross section of the large-opening torsion model of the fuselage as torsion deformation key points.
Further, the obtaining the displacement component of the y axis and the z axis at each torsional deformation key point based on the expression of the displacement component includes:
torsional deformation key points a and a', whose deformation along the y-axis is:
Figure BDA0002868653230000041
its deformation along the z-axis is:
Figure BDA0002868653230000042
at the torsional deformation key points B and B', the deformation along the y-axis is:
Figure BDA0002868653230000043
its deformation along the z-axis is:
Figure BDA0002868653230000044
among four angular points of the cross section of the large-opening torsion model of the fuselage, the left lower angular point and the right lower angular point are A and A' respectively; the upper left corner point and the upper right corner point are B and B' respectively.
Further, a torsional deformation of the entire fuselage wide opening structure is thereby obtained, including:
representing the torsional deformation magnitude of the whole model by the torsional deformation of the determined torsional deformation key point;
the torsional deformation at each torsional deformation key point is calculated at x = L, so that the torsional deformation at the key point of the calculated section with the largest torsional deformation is calculated, which also represents the largest torsional deformation of the entire model.
Compared with the prior art, the invention has the following technical characteristics:
1. according to the invention, through deep research on a large opening structure at the lower part of a rectangular section fuselage of the airplane under a torsional load, an expression of torsional deformation of the structure is obtained, key parameters influencing the torsional deformation are obtained, and theoretical support is provided for controlling the torsional deformation.
2. The method is characterized in that the key parameters of the torsional deformation are obtained through optimization of finite element calculation software, when the load, the appearance size and the opening size are changed in the finite element calculation, a finite element model needs to be re-established, the grid is divided again, the optimization calculation is loaded, the calculation iteration process is long, the workload is large, and the key parameters influencing the torsional deformation are not clear in the finite element method. By adopting the method for determining the parameters through the formula, the key parameters of the torsional deformation can be quickly obtained no matter how the size parameters of the large opening change, and the working efficiency is greatly improved.
Drawings
Fig. 1 (a), (b) and (c) are respectively a front view, a right view and a perspective structure schematic diagram of a torsion model of a large opening structure of a rectangular section fuselage;
FIG. 2 is a schematic view of the fan area distribution;
FIG. 3 is a schematic view of torsional deformation;
FIG. 4 is a schematic view of torsional deformation along the y-axis;
FIG. 5 is a schematic view of torsional deformation along the z-axis;
FIG. 6 is a schematic flow chart of the method of the present invention.
Detailed Description
Referring to fig. 1, the invention discloses a method for calculating torsional deformation of a large opening structure of a rectangular thin-wall machine body, which comprises the following steps:
step 1, establishing a torsion model of a rectangular section fuselage large opening structure
According to the shape and the size of the actual large opening structure of the machine body, establishing a structural model of the large opening structure of the machine body, as shown in figure 1; in the structural model, for the reinforcing frames at two ends of the actual large-opening structure, because the reinforcing frames at two ends have the same constraint on the large-opening structure when the large-opening structure is subjected to torsional load, the reinforcing frames are simplified into a model structure in which one reinforcing frame is connected with the large opening in the structural model; the other reinforcing frame is connected with the large opening and used for analyzing the model structure in the same process.
Setting a restraint end face to simulate a reinforcing frame at the end part of a large-opening structure of an actual structure, wherein the end face of the large-opening structure model is superposed with the restraint end face, the end face is used as a fixed end, and the other end face is used as a loading end.
Firstly, determining an origin O of a coordinate axis, wherein the method comprises the following steps:
taking a symmetrical surface of the large opening structure as a reference, wherein the symmetrical surface vertically divides the end surface of the large opening structure; on the intersecting line of the symmetrical surface and the end surface, the distance z from the top of the large opening structure is taken h Point (c) is regarded as point O, z h The calculation formula of (2) is as follows:
Figure BDA0002868653230000051
where h denotes the height of the large-opening structure and b denotes the width of the large-opening structure.
In the above formula, the distance from the top surface z of the large opening structure h When the large-opening structure is twisted, the inventors have analyzed and calculated that the normal stress is 0 and the shear stress is the maximum, and then the point on the intersection line corresponding to the position is determined as the point O.
Based on the origin O, determining that the length direction of the large opening structure is an x axis, the height direction is a z axis and points upwards, and the y axis is determined according to a right-hand coordinate system rule; taking an actual airplane as a reference, the x axis is generally the reverse heading of the airplane, the y axis is the right side of the airplane body, and the z axis is the height direction of the airplane body.
For the large-opening structure model, applying a torsional load M around the x axis to the large-opening structure model at the loading end t Thereby establishing a torsion model.
Step 2, calculating the cross section characteristic related parameters of the fuselage large opening structure model
Torsional load M applied to large-opening structure model t Then torsional deformation occurs; determining a torsional center position P of torsion on a z-axis, taking the torsional center P as a main pole point, taking an intersection point K of the z-axis and the upper part of the large-opening structure model as a main zero point, taking a vertical distance from any point Q to P on a section as r, and defining the integral of the vertical distance r from the main zero point K to the point Q along the arc length of the profile of the section as a fanning area A w
Wherein, the distance m =3h from the torsional center position P to the top of the large-opening structure model 2 /(b+6h)。
For example, for a point B 'on the cross section, the integral direction of the corresponding sectorial area during calculation is shown by the arrow in fig. 2, the integral starting point is the intersection point of the z-axis and the top of the large opening model, and the integral ending point is the point B'.
Based on the fanning area A w Calculating the main sectorial moment of inertia I of the section of the large-opening model w (ii) a Principal fan moment of inertia I w Is: - Ω A w 2 dA, wherein dA represents the integral infinitesimal area, and Ω represents the cross-sectional area of the large opening of the fuselage; a is prepared from w After substituting the foregoing equation, the following equation is used:
Figure BDA0002868653230000061
where t represents the wall thickness of the large opening model.
Step 3, calculating the torsion angle of the large opening structure model
Under external load M t Under the action, the control equation of the torsion angle at different calculated section positions is as follows:
Figure BDA0002868653230000062
in the above formula, x represents the distance between the position of the calculated profile, which is a profile perpendicular to the x axis, and the constraining end face; l represents the length of the fuselage large opening model and E is the modulus of elasticity of the structural material.
Step 4, calculating the torsional deformation of the large-opening structure model
The large-opening structure model is subjected to torsional load M t Then, the rotation will occur around the point P of the torsional center, as shown in FIG. 3;
any point on the large-opening structure torsion model section is marked as S, the position of the S point after torsion deformation is S', and the distance from the S point to the torsion center P point is r; the component of the S distance P point along the z-axis is r z (ii) a The component of the S distance P point along the y axis is r y (ii) a θ is the angle between PS and y-axis, then:
the deformation amount of the S point is:
Figure BDA0002868653230000071
the displacement components of the S point torsional deformation along the y axis and the z axis are respectively as follows:
Figure BDA0002868653230000072
will I w With expressions substituted in the above formula
Figure BDA0002868653230000075
The displacement components of the S point torsional deformation along the y axis and the z axis are respectively as follows:
Figure BDA0002868653230000073
the displacement deformation along the y and z axes of the torsional deformation is schematically shown in fig. 4 and 5.
According to the formula, the torsional deformation of any point on the large-opening structure torsional model section can be calculated.
Determining a torsional deformation key point in a large-opening structure torsional model; in this embodiment, the torsional deformation key points are: four angular points of the cross section of the large-opening torsion model of the fuselage, wherein the left lower angular point and the right lower angular point are A and A' respectively; the upper left corner point and the upper right corner point are B and B' respectively.
Since the torsional deformation key point can reflect the extreme value of the torsional deformation of the section of the large-opening structure model, for example, the torsional deformation of the point A along the y axis and the z axis is the maximum value, the deformation of the point B along the y axis is the minimum value, and the deformation along the z axis is the reverse maximum value, the scheme represents the torsional deformation magnitude of the whole model by the determined torsional deformation of the torsional deformation key point:
torsional deformation key points a and a', whose deformation along the y-axis is:
Figure BDA0002868653230000074
its deformation along the z-axis is:
Figure BDA0002868653230000081
at the torsional deformation key points B and B', the deformation along the y-axis is:
Figure BDA0002868653230000082
its deformation along the z-axis is:
Figure BDA0002868653230000083
in the above formula, when x is L, the value of torsional deformation is maximum; in actual calculation, the torsional deformation of each torsional deformation key point can be calculated at x = L, so that the torsional deformation of the key point of the calculation section with the largest torsional deformation is calculated, and the maximum torsional deformation of the whole model is represented.
According to the method, the torsional deformation expression of the large-opening structure model with any size under the action of the torque can be determined, and the method can be used for controlling the torsional deformation of the structure in the structure design process; for example, for a certain actual large-opening structure, the torsional deformation of the corresponding torsional deformation key point can be obtained only by bringing the relevant structure parameters into the expression of the torsional deformation key point, and then whether the design requirements are met is evaluated; when the structural design guidance is not satisfied, the parameters can be quickly adjusted through a formula, and the structural design guidance is of great significance.
The embodiment is as follows:
determining the torsional deformation of a certain fuselage cabin structure.
(1) Determining a torsion model
The torsion model shown in fig. 1 is simplified from the actual structure, and the respective dimensional parameters are determined.
Width b =2440mm, height h =2060mm, wall thickness t =5.8mm, opening length L =5000mm, and resistance to torsional load M t =10 9 N·mm。
The y-axis position is determined, as shown in fig. 1, at a distance from the upper skin of:
Figure BDA0002868653230000084
the material is 2A12-T4, and the elastic modulus of the material is E =71000MPa.
(2) Calculating torsional deformation
x =5000mm section:
Figure BDA0002868653230000091
Figure BDA0002868653230000092
Figure BDA0002868653230000093
Figure BDA0002868653230000094
x =2500mm section:
Figure BDA0002868653230000095
Figure BDA0002868653230000096
Figure BDA0002868653230000097
Figure BDA0002868653230000098
and solving the buckling deformation at the position of any section x, and substituting the coordinates x of the section position into a deformation expression.
The above embodiments are only used for illustrating the technical solutions of the present application, and not for limiting the same; although the present application has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; such modifications and substitutions do not substantially depart from the spirit and scope of the embodiments of the present application, and are intended to be included within the scope of the present application.

Claims (3)

1. A method for calculating torsional deformation of a large opening structure of a rectangular thin-wall machine body is characterized by comprising the following steps:
according to the shape and the size of an actual large opening structure of the machine body, a structural model of the large opening of the machine body is established, and in the structural model, reinforcing frames at two ends of the actual large opening structure are simplified into a model structure connected with the large opening through one of the reinforcing frames; setting a restraint end face to simulate a reinforcing frame at the end part of a large-opening structure of an actual structure, wherein the end face of a large-opening structure model is superposed with the restraint end face, the end face is used as a fixed end, and the other end face is used as a loading end; determining an origin of a coordinate axis in the structural model, and then establishing a coordinate system; applying a torsional load around an x axis to the large-opening structure model at the loading end so as to establish a torsional model;
calculating relevant parameters of the section characteristics of the torsion model of the large-opening structure of the fuselage, including the fanning area and the main fanning moment of inertia;
determining a torsion angle control equation at different section positions under the action of an external load;
determining an expression of displacement components of any point on the section of the large-opening structure torsion model along the y axis and the z axis after torsion deformation;
determining torsional deformation key points in a large-opening structure torsional model, and obtaining y-axis and z-axis displacement components at each torsional deformation key point based on the expression of the displacement components, thereby obtaining the torsional deformation of the whole large-opening structure of the machine body;
determining an origin of a coordinate axis in the structural model, and then establishing a coordinate system, wherein the coordinate system comprises:
taking a symmetrical surface of the large opening structure as a reference, wherein the symmetrical surface vertically divides the end surface of the large opening structure; taking the top z of the large-distance opening structure on the intersection line of the symmetrical surface and the end surface h Point (c) is regarded as point O, z h The calculation formula of (c) is:
Figure FDA0003802163570000011
wherein h represents the height of the large opening structure, b represents the width of the large opening structure;
based on the origin O, determining that the length direction of the large opening structure is an x axis, the height direction is a z axis and points upwards, and the y axis is determined according to a right-hand coordinate system rule;
the calculation process of the fanning area and the main fanning inertia moment is as follows:
torsional load M borne by large-opening structure torsional model t Then torsional deformation occurs; determining the torsional center position P on the z-axis, taking the torsional center P as a main pole, taking the intersection point D of the z-axis and the upper part of the large-opening structure model as a main zero point, and taking the cross section as a main zero pointIt is intended that the vertical distance from point Q to P is defined as r, and the integral of the vertical distance r from the main zero point D to point Q along the arc length of the cross-sectional profile is defined as the fan-shaped area A w
Based on the fanning area A w Calculating the main fan-shaped moment of inertia I of the section of the large-opening model w (ii) a Principal fan moment of inertia I w Is: - Ω A w 2 dA, wherein dA represents the integral infinitesimal area, and Ω represents the cross-sectional area of the large opening of the fuselage; a is to be w After substituting the foregoing equation, the following equation is used:
Figure FDA0003802163570000021
wherein t represents the wall thickness of the large opening model;
the torsion angle control equation at different section positions is expressed as:
Figure FDA0003802163570000022
in the above formula, x represents the distance between the position of the calculated profile, which is a profile perpendicular to the x axis, and the constraining end face; l represents the length of the fuselage large opening model, and E is the modulus of elasticity of the structural material;
the expression for determining the displacement components of any point on the large-opening structure torsion model section along the y axis and the z axis after torsion deformation comprises the following steps:
any point on the large-opening structure torsion model section is marked as S, the position of the S point after torsion deformation is S', and the distance from the S point to the torsion center P point is r; the component of the S distance P along the z-axis is r z (ii) a The component of the S distance P point along the y axis is r y (ii) a θ is the angle between PS and y-axis, then:
the deformation amount of the S point is:
Figure FDA0003802163570000031
the displacement components of the S point torsional deformation along the y axis and the z axis are respectively as follows:
Figure FDA0003802163570000032
will I w With expressions substituted in the above formula
Figure FDA0003802163570000038
The displacement components of the S point torsional deformation along the y axis and the z axis are respectively as follows:
Figure FDA0003802163570000033
the obtaining of the displacement components of the y axis and the z axis at each torsional deformation key point based on the expression of the displacement components comprises:
torsional deformation key points a and a', whose deformation along the y-axis is:
Figure FDA0003802163570000034
its deformation along the z-axis is:
Figure FDA0003802163570000035
at the torsional deformation key points B and B', the deformation along the y-axis is:
Figure FDA0003802163570000036
its deformation along the z-axis is:
Figure FDA0003802163570000037
among four angular points of the cross section of the large-opening torsion model of the fuselage, the left lower angular point and the right lower angular point are A and A' respectively; the upper left corner point and the upper right corner point are B and B' respectively.
2. The method for calculating the torsional deformation of the large-opening structure of the rectangular thin-walled fuselage according to claim 1, wherein the determining the torsional deformation key points in the large-opening structure torsional model comprises the following steps:
and taking four corner points of the cross section of the large-opening torsion model of the fuselage as torsion deformation key points.
3. The method for calculating the torsional deformation of the large opening structure of the rectangular thin-walled fuselage according to claim 1, wherein the obtaining of the torsional deformation of the entire large opening structure of the fuselage therefrom comprises:
representing the torsional deformation magnitude of the whole model by the torsional deformation of the determined torsional deformation key point;
the torsional deformation at each torsional deformation key point is calculated at x = L, so that the torsional deformation at the key point of the calculated section with the largest torsional deformation is calculated, which also represents the largest torsional deformation of the entire model.
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