CN112711801B - Rectangular thin-wall machine body large-opening structure torsion load distribution calculation method - Google Patents

Rectangular thin-wall machine body large-opening structure torsion load distribution calculation method Download PDF

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CN112711801B
CN112711801B CN202011610037.8A CN202011610037A CN112711801B CN 112711801 B CN112711801 B CN 112711801B CN 202011610037 A CN202011610037 A CN 202011610037A CN 112711801 B CN112711801 B CN 112711801B
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苏雁飞
李明强
张平贵
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AVIC First Aircraft Institute
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Abstract

The invention discloses a method for calculating the distribution of torsional load 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 a fanning area, a main fanning inertia moment, a fanning static moment, a section normal stress and a section shear stress; in the torsion model section of the large-opening structure of the fuselage, expressions of bending moment, axial force and shearing force of the left side edge, the right side edge and the top edge are respectively determined, and therefore the torsion load distribution of the large-opening structure is calculated. By adopting the method for determining the parameters in the formula, the distribution condition of the torsional load can be quickly obtained no matter how the size parameters of the large opening change, and the working efficiency is effectively improved.

Description

Rectangular thin-wall machine body large-opening structure torsion load distribution calculation method
Technical Field
The invention belongs to the field of aviation structure design, and particularly relates to a method for calculating torsional load distribution of a large-opening structure of a rectangular thin-wall fuselage.
Background
The large opening structure cuts off the force transmission path of the airplane structure, which is a difficult point of airplane design. The conventional large opening of the circular fuselage is based on a small number of design bases, while the rectangular opening is a special cabin opening and is a novel structural form, the design experience in model design is lacked, and the introduction of the structure of the type is lacked in the design information of the airplane.
Compared with the traditional circular fuselage structure of the airplane, the rectangular fuselage section is a special airplane structure form, the rectangular fuselage with a large opening is more difficult in the design of the special airplane structure, and the force transmission analysis under the torsional load is more complicated than that under other loads; 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. Load analysis and load distribution determination are the premise and the basis of structural arrangement, most of the existing aircraft design related information is directed to conventional aircraft layout, and no description is provided for special-form layout such as a large opening with a rectangular section.
Disclosure of Invention
The invention aims to provide a method for calculating the torsional load distribution of a large-opening structure of a rectangular thin-wall machine body, which provides a basis for determining structural arrangement and is used for guiding the structural design of the large-opening machine body of the machine body.
In order to realize the task, the invention adopts the following technical scheme:
a method for calculating torsional load distribution 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 constraint 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 constraint 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 a fanning area, a main fanning inertia moment, a fanning static moment, a section normal stress and a section shear stress;
in the torsion model section of the large-opening structure of the fuselage, expressions of bending moment, axial force and shearing force of the left side edge, the right side edge and the top edge are respectively determined, and therefore the torsion load distribution of the large-opening structure is calculated.
Further, determining an origin of coordinate axes 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 (2) is as follows:
Figure BDA0002868217000000021
wherein h represents the height of the large opening structure, 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, the main fanning inertia moment and the fanning static moment 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 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 composed of integral number of Ω A w 2 dA, wherein dA represents an integral infinitesimal area, and Ω represents a cross-sectional area of a large opening of the fuselage; a is to be w After substituting the preceding formula, the formula is as follows:
Figure BDA0002868217000000022
wherein t represents the wall thickness of the large-opening structure torsion model;
calculating the fan static distance S of the large-opening torsion model section w ＝∫A w dA, where dA represents the integral of the large open area of the fuselage.
Further, the profile normal stress σ w The expression is as follows:
Figure BDA0002868217000000031
in the above formula, A w For the fan-shaped area of the calculated section, x represents the distance between the section position and the constrained end surface, and L represents the length of the torsion model of the large opening structure of the fuselage.
Further, the cross sectional shear stress τ w The expression is as follows:
Figure BDA0002868217000000032
in the above equation, t represents the wall thickness of the large opening model.
Further, in the torsion model section of the large opening structure of the fuselage, expressions of bending moment, axial force and shearing force of the top edge are respectively as follows:
bending moment M of the top side z-up Comprises the following steps:
Figure BDA0002868217000000033
axial force F of the top edge x-up Comprises the following steps:
F x-up ＝0
the top edge shear force is:
F y ＝0。
further, in the torsion model section of the large opening structure of the fuselage, the expressions of the bending moment, the axial force and the shearing force of the left side are respectively as follows:
bending moment M of left side yL Comprises the following steps:
Figure BDA0002868217000000034
axial force F of the left side xL Comprises the following steps:
Figure BDA0002868217000000035
the shear force of the left side is:
Figure BDA0002868217000000036
further, in the torsion model section of the large opening structure of the fuselage, the expressions of the bending moment, the axial force and the shearing force of the right side are respectively as follows:
axial force F of the right side xR Comprises the following steps:
Figure BDA0002868217000000041
bending moment M of right side edge yR Comprises the following steps:
Figure BDA0002868217000000042
the right side shear force is:
Figure BDA0002868217000000043
compared with the prior art, the invention has the following technical characteristics:
according to the invention, the load transfer rule of each component and the calculation method of each component load are obtained by modeling and deeply researching the large opening structure at the lower part of the rectangular section fuselage of the airplane, and the method has important guiding significance for determining the structural arrangement and structural design of the large opening rectangular fuselage. By adopting the method for determining the parameters in the formula, the distribution condition of the torsional load can be quickly obtained no matter how the size parameters of the large opening change, and the working efficiency is effectively improved.
Drawings
Fig. 1 (a), (b), and (c) are respectively a front view, a right view, and a perspective view of a torsion model of a large opening structure of a rectangular cross-section fuselage;
FIG. 2 is a schematic illustration of a calculated sector area of a cross-section;
FIG. 3 is a schematic illustration of a calculated sectorial static moment of a cross section;
FIG. 4 is a cross-sectional normal stress and load profile;
FIG. 5 is a cross-sectional shear stress and load profile;
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 the distribution of torsional load of a large opening structure of a rectangular thin-walled fuselage, 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, a structural model of the large opening structure of the machine body is established, 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 the same as the analysis process of the model structure connected with the large opening.
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 model as a reference, wherein the symmetrical surface vertically subdivides 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 (c) is:
Figure BDA0002868217000000051
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 The position of (1) is that under the condition of large opening structure torsion, the inventor obtains a positive response through analysis and calculationThe force is 0 and the shear stress is maximum, 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 the direction is upward, 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 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 。
Wherein the distance between the torsional center position P and the top of the large-opening structure model is m =3h 2 /(b+6h)。
For example, for a point B 'on the cross section, the corresponding sectorial area is calculated, the starting point of the integration is the intersection point D of the z-axis and the top of the large opening model, and the ending point of the integration is the point B'.
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 an integral infinitesimal area, and Ω represents a cross-sectional area of a large opening of the fuselage; a is to be w After substituting the preceding formula, the formula is as follows:
Figure BDA0002868217000000061
where t represents the wall thickness of the large opening model.
Calculating the sectorial static distance S of the model section of the large-opening structure w ＝∫ Ω A w dA, where dA integrates the area of the infinitesimal and Ω represents the integration region, i.e. the area of the large opening cross section of the fuselage.
Cross sectional normal stress σ w The expression is as follows:
Figure BDA0002868217000000062
in the above formula, A w For the fan-shaped area of the calculated section, x represents the distance between the section position and the constrained end surface, and L represents the length of the torsion model of the large opening structure of the fuselage.
Cross sectional shear stress τ w The expression is as follows:
Figure BDA0002868217000000063
in the above equation, t represents the wall thickness of the large opening model (same as the parameter t).
Step 3, calculating the section load of the large opening structure model
As shown in fig. 4, in the fuselage large opening structure torsion model section, expressions of bending moment, axial force, and shear force of the left side edge, the right side edge, and the top edge (corresponding to the upper skin, the left side skin, and the right side skin of the actual structure) are determined, respectively:
on the sides (left side, right side and top side) where the bending moment is to be calculated, x represents the distance of the section (section perpendicular to the x-axis) passing through the calculated position on that side from the constraining end face, then:
the bending moment of the top side is the integral of the product of the normal stress and the distance area of each point on the top side, namely ^ integral Ω σ w * y dA, where dA represents the area of the integral infinitesimal and y represents the calculated distance of the point to the z-axis; omega denotes the area of the large open top edge of the fuselage, will be w The expression is brought into the above formula to obtain the bending moment M of the top edge z-up Comprises the following steps:
Figure BDA0002868217000000071
the axial force of the top edge is the integral of the product of the positive stress and the area of each point on the top edge, i.e. [ integral ] Ω σ w * dA, will w Substituting the expression into the above formula to obtain the axial force F of the top edge x-up Comprises the following steps:
F x-up ＝0
the shearing force of the top edge is the integral of the product of the shearing stress and the area of each point on the top edge, namely ^ integral ^ Ω τ w * dA, d.t. w Substituting the expression into the above formula to obtain the top edge shearing force as follows:
F y ＝0
the bending moment of the left side edge is the integral of the product of the positive stress and the distance area of each point on the left side edge, namely ^ integral Ω σ w * z dA, z representing the calculated distance of the point to the y-axis; Ω represents the left side region of the large opening of the fuselage, and σ represents w The expression is substituted into the above formula to obtain the bending moment M of the left side edge yL Comprises the following steps:
Figure BDA0002868217000000072
the expression of the axial force of the left side edge is the same as the axial force of the front top edge, F xL Comprises the following steps:
Figure BDA0002868217000000073
axial force F of the right side xR Comprises the following steps:
Figure BDA0002868217000000074
bending moment M of right side edge yR Comprises the following steps:
Figure BDA0002868217000000075
the shear force of the left side and the right side is as follows:
Figure BDA0002868217000000076
shear force and external load M from left and right sides t Balance, load distribution characteristics:
for the calculated profile, the axial force F x Comprises the following steps:
F x ＝F x-up +F xL +F xR ＝0
for the calculated profile, bending moment M y Comprises the following steps:
M y ＝M yL +M yR ＝0
for the calculated profile, bending moment M z Comprises the following steps:
M z ＝M z-up -F xL ·b＝0
the total load of the cross section is 0 respectively, but the distributed load of each part is not 0.
According to the method, the load distribution 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 internal force transmission analysis of the structure and guiding the structural strength design. When the load at the position of any section x is solved, the distance x between the calculated section and the constraint end face is substituted into the bending moment, axial force and shearing force expression.
The embodiment is as follows:
in one embodiment of the present invention, the load distribution of a certain fuselage cabin structure is determined by the following calculation process:
(1) Determining a torsion model
The torsion model shown in fig. 1 is simplified according to the actual structure, and the 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 determination, as shown in FIG. 1, is at a distance from the top edge of:
Figure BDA0002868217000000081
(2) Calculating the load at the x =2500mm position
Bending moment M of the top side z-up Comprises the following steps:
Figure BDA0002868217000000082
axial force F of the top side x-up Comprises the following steps:
F x-up ＝0
axial force F of the left side xL Comprises the following steps:
Figure BDA0002868217000000091
bending moment M of left side relative to y axis yL Comprises the following steps:
Figure BDA0002868217000000092
axial force F of the right side xR Comprises the following steps:
Figure BDA0002868217000000093
bending moment M of right side edge to y axis yR Comprises the following steps:
Figure BDA0002868217000000094
the total shear at the top edge is:
F y ＝0
the shear force of the left side and the right side is as follows:
Figure BDA0002868217000000095
shear force and external load M from left and right sides t And (4) balancing.
(3) Calculating the load
At x =0, the load is maximum, with:
bending moment M of the top side z-up Comprises the following steps:
Figure BDA0002868217000000096
axial force F of the top edge x-up Comprises the following steps:
F x-up ＝0
the total shear at the top edge is:
F y ＝0
axial force F of the left side xL Comprises the following steps:
Figure BDA0002868217000000101
bending moment M of left side relative to y axis yL Comprises the following steps:
Figure BDA0002868217000000102
axial force F of the right side xR Comprises the following steps:
Figure BDA0002868217000000103
bending moment M of right side yR Comprises the following steps:
Figure BDA0002868217000000104
the shearing force of the left side and the right side is as follows:
Figure BDA0002868217000000105
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 (1)

1. A method for calculating torsional load distribution 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 constraint 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 constraint 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 a fanning area, a main fanning inertia moment, a fanning static moment, a section normal stress and a section shear stress;
in the section of the torsion model of the large-opening structure of the machine body, expressions of bending moment, axial force and shearing force of the left side edge, the right side edge and the top edge are respectively determined, and therefore the torsion load distribution of the large-opening structure is calculated;
determining an origin of a coordinate axis in the structural model, and then establishing a coordinate system, 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; 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 FDA0003802312570000011
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 the direction is upward, and the y axis is determined according to a right-hand coordinate system rule;
the calculation process of the fanning area, the main fanning inertia moment and the fanning static distance 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 composed of integral number of 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 FDA0003802312570000021
wherein t represents the wall thickness of the large-opening structure torsion model;
calculating the fan static distance S of the large-opening torsion model section w ＝∫A w dA, where dA represents the integral of the large opening area of the fuselage;
the profile normal stress σ w The expression is as follows:
Figure FDA0003802312570000022
in the above formula, A w Calculating the fan-shaped area of the section, wherein x represents the distance between the section position and the constraint end surface, and L represents the length of the torsion model of the large opening structure of the fuselage;
cross sectional shear stress tau w The expression is as follows:
Figure FDA0003802312570000023
in the above formula, t represents the wall thickness of the large opening model;
in the section of the torsion model of the large opening structure of the machine body, expressions of bending moment, axial force and shearing force of the top edge are respectively as follows:
bending moment M of the top side z-up Comprises the following steps:
Figure FDA0003802312570000031
axial force F of the top edge x-up Comprises the following steps:
F x-up ＝0
the top edge shear force is:
F y ＝0；
in the torsion model section of the large-opening structure of the fuselage, the expressions of the bending moment, the axial force and the shearing force of the left side are respectively as follows:
bending moment M of left side yL Comprises the following steps:
Figure FDA0003802312570000032
axial force F of the left side xL Comprises the following steps:
Figure FDA0003802312570000033
the shear force of the left side is:
Figure FDA0003802312570000034
in the torsion model section of the large-opening structure of the fuselage, the expressions of the bending moment, the axial force and the shearing force of the right side are respectively as follows:
axial force F of the right side xR Comprises the following steps:
Figure FDA0003802312570000035
bending moment M of right side yR Comprises the following steps:
Figure FDA0003802312570000041
the shear force of the right side edge is:
Figure FDA0003802312570000042
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