CN108090265B - Stress calculation method of common frame of airplane body under bending load - Google Patents

Stress calculation method of common frame of airplane body under bending load Download PDF

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CN108090265B
CN108090265B CN201711297855.5A CN201711297855A CN108090265B CN 108090265 B CN108090265 B CN 108090265B CN 201711297855 A CN201711297855 A CN 201711297855A CN 108090265 B CN108090265 B CN 108090265B
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stress
skin
common frame
fuselage
airplane
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薛应举
张引利
冯雅君
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Xian Aircraft Design and Research Institute of AVIC
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Abstract

The invention relates to a stress calculation method of a common frame of an airplane body under the action of bending load, belonging to the field of flightThe technical field of machine structural strength analysis comprises the following steps: step 1: calculating the bending moment M of the overall load of the airplane at a common frame and the positive stress sigma generated on the skin and the stringer of the airplane body by the bending moment M; step 2: the resultant force F of the positive stress sigma generated on the skin and the stringer is equivalent to an axial force which generates a tangent plane load qm(ii) a And step 3: according to the tangent plane load qmDetermining the maximum bending moment M in the frame planemax(ii) a And 4, step 4: according to the maximum bending moment MmaxFinding the common frame stress sigmaq. The stress calculation method of the common frame of the airplane under the bending load overcomes the defects of the commonly used finite element method at present, so that the calculation is simpler and more convenient; in addition, by the method, the stress of the common frame can be calculated without waiting for the structural design to be completed in the initial design stage of the airplane, so that the design working progress is greatly advanced.

Description

Stress calculation method of common frame of airplane body under bending load
Technical Field
The invention belongs to the technical field of aviation structure strength analysis, and particularly relates to a stress calculation method of an airplane common frame under bending load.
Background
The common frame is the most common structure on the airplane, and the common frame is used for bearing the load on the airplane, keeping the appearance of the airplane body complete and providing support for the skin of the airplane body. The strength analysis of the common frame is an important content of the structural strength analysis of the airplane, and is a basic condition for ensuring the safety of the airplane, and the condition for obtaining the stress of the common frame is a precondition for the strength analysis. The conventional analysis method is to use a finite element method to complete huge and complicated analysis by a computer, but the analysis method needs to wait until the structural design is completed, so that the strong design work is delayed and repeated. Therefore, it is desirable to have a calculation method that can simply and rapidly complete the calculation of the stress of the common frame at the initial stage of the design of the airplane.
Disclosure of Invention
The invention aims to provide a stress calculation method of a common frame of an airplane body under a bending load, and the stress calculation method is used for solving the problems of lag in calculation process, low calculation accuracy, long calculation time and the like in the prior art.
In order to achieve the purpose, the invention adopts the technical scheme that: a stress calculation method of a common frame of an airplane fuselage under the action of bending load is characterized by comprising the following steps:
step 1: calculating the bending moment M of the total load of the airplane at a common frame and the positive stress sigma generated on the skin and the stringer of the airplane body by the bending moment M;
step 2: the resultant force F of the positive stress sigma generated on the skin and the stringer is equivalent to an axial force which generates a tangent plane load qm；
And step 3: according to the tangent plane load qmDetermining the maximum bending moment M in the frame planemax；
And 4, step 4: according to the maximum bending moment MmaxFinding the common frame stress sigmaq。
Further, the positive stress σ in the step 1 is represented by the formula
Figure BDA0001500658440000011
Obtaining;
wherein the moment of inertia I ═ sigma (f) of the fuselage reduction profilectp+φδ0b)y2
In the formula: y is the distance from the neutral axis of the reducing profile to any stringer, fctpIs the stringer cross-sectional area, b is the stringer spacing, δ0The thickness of the fuselage skin is taken as the thickness of the fuselage skin,
Figure RE-GDA0001582634500000021
the skin shrinkage reduction coefficient of the compression area of the fuselage,
Figure RE-GDA0001582634500000022
the critical stress of the skin, the elastic modulus of the E material and the radius of the fuselage.
Further, the section load q in the step 2mBy the formula
Figure BDA0001500658440000023
Obtaining:
wherein: effective thickness delta phi delta of fuselage skin0+fctp/b，
In the formula: a is the frame distance of the fuselage, and rho is the curvature radius of the fuselage;
finally obtaining the section load
Figure BDA0001500658440000024
Further, the maximum bending moment M in the step 3maxBy applying a tangential load qmThe integral is obtained along the general frame of the fuselage,
Figure BDA0001500658440000025
when y is the maximum value R, the maximum bending moment Mmax＝0.23qmR2。
Further, the common frame stress σ in the step 4qBy the formula
Figure BDA0001500658440000026
Obtaining:
in the above formula: i ismThe moment of inertia of the common frame, and delta y is the distance from the centroid of the common frame to the edge strip.
The stress calculation method of the common frame of the airplane under the bending load overcomes the defects of a finite element method commonly used at present, so that the calculation is simpler and more convenient; in addition, by the method, the stress of the common frame can be calculated without waiting for the structural design to be completed in the initial design stage of the airplane, so that the design working progress is greatly advanced.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and together with the description, serve to explain the principles of the invention.
FIG. 1 is a schematic illustration of an exemplary configuration of an aircraft fuselage;
FIG. 2 is a schematic cross-sectional view of a typical general block of an aircraft;
FIG. 3 is a force diagram of a typical frame of an aircraft under bending loads;
FIG. 4 is a plot of the tangential loading produced on a conventional frame with bending loads;
FIG. 5 is a graph of bending moment produced by a tangential load on a conventional frame;
fig. 6 is a general frame deformation diagram.
Reference numerals:
1-common frame, 2-skin, 3-stringer.
Detailed Description
In order to make the implementation objects, technical solutions and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention will be described in more detail below with reference to the accompanying drawings in the embodiments of the present invention.
As shown in the schematic diagram of the aircraft fuselage structure shown in fig. 1, a common frame 1 is a main force bearing component of the aircraft fuselage structure, a plurality of circles of the common frame 1 are arranged in parallel, then a truss strip 3 arranged in parallel with the axis of the fuselage penetrates through the parallel common frame 1 to complete the fixation of the structure, and a skin 2 is laid on the outer side of the common frame 1, so that the aircraft fuselage structure is formed.
As shown in fig. 2, the general frame 1 is composed of an L-shaped frame connected to the skin 2 at the lower side and an X-shaped frame at the upper side, and the supporting force of the skin 2 needs to be considered in the calculation of the strength.
For this purpose, the method for calculating the stress of a conventional frame of an aircraft fuselage under bending load according to the invention is further explained below with a set of specific data.
As shown in fig. 3 to 6: e70000 MPa, M4X 109N·mm，R＝2000mm， a＝500mm，b＝180mm，δ01.8mm, 80mm for a common frame height h, fctp＝210mm2，Im＝176986mm4And calculating the stress of the common frame.
The invention discloses a stress calculation method of a common frame of an airplane body under bending load, which specifically comprises the following steps:
step 1: calculating the positive stress sigma generated on the fuselage skin and the stringer of the common frame of the airplane under the action of the bending moment M, wherein the positive stress sigma is calculated according to a formula
Figure BDA0001500658440000031
Obtaining;
wherein the moment of inertia I ═ sigma (f) of the fuselage reduction profilectp+φδ0b)y2
In the formula: y is the distance from the neutral axis of the reducing profile to any stringer, fctpIs the stringer cross-sectional area, b is the stringer spacing, δ0The thickness of the fuselage skin is taken as the thickness of the fuselage skin,
Figure RE-GDA0001582634500000041
the skin shrinkage reduction coefficient of the compression area of the fuselage,
Figure RE-GDA0001582634500000042
the critical stress of the skin, the elastic modulus of the E material and the radius of the fuselage.
The skin critical stress can be obtained by adopting a successive approximation method:
Figure BDA0001500658440000043
first approximation at skin critical stress σmAnd if the skin and stringer stress sigma is 35MPa nearby, then:
fuselage compression zone skin shrinkage reduction factor
Figure BDA0001500658440000044
Effective thickness delta phi delta of fuselage skin0+fctp/b＝0.995×1.8+210/180＝2.96
Moment of inertia I ═ Σ (f) of the fuselage reduction profilectp+φδ0b)y2＝74333701374mm4
Skin and stringer positive stress
Figure BDA0001500658440000045
And the second approximation, namely the stress sigma of the skin and the stringer is 107.62MPa, then:
fuselage compression zone skin shrinkage reduction factor
Figure BDA0001500658440000046
Effective thickness delta phi delta of fuselage skin0+fctp/b＝0.567×1.8+210/180＝2.19
Moment of inertia I ═ Σ (f) of the fuselage reduction profilectp+φδ0b)y2＝54990703089mm4
Skin and stringer positive stress
Figure BDA0001500658440000047
The third approximation, let the skin and stringer stress σ be 145.48MPa, then:
fuselage compression zone skin shrinkage reduction factor
Figure BDA0001500658440000048
Effective thickness delta phi delta of fuselage skin0+fctp/b＝0.488×1.8+210/180＝2.05
Moment of inertia I ═ Σ (f) of the fuselage reduction profilectp+φδ0b)y2＝51399728717mm4
Skin and stringer positive stress
Figure BDA0001500658440000051
The fourth approximation, let the skin and stringer stress σ be 155.64MPa, then:
fuselage compression zone skin shrinkage reduction factor
Figure BDA0001500658440000052
Effective thickness delta phi delta of fuselage skin0+fctp/b＝0.472×1.8+210/180＝2.02
Moment of inertia I ═ Σ (f) of the fuselage reduction profilectp+φδ0b)y2＝50666690059mm4
Skin and stringer positive stress
Figure BDA0001500658440000053
In the fifth approximation, let the skin and stringer stress σ be 157.89MPa, then:
fuselage compression zoneCoefficient of skin shrinkage reduction
Figure BDA0001500658440000054
Effective thickness delta phi delta of fuselage skin0+fctp/b＝0.468×1.8+210/180＝2.01
Moment of inertia I ═ Σ (f) of the fuselage reduction profilectp+φδ0b)y2＝50516809008mm4
Skin and stringer positive stress
Figure BDA0001500658440000055
The final value can be determined if the difference between the values obtained by the last two solutions (fifth and fourth approximations, (158.36-157.89)/157.89 is 0.29%) is less than 0.3%, and is very close to the difference.
Step 2: q is foundmBut q ismOnly an intermediate value is needed, evaluation is not needed, and the maximum bending moment M can be directly solvedmax；
Figure BDA0001500658440000056
And step 3: finding the common frame stress sigmaq。
Figure BDA0001500658440000057
The invention relates to a stress calculation method of an ordinary frame of an airplane body under the action of bending load, which starts with the fact that the airplane body bears the total load, and gradually deduces the tangential plane load and tangential plane bending moment generated on the ordinary frame by the load until the stress generated on the ordinary frame by the load. By utilizing the stress calculation method, whether the bending rigidity of the common frame of the airplane is enough or not can be calculated, whether the section of the common frame is damaged or not can be calculated, and the structural design of the common frame of the airplane can be guided. According to the stress calculation method of the common frame of the airplane under the bending load, which is provided by the invention, the defects of the commonly used finite element method at present are overcome, so that the calculation is simpler and more convenient; in addition, the stress calculation method can be used for calculating the stress of the common frame without waiting for the structural design to be finished in the initial stage of airplane design, so that the design working progress is greatly advanced.
The above description is only for the best mode of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.

Claims (1)

1. A stress calculation method of a common frame of an airplane fuselage under the action of bending load is characterized by comprising the following steps:
step 1: calculating the bending moment M of the total load of the airplane at a common frame and the positive stress sigma generated on the skin and the stringer of the airplane body by the bending moment M, and the positive stress
Figure FDA0002974797960000011
Moment of inertia I ═ Σ (f) of the fuselage reduction profilectp+φδ0b)y2Y is the distance from the neutral axis of the reduced profile to any stringer, fctpIs the stringer cross-sectional area, b is the stringer spacing, δ0The thickness of the fuselage skin is taken as the thickness of the fuselage skin,
Figure FDA0002974797960000012
the skin shrinkage reduction coefficient of the compression area of the fuselage,
Figure FDA0002974797960000013
the critical stress of the skin, the elastic modulus of the E material and the radius of the fuselage are shown as R;
step 2: the resultant force F of the positive stress sigma generated on the skin and the stringer is equivalent to an axial force which generates a tangent plane load qmTangential surface load
Figure FDA0002974797960000014
Wherein a is the frame pitch of the fuselage, delta is the effective thickness of the skin of the fuselage, and delta is phi delta0+fctp/b；
And step 3: according to the tangent plane load qmDetermining the maximum bending moment M in the frame planemaxMaximum bending moment
Figure FDA0002974797960000015
And 4, step 4: according to the maximum bending moment MmaxFinding the common frame stress sigmaqStress, stress
Figure FDA0002974797960000016
Wherein, ImThe moment of inertia of the common frame, and delta y is the distance from the centroid of the common frame to the edge strip.
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