CN113753258B - Bolt-mounted aircraft windshield glass small deflection calculation method - Google Patents

Bolt-mounted aircraft windshield glass small deflection calculation method Download PDF

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CN113753258B
CN113753258B CN202111106668.0A CN202111106668A CN113753258B CN 113753258 B CN113753258 B CN 113753258B CN 202111106668 A CN202111106668 A CN 202111106668A CN 113753258 B CN113753258 B CN 113753258B
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deflection
windshield glass
small deflection
bolt
function
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CN113753258A (en
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张佩
吴保胜
张丽
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AVIC First Aircraft Institute
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64F—GROUND OR AIRCRAFT-CARRIER-DECK INSTALLATIONS SPECIALLY ADAPTED FOR USE IN CONNECTION WITH AIRCRAFT; DESIGNING, MANUFACTURING, ASSEMBLING, CLEANING, MAINTAINING OR REPAIRING AIRCRAFT, NOT OTHERWISE PROVIDED FOR; HANDLING, TRANSPORTING, TESTING OR INSPECTING AIRCRAFT COMPONENTS, NOT OTHERWISE PROVIDED FOR
    • B64F5/00—Designing, manufacturing, assembling, cleaning, maintaining or repairing aircraft, not otherwise provided for; Handling, transporting, testing or inspecting aircraft components, not otherwise provided for
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64C—AEROPLANES; HELICOPTERS
    • B64C1/00—Fuselages; Constructional features common to fuselages, wings, stabilising surfaces or the like
    • B64C1/14—Windows; Doors; Hatch covers or access panels; Surrounding frame structures; Canopies; Windscreens accessories therefor, e.g. pressure sensors, water deflectors, hinges, seals, handles, latches, windscreen wipers
    • B64C1/1476—Canopies; Windscreens or similar transparent elements
    • B64C1/1492—Structure and mounting of the transparent elements in the window or windscreen
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Abstract

The application belongs to the field of laminated glass windshields for aircraft, and particularly relates to a bolt-mounted aircraft windshield glass small deflection calculation method. The method comprises the steps of firstly, obtaining a bending stiffness matrix of windshield glass according to a stiffness theory of a laminated plate in composite material mechanics; step two, acquiring a small deflection motion control equation of the windshield glass under the action of airtight load according to a basic differential equation of small deflection bending of the thin plate; step three, simplifying the boundary conditions of the windshield glass installed by bolts into four-side clamped boundary conditions; and step four, generating a deflection function into a deflection interview function meeting four-side clamped boundary conditions, and bringing the deflection function into a small deflection motion control equation to obtain a small deflection calculation formula suitable for the bolt-mounted aircraft windshield glass. According to the method, the thickness and the parameter design of each layer of the windshield glass can be conveniently and rapidly installed through the guide bolt, and compared with a simulation calculation and experiment method, a great amount of manpower, material resources and financial resources in the structural design link of the windshield glass can be saved.

Description

Bolt-mounted aircraft windshield glass small deflection calculation method
Technical Field
The application belongs to the field of laminated glass windshields for aircraft, and particularly relates to a bolt-mounted aircraft windshield glass small deflection calculation method.
Background
The aircraft windshield glass is a sandwich glass structure formed by mixing glass and an adhesive layer. For this laminated glass structure, most of the researches at present mainly use a method of combining finite element analysis and experiments to research the performance, so that the theoretical research is less, and the theoretical research is less for the specific application scene of the bolt-type aircraft windshield glass.
It is therefore desirable to have a solution that overcomes or at least alleviates at least one of the above-mentioned drawbacks of the prior art.
Disclosure of Invention
The purpose of the application is to provide a bolt-mounted aircraft windshield glass small deflection calculation method, so as to solve at least one problem existing in the prior art.
The technical scheme of the application is as follows:
a method of bolt-mounted aircraft windshield glass small deflection calculation comprising:
step one, obtaining a bending stiffness matrix of windshield glass according to a stiffness theory of a laminated plate in composite material mechanics;
step two, acquiring a small deflection motion control equation of the windshield glass under the action of airtight load according to a basic differential equation of small deflection bending of the thin plate;
step three, simplifying the boundary conditions of the windshield glass installed by bolts into four-side clamped boundary conditions;
and step four, generating a deflection function into a deflection interview function meeting four-side clamped boundary conditions, and bringing the deflection function into a small deflection motion control equation to obtain a small deflection calculation formula suitable for the bolt-mounted aircraft windshield glass.
In at least one embodiment of the present application, in step one, the obtaining the bending stiffness matrix of the windshield according to the stiffness theory of the laminate in the composite mechanics includes:
bending stiffness matrix D ij The method comprises the following steps:
Figure BDA0003272693810000021
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure BDA0003272693810000022
to reduce the stiffness matrix, Z k 、Z k-1 Coordinates of each monolayer in the thickness direction are respectively, and the origin of the coordinates in the thickness direction is positioned on the middle plane;
in the case of an isotropic material,
Figure BDA0003272693810000023
the matrix is expressed as:
Figure BDA0003272693810000024
Figure BDA0003272693810000025
Figure BDA0003272693810000026
Figure BDA0003272693810000027
wherein E is the elastic modulus and mu is the Poisson's ratio.
In at least one embodiment of the present application, in the second step, the obtaining a small deflection motion control equation of the windshield glass under the airtight load according to the basic differential equation of the small deflection bending of the thin plate includes:
at small deflection, the longitudinal displacement of the middle plane of the structure is zero, i.e. u=v=0, and epsilon can be obtained x ＝ε y ＝γ xy =0, then there is:
Figure BDA0003272693810000028
wherein u and v are displacements in two mutually perpendicular x and y directions in the structure, ε x 、ε y 、γ xy Strain in x, y direction and shear strain in longitudinal plane, M x 、M y 、M xy Is the internal moment of unit width on the cross section of the laminated plate,
Figure BDA0003272693810000029
Figure BDA00032726938100000210
strain, curvature and twist rate of the mid-plane respectively;
at airtight load q 0 Under the action, the small deflection motion control equation of the windshield glass is as follows:
Figure BDA00032726938100000211
bringing the bending stiffness matrix of the windshield glass into a small deflection motion control equation to obtain the following components:
Figure BDA00032726938100000212
in at least one embodiment of the present application, in step three, the simplifying the bolted windshield boundary condition to a four-sided clamped boundary condition includes:
the bolt-mounted glass boundary section is simplified into four-side clamped boundary conditions;
namely:
ω x＝0 ＝ω x＝a ＝ω y＝0 ＝ω y＝b ＝0
Figure BDA0003272693810000031
where a is the length of the windscreen and b is the width of the windscreen.
In at least one embodiment of the present application, in the fourth step, the generating the deflection function into a deflection interview function satisfying a four-sided clamped boundary condition, and bringing the deflection interview function into a small deflection motion control equation, and obtaining a small deflection calculation formula suitable for the bolt-type aircraft windshield glass includes:
let the deflection function at the point (x, y) of the laminated glass be:
Figure BDA0003272693810000032
the deflection function meets the boundary condition of four sides clamped, and brings the deflection function into a Galerkin equation:
Figure BDA0003272693810000033
thereby obtaining undetermined parameter C:
Figure BDA0003272693810000034
the formula for the small deflection calculation for a bolt-mounted aircraft windshield is:
Figure BDA0003272693810000035
the invention has at least the following beneficial technical effects:
the bolt-type installed small deflection calculation method for the aircraft windshield glass can guide the thickness and parameter design of each layer of the bolt-type installed windshield glass conveniently and rapidly, and compared with simulation calculation and experimental methods, the bolt-type installed small deflection calculation method for the aircraft windshield glass can save a large amount of manpower, material resources and financial resources in the structural design link of the windshield glass.
Drawings
FIG. 1 is a schematic cross-sectional view of a glass boundary of a bolt-on mounting according to one embodiment of the present application;
fig. 2 is a schematic view of coordinates of each single layer in the thickness direction according to an embodiment of the present application.
Detailed Description
In order to make the purposes, technical solutions and advantages of the implementation of the present application more clear, the technical solutions in the embodiments of the present application will be described in more detail below with reference to the accompanying drawings in the embodiments of the present application. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are some, but not all, of the embodiments of the present application. The embodiments described below by referring to the drawings are exemplary and intended for the purpose of explaining the present application and are not to be construed as limiting the present application. All other embodiments, which can be made by one of ordinary skill in the art based on the embodiments herein without making any inventive effort, are intended to be within the scope of the present application. Embodiments of the present application are described in detail below with reference to the accompanying drawings.
In the description of the present application, it should be understood that the terms "center," "longitudinal," "lateral," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," and the like indicate orientations or positional relationships based on the orientations or positional relationships illustrated in the drawings, merely to facilitate description of the present application and simplify the description, and do not indicate or imply that the device or element being referred to must have a specific orientation, be configured and operated in a specific orientation, and therefore should not be construed as limiting the scope of protection of the present application.
The present application is described in further detail below with reference to fig. 1-2.
The application provides a bolt-mounted aircraft windshield glass small deflection calculation method, which comprises the following steps:
step one, obtaining a bending stiffness matrix of windshield glass according to a stiffness theory of a laminated plate in composite material mechanics;
step two, acquiring a small deflection motion control equation of the windshield glass under the action of airtight load according to a basic differential equation of small deflection bending of the thin plate;
step three, simplifying the boundary conditions of the windshield glass installed by bolts into four-side clamped boundary conditions;
and step four, generating a deflection function into a deflection interview function meeting four-side clamped boundary conditions, and bringing the deflection function into a small deflection motion control equation to obtain a small deflection calculation formula suitable for the bolt-mounted aircraft windshield glass.
As shown in fig. 1, the aircraft windshield glass is a laminated glass structure formed by mixing glass and glue layers, generally consists of three layers of glass and two layers of PU glue layers, and is mounted on a pressing plate through bolts. The glass and the adhesive layer are firmly bonded, and the thickness dimension of the structure is much smaller than the minimum dimension in the longitudinal direction, so that the basic assumption of the laminated board classical theory is met.
According to the bolt-mounted aircraft windshield glass small deflection calculation method, firstly, a bending stiffness matrix of the windshield glass is obtained according to a stiffness theory of a laminated plate in composite mechanics:
bending stiffness matrix D ij The method comprises the following steps:
Figure BDA0003272693810000051
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure BDA0003272693810000052
to reduce the stiffness matrix, Z k 、Z k-1 Coordinates of each single layer in the thickness direction are respectively shown in fig. 2, and the origin of the coordinates in the thickness direction is located on the middle plane;
in the case of an isotropic material,
Figure BDA0003272693810000053
the matrix is expressed as:
Figure BDA0003272693810000054
Figure BDA0003272693810000055
Figure BDA0003272693810000056
Figure BDA0003272693810000057
wherein E is the elastic modulus and mu is the Poisson's ratio.
Then, combining the obtained bending stiffness matrix, and obtaining a small deflection motion control equation of the windshield glass under the action of the airtight load according to a basic differential equation of small deflection bending of the thin plate, wherein the small deflection motion control equation comprises the following steps of:
at small deflection, the longitudinal displacement of the middle plane of the structure is zero, i.e. u=v=0, and epsilon can be obtained x ＝ε y ＝γ xy =0, then there is:
Figure BDA0003272693810000058
wherein u and v are displacements in two mutually perpendicular x and y directions in the structure, ε x 、ε y 、γ xy Respectively x and yStrain in the direction and shear strain in the longitudinal plane, M x 、M y 、M xy Is the internal moment of unit width on the cross section of the laminated plate,
Figure BDA0003272693810000059
Figure BDA00032726938100000510
respectively the strain, curvature and torsion rate of the middle surface, D ij Is a bending stiffness matrix;
basic differential equation for small deflection bending of sheet at hermetic load q 0 Under the action, the small deflection motion control equation of the windshield glass is as follows:
Figure BDA00032726938100000511
bringing the bending stiffness matrix of the windshield glass into a small deflection motion control equation to obtain the following components:
Figure BDA00032726938100000512
according to the bolt-mounted aircraft windshield glass small deflection calculation method, the bolt-mounted windshield glass boundary conditions can be simplified into four-side clamped boundary conditions, and the method comprises the following steps of:
the bolt-mounted glass boundary section is simplified into four-side clamped boundary conditions;
namely:
ω x＝0 ＝ω x＝a ＝ω y＝0 ＝ω y＝b ＝0
Figure BDA0003272693810000061
where a is the length of the windscreen and b is the width of the windscreen.
According to the bolt-type installed aircraft windshield glass small deflection calculation method, a deflection function is generated into a deflection interview function meeting four-side clamped boundary conditions, and the deflection interview function is brought into a small deflection motion control equation to obtain a small deflection calculation formula of the aircraft windshield glass suitable for bolt-type installation, and the method specifically comprises the following steps:
let the deflection function at the point (x, y) of the laminated glass be:
Figure BDA0003272693810000062
the deflection function meets the boundary condition of four sides clamped, and brings the deflection function into a Galerkin equation:
Figure BDA0003272693810000063
thereby obtaining undetermined parameter C:
Figure BDA0003272693810000064
the formula for the small deflection calculation for a bolt-mounted aircraft windshield is:
Figure BDA0003272693810000065
according to the bolt-mounted aircraft windshield glass small deflection calculation method, the bending stiffness matrix of the windshield glass can be obtained according to the stiffness theory of the laminated plate in the composite material mechanics. The basic differential equation of the small deflection bending of the sheet is combined with the bending stiffness matrix, so that a small deflection motion control equation of the windshield glass under the action of airtight load can be obtained, the boundary condition of the windshield glass mounted by the bolts is simplified into a four-side clamped boundary condition, the deflection function is generated into a deflection surface test function meeting the four-side clamped boundary condition, and the deflection surface test function is brought into the small deflection motion control equation, so that a small deflection calculation formula suitable for the aircraft windshield glass mounted by the bolts can be obtained.
According to the bolt-type installed small deflection calculation method for the aircraft windshield glass, theoretical deduction is performed on deformation deflection of the aircraft windshield glass in the bolt-type common installation mode under airtight load, the small deflection calculation method suitable for the bolt-type installed aircraft windshield glass is summarized, thickness and parameter design of each layer of the bolt-type installed windshield glass can be conveniently and rapidly guided, and compared with simulation calculation and experimental methods, a great amount of manpower, material resources and financial resources in structural design links of the windshield glass can be saved.
The foregoing is merely specific embodiments of the present application, but the scope of the present application is not limited thereto, and any changes or substitutions easily conceivable by those skilled in the art within the technical scope of the present application should be covered in the scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.

Claims (1)

1. A method of calculating a small deflection of a bolt-mounted aircraft windshield, comprising:
step one, obtaining a bending stiffness matrix of windshield glass according to a stiffness theory of a laminated plate in composite material mechanics;
step two, acquiring a small deflection motion control equation of the windshield glass under the action of airtight load according to a basic differential equation of small deflection bending of the thin plate;
step three, simplifying the boundary conditions of the windshield glass installed by bolts into four-side clamped boundary conditions;
generating a deflection function into a deflection interview function meeting four-side clamped boundary conditions, and bringing the deflection function into a small deflection motion control equation to obtain a small deflection calculation formula suitable for the bolt-mounted aircraft windshield glass;
in the first step, the obtaining the bending stiffness matrix of the windshield glass according to the stiffness theory of the laminated plate in the composite mechanics comprises the following steps:
bending stiffness matrix D ij The method comprises the following steps:
Figure FDA0004270089880000011
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure FDA0004270089880000012
to reduce the stiffness matrix, Z k 、Z k-1 Coordinates of each monolayer in the thickness direction are respectively, and the origin of the coordinates in the thickness direction is positioned on the middle plane;
in the case of an isotropic material,
Figure FDA0004270089880000013
the matrix is expressed as:
Figure FDA0004270089880000014
Figure FDA0004270089880000015
Figure FDA0004270089880000016
Figure FDA0004270089880000017
wherein E is elastic modulus, and mu is Poisson's ratio;
in the second step, the obtaining a small deflection motion control equation of the windshield glass under the action of the airtight load according to the basic differential equation of the small deflection bending of the thin plate comprises the following steps:
at small deflection, the longitudinal displacement of the middle plane of the structure is zero, i.e. u=v=0, and epsilon can be obtained x ＝ε y ＝γ xy =0, then there is:
Figure FDA0004270089880000021
wherein u and v are displacements in two mutually perpendicular x and y directions in the structure, ε x 、ε y 、γ xy Strain in x, y direction and shear strain in longitudinal plane, M x 、M y 、M xy Is the internal moment of unit width on the cross section of the laminated plate,
Figure FDA0004270089880000022
Figure FDA0004270089880000023
strain, curvature and twist rate of the mid-plane respectively;
at airtight load q 0 Under the action, the small deflection motion control equation of the windshield glass is as follows:
Figure FDA0004270089880000024
bringing the bending stiffness matrix of the windshield glass into a small deflection motion control equation to obtain the following components:
Figure FDA0004270089880000025
in the third step, the simplification of the bolt-mounted windshield glass boundary condition to a four-sided clamped boundary condition includes:
the bolt-mounted glass boundary section is simplified into four-side clamped boundary conditions;
namely:
ω x＝0 ＝ω x＝a ＝ω y＝0 ＝ω y＝b ＝0
Figure FDA0004270089880000026
wherein a is the length of the windshield and b is the width of the windshield;
in the fourth step, the deflection function is generated into a deflection surface test function meeting four-side clamped boundary conditions, and the deflection surface test function is brought into a small deflection motion control equation, so that a small deflection calculation formula suitable for the bolt-mounted aircraft windshield glass is obtained, wherein the small deflection calculation formula comprises the following steps:
let the deflection function at the point (x, y) of the laminated glass be:
Figure FDA0004270089880000027
the deflection function meets the boundary condition of four sides clamped, and brings the deflection function into a Galerkin equation:
Figure FDA0004270089880000028
thereby obtaining undetermined parameter C:
Figure FDA0004270089880000029
the formula for the small deflection calculation for a bolt-mounted aircraft windshield is:
Figure FDA0004270089880000031
CN202111106668.0A 2021-09-22 2021-09-22 Bolt-mounted aircraft windshield glass small deflection calculation method Active CN113753258B (en)

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Family Cites Families (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
GB1060031A (en) * 1965-01-06 1967-02-22 British Aircraft Corp Ltd Improvements in mountings for aircraft windscreens
US6029933A (en) * 1997-08-01 2000-02-29 The Boeing Company Fire resistant pressure relief panel assembly
DE102008056702B4 (en) * 2008-11-11 2014-04-03 Airbus Operations Gmbh airplane window
US20110240188A1 (en) * 2008-12-11 2011-10-06 Bae Systems Plc Aircraft transparency protection
CN211783345U (en) * 2020-03-16 2020-10-27 成都桐林铸造实业有限公司 Curvature detection device
CN113187087B (en) * 2021-04-19 2022-04-08 西南交通大学 High-falling object flexible glass protective net with landscape function and design method thereof

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