Method and device for calculating critical stress of wallboard under stretching and compression coupling action

Abstract

The invention provides a method for calculating critical stress of a wallboard under the action of stretching and compression coupling, and belongs to the technical field of airplane structural strength analys.The method comprises the steps that a theoretical model of the wallboard under the action of stretching and compression coupling is established, and structural parameters of the wallboard are obtained; based on the theoretical model under the stretching and compression coupling effect, constructing a buckling condition expression of the wallboard under the stretching and compression coupling effect; constructing a material characteristic parameter expression, and obtaining material characteristic parameters based on the material characteristic parameter expression; constructing a critical coefficient expression, and obtaining a minimum critical coefficient under a specified compression-pull load ratio based on the critical coefficient expression; based on the critical coefficient expression and the buckling condition expression, a critical stress expression of the wallboard under the stretching and compression coupling effect is obtained, and the critical stress is obtained according to the minimum critical coefficient, the material characteristic parameter D and the wallboard structure parameter.

Description

Technical Field

[0001] This application belongs to the field of aircraft structural strength analysis technology, and specifically relates to a method and apparatus for calculating the critical stress of a panel under the coupled action of tension and compression. Background Technology

[0002] As a widely used load-bearing structure in aircraft, fuselage skin panels typically need to withstand complex stresses in multiple directions. Especially during flight, these panels must withstand not only axial compressive loads but also spanwise tensile loads. This coupling of tension and compression significantly increases the risk of panel instability, directly impacting the stability and safety of the aircraft structure. Therefore, ensuring sufficient stability and strength of the panels under tension-compression coupling is not only a fundamental requirement for aircraft design but also a crucial basis for improving overall performance.

[0003] In existing technologies, the finite element method (FEM) can generally be used to perform stress analysis, strength calculation, and structural optimization of the stress state of a wall panel under coupled tension and compression. However, when the structural dimensions of the wall panel change, a new finite element simulation model needs to be established. Especially during the design phase, repeated modifications to the design inevitably increase the computational workload and extend the design cycle. Another method is to use theoretical models, but most of these methods only cover uniaxial stress states. While they can accurately predict buckling stress under uniaxial compression, they cannot effectively handle the complex stress state of the wall panel under coupled tension and compression. Summary of the Invention

[0004] The purpose of this application is to provide a method and apparatus for calculating the critical stress of a wall panel under tension and compression coupling, so as to solve or alleviate at least one of the problems in the prior art.

[0005] On the one hand, the technical solution of this application is: a method for calculating the critical stress of a wall panel under tension and compression coupling, including...

[0006] A theoretical model of the wall panel under tension and compression coupling was established, and the structural parameters of the wall panel were obtained.

[0007] Based on the theoretical model under tension and compression coupling, an expression for the buckling condition of the wall panel under tension and compression coupling is constructed.

[0008] Construct material characteristic parameter expressions, and obtain material characteristic parameters based on material characteristic parameter expressions;

[0009] Construct a critical coefficient expression, and obtain the minimum critical coefficient under a specified compressive-tensile load ratio based on the critical coefficient expression;

[0010] Based on the expressions for critical coefficients and buckling conditions, the expression for critical stress of the wall panel under tension and compression coupling is obtained. The critical stress is then obtained based on the minimum critical coefficient, material characteristic parameter D, and wall panel structural parameters.

[0011] Preferably, in the theoretical model of the wall panel under the coupled action of tension and compression, the four sides of the wall panel are simply supported. According to the left-hand coordinate system, the x-axis is horizontally to the right along the upper side of the wall panel, the y-axis is vertically downward along the left side of the wall panel, and the origin of the coordinate system is located at the left vertex of the wall panel. The structural parameters of the wall panel include the length, width, and thickness of the wall panel, as well as the elastic modulus and Poisson's ratio of the material.

[0012] Preferably, the process of constructing the buckling condition expression of the wall panel under tension and compression coupling based on the theoretical model under tension and compression coupling is as follows:

[0013] First, based on compressive stress σ x With tensile stress σ y Given the relationship between compressive stress and tensile stress, let compressive stress be positive and tensile stress be negative. Then, compressive stress and tensile stress satisfy: σ x= -βσ y In the formula, β is the ratio of compressive to tensile load;

[0014] The deflection ω at any point on the wall panel can be expressed as a trigonometric series as follows: In the formula: m and n are positive integers, A mn Here are the coefficients of the trigonometric functions, a is the length of the panel, and b is the width of the panel.

[0015] The differential equation for the buckling of the wall panel is: In the formula, D is the material characteristic parameter, ▽ is x, E is the elastic modulus, δ is the wall thickness, and μ is Poisson's ratio;

[0016] Substituting the deflection expression into the buckling differential equation, and considering that the buckling condition must be satisfied for any x and y, therefore:

[0017] ;

[0018] After simplification, the expression for the compression condition is obtained as follows: .

[0019] Preferably, the expression for the material characteristic parameters is: In the formula, D is a material characteristic parameter.

[0020] Preferably, the expression for the critical coefficient is... In the formula, K is the critical coefficient;

[0021] By adjusting the values ​​of positive integers m and n, multiple critical coefficients are obtained under a specified compressive-tensile load ratio. The critical coefficient with the smallest absolute value is selected from the multiple critical coefficients to obtain the minimum critical coefficient.

[0022] Preferably, the critical stress expression is: In the formula, σ x,cr This is the critical stress.

[0023] On the other hand, the technical solution provided in this application is: a device for calculating the critical stress of a wall panel under tension and compression coupling, including...

[0024] The parameter acquisition module is used to establish a theoretical model of the wall panel under the coupled action of tension and compression, and to acquire the structural parameters of the wall panel.

[0025] The buckling construction module is used to construct the buckling condition expression of the wall panel under the coupling action of tension and compression based on the theoretical model under the coupling action of tension and compression.

[0026] The material parameter module is used to construct material characteristic parameter expressions and obtain material characteristic parameters based on these expressions.

[0027] The critical coefficient module is used to construct the critical coefficient expression, and based on the critical coefficient expression, the minimum critical coefficient under a specified compressive-tensile load ratio is obtained;

[0028] The critical stress calculation module is used to obtain the critical stress expression of the wall panel under the coupled action of tension and compression based on the critical coefficient expression and the buckling condition expression. The critical stress is obtained according to the minimum critical coefficient, the material characteristic parameter D and the wall panel structural parameters.

[0029] Preferably, in the theoretical model of the wall panel under the coupled action of tension and compression, the four sides of the wall panel are simply supported. According to the left-hand coordinate system, the x-axis is horizontally to the right along the upper side of the wall panel, the y-axis is vertically downward along the left side of the wall panel, and the origin of the coordinate system is located at the left vertex of the wall panel. The structural parameters of the wall panel include the length, width, and thickness of the wall panel, as well as the elastic modulus and Poisson's ratio of the material.

[0030] Preferably, the process of constructing the buckling condition expression of the wall panel under tension and compression coupling based on the theoretical model under tension and compression coupling is as follows:

[0031] First, based on compressive stress σ x With tensile stress σ y Given the relationship between compressive stress and tensile stress, let compressive stress be positive and tensile stress be negative. Then, compressive stress and tensile stress satisfy: σ x= -βσ y In the formula, β is the ratio of compressive to tensile load;

[0032] The deflection ω at any point on the wall panel can be expressed as a trigonometric series as follows: In the formula: m and n are positive integers, A mn Here are the coefficients of the trigonometric functions, a is the length of the panel, and b is the width of the panel.

[0033] The differential equation for the buckling of the wall panel is: In the formula, D is the material characteristic parameter, ▽ is x, E is the elastic modulus, δ is the wall thickness, and μ is Poisson's ratio;

[0034] Substituting the deflection expression into the buckling differential equation, and considering that the buckling condition must be satisfied for any x and y, therefore:

[0035] ;

[0036] After simplification, the expression for the compression condition is obtained as follows: .

[0037] Preferably, the expression for the material characteristic parameters is: In the formula, D is a material characteristic parameter.

[0038] Preferably, the expression for the critical coefficient is... In the formula, K is the critical coefficient;

[0039] By adjusting the values ​​of positive integers m and n, multiple critical coefficients are obtained under a specified compressive-tensile load ratio. The critical coefficient with the smallest absolute value is selected from the multiple critical coefficients to obtain the minimum critical coefficient.

[0040] Preferably, the critical stress expression is: In the formula, σ x,cr This is the critical stress.

[0041] Thirdly, this application provides an electronic device, comprising:

[0042] One or more processors;

[0043] Memory;

[0044] One or more applications, which are stored in the memory and configured to be executed by the one or more processors, are configured to implement the critical stress calculation method for a wall panel under tension and compression coupling as described in any of the preceding claims.

[0045] Finally, this application provides a computer-readable storage medium, characterized in that the computer-readable storage medium stores at least one instruction, at least one program, code set, or instruction set, wherein the at least one instruction, the at least one program, the code set, or the instruction set is loaded and executed by a processor to implement the critical stress calculation method for a wall panel under tensile and compressive coupling as described in any of the preceding claims.

[0046] This application theoretically analyzes the buckling of a wall panel under the coupled effects of tension and compression, and obtains the expression for the critical stress of this type of structure. Based on this, the key parameters affecting the critical stress can be obtained. The critical pressure can be easily calculated through the key parameters, providing theoretical support for the stability of the wall panel under tension and compression, making up for the shortcomings of conventional methods, and improving the efficiency of scheme iteration and parameter optimization. Attached Figure Description

[0047] To more clearly illustrate the technical solutions provided in this application, the accompanying drawings will be briefly described below. Obviously, the drawings described below are merely some embodiments of this application.

[0048] Figure 1 This is a schematic diagram illustrating the method for calculating the critical stress of the wall panel under the coupled action of tension and compression according to this application.

[0049] Figure 2 This is a schematic diagram showing the wall panel in this application subjected to the combined effects of tension and compression coupling.

[0050] Figure 3 The critical parameter K in one embodiment of this application varies with the ratio of the wall panel length to its width.

[0051] Figure 4 This is a schematic diagram of the critical stress calculation device for the wall panel under the coupled action of tension and compression according to this application. Detailed Implementation

[0052] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions in the embodiments of this application will be described in more detail below with reference to the accompanying drawings.

[0053] To facilitate convenient and rapid stability calculation of wall panels under tension and compression coupling, this application provides a method and apparatus for calculating the critical stress of wall panels under tension and compression coupling. By using the critical stress expression of this type of structure, the key parameters affecting the critical stress of the wall panel can be obtained accurately and quickly, thus providing theoretical support for the stability calculation of wall panels under tension and compression coupling.

[0054] like Figure 1As shown, this application first provides a method for calculating the critical stress of a wall panel under tensile and compressive coupling. The method uses the equilibrium method to calculate the critical stress of the wall panel under tensile and compressive coupling, which includes the following process:

[0055] Step S1: Establish a theoretical model of the wall panel under the coupled action of tension and compression, and obtain the structural parameters of the wall panel.

[0056] like Figure 2 The figure shows the theoretical model of the wall panel under the combined action of tension and compression in this application. The wall panel is simply supported on all four sides and is subjected to a compressive stress σ in the transverse direction. x Longitudinal tensile stress σ y The coordinates of the theoretical model of the wall panel are defined as follows: according to the left-hand coordinate system, the x-axis extends horizontally to the right along the upper side of the wall panel, the y-axis extends vertically downward along the left side of the wall panel, and the origin O is located at the left vertex of the wall panel.

[0057] The structural parameters of the wall panel include its length, width, thickness, and the elastic modulus and Poisson's ratio of the material.

[0058] Step S2: Based on the theoretical model of the wall panel in Step S1, construct the buckling condition expression of the wall panel under the coupled action of tension and compression.

[0059] First, based on compressive stress σ x With tensile stress σ y Given the relationship between compressive stress and tensile stress, let compressive stress be positive and tensile stress be negative. Then, compressive stress and tensile stress satisfy: σ x= -βσ y In the formula, β is the compressive-tensile load ratio.

[0060] The deflection ω at any point on the wall panel can be expressed as a trigonometric series as follows: In the formula: m and n are positive integers, A mn denoted by , where 'a' is the length of the panel and 'b' is the width of the panel.

[0061] The differential equation for the buckling of the wall panel is: In the formula, D is the material characteristic parameter, ▽ 4 For biharmonic operators, E is the elastic modulus, δ is the wall thickness, and μ is Poisson's ratio.

[0062] Substituting the deflection expression into the buckling differential equation, and considering that the buckling condition must be satisfied for any x and y, therefore:

[0063] ;

[0064] After simplification, the expression for the compression condition can be obtained as follows: .

[0065] Step S3: Construct the material characteristic parameter expression, and obtain the material characteristic parameter D based on the material characteristic parameter expression.

[0066] In this application, the material characteristic parameter D is obtained from the material parameters and thickness of the wall panel: .

[0067] Step S4: Construct the critical coefficient expression, and obtain the minimum critical coefficient under the specified compressive-tensile load ratio based on the critical coefficient expression.

[0068] In this application, the expression for the critical coefficient K is: ;

[0069] By taking different integer values ​​for m and n, we can obtain different values ​​for the critical coefficient K. The critical coefficient with the smallest absolute value is the minimum critical coefficient. Figure 3 The figure shows curves of the critical coefficient K for different aspect ratios a / b, and the K value can be found directly from this figure.

[0070] Step S5: Based on the expression for the critical coefficient and the expression for the buckling condition, the expression for the critical stress of the wall panel under the coupled action of tension and compression is obtained. The critical stress is obtained according to the minimum critical coefficient, the material characteristic parameter D, and the structural parameters of the wall panel.

[0071] Substituting the expression for the critical coefficient into the expression for the buckling condition, we obtain the expression for the critical stress: .

[0072] The method of this application will be further described in detail below with a specific example. In this embodiment of the application, the structural parameters of the wall panel include: length a = 500 mm, width b = 180 mm, thickness δ = 2 mm, material is aluminum alloy, Young's modulus E = 70000 MPa, Poisson's ratio μ = 0.33. The wall panel is subjected to a compressive stress σ in the transverse direction. x Under longitudinal tensile stress σ y Find σ. y / σ x The critical stress σ of the wall panel when = -0.5 x,cr .

[0073] First, the critical coefficient K is determined based on the above structural parameter data:

[0074] .

[0075] By taking different integer values ​​for m and n in turn, different values ​​of the critical coefficient K are obtained, as shown in Table 1.

[0076] Table 1. K values ​​for different m and n

[0077]

[0078] Table 1 shows that the minimum critical coefficient K is K=10.53.

[0079] It can also be found from the curve of the critical parameter K changing with the ratio of the wall panel length to the width.

[0080] Then calculate the material characteristic parameter D:

[0081] .

[0082] Finally, the critical stress σ is calculated based on the critical stress expression. x,cr :

[0083] .

[0084] The method of this application theoretically analyzes the buckling of the wall panel under the coupled action of tension and compression, and obtains the expression of the critical stress of this type of structure. Based on this, the key parameters affecting the critical stress can be obtained. The critical pressure can be easily calculated through the key parameters, which provides theoretical support for the stability of the wall panel under tension and compression, makes up for the shortcomings of conventional methods, and improves the efficiency of scheme iteration and parameter optimization.

[0085] like Figure 4 As shown, this application also provides a device for calculating the critical stress of a wall panel under tensile and compressive coupling, the device 100 comprising:

[0086] The parameter acquisition module 101 is used to establish a theoretical model of the wall panel under the coupled action of tension and compression, and to acquire the structural parameters of the wall panel.

[0087] The buckling construction module 102 is used to construct the buckling condition expression of the wall panel under the coupling action of tension and compression based on the theoretical model under the coupling action of tension and compression.

[0088] The material parameter module 103 is used to construct material characteristic parameter expressions and obtain material characteristic parameters based on the material characteristic parameter expressions;

[0089] Critical coefficient module 104 is used to construct the critical coefficient expression and obtain the minimum critical coefficient under a specified compressive-tensile load ratio based on the critical coefficient expression.

[0090] The critical stress calculation module 105 is used to obtain the critical stress expression of the wall panel under the coupled action of tension and compression based on the critical coefficient expression and the buckling condition expression, and to obtain the critical stress according to the minimum critical coefficient, the material characteristic parameter D and the wall panel structural parameters.

[0091] The processing procedures of each module of the critical stress calculation device for the wall panel under tension and compression coupling can refer to the calculation method for the critical stress of the wall panel under tension and compression coupling described above, and will not be repeated here.

[0092] In addition, this application also provides an electronic device, which includes:

[0093] One or more processors;

[0094] Memory;

[0095] One or more applications, which are stored in the memory and configured to be executed by the one or more processors, are configured to implement the critical stress calculation method for a wall panel under tension and compression coupling as described in any of the preceding claims.

[0096] Finally, this application also provides a computer-readable storage medium, characterized in that the computer-readable storage medium stores at least one instruction, at least one program, code set, or instruction set, wherein the at least one instruction, the at least one program, the code set, or the instruction set is loaded and executed by a processor to implement the critical stress calculation method for a wall panel under tensile and compressive coupling as described above.

[0097] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for calculating the critical stress of a wall panel under coupled tension and compression, characterized in that, include A theoretical model of the wall panel under tension and compression coupling was established, and the structural parameters of the wall panel were obtained. Based on the theoretical model under tension and compression coupling, an expression for the buckling condition of the wall panel under tension and compression coupling is constructed. Construct material characteristic parameter expressions, and obtain material characteristic parameters based on material characteristic parameter expressions; Construct a critical coefficient expression, and obtain the minimum critical coefficient under a specified compressive-tensile load ratio based on the critical coefficient expression; Based on the expressions for critical coefficients and buckling conditions, the expression for critical stress of the wall panel under tension and compression coupling is obtained. The critical stress is then obtained based on the minimum critical coefficient, material characteristic parameter D, and wall panel structural parameters.

2. The method for calculating the critical stress of a wall panel under tension and compression coupling as described in claim 1, characterized in that, In the theoretical model of the wall panel under the coupled action of tension and compression, the four sides of the wall panel are simply supported. According to the left-hand coordinate system, the x-axis is horizontally to the right along the upper side of the wall panel, and the y-axis is vertically downward along the left side of the wall panel. The origin of the coordinate system is located at the left vertex of the wall panel. The structural parameters of the wall panel include the length, width, and thickness of the wall panel, as well as the elastic modulus and Poisson's ratio of the material.

3. The method for calculating the critical stress of a wall panel under tension and compression coupling as described in claim 2, characterized in that, The process of constructing the buckling condition expression for the wall panel under tension-compression coupling based on the theoretical model is as follows: First, based on compressive stress σ x With tensile stress σ y Given the relationship between compressive stress and tensile stress, let compressive stress be positive and tensile stress be negative. Then, compressive stress and tensile stress satisfy: σ x= -βσ y In the formula, β is the ratio of compressive to tensile load; The deflection ω at any point on the wall panel can be expressed as a trigonometric series: In the formula: m and n are positive integers, A mn Here are the coefficients of the trigonometric functions, a is the length of the panel, and b is the width of the panel. The differential equation for the buckling of the wall panel is: In the formula, D is the material characteristic parameter, ▽ 4 For biharmonic operators, E is the elastic modulus, δ is the wall thickness, and μ is Poisson's ratio; Substituting the deflection expression into the buckling differential equation, and considering that the buckling condition must be satisfied for any x and y, therefore: ； After simplification, the expression for the compression condition is obtained as follows: .

4. The method for calculating the critical stress of a wall panel under tension and compression coupling as described in claim 3, characterized in that, The expression for the material characteristic parameters is: In the formula, D is a material characteristic parameter.

5. The method for calculating the critical stress of a wall panel under tension and compression coupling as described in claim 4, characterized in that, The expression for the critical coefficient In the formula, K is the critical coefficient; By adjusting the values ​​of positive integers m and n, multiple critical coefficients are obtained under a specified compressive-tensile load ratio. The critical coefficient with the smallest absolute value is selected from the multiple critical coefficients to obtain the minimum critical coefficient.

6. The method for calculating the critical stress of a wall panel under tension and compression coupling as described in claim 5, characterized in that, The expression for the critical stress is as follows: In the formula, σ x,cr This is the critical stress.

7. A device for calculating the critical stress of a wall panel under coupled tension and compression, characterized in that, include The parameter acquisition module is used to establish a theoretical model of the wall panel under the coupled action of tension and compression, and to acquire the structural parameters of the wall panel. The buckling construction module is used to construct the buckling condition expression of the wall panel under the coupling action of tension and compression based on the theoretical model under the coupling action of tension and compression. The material parameter module is used to construct material characteristic parameter expressions and obtain material characteristic parameters based on these expressions. The critical coefficient module is used to construct the critical coefficient expression, and based on the critical coefficient expression, the minimum critical coefficient under a specified compressive-tensile load ratio is obtained; The critical stress calculation module is used to obtain the critical stress expression of the wall panel under the coupled action of tension and compression based on the critical coefficient expression and the buckling condition expression. The critical stress is obtained according to the minimum critical coefficient, the material characteristic parameter D and the wall panel structural parameters.

8. The critical stress calculation device for a wall panel under tension and compression coupling as described in claim 7, characterized in that, In the theoretical model of the wall panel under the coupled action of tension and compression, the four sides of the wall panel are simply supported. According to the left-hand coordinate system, the x-axis is horizontally to the right along the upper side of the wall panel, and the y-axis is vertically downward along the left side of the wall panel. The origin of the coordinate system is located at the left vertex of the wall panel. The structural parameters of the wall panel include the length, width, and thickness of the wall panel, as well as the elastic modulus and Poisson's ratio of the material.

9. The critical stress calculation device for a wall panel under tension and compression coupling as described in claim 8, characterized in that, The process of constructing the buckling condition expression for the wall panel under tension-compression coupling based on the theoretical model is as follows: First, based on compressive stress σ x With tensile stress σ y Given the relationship between compressive stress and tensile stress, let compressive stress be positive and tensile stress be negative. Then, compressive stress and tensile stress satisfy: σ x= -βσ y In the formula, β is the ratio of compressive to tensile load; The deflection ω at any point on the wall panel can be expressed as a trigonometric series: In the formula: m and n are positive integers, A mn Here are the coefficients of the trigonometric functions, a is the length of the panel, and b is the width of the panel. The differential equation for the buckling of the wall panel is: In the formula, D is the material characteristic parameter, ▽ 4 For biharmonic operators, E is the elastic modulus, δ is the wall thickness, and μ is Poisson's ratio; Substituting the deflection expression into the buckling differential equation, and considering that the buckling condition must be satisfied for any x and y, therefore: ； After simplification, the expression for the compression condition is obtained as follows: .

10. The critical stress calculation device for a wall panel under tension and compression coupling as described in claim 9, characterized in that, The expression for the material characteristic parameters is: In the formula, D is a material characteristic parameter.

11. The method for calculating the critical stress of a wall panel under tension and compression coupling as described in claim 10, characterized in that, The expression for the critical coefficient In the formula, K is the critical coefficient; By adjusting the values ​​of positive integers m and n, multiple critical coefficients are obtained under a specified compressive-tensile load ratio. The critical coefficient with the smallest absolute value is selected from the multiple critical coefficients to obtain the minimum critical coefficient.

12. The critical stress calculation device for a wall panel under tension and compression coupling as described in claim 11, characterized in that, The expression for the critical stress is as follows: In the formula, σ x,cr This is the critical stress.

13. An electronic device, characterized in that, include: One or more processors; Memory; One or more applications, which are stored in the memory and configured to be executed by the one or more processors, are configured to implement the method for calculating the critical stress of a wall panel under tensile and compressive coupling as described in any one of claims 1 to 6.

14. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores at least one instruction, at least one program, code set, or instruction set, wherein the at least one instruction, the at least one program, the code set, or instruction set is loaded and executed by a processor to implement the method for calculating the critical stress of a wall panel under tensile and compressive coupling as described in any one of claims 1 to 6.

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