A shell element design method for reliability study of aviation thin shell structures

Abstract

This application belongs to the field of shell unit design. It is a shell unit design method for the reliability research of aviation thin-shell structures. After discretizing the aviation thin-walled structure, each unit must be given a certain geometric size and material parameter to form a normal distribution or random distribution probability model, and a random finite element model is formed in conjunction with the unit stiffness matrix to perform probability random distribution finite element stiffness calculation. Based on the traditional analytical expression of each unit stiffness, the probability random distribution condition is introduced, so that the simulation analysis of the aviation plate and shell structure can take into account the influence of uncertain factors in process manufacturing, avoiding the adverse effects of the traditional safety factor method on the structural design, and reducing the cumbersome process of preparing a large number of input files for structural reliability analysis using deterministic analysis units, which can accelerate the iterative process of structural reliability design.

Description

Technical Field

[0001] The present application belongs to the field of shell element design, and in particular relates to a shell element design method for reliability research of aviation thin shell structures. Background Art

[0002] There are many factors that affect the economy or safety of aircraft structures, some of which have obvious and non-negligible randomness. However, in the current safety life design, durability and damage tolerance design, isolated and deterministic methods are used. Reliability is the ability of a product to complete its intended function under specified conditions within a specified time. With the deepening of research on structural reliability theory, the classical structural reliability theory has been fully developed. The structural design method based on probability theory has gradually been accepted by the engineering community. From the 1970s to the 1980s, the structural reliability theory was perfected and adopted by the codes and standards of various countries. Since C.A. Cornell proposed the second-order moment method, N.C. Lind deduced a complete set of load and resistance safety factors. This research linked reliability analysis with practical acceptable design methods. Random finite elements can more accurately reflect the influence of load uncertainty and material property heterogeneity on the structure. This influence is reflected by the mean value and covariance of unit stress. These stress effects are applied to the analysis and calculation of structural reliability, and the reliability index (or failure probability) of the structure is used to finally represent the influence of these uncertainties on the structure. However, this design based on statistical rules is difficult to accurately reflect the thickness distribution of the wall panel.

[0003] Therefore, a shell element design method suitable for reliability research of aviation thin shell structures is needed. Summary of the invention

[0004] The purpose of this application is to provide a shell unit design method for reliability research of aviation thin shell structures to solve the problem that the finite element analysis process based on determining the size to establish the unit stiffness matrix cannot reflect the thickness distribution of the wall panel.

[0005] The technical solution of the present application is: a shell unit design method for reliability research of aviation thin shell structures, comprising:

[0006] A bilinear model is established based on the characteristics of the aviation thin-walled structure design object;

[0007] The geometric dimensions and material parameters of each unit are obtained through the bilinear model, and then the normal distribution or random distribution probability model of each unit thickness is calculated based on the geometric dimensions and material parameters in the bilinear model to form a stress-strength interference model and determine whether the structure has failed. If not, the model parameters that meet the normal distribution or random distribution probability are input into the finite element solver to build a structural parameter probability analysis model;

[0008] The unit stiffness matrix corresponding to the aviation thin-walled structure is constructed according to the random model input parameters and the unit stiffness analytical expression;

[0009] The structural parameter probability analysis model is combined with the unit stiffness matrix to form a random finite element model, and the finite element stiffness analysis is performed through the thickness probability distribution to form the unit stiffness response value of the current analysis step;

[0010] The random thickness probability distribution is repeatedly generated in the random finite element model, and the finite element stiffness calculation is performed. After multiple rounds of automatic iteration, the stress distribution model of the thin-walled structure is formed. Finally, the reliability R of the aviation thin-walled structure is calculated through the stress-strength interference model and sent to the user.

[0011] Preferably, the relational expression of the unit stiffness matrix is:

[0012] ;

[0013] ;

[0014] ;

[0015] In the formula, are the tension / compression per unit length of the laminate section perpendicular to the x-axis, the tension / compression per unit length of the laminate section perpendicular to the y-axis, and the shear force; They are the bending moment around the x-axis per unit length of the laminate section, the bending moment around the y-axis per unit length of the laminate section, and the torque; are the normal strain and shear strain of the mid-surface of the laminate along the x-direction and the mid-surface of the laminate along the y-direction, respectively; are the curvature and distortion rate of the mid-surface of the laminate along the x direction and the mid-surface of the laminate along the y direction respectively; A ij , B ij , D ij are the matrix items corresponding to the in-plane stiffness matrix, coupling stiffness matrix and bending stiffness matrix of the laminate, i=1, 2, 6, j=1, 2, 6; Q x , Q y is the in-plane unit shear load along the x direction and along the y direction; S ij is the shear stiffness coefficient, i=1-2, j=1-2; are the in-plane shear strains of the xz and yz planes, respectively.

[0016] Preferably, finite element stiffness analysis is performed through thickness probability distribution, specifically:

[0017] ;

[0018] ;

[0019] ;

[0020] ;

[0021] Where A, B, and D are the in-plane stiffness matrix, coupling stiffness matrix, and bending stiffness matrix of the laminate, respectively; represents transverse shear; is the eccentric modulus of the kth layer, is the shear modulus of the kth layer, N is the number of single layers; is the coordinate of the lower surface of a single layer; is the coordinate of the upper surface of a single layer; is the thickness of the kth monolayer; is the coordinate of the reference surface; is the thickness of the k-1th monolayer; Indicates The number of individual layers in a stratum; Indicates The thickness of each layer; is the number of layers; For the The eccentric stiffness coefficient of each layer; Indicates The average distance from the mid-surface of each single layer in a layer to the reference plane; Indicates The mean square value of the distance from the mid-surface of each single layer in a layer to the reference plane.

[0022] Preferably, the unit stiffness matrix is:

[0023] ;

[0024] In the formula, represents the corresponding item of the element elasticity matrix; , is the center of gravity of the unit; is the radius of inertia in the x and y directions relative to the unit corner point, is the product of inertia.

[0025] Preferably, the specific method of establishing the bilinear model is: discretizing the thin-walled structure to form a plurality of units, and assigning each unit a certain geometric size and material parameter.

[0026] Preferably, the geometric dimensions and material parameters are measured by actually measuring the physical model, digital model or real object, and then calculating the mean μ, standard deviation σ and coefficient of variation COV of the corresponding parameters of each unit.

[0027] Preferably, the specific design method of the normal distribution or random distribution probability model of each unit thickness is:

[0028] Each module is marked separately, and the actual thickness distribution of each module is obtained. The maximum load, minimum load, maximum structural strength and minimum structural strength that the corresponding module can withstand are obtained through load calculation. The corresponding load probability density function and structural strength probability density function are obtained through statistics.

[0029] Preferably, the specific method for judging whether the structure has failed is: setting a structural failure threshold, calculating the area of ​​the damage zone by means of the load probability density function and the structural strength probability density function, judging whether the area of ​​the damage zone exceeds the structural failure threshold, if not, judging that the structure has not failed; if yes, judging that the structure has failed.

[0030] The shell unit design method for the reliability research of aviation thin shell structures in the present application introduces a probabilistic random distribution condition on the basis of the traditional analytical expression of the stiffness of each unit, so that the simulation analysis of the aviation plate and shell structure can take into account the influence of uncertain factors in the process manufacturing, avoiding the adverse effect of the traditional safety factor method on the structural design, and at the same time reducing the tedious process of preparing a large number of input files for structural reliability analysis using deterministic analysis units, which can accelerate the iterative process of structural reliability design. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to more clearly illustrate the technical solution provided by the present application, the following is a brief introduction to the accompanying drawings. Obviously, the accompanying drawings described below are only some embodiments of the present application.

[0032] Figure 1 This is a schematic diagram of the overall process of this application;

[0033] Figure 2 This is a schematic diagram of the stress-strength interference model of this application;

[0034] Figure 3 A schematic diagram of normal distribution parameters for this application;

[0035] Figure 4 Schematic diagram of the Z coordinates of each single layer of the laminate of this application. DETAILED DESCRIPTION

[0036] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0037] A shell element design method for the reliability study of aviation thin shell structures. With the lean requirements of aviation structural design, the traditional design method based on deterministic models has shown corresponding limitations. Aerospace engineers have been seeking aircraft structures that meet various performance and use requirements. With the development of computer technology, finite element technology and optimization technology, many structural reliability analysis methods have been developed and applied to aircraft structural design. In traditional structural optimization, all parameters are considered to be certain. Since the load and strength in the actual structure are not determined in advance, it is now widely believed that structural problems are non-deterministic. Therefore, some parameters must be regarded as random variables, and a reliability-based design method should be adopted, that is, the structural design must be carried out on the basis of reliability analysis; traditionally, the design of aircraft mostly adopts a deterministic design method, that is, the safety factor method, which has the advantages of simplicity and ease in engineering applications and is widely adopted by designers. However, the safety factor method also has an adverse effect on structural design. First of all, the safety factor method is conservative. In order to ensure sufficient design strength, a larger safety factor is often used, resulting in overweight structure, which has a great impact on the performance of aircraft structure. In the past, the reliability research of aviation structure adopted the research ideas based on mathematical statistics principles such as Monte Carlo simulation method, and established a large number of sample points for analysis. For large and complex aviation structures, it is obviously very complicated to prepare the input model manually, which is a waste of manpower. Using the design method provided by this scheme, only statistical parameters such as mean μ, standard deviation σ and coefficient of variation COV of the design part need to be provided, and the system can automatically complete the research on the response of thickness process parameters to structural performance for thin-walled structures. The application of this scheme in the domestic independent structural analysis system SABRE shows that it can effectively improve the efficiency of structural reliability research using component geometric scale as statistical variable and shorten the design cycle of uncertain influence research.

[0038] like Figure 1 , including the following steps:

[0039] Step S100, firstly establishing a bilinear model according to the design object characteristics of the aviation thin-walled structure;

[0040] Thin-walled structure design takes the structure itself as the object, discretizes the thin-walled structure to form several units, and assigns each unit a certain geometric dimension and material parameter, where the geometric dimension and material parameter are measured by physical model, digital model or real object, and then the mean μS, standard deviation σ and coefficient of variation COV of the corresponding parameters of each unit are calculated. After the thin-walled structure is discretized, a bilinear model is established to represent the geometric design domain of the thin-walled structure.

[0041] In the existing solution process for each unit, the thickness value of the midpoint of each unit is assigned to represent the entire unit. However, in the actual measurement process, the thickness of each unit at each position is not the same, which leads to deviations in the actual solution.

[0042] Step S200: The base point thickness data in different units may be normally distributed or randomly distributed, so a probability analysis model is established to determine the thickness distribution range, specifically: the geometric dimensions and material parameters of each unit are obtained through a bilinear model, and then the normal distribution or random distribution probability model of the thickness of each unit is calculated according to the geometric dimensions and material parameters in the bilinear model, a stress-strength interference model is formed, and it is judged whether the structure fails. If not, the model parameters that meet the normal distribution or random distribution probability are input into the finite element solver, and a structural parameter probability analysis model is constructed, and then the random model input parameters are generated through the structural parameter probability analysis model;

[0043] The specific design method of the normal distribution or random distribution probability model of each unit thickness is:

[0044] Each module is marked separately, and the actual thickness distribution of each module is obtained. The maximum load, minimum load, maximum structural strength and minimum structural strength that the corresponding module can withstand are obtained through load calculation. The corresponding load probability density function and structural strength probability density function are obtained through statistics.

[0045] Whether the structure fails in the stress-strength interference model depends on the relationship between the structure (or load) and the material (or structure) strength. The load is represented by L and the structural strength is represented by S. , represent the load probability density function and the structural strength probability density function respectively. Figure 2 Corresponding to , , the shaded part indicates the interference area, which is the possible damage area of ​​the structure. Figure 3 Schematic diagram of load and structural strength following normal distribution.

[0046] Preferably, the specific method for judging whether the structure has failed is: setting a structural failure threshold, calculating the area of ​​the damage zone by means of the load probability density function and the structural strength probability density function, judging whether the area of ​​the damage zone exceeds the structural failure threshold, if not, judging that the structure has not failed; if yes, judging that the structure has failed.

[0047] The random model input parameters include the random corresponding mean; the normal distribution standard deviation; the minimum truncation value of the random corresponding mean, which is taken when the random value is less than the minimum truncation value; the maximum truncation value of the random corresponding mean, which is taken when the random value is greater than the maximum truncation value; the random number generator used for initialization; and the distribution type, including random distribution and normal distribution.

[0048] The random model input parameters generate random numbers between the maximum load and the minimum load, and between the maximum structural strength and the minimum structural strength for finite element stiffness analysis.

[0049] Step S300, construct the unit stiffness matrix corresponding to the aviation thin-walled structure according to the random model input parameters and the unit stiffness analytical expression. Specifically, when the aviation thin-walled structure is made of metal materials, the existing unit stiffness matrix is ​​used; when the aviation thin-walled structure is made of composite materials, the unit stiffness matrix with thickness as a variable is established through shell elements;

[0050] The element stiffness matrix is ​​shown as follows;

[0051] ;

[0052] In the formula, represents the corresponding item of the element elasticity matrix; , is the center of gravity of the unit; is the radius of inertia in the x and y directions relative to the unit corner point, is the product of inertia.

[0053] Step S400, combining the structural parameter probability analysis model with the unit stiffness matrix to form a random finite element model, performing finite element stiffness analysis through thickness probability distribution, and forming a unit stiffness response value of the current analysis step;

[0054] like Figure 4 , because there is a large uncertainty in the distribution thickness of the laminate when it is made of composite materials, and the relationship between the stiffness and thickness of the composite material is relatively complex, the relationship between the unit stiffness matrix is:

[0055] ;

[0056] ;

[0057] ;

[0058] In the formula, are the tension / compression per unit length of the laminate section perpendicular to the x-axis, the tension / compression per unit length of the laminate section perpendicular to the y-axis, and the shear force; They are the bending moment around the x-axis per unit length of the laminate section, the bending moment around the y-axis per unit length of the laminate section, and the torque; are the normal strain and shear strain of the mid-surface of the laminate along the x-direction and the mid-surface of the laminate along the y-direction, respectively; are the curvature and distortion rate of the mid-surface of the laminate along the x direction and the mid-surface of the laminate along the y direction respectively; A ij , B ij , D ij are the matrix items corresponding to the in-plane stiffness matrix, coupling stiffness matrix and bending stiffness matrix of the laminate, i=1, 2, 6, j=1, 2, 6; Q x , Q y is the in-plane unit shear load along the x direction and along the y direction; S ij is the shear stiffness coefficient, i=1-2, j=1-2; are the in-plane shear strains of the xz and yz planes, respectively.

[0059] Based on the layered concept, the relationship tree of the stiffness coefficient of the laminate with thickness as the variable is shown as follows:

[0060] ;

[0061] ;

[0062] ;

[0063] ;

[0064] Where: A, B, D are the in-plane stiffness matrix, coupling stiffness matrix and bending stiffness matrix of the laminate respectively; Represents transverse shear, collectively referred to as shear stiffness.

[0065] — eccentric modulus of the kth layer, — shear modulus of the kth layer, N — number of single layers;

[0066] —Coordinates of the lower surface of a single layer;

[0067] —Coordinates of the upper surface of a single layer;

[0068] —thickness of the kth monolayer;

[0069] — coordinates of the reference surface;

[0070] —Thickness of the k-1th monolayer.

[0071] :Indicates the The number of individual layers in a stratum;

[0072] :Indicates the The thickness of each layer;

[0073] - the number of layers;

[0074] —No. The eccentric stiffness coefficient of each layer.

[0075] :Indicates the The average distance from the mid-surface of each single layer in a layer to the reference plane.

[0076] :Indicates the The mean square value of the distance from the mid-surface of each single layer in a layer to the reference plane.

[0077] Step S500, repeatedly generate random thickness probability distribution in the random finite element model, perform finite element stiffness calculation, form a thin-walled structure stress distribution model after multiple rounds of automatic iteration, and finally calculate the reliability R of the aviation thin-walled structure through the thin-walled structure stress distribution model and send it to the user.

[0078] Through the above design, the probabilistic random distribution condition is introduced on the basis of the traditional analytical expression of stiffness of each unit, so that the simulation analysis of aviation plate and shell structures can take into account the influence of uncertain factors in process manufacturing, avoiding the adverse effects of the traditional safety factor method on structural design, and reducing the cumbersome process of preparing a large number of input files for structural reliability analysis using deterministic analysis units, which can accelerate the iterative process of structural reliability design. This solution has been verified in domestic independent structural analysis software.

[0079] Finally, it should be noted that: the drawings of the embodiments disclosed in the present invention only involve structures related to the embodiments disclosed in the present invention, and other structures can refer to the general design. In the absence of conflict, the same embodiment and different embodiments of the present invention can be combined with each other;

[0080] Finally: The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A shell element design method for reliability research of aviation thin shell structures, characterized in that: include: A bilinear model is established based on the characteristics of the aviation thin-walled structure design object; The geometric dimensions and material parameters of each unit are obtained through the bilinear model, and then the normal distribution or random distribution probability model of the thickness of each unit is calculated according to the geometric dimensions and material parameters in the bilinear model to form a stress-strength interference model and determine whether the structure has failed. If not, the model parameters that meet the normal distribution or random distribution probability are input into the finite element solver to build a structural parameter probability analysis model, and then the random model input parameters are generated through the structural parameter probability analysis model; The unit stiffness matrix corresponding to the aviation thin-walled structure is constructed according to the random model input parameters and the unit stiffness analytical expression; The structural parameter probability analysis model is combined with the unit stiffness matrix to form a random finite element model, and the finite element stiffness analysis is performed through the thickness probability distribution to form the unit stiffness response value of the current analysis step; Repeatedly generate random thickness probability distribution in the random finite element model, perform finite element stiffness calculation, and form a thin-walled structure stress distribution model after multiple rounds of automatic iteration. Finally, calculate the reliability R of the aviation thin-walled structure through the stress-strength interference model and send it to the user; The analytical expression of the unit stiffness is: Where N x , N y , N xy are the tension / compression per unit length of the laminate section perpendicular to the x-axis, the tension / compression per unit length of the laminate section perpendicular to the y-axis, and the shear force; M x , M y , M xy They are the bending moment around the x-axis per unit length of the laminate section, the bending moment around the y-axis per unit length of the laminate section, and the torque; are the normal strain and shear strain of the mid-surface of the laminate along the x direction and the mid-surface of the laminate along the y direction, respectively; K x , K y , K xy are the curvature and distortion rate of the mid-surface of the laminate along the x direction and the mid-surface of the laminate along the y direction respectively; A ij , B ij , D ij are the matrix items corresponding to the in-plane stiffness matrix, coupling stiffness matrix and bending stiffness matrix of the laminate, i = 1, 2, 6, j = 1, 2, 6; Q x , Q y is the in-plane unit shear load along the x direction and along the y direction; S ij is the shear stiffness coefficient, i = 1-2, j = 1-2; τ xz , τ yz are the in-plane shear strains of the xz and yz planes, respectively; The specific method of establishing the bilinear model is: discretizing the thin-walled structure to form a number of units, and assigning each unit a certain geometric size and material parameters; The geometric dimensions and material parameters are obtained by actually measuring the physical model, digital model or real object, and then calculating the mean μ, standard deviation σ and coefficient of variation COV of the corresponding parameters of each unit to establish a bilinear model.

2. The shell element design method for reliability research of aviation thin shell structure according to claim 1, characterized in that: Where A, B, and D are the in-plane stiffness matrix, coupling stiffness matrix, and bending stiffness matrix of the laminate, respectively; G represents transverse shear; is the eccentric modulus of the kth layer, S k is the shear modulus of the kth layer, N is the number of single layers; z k-1 =C ref +D k-1 is the coordinate of the lower surface of the single layer; z k =z k-1 +t k is the coordinate of the upper surface of the single layer; t k is the thickness of the kth monolayer; C ref is the coordinate of the reference plane; D k-1 is the thickness of the k-1th monolayer; m k represents the number of single layers in the kth layer; T k represents the thickness of the kth layer; L is the number of layers; is the eccentric stiffness coefficient of the i-th layer; It represents the average distance from the mid-surface of each single layer in the kth layer to the reference plane; It represents the mean square value of the distance from the mid-surface of each single layer in the kth layer to the reference plane.

3. The shell element design method for reliability research of aviation thin shell structure according to claim 2, characterized in that: The element stiffness matrix is: Where D ij represents the corresponding item of the unit elasticity matrix, where i = 1, 3, j = 1, 3; is the centroid position of the unit; ρ x , y is the radius of inertia in the x and y directions relative to the unit corner point, ρ xy is the product of inertia.

4. The shell element design method for reliability research of aviation thin shell structure according to claim 1, characterized in that: The specific design method of the normal distribution or random distribution probability model of each unit thickness is: Each module is marked separately, and the actual thickness distribution of each module is obtained. The maximum load, minimum load, maximum structural strength and minimum structural strength that the corresponding module can withstand are obtained through load calculation. The corresponding load probability density function and structural strength probability density function are obtained through statistics.

5. The shell element design method for reliability research of aviation thin shell structure according to claim 1, characterized in that: The specific method for judging whether the structure has failed is as follows: setting a structural failure threshold, calculating the area of ​​the damage zone through the load probability density function and the structural strength probability density function, and judging whether the area of ​​the damage zone exceeds the structural failure threshold. If not, the structure is judged not to have failed; if so, the structure is judged to have failed.

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