Strong nonlinear point load and surface load conversion method

Abstract

The invention belongs to the field of anti-impact design of aircraft structures, and particularly relates to a strong nonlinear point load and surface load conversion method, which comprises the following steps of: S1, generating a water pressure load curved surface spline interpolation function according to pressure measuring point coordinates on the bottom surface of a fuselage and corresponding pressure values; s2, fitting a pressure distribution curved surface according to a curved surface spline interpolation function; s3, obtaining a pressure value of a finite element node of each surface element on the finite element model of the bottom surface of the fuselage according to the pressure distribution curved surface; and S4, according to the pressure value corresponding to the finite element node on each surface element, performing integration on each surface element to obtain surface loads of all the surface elements and point loads at the finite element nodes.

Description

Technical Field

[0001] The present application belongs to the field of aircraft structure impact resistance design, and in particular relates to a method for converting strongly nonlinear point loads and surface loads. Background Art

[0002] The strong nonlinear water loads obtained from the landing / water-skiing test of the surface aircraft or the water entry test of the cabin section are mainly presented as a limited number of pressure point loads on the bottom of the ship, while in fact the loads applied by the structural strength verification and strength test are surface loads. The point load-surface load conversion relationship is established, and the three-dimensional bottom surface load distribution is obtained through the load distribution and changes of the limited points, forming a point load to surface load conversion method.

[0003] The technology closest to the present invention is a method for equivalently distributing aircraft aerodynamic loads to finite element nodes. The aircraft wing structure bears aerodynamic external loads, and the pressure distribution at a series of discrete points and the total load and total moment of the wing are given according to experiments or theoretical calculations. When the wing structure is subjected to finite element analysis, these pressure points and the nodes of the finite element model do not overlap, and the aerodynamic load needs to be converted from the aerodynamic nodes to the finite element nodes. For two-dimensional loads, according to the pressure values ​​at known aerodynamic points, the pressure distribution surface is fitted through the thin plate spline interpolation function, and the pressure value at each finite element node is obtained from the surface. The pressure is then integrated on the unit to obtain the load interpolation method on the finite element node. The thin plate spline surface interpolation widely used in aerospace engineering is used. For three-dimensional loads, the concentrated force is directly integrated on the aerodynamic grid, and then distributed to the finite element model according to the principle of nearest distribution. The disadvantages of the prior art: the total wing load obtained according to the prior art is somewhat different from the test results. For large load conditions, the error can be controlled within 10%; for small load conditions, the error is larger, exceeding 10%; the existing interpolation method has poor adaptability to problems where aerodynamic data changes dramatically and has singular distributions. Summary of the invention

[0004] In order to solve the above problems, the present application provides a method for transforming strongly nonlinear point loads and surface loads, including:

[0005] Step S1: Generate a water pressure load surface spline interpolation function according to the coordinates of the pressure measuring points on the bottom surface of the fuselage and the corresponding pressure values;

[0006] Step S2: fitting the pressure distribution surface according to the surface spline interpolation function;

[0007] Step S3: obtaining the pressure value of each finite element node of the finite element model of the bottom surface of the fuselage from the pressure distribution surface;

[0008] Step S4: According to the pressure value corresponding to the finite element node on each surface element, integrate on each surface element to obtain the surface load of all surface elements and the point load at the finite element node.

[0009] Preferably, the surface elements of the finite element model include quadrilateral elements or triangular elements.

[0010] Preferably, the method for calculating the surface load of the triangular unit and the point load at the finite element node includes:

[0011] Let the pressure values ​​of the three finite element nodes of the triangular unit be qi, qj, and qk respectively. Determine the water pressure distribution plane q based on qi, qj, and qk. Integrate the water pressure distribution plane q over the triangular domain to obtain the surface load on the triangular block.

[0012] Preferably, the water pressure distribution plane equation of the water pressure distribution plane q is set to:

[0013] q=α+βx+γz;

[0014] Among them, α, β, γ are all unknown coefficients, x is the horizontal coordinate, and y is the vertical coordinate.

[0015] Preferably, the coordinates of the finite element nodes with pressure values ​​of qjqi are set to (a, 0), the coordinates of the finite element nodes with pressure values ​​of qk are set to (b, c), and the coordinates of the finite element nodes with pressure values ​​of qj are set to the origin. Substituting the coefficients to be solved, the water pressure distribution plane equation of the water pressure distribution plane q is obtained as follows:

[0016]

[0017] Preferably, the surface load calculation formula of the water pressure distribution plane q is:

[0018]

[0019] S is the area of ​​the triangle.

[0020] Preferably, the pressure center is the equivalent action point of the total load of the surface element, and the pressure center calculation formula of the water pressure distribution plane q is:

[0021]

[0022] Preferably, the method for calculating the point load at the finite element node includes:

[0023] The triangle unit is considered to be composed of three sub-triangle units superimposed;

[0024] The pressure values ​​of the finite element nodes of the first sub-triangular element are: q i ≠0,q j =q k =0;

[0025] The pressure values ​​of the finite element nodes of the second sub-triangular unit are: q i =0,q j ≠0,q k =0;

[0026] The pressure values ​​of the finite element nodes of the third sub-triangular unit are: q i =q j =0,q k ≠0.

[0027] Preferably, the surface loads of the triangular finite element nodes are:

[0028]

[0029] Where: q0 = q i +q j +q k .

[0030] Preferably, the surface load of the quadrilateral unit and the point load at the finite element node are obtained by splitting into a plurality of triangular units and integrating them respectively.

[0031] Preferably, the surface load of the quadrilateral unit and the point load at the finite element node are obtained by splitting into four triangular units and integrating them respectively.

[0032] Preferably, the pressure measuring points on the bottom surface of the fuselage are distributed in a matrix, wherein the distance between two adjacent pressure measuring points distributed along the heading direction is 1.5 to 2 times the distance between two adjacent pressure measuring points distributed along the span direction.

[0033] Preferably, the pressure value of the pressure measuring point on the bottom surface of the fuselage is obtained by screening through a design point method, a parameter analysis and selection method, a single value envelope method or a combined envelope method.

[0034] The present application establishes a point load-surface load conversion relationship, and obtains a three-dimensional ship bottom surface load distribution method through the load distribution and change of finite points by combining theoretical analysis, simulation, model test and other technical means. The present invention provides a strong nonlinear point load and surface load conversion method for structural design and strength verification. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 This is a flow chart of a method for converting strongly nonlinear point loads and surface loads in a preferred embodiment of the present application.

[0036] Figure 2 This is a schematic diagram of an integral triangle in a preferred embodiment of the present application. DETAILED DESCRIPTION

[0037] In order to make the technical solution and advantages of the present application clearer, the technical solution of the present application will be further described in detail in detail and in detail in conjunction with the accompanying drawings. It can be understood that the specific embodiments described here are only partial embodiments of the present application, which are only used to explain the present application, not to limit the present application. It should be noted that, for the convenience of description, only the parts related to the present application are shown in the accompanying drawings, and other related parts can refer to the general design. In the absence of conflict, the embodiments in the present application and the technical features in the embodiments can be combined with each other to obtain new embodiments.

[0038] (1) Aircraft water landing dynamics model test

[0039] Aircraft ditching on water is a water impact problem. The aircraft will be subjected to huge impact loads in the initial transient period of entering the water. During the entire ditching process, the aircraft structure will continuously arouse the movement of the fluid medium. At the same time, the fluid medium will exert various reaction forces on the aircraft structure. This is a structural water impact dynamics problem. The theoretical analysis of ditching on water involves changes in the shape of the water surface boundary, which is a rather complex nonlinear problem.

[0040] The dynamic similarity model test has been widely used to study the performance of aircraft forced landing. The model design and production should meet both geometric similarity and motion similarity. According to the similarity conditions and similarity criteria, the model's size, center of gravity, weight, moment of inertia and other parameters should meet the corresponding proportional relationship in Table 1.

[0041]

[0042] (2) Water load measurement

[0043] In a water load model test of an aircraft forced landing, 32 pressure sensors are arranged on the lower surface of the fuselage, and the sensors are distributed according to the frame station. The installation positions of some pressure sensors are shown in Figure 1 , the X axis is on the horizontal line of the aircraft structure, and its direction is opposite to the heading; the Y axis is perpendicular to the symmetry plane of the aircraft, and points to the right; the Z axis is on the symmetry plane of the aircraft, and points vertically upward. The coordinates of the pressure sensors of each channel are shown in Table 2.

[0044]

[0045]

[0046] (3) Screening of water load conditions

[0047] The hydrodynamic load changes instantaneously when the aircraft enters the water. If each instantaneous load in the time history method is taken into account, the number of load points will be very large, which is impractical and difficult to achieve in engineering practice. Therefore, it is necessary to screen the loads from such a vast data pile according to certain principles to obtain limited load design severe conditions to provide strength verification calculations. This can not only ensure that the severe conditions of the loads are not missed, but also greatly reduce the workload of calculations. Four methods are used for load screening: design point method, parameter analysis and selection method, single value envelope method and combination envelope method. The first three are classic screening methods, and the combination envelope method is a supplement to the classic method.

[0048] (4) Load distribution calculation method

[0049] ① Water load provision form

[0050] During the aircraft entry into water, the bottom surface of the fuselage is the first to contact with water and the bottom surface is always interacting with water during the entry into water. The pressure distribution on the bottom surface changes with time. The strong nonlinear water load obtained from the water surface aircraft landing / hydroplaning test or the cabin entry into water test is given in the form of a finite number of pressure point loads and pressure measurement point coordinates.

[0051] ② Load sharing method

[0052] Firstly, the water pressure load surface spline interpolation function is generated according to the coordinates of the pressure measuring points and the pressure values ​​on the bottom surface of the fuselage; and the pressure distribution surface is fitted by using the surface spline interpolation function;

[0053] The pressure value of each finite element node on the bottom surface is obtained from the curved surface, and then integrated on the quadrilateral unit and triangular unit of the finite element element to obtain the small block surface load and the point load at the finite element node.

[0054] It can be divided into the following steps:

[0055] a) Generate a surface spline interpolation function based on the pressure values ​​of a limited number of water pressure measuring points;

[0056] b) Determine the pressure value at the finite element node by using the surface spline function interpolation;

[0057] c) Integrate on the quadrilateral and triangular surface element grids to obtain small block surface loads and finite element node loads.

[0058] Surface spline function is a mathematical method for interpolating functions of two independent variables. The calculation of bottom water load can be done by using the surface spline function method developed by Harder and Desmaras in 1972. This section takes the XOY plane as an example.

[0059] Assume that at N independent points (x j ,yj )(j=1,2,……,N) j Given, the general surface spline function can be expressed as:

[0060]

[0061] Where:

[0062] r i 2 =(xx i ) 2 +(yy i ) 2 (2)

[0063] ε is a small quantity, which is set for calculating high-order derivatives and controlling the rapidity of surface curvature changes. General requirements:

[0064] ε< <min(r i 2 )(i=1,2,……,N;r i is a non-zero value) (3)

[0065] Coefficient F i and a0, a1, a2 are determined by the following linear equations:

[0066]

[0067] Where:

[0068]

[0069] C j The weight added for the surface smoothing requirement, C j Take 0.

[0070] Representing equation (4) in matrix form, we have:

[0071]

[0072] The first-order partial derivative is:

[0073]

[0074] Equation group (6) has the following three characteristics:

[0075] a) The order is high, its order is N+3;

[0076] b) The coefficient matrix is ​​symmetric;

[0077] c) Diagonal elements may be zero.

[0078] Solving equation (6), we get Fi Substituting a0, a1, a2 into (1), we can obtain the surface spline interpolation function of the water pressure distribution.

[0079] The surface elements in the finite element model, whether quadrilateral elements or triangular elements, can be divided into one or several triangular elements. The calculation of unit node loads is based on triangular elements.

[0080] Assume that the water pressures on the three corner points of the triangular unit are qi, qj, and qk, respectively. The water pressure distribution plane q can be determined based on qi, qj, and qk. By integrating q over the triangular domain, the load on the triangular block can be obtained. For the sake of simplicity in formula derivation, the origin is set at point i and the X-axis is the line connecting ij. Figure 2 . This section takes the XOZ plane as an example.

[0081] The water pressure distribution plane equation is:

[0082] q=α+βx+γz (8)

[0083] Depend on:

[0084]

[0085] We can get:

[0086] α=q i (10)

[0087]

[0088] Substituting (10) to (12) into (8), we can obtain:

[0089]

[0090] Total load:

[0091]

[0092] Heart Pressure:

[0093]

[0094] For the water pressure distribution on the triangular area, the distribution superposition method can also be used to calculate the water pressure distribution on the triangular area. The specific process is as follows:

[0095] For q i ,q j ,q k The resulting water pressure distribution plane q can be obtained by q i ≠0,q j =q k =0 and q i =0,q j ≠0,qk =0;q i =q j =0,q k ≠0 is the superposition of three pyramidal distributions; therefore, the loads at the three corner points can be formed by the superposition of the above three loads distributed at each corner point.

[0096] After derivation, the loads at the three corner points of the triangle are:

[0097]

[0098] Where: q0 = q i +q j +q k ,q i ,q j ,q k are the pressure values ​​of the three corner points of the triangle, and S is the area of ​​the triangle.

[0099] It can be seen from formula (17) that the corner point load on the triangular block is only related to the pressure values ​​at the three local corner points and the area of ​​the triangular block.

[0100] For a quadrilateral unit, it is divided into four triangles along two diagonals in load calculation. The loads at each point are obtained by integrating the four triangular units respectively. After superposition, the loads are divided by 2 to obtain the loads at each node of the quadrilateral.

[0101] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application shall be based on the protection scope of the claims.

Claims

1. A method for transforming strongly nonlinear point loads and surface loads, characterized in that: include: Step S1: Generate a water pressure load surface spline interpolation function according to the coordinates of the pressure measuring points on the bottom surface of the fuselage and the corresponding pressure values; Step S2: fitting the pressure distribution surface according to the surface spline interpolation function; Step S3: obtaining the pressure value of each finite element node of the finite element model of the bottom surface of the fuselage from the pressure distribution surface; Step S4: According to the pressure value corresponding to the finite element node on each surface element, integrate on each surface element to obtain the surface load of all surface elements and the point load at the finite element node.

2. The method for converting strong nonlinear point loads to surface loads according to claim 1, characterized in that: The surface elements of the finite element model include quadrilateral elements or triangular elements.

3. The method for converting strong nonlinear point load to surface load as claimed in claim 2, characterized in that: Methods for calculating point loads on triangular element surfaces and finite element nodes include: Let the pressure values ​​of the three finite element nodes of the triangular unit be qi, qj, and qk respectively. Determine the water pressure distribution plane q based on qi, qj, and qk. Integrate the water pressure distribution plane q over the triangular domain to obtain the surface load on the triangular block.

4. The method for converting strong nonlinear point load to surface load as claimed in claim 3, characterized in that: The water pressure distribution plane equation of the water pressure distribution plane q is set as: q=α+βx+γz; Among them, α, β, γ are all unknown coefficients, x is the horizontal coordinate, and y is the vertical coordinate.

5. The method for converting strong nonlinear point load to surface load according to claim 4, characterized in that: The coordinates of the finite element nodes with pressure values ​​of qjqi are set to (a, 0), the coordinates of the finite element nodes with pressure values ​​of qk are set to (b, c), and the coordinates of the finite element nodes with pressure values ​​of qj are set to the origin. Substituting the unknown coefficients into the solution, the water pressure distribution plane equation of the water pressure distribution plane q is obtained as follows:

6. The method for converting strong nonlinear point load to surface load according to claim 5, characterized in that: The surface load calculation formula of the water pressure distribution plane q is: S is the area of ​​the triangle.

7. The method for converting strong nonlinear point load to surface load according to claim 6, characterized in that: The calculation formula for the pressure center of the water pressure distribution plane q is:

8. The method for converting strong nonlinear point load to surface load according to claim 6, characterized in that: Methods for calculating point loads at finite element nodes include: The triangle unit is considered to be composed of three sub-triangle units superimposed; The pressure values ​​of the finite element nodes of the first sub-triangular unit are: q i ≠0,q j =q k =0; The pressure values ​​of the finite element nodes of the second sub-triangular unit are: q i =0,q j ≠0,q k =0; The pressure values ​​of the finite element nodes of the third sub-triangular unit are: q i =q j =0,q k ≠0.

9. The method for converting strong nonlinear point load to surface load according to claim 8, characterized in that: The point loads of the triangular finite element nodes are: Where: q0 = q i +q j +q k .

10. The method for converting strong nonlinear point load to surface load according to claim 6, characterized in that: The surface loads of the quadrilateral elements and the point loads at the finite element nodes are obtained by splitting them into multiple triangular elements and integrating them separately.

11. The method for converting strong nonlinear point load to surface load according to claim 10, characterized in that: The surface load of the quadrilateral element and the point load at the finite element node are obtained by splitting it into 4 triangular elements and integrating them separately.

12. The method for converting strong nonlinear point load to surface load according to claim 10, characterized in that: The pressure measuring points on the bottom surface of the fuselage are distributed in a matrix, wherein the distance between two adjacent pressure measuring points distributed along the heading direction is 1.5 to 2 times the distance between two adjacent pressure measuring points distributed along the span direction.

13. The method for converting strong nonlinear point load to surface load according to claim 10, characterized in that: The pressure values ​​of the pressure measuring points on the bottom surface of the fuselage are obtained by screening through the design point method, parameter analysis and selection method, single value envelope method or combined envelope method.

Images