A design optimization method for lightening holes in aircraft tooling

Abstract

The present invention discloses a design optimization method for aircraft tooling lightening holes, belonging to the technical field of aircraft tooling design. The method comprises the following steps: obtaining the load-bearing conditions of each beam on a tooling without lightening holes; simplifying the beams on the tooling into statically indeterminate beams with fixed ends, transforming them into equivalent statically determinate systems when solving the problem, moving the load to the midpoint of the beam according to the force translation theorem, and then calculating the deformation of the beam by superimposing the deformation effects of each section to derive the maximum deformation equation of a cantilever beam with lightening holes when subjected to a concentrated force; determining the stiffness requirements and weight reduction goals of the tooling, and clarifying the limiting conditions of the lightening hole parameters; determining the beam load transfer relationship and determining different optimization strategies based on different load transfer methods; using orthogonal experiments to determine the degree of influence of the lightening hole parameters on the optimization goal, and optimizing the design of the tooling lightening holes based on the test results. The present invention provides new ideas and methods for the design of tooling lightening holes.

Description

Technical Field

[0001] The present invention relates to the field of aircraft tooling design, and in particular to a design optimization method for a lightening hole of an aircraft tooling. Background Art

[0002] Aircraft manufacturing utilizes a wide variety of tooling. To ensure precision, tooling designs often incorporate a large safety factor to guarantee rigidity. This, however, significantly increases tooling weight, making it difficult to transport the product while holding the tooling. For completed tooling, adding lightening holes to the original structure can effectively reduce weight while maintaining rigidity.

[0003] The design of lightening holes for aircraft tooling generally relies on engineering experience combined with finite element calculations. This design method has the following problems: 1) The design iteration cycle is long and the threshold for designers is high; 2) There is a lack of evaluation indicators, making it difficult to evaluate the pros and cons of design solutions; 3) There is a lack of systematic design methods, and the design solutions for lightening holes vary from person to person, and the design concepts and ideas are difficult to preserve and pass on. At present, there are optimization design methods for lightening holes in thin plate structures in the aerospace field in China. Representative examples include Hao Peng [1] and others who optimized lightening holes in skin truss structures based on neural networks, and Liu Hai [2] who optimized the number of lightening holes in anti-shear thin plates using the finite element method. There is no method for designing and optimizing lightening holes for aircraft tooling by combining theoretical calculations with orthogonal experiments. Summary of the Invention

[0004] The present invention aims to solve the problem in the prior art that the heavy weight of the tooling makes it difficult to transport products while the tooling is held. A design optimization method for lightening holes in aircraft tooling is proposed, which takes the ratio of tooling stiffness to weight as the optimization target and provides designers with an effective reference for the size and distribution of the lightening holes.

[0005] In order to achieve the above-mentioned object of the invention, the technical solution of the present invention is as follows:

[0006] A design optimization method for a lightening hole of an aircraft tooling, characterized by comprising the following steps:

[0007] Step a, obtaining the load condition of each beam on the fixture without lightening holes;

[0008] Step b: Simplify the beam on the fixture into a statically indeterminate beam with both ends fixed. When solving, transform it into an equivalent statically determinate system. Move the load obtained in step a to the midpoint of the beam according to the translation theorem of force. Then calculate the deformation of the beam by superposing the deformation effects of each section.

[0009] Step c, deriving the maximum deformation formula of the cantilever beam with rectangular lightening holes when subjected to concentrated force, and combining it with step b, obtaining the stiffness of the statically indeterminate beam with rectangular lightening holes with both ends fixed;

[0010] Step d: Determine the tooling stiffness requirements and weight reduction targets based on tooling design requirements and actual needs, and clearly define the constraints for reducing hole parameters;

[0011] Step e: using orthogonal test to determine the influence of the lightening hole parameters on the optimization target, and optimizing the design of the tooling lightening hole according to the test results.

[0012] Furthermore, the method of obtaining the load-bearing condition of each beam on the tooling without lightening holes includes: measuring the weight and center of the product on the tooling, simplifying the product into mass points based on the measurement results, connecting it to the tooling joints according to the actual connection form, and reading the load conditions borne by each beam constituting the tooling.

[0013] Furthermore, the maximum deformation of the cantilever beam with the lightening hole when subjected to concentrated force is equal to the sum of the deformation of the cantilever beam caused by the concentrated force, the deformation of the cantilever beam caused by the bending internal force and the additional moment, and the deformation of the cantilever beam caused by the shear internal force.

[0014] Furthermore, for thin-walled hollow beams, the maximum deformation of cantilever beams with lightening holes under concentrated force should also be corrected by adding the value

[0015]

[0016] Where n is the number of lightening holes, i=1 when n is an odd number, and i=2 when n is an even number; δ1 is the hole length, δ2 is the spacing between two adjacent lightening holes; I1 is the moment of inertia of the section without lightening holes, I2 is the moment of inertia of the section with lightening holes; k is the correction coefficient.

[0017] Furthermore, in step e, different optimization strategies are determined according to different load transfer modes of the beams; the beams that transmit loads sequentially are defined as a "series" relationship; when the beams are in a "series" relationship, the optimization strategy is to design the parameters of the lightening holes to optimize the specific stiffness of the beams; the beams that share the load are defined as a "parallel" relationship; when the beams are in a "parallel" relationship, the optimization strategy is not only to design the parameters of the lightening holes to optimize the specific stiffness of the beams, but also to ensure that the stiffness of the parallel beams remains consistent after the lightening holes are added, maintain structural symmetry, promote uniform load distribution, and avoid additional bending moments.

[0018] Furthermore, in step d, based on the stiffness requirements of the tooling, the load Ω required to produce unit deflection under unit mass is used to express the specific stiffness of the structure. The larger the Ω, the greater the specific stiffness of the structure, and the smaller the Ω, the smaller the specific stiffness of the structure. The expression is:

[0019]

[0020] Where F is the concentrated load, ω cis the total deformation of the beam, and m is the mass of the beam.

[0021] Furthermore, the lightening hole parameters include the width, length and number of the lightening holes, and the restrictions on the lightening holes include: the length of the lightening hole does not exceed 10% of the total length of the beam; the width of the lightening hole does not exceed 80% of the width of the beam.

[0022] Furthermore, in step f, the width, length and number of the lightening holes are used as factors, the number of levels x is set according to the precision of the calculation, a factor level table is established, and the specific stiffness and range of each beam are calculated; according to the calculation results, the factors with a greater impact on the target are prioritized in order, and the factors with a smaller impact on the target are weakened, and finally the design results of the tooling lightening holes are obtained.

[0023] Furthermore, the deformation of the cantilever beam with the lightening hole caused by the concentrated force F / 2 includes bending deformation caused by the concentrated force and shear deformation caused by the concentrated force.

[0024] Furthermore, the cantilever beam with a lightening hole is deformed by the concentrated force F / 2, and the bending deformation ω caused by the concentrated force is M for:

[0025]

[0026] Where: ω1 is the displacement of the first segment due to deformation under the action of concentrated force, ω1 * is the displacement of the first segment due to bending under the action of concentrated force, ω i is the displacement of the i-th segment due to deformation under the action of concentrated force, ω i * is the displacement of the i-th segment due to bending under the action of concentrated force, ω 2n+1 is the displacement of the 2n+1 segment due to deformation under the action of concentrated force;

[0027] Shear deformation ω caused by concentrated force F for:

[0028]

[0029] Where h1 is the height of the outer section of the beam, h2 is the height of the inner section of the beam, G is the shear modulus of the material, n is the number of lightening holes, δ1 is the length of the lightening hole, δ2 is the spacing between two adjacent lightening holes, δ3 is the width of the lightening hole, I1 is the moment of inertia of the section without lightening holes, and I2 is the moment of inertia of the section with lightening holes.

[0030] Furthermore, the bending deformation and shear deformation of the cantilever beam caused by the internal moment and additional moment are and 0, the total deformation caused by the bending moment for:

[0031]

[0032] in: is the displacement of the first segment due to deformation under the action of internal moment Me and additional moment M*, is the displacement of the first segment due to bending under the action of internal moment Me and additional moment M*, is the displacement of the i-th segment due to deformation under the action of internal moment Me and additional moment M*, is the displacement of segment i due to bending under the action of internal moment Me and additional moment M*; It is the displacement of the 2n+1 segment due to deformation under the action of internal moment Me and additional moment M*.

[0033] In summary, the present invention has the following advantages:

[0034] 1. This invention provides a set of design and optimization strategies for tooling lightening holes. The load-bearing conditions of the tooling beam are calculated, and then the relationship between the lightening hole design parameters and the tooling beam stiffness and weight is established. The relationship between the design parameters and product indicators is clarified. Finally, the orthogonal test method is used to determine the degree of influence of different parameters on the indicators. Then, single-objective optimization is carried out in descending order to achieve the optimal design of the tooling lightening holes.

[0035] 2. The method of the present invention establishes the relationship between the size and distribution of the tooling lightening holes and the stiffness and weight of the tooling beam through the beam bending and shear deformation formulas in mechanics. The ratio of tooling stiffness to weight is used as the optimization target, providing designers with an effective reference for the size and distribution of lightening holes.

[0036] 3. The method of the present invention derives the maximum deformation formula of the cantilever beam by superposing the deformation effects of each section, transforms the two-end beam into an equivalent statically determinate system of a statically indeterminate structure, and provides the derivation process of the relationship formula between the design parameters of the lightening hole and the maximum deformation of the tooling beam, providing a reference for designers;

[0037] 4. After determining the parameter range of the lightening hole according to actual needs, the present invention optimizes the parameters through orthogonal experiments to obtain the lightening hole design parameters that meet the stiffness requirements and have the lightest weight. This method has the advantages of high computational efficiency and simple operation, providing new ideas and methods for tooling designers.

[0038] 5. The present invention also proposes a correction method for deriving the maximum deformation formula of a cantilever beam based on the superposition method of segment-by-segment deformation effects. This correction is made for thin-walled hollow beam structures to make the design results more reliable.

[0039] 6. The present invention divides the beams that make up the tooling into "series" and "parallel" relationships according to the load transfer method, and selects different optimization strategies for different load transfer methods to obtain better design effects. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a schematic diagram of the lightening hole parameters;

[0041] Figure 2 It is the schematic diagram of converting a beam fixed at both ends into its equivalent statically determinate system;

[0042] Figure 3 This is the principle diagram of the segment-by-segment deformation superposition method;

[0043] Figure 4 It is a flow chart of the lightening hole design method. DETAILED DESCRIPTION

[0044] In order to more clearly illustrate the present invention, the present invention is further described below in conjunction with preferred embodiments and drawings. Those skilled in the art should understand that the following specific description is illustrative rather than restrictive and should not be used to limit the scope of protection of the present invention.

[0045] The present invention provides a design optimization method for aircraft tooling lightening holes, such as Figure 4 As shown, the following steps are included:

[0046] Step 1: Calculate the load-bearing conditions of each beam on the fixture without lightening holes.

[0047] (1) Measure product weight information

[0048] This step may be implemented by, but is not limited to, using 3D modeling software to create a product model mounted on the tooling, assigning material properties, and then measuring the weight and center of gravity of the product on the tooling.

[0049] (2) Loading

[0050] According to the weight and center of gravity measured in step (1), the product is simplified into mass points and connected to the tooling joints according to the actual connection form. The calculation method of this step can be, but is not limited to, the finite element method.

[0051] (3) Result reading: Read the load borne by each beam that makes up the tooling.

[0052] Step 2: Derive the maximum deformation equation of the beam

[0053] The design parameters of the tooling lightening hole are as follows: Figure 1 shown.

[0054] Most of the beams on the fixture are connected by welding. When calculating, they can be simplified into statically indeterminate beams with both ends fixed. When solving, they can be transformed into statically determinate equivalent systems (the transformation principle is as follows Figure 2 ), where A, B, and C represent the endpoints of the beam.

[0055] The load obtained in step 1 is moved to the midpoint of the beam according to the force translation theorem, and then the deformation of the beam is calculated according to the segment-by-segment deformation effect superposition method (the principle is as follows Figure 3 ).

[0056] The maximum deformation formula of a cantilever beam with a lightening hole when subjected to concentrated force is:

[0057]

[0058] Where, ω c is the maximum deformation of the cantilever beam, ω Z is the deformation of the cantilever beam caused by the concentrated force, is the deformation of the cantilever beam due to the bending internal force, is the deformation of the cantilever beam due to the internal force of shear force.

[0059] Bending deformation ω caused by concentrated force F / 2 M for:

[0060]

[0061] Where: ω1 is the displacement of the first segment due to deformation under the action of concentrated force, ω1 * is the displacement of the first segment due to bending under the action of concentrated force, ω i is the displacement of the i-th segment due to deformation under the action of concentrated force, ω i * is the displacement of the i-th segment due to bending under the action of concentrated force, ω 2n+1 is the displacement of the 2n+1 segment due to deformation under the action of concentrated force.

[0062]

[0063] Where F is the magnitude of the concentrated force, E is the elastic modulus of the material, I1 is the moment of inertia of the section without the lightening hole, I2 is the moment of inertia of the section with the lightening hole, l1 is the distance from the end point of the beam to the edge of the first lightening hole, and L is the total length of the beam.

[0064]

[0065] Where n is the number of lightening holes, δ1 is the length of the lightening hole, δ2 is the spacing between two adjacent lightening holes, and δ3 is the width of the lightening hole.

[0066] Shear deformation ω caused by concentrated forceF for:

[0067]

[0068] Where h1 is the height of the outer section of the beam, h2 is the height of the inner section of the beam, G is the shear modulus of the material, and the total deformation caused by the concentrated force ω Z for:

[0069] ω Z =ω M +ω F ;

[0070] ω M is the bending deformation caused by concentrated force, ω F Shear deformation caused by concentrated force.

[0071] Similarly, the bending deformation of the cantilever beam caused by the internal moment Me and the additional moment M* is According to the symmetry of the beam, the deformation caused by the shear internal force is 0, so the total deformation caused by the bending moment is for:

[0072]

[0073] in: is the displacement of the first segment due to deformation under the action of internal moment Me and additional moment M*, is the displacement of the first segment due to bending under the action of internal moment Me and additional moment M*, is the displacement of the i-th segment due to deformation under the action of internal moment Me and additional moment M*, is the displacement of the i-th segment due to bending under the action of internal moment Me and additional moment M*. It is the displacement of the 2n+1 segment due to deformation under the action of internal moment Me and additional moment M*.

[0074]

[0075] When the structure is a thin-walled hollow beam, the calculation results must be corrected. If it is not a thin-walled hollow beam, no correction is required. Assuming the correction coefficient k, the correction formula can be expressed as:

[0076]

[0077] Where, when n is an odd number, i=1, and when n is an even number, i=2. The final total deformation result is the total deformation caused by the concentrated force + the total deformation caused by the internal moment Me and the additional moment M* + the correction deformation, that is:

[0078]

[0079] Step 3: Determine optimization goals and constraints

[0080] (1) Determine the optimization target of tooling

[0081] Determine the tooling stiffness requirements and weight reduction targets based on tooling design requirements and actual needs.

[0082] The calculation formula for the mass of a beam with a lightened hole is as follows:

[0083] M=V(n,l,l1,δ1,δ2,δ3,t,h1,h2,b1,b2)ρ (2)

[0084] Where M represents the mass of the beam, ρ is the material density, and V is the volume of the beam. The volume is expressed as follows:

[0085] V=[l1+l2+(n-1)δ2](b1h1-b2h2)+nδ1(b1h1-b2h2-2tδ3) (3)

[0086] The specific stiffness of a structure can be expressed by the load Ω required to produce unit deflection under unit mass. The larger the Ω, the greater the specific stiffness of the structure, and the smaller the Ω, the smaller the specific stiffness of the structure. The expression is:

[0087]

[0088] Where F is the concentrated load, ω c is the total deformation of the beam, and m and M are the mass of the beam.

[0089] (2) Clearly reduce the constraints on hole parameters

[0090] After the design is completed, the tooling only has three variables: n, δ1, and δ3. max , n max To reduce the number of holes at most; to prevent the local strength of the tooling from being insufficient, the length of the hole δ1 is generally not more than 10% of the total length of the beam, δ1∈0~0.1*L; the width of the hole δ3 is not more than 80% of the beam width, that is, δ3∈

[0091] 0~0.8*h1.

[0092] Step 4: Determine the beam load relationship and formulate an optimization strategy

[0093] According to the load transfer method, beams that share the load are considered in a "parallel" relationship; beams that transfer the load sequentially are considered in a "series" relationship. For beams in a "series" relationship, the optimization strategy is to design the lightening hole parameters to optimize the beam's specific stiffness. For beams in a "parallel" relationship, the optimization strategy not only requires designing the lightening hole parameters to optimize the beam's specific stiffness, but also ensures that the stiffness of the parallel beams remains consistent after adding lightening holes, maintaining structural symmetry, promoting even load distribution, and avoiding additional bending moments.

[0094] Step 5: Orthogonal test to determine the degree of influence on optimization target

[0095] The orthogonal test method is adopted, with the width, length and number of the lightening holes as factors, and the number of levels x is set according to the precision of the calculation. The factor level table is established as shown in Table 1, and the specific stiffness and range of each beam are calculated as shown in Table 2.

[0096] Orthogonal table for optimizing design parameters of lightening holes

[0097]

[0098]

[0099] 3-factor x-level orthogonal table

[0100]

[0101] Step 6: Optimize the design of tooling lightening holes

[0102] The range obtained in step 5 represents the degree of influence of the three factors on the optimization objective. The larger the range, the stronger the influence of the factor on the optimization objective. During the optimization design, factors with greater influence on the objective are prioritized, and factors with less influence are weakened, ultimately resulting in the design result of the tooling lightening hole.

[0103] Example

[0104] The following is an explanation of this method using specific data.

[0105] ① Calculate the load-bearing condition of each beam on the fixture without lightening holes:

[0106] In this embodiment, a finite element model of the tooling is established using beam elements. Calculations show that the load borne by the beam to be optimized is 1200 N, and the load position is 200 mm from the geometric center of the beam. Based on the force translation theorem, this is converted into a concentrated force of 1200 N and a bending moment of 240 N·m at the geometric center of the beam.

[0107] ② The maximum deformation equation of the beam is derived, and after comparison and correction with the calculation results of the finite element shell unit, the two parameters k1=275 and k2=240 in the deformation correction formula are obtained.

[0108] ③Determine optimization goals and constraints

[0109] In this embodiment, the weight reduction target of a single beam is 10%, the length of a single hole satisfies 0<δ1≤230 mm, and the width of a single hole satisfies 0<δ3≤85 mm.

[0110] ④ Determine the beam load relationship and formulate optimization strategies

[0111] In this embodiment, the beams to be optimized are in a "serial" relationship for sequentially transmitting loads, so it is only necessary to consider achieving the optimal specific stiffness of the beam after adding the lightening holes.

[0112] The beam to be optimized is 2000mm long, 5mm thick, with a 100mm height and length for the outer rectangle of the beam section, and a 90mm height and length for the inner rectangle of the beam section. That is, l = 2000, t = 5, b1 = h1 = 100, and b2 = h2 = 90.

[0113] ⑤ Orthogonal test to determine the degree of influence on optimization target

[0114] In order to ensure the symmetry of the structure, avoid additional torque, and reduce the uniform distribution of holes, there is a geometric relationship: δ2 = l1 = l-nδ1, so there are 3 independent factors.

[0115] Factor Level Table

[0116] Factor 1 Factor 2 Factor 3 n(number of holes) <![CDATA[δ1 (hole length)]]> <![CDATA[δ3 (hole width)]]> Level 1 2 230 40 Level 2 4 200 55 Level 3 6 170 70 Level 4 8 140 85

[0117] A 3-factor 4-level orthogonal table was established, and the specific stiffness of each beam was calculated. The results are as follows:

[0118] 3 factors and 4 levels orthogonal table

[0119]

[0120]

[0121] ⑥Optimize the design of tooling to reduce holes

[0122] From the orthogonal test, it can be seen that the importance of factors affecting the specific stiffness of this group of beam structures is ranked as number of holes > hole length > hole width. Therefore, when considering tooling weight reduction, it is preferred to increase the hole width while meeting the requirements, and try not to increase the number of holes.

[0123] According to the parameter optimization principle obtained from the orthogonal experiment, in this case, the hole width δ3 = 85, δ1 = 230, and n = 2 were selected as the parameters for the lightening hole. The calculated weight reduction ratio was 10.29%, which met the optimization target requirements.

[0124] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any form. Any simple modification or equivalent change made to the above embodiment based on the technical essence of the present invention shall fall within the scope of protection of the present invention.

Claims

1. A design optimization method for aircraft tooling lightening holes, characterized in that: The steps include: Step a, obtaining the load condition of each beam on the fixture without lightening holes; Step b: Simplify the beam on the fixture into a statically indeterminate beam with both ends fixed. When solving, transform it into an equivalent statically determinate system. Move the load obtained in step a to the midpoint of the beam according to the translation theorem of force. Then calculate the deformation of the beam by superposing the deformation effects of each section. Step c, deriving the maximum deformation formula of the cantilever beam with rectangular lightening holes when subjected to concentrated force, and combining it with step b, obtaining the stiffness of the statically indeterminate beam with rectangular lightening holes with both ends fixed; Step d: Determine the tooling stiffness requirements and weight reduction targets based on tooling design requirements and actual needs, and clearly define the constraints for reducing hole parameters; Step e: using orthogonal test to determine the influence of the lightening hole parameters on the optimization target, and optimizing the design of the tooling lightening hole according to the test results.

2. The design optimization method for aircraft tooling lightening holes according to claim 1, characterized in that: The method of obtaining the load-bearing condition of each beam on the tooling without lightening holes includes: measuring the weight and center of the product on the tooling, simplifying the product into mass points based on the measurement results, connecting the product to the tooling joint according to the actual connection form, and reading the load borne by each beam constituting the tooling.

3. The design optimization method for aircraft tooling lightening holes according to claim 1, characterized in that: Maximum deformation of a cantilever beam with a lightening hole when subjected to concentrated force ω c Equal to the deformation of the cantilever beam caused by the concentrated force ω Z , deformation of the cantilever beam due to bending internal force and the deformation of the cantilever beam due to shear internal forces sum.

4. The design optimization method for aircraft tooling lightening holes according to claim 3, characterized in that: For thin-walled hollow beams, cantilever beams with lightening holes should also add a correction value to the maximum deformation when subjected to concentrated force. Where n is the number of lightening holes, i=1 when n is an odd number, and i=2 when n is an even number; δ1 is the hole length, and δ2 is the spacing between two adjacent lightening holes; I1 is the moment of inertia of the section without the lightening hole, I2 is the moment of inertia of the section with the lightening hole; k is the correction coefficient; E is the elastic modulus of the material, and L is the total length of the beam.

5. The design optimization method for aircraft tooling lightening holes according to claim 1, characterized in that: In step e, different optimization strategies are determined according to different load transfer modes of the beam; Beams that transmit loads sequentially are defined as being in a "series" relationship. When this relationship exists, the optimization strategy involves designing the parameters of the lightening holes to optimize the beam's specific stiffness. Beams that share the load are defined as being in a "parallel" relationship. In addition to designing the parameters of the lightening holes to optimize the beam's specific stiffness, the optimization strategy also involves ensuring that the stiffness of the parallel beams remains consistent after adding lightening holes, maintaining structural symmetry, and evenly distributing the load to avoid generating additional bending moments.

6. The design optimization method for aircraft tooling lightening holes according to claim 1, characterized in that: In step d, based on the stiffness requirements of the tooling, the load Ω required to produce unit deflection under unit mass is used to express the specific stiffness of the structure. The larger the Ω, the greater the specific stiffness of the structure, and the smaller the Ω, the smaller the specific stiffness of the structure. The expression is: Where F is the concentrated load, ω c is the total deformation of the beam, and m is the mass of the beam.

7. The design optimization method for aircraft tooling lightening holes according to claim 1 or 5, characterized in that: The lightening hole parameters include the width, length and number of the lightening holes. The restrictions on the lightening holes include: the length of the lightening hole does not exceed 10% of the total length of the beam; the width of the lightening hole does not exceed 80% of the beam width.

8. The design optimization method for aircraft tooling lightening holes according to claim 1, characterized in that: In step f, the width, length, and number of the lightening holes are used as factors, the number of levels x is set according to the precision of the calculation, a factor level table is established, and the specific stiffness and range of each beam are calculated; according to the calculation results, the factors with a greater impact on the target are prioritized in order, and the factors with a smaller impact on the target are weakened, and finally the design results of the tooling lightening holes are obtained.

9. The design optimization method for aircraft tooling lightening holes according to claim 3, characterized in that: The deformation of the cantilever beam with a lightening hole caused by the concentrated force F / 2 includes bending deformation caused by the concentrated force and shear deformation caused by the concentrated force.

10. The design optimization method for aircraft tooling lightening holes according to claim 9, characterized in that: The bending deformation ω caused by the concentrated force is the deformation of the cantilever beam with a lightening hole caused by the concentrated force F / 2. M for: Where: ω1 is the displacement of the first segment due to deformation under the action of concentrated force, ω1 * is the displacement of the first segment due to bending under the action of concentrated force, ω i is the displacement of the i-th segment due to deformation under the action of concentrated force, ω i * is the displacement of the i-th segment due to bending under the action of concentrated force, ω 2n+1 is the displacement of the 2n+1 segment due to deformation under the action of concentrated force; Shear deformation ω caused by concentrated force F for: Where h1 is the height of the outer section of the beam, h2 is the height of the inner section of the beam, G is the shear modulus of the material, n is the number of lightening holes, δ1 is the length of the lightening hole, δ2 is the spacing between two adjacent lightening holes, δ3 is the width of the lightening hole, I1 is the moment of inertia of the section without lightening holes, and I2 is the moment of inertia of the section with lightening holes.

11. The design optimization method for aircraft tooling lightening holes according to claim 3, characterized in that: The bending deformation and shear deformation of the cantilever beam caused by the internal moment and additional moment are and 0, the total deformation caused by the bending internal force for: in: is the displacement of the first segment due to deformation under the action of internal moment Me and additional moment M*, is the displacement of the first segment due to bending under the action of internal moment Me and additional moment M*, is the displacement of the i-th segment due to deformation under the action of internal moment Me and additional moment M*, is the displacement of segment i due to bending under the action of internal moment Me and additional moment M*; It is the displacement of the 2n+1 segment due to deformation under the action of internal moment Me and additional moment M*.

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