A structural strength optimization method based on triangular fractal algorithm

Abstract

This invention discloses a structural strength optimization method based on a triangular fractal algorithm, relating to the field of structural optimization design in civil engineering. The method includes the following steps: Ⅰ. Setting the geometric and material parameters of initial members and calculating their buckling critical load and specific strength; Ⅱ. Setting the geometric and material parameters of the reinforced members in the first iteration and calculating their buckling critical load and specific strength after iteration; Ⅲ. In each iteration, changing the radius of the added members, calculating the maximum specific strength of the triangular fractal structure in each iteration, and recording the corresponding member radius. The fractal structure generated after multiple iterations of this invention can withstand greater loads and has higher strength. It maintains increased strength even with further increases in the number of iterations, making the structure less prone to failure. The fractal structure generated after multiple iterations can withstand greater loads and has higher strength, which is helpful for optimizing engineering solutions.

Description

Technical Field

[0001] This invention relates to the field of structural optimization design in civil engineering, and specifically to a structural strength optimization method based on a triangular fractal algorithm. Background Technology

[0002] In recent years, fractal algorithms have gained attention in structural optimization design, enabling the construction of complex planar and three-dimensional structures. Fractal structures have been applied in the civil engineering industry. Under certain load conditions, fractal structures offer efficiency advantages over traditional non-fractal structures. Using tetrahedral and octahedral fractal algorithms can increase mass-to-strength ratio, achieving higher structural strength with less material, thus creating more robust structures and facilitating the development of new engineering solutions. However, existing technologies have shortcomings in structural strength optimization. The structural strength of tetrahedral and octahedral fractal algorithms does not continuously increase with the number of iterations. As iterations progress, tetrahedral and octahedral fractal structures become more complex, leading to an increase in failure modes, structural damage, and a decrease in strength. It is necessary to avoid using such complex structures to ensure a continuous increase in structural strength with increasing iterations and to prevent failure. Summary of the Invention

[0003] The purpose of this invention is to address the shortcomings of existing technologies and provide a structural strength optimization method based on the triangular fractal algorithm.

[0004] This invention proposes a structural strength optimization method based on a triangular fractal algorithm. The technical solution adopted to solve the technical problem is as follows:

[0005] Ⅰ. Set the geometric and material parameters of the initial members, and calculate the buckling critical load and specific strength of the initial members;

[0006] II. Set the geometric and material parameters of the reinforced member in the first iteration, and calculate the critical buckling load and specific strength of the member after the iteration;

[0007] III. During each iteration, change the radius of the added members, calculate the maximum specific strength of the triangular fractal structure during each iteration, and record the corresponding member radii;

[0008] IV. Determine whether the preset iteration optimization stopping condition has been met. After the iteration stops, output the optimized geometric parameters of each member.

[0009] As a further aspect of the present invention, the geometric parameters of the rod in step I specifically include the length L, radius R, and effective length factor K of the rod, wherein the effective length factor K is a constant;

[0010] The material parameters of the rod include Young's modulus E and the moment of inertia J of the rod section.

[0011] As a further aspect of the present invention, the specific calculation formula for the buckling critical load of the member in step I is as follows:

[0012]

[0013] In the formula, J y R represents the moment of inertia of the member's cross section at the y-th iteration, with the initial moment of inertia being J0; y P represents the radius of the member in the y-th iteration, with the initial member radius being R0; by This represents the buckling critical load of the member at the y-th iteration, with the initial buckling critical load being P. b0 E represents the Young's modulus of the rod; K represents the effective length factor; L x This represents the length of the member, with an initial member length of L0; m n ρ represents the mass of the rod in the nth iteration, with the initial mass of the rod being m0; ρ represents the density of the rod.

[0014] As a further aspect of the present invention, the specific formula for calculating the specific strength of the rod in step I is as follows:

[0015]

[0016]

[0017] In the formula, f represents specific strength; 4 n This represents the length of the reinforced member in the nth iteration, and its length is... m0 represents the initial mass of the member, which is consistent with the meaning of m0 in formula (2); m n This represents the mass of the rod in the nth iteration, and is related to m in formula (2). n The meanings are the same.

[0018] As a further aspect of the present invention, the specific steps for changing the radius of the added rod in step III and calculating the maximum specific strength of the triangular fractal structure in each iteration are as follows:

[0019] S1.1: Set the radius increment. At the beginning of each iteration, the radius of the newly added members is gradually adjusted according to the preset radius increment using a binary search method, and the moment of inertia of the members is updated after each adjustment.

[0020] S1.2: Recalculate the critical load of the reinforced structure using the buckling critical load formula, and count the total mass of the structure under the current reinforcement scheme. Calculate the specific strength after changing the radius of the members multiple times, compare the calculated specific strengths of each group, select the one with the largest specific strength, and record its corresponding optimal radius value.

[0021] As a further aspect of the present invention, the specific steps for the specific strength after changing the radius of the rod in S1.2 are as follows:

[0022]

[0023] In the formula, f′ represents the specific strength after changing the radius of the rod; ρ represents the density of the rod; L0 represents the initial length of the rod; R0 represents the initial radius of the rod; R1 represents the radius of the rod after the first iteration; i represents the i-th iteration; and j represents the total number of iterations.

[0024] As a further aspect of the present invention, the iterative optimization stopping condition in step IV is that the maximum specific strength of the triangular fractal structure is not greater than 1 during the first iteration, and the iterative stopping condition for non-first iterations is that the maximum specific strength of the fractal component is not greater than the maximum specific strength recorded up to the last iteration.

[0025] The beneficial effects of this invention are:

[0026] Unlike non-fractal structural members, which fail due to buckling under small loads, the fractal structure generated by this invention after multiple iterations can withstand larger loads and has higher strength. The fractal structure generated by the triangular fractal algorithm avoids the situation where the structural strength does not increase with the number of iterations, which is the case with tetrahedral and octahedral fractal algorithms. It can maintain the increase in strength as the number of iterations increases, and the structure is not prone to failure. At the same time, this optimization method is applicable to various materials, consumes less material during construction, and has high construction efficiency. Therefore, adopting this method helps to optimize engineering solutions. Attached Figure Description

[0027] The present invention will now be further described with reference to the accompanying drawings.

[0028] Figure 1 This is a framework diagram of a structural strength optimization method based on the triangular fractal algorithm. Detailed Implementation

[0029] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0030] Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0031] This embodiment of the invention provides a structural strength optimization method based on a triangular fractal algorithm. See also... Figure 1 , Figure 1 This is a framework diagram of a structural strength optimization method based on a triangular fractal algorithm provided in an embodiment of the present invention. The method includes the following steps:

[0032] Set the geometric and material parameters of the initial member, and calculate the buckling critical load and specific strength of the initial member.

[0033] In this embodiment, the geometric parameters of the rod specifically include the rod's length L, radius R, and effective length factor K, where the effective length factor K is a constant. The material parameters of the rod include Young's modulus E and the moment of inertia J of the rod's cross section.

[0034] It should be further explained that the specific calculation formula for the critical buckling load of the member is as follows:

[0035]

[0036] In the formula, J y R represents the moment of inertia of the member's cross section at the y-th iteration, with the initial moment of inertia being J0; y P represents the radius of the member in the y-th iteration, with the initial member radius being R0; by This represents the buckling critical load of the member at the y-th iteration, with the initial buckling critical load being P. b0 E represents the Young's modulus of the rod; K represents the effective length factor; L x This represents the length of the member, with an initial member length of L0; m n ρ represents the mass of the rod in the nth iteration, with the initial mass of the rod being m0; ρ represents the density of the rod.

[0037] The specific formula for calculating the specific strength of a member is as follows:

[0038]

[0039] In the formula, f represents specific strength; 4 n This represents the length of the reinforced member in the nth iteration, and its length is... m0 represents the initial mass of the member, which is consistent with the meaning of m0 in formula (2); m n This represents the mass of the rod in the nth iteration, and is related to m in formula (2). n The meanings are the same.

[0040] Set the geometric and material parameters of the reinforced member in the first iteration, and calculate the critical buckling load and specific strength of the member after the iteration.

[0041] In each iteration, the radius of the added members is changed, the maximum specific strength of the triangular fractal structure is calculated in each iteration, and the corresponding member radius is recorded.

[0042] Specifically, a radius increment is set. At the beginning of each iteration, the radius of the newly added members is gradually adjusted according to the preset radius increment using a binary search method. After each adjustment, the moment of inertia of the member section is updated. The critical load of the reinforced structure is recalculated using the buckling critical load formula. The total mass of the structure under the current reinforcement scheme is also calculated. The specific strength after changing the member radius is calculated multiple times. The specific strength is calculated multiple times and compared with each group of calculated specific strengths. The one with the largest specific strength is selected and its corresponding optimal radius value is recorded.

[0043] It should be further explained that the specific steps for changing the specific strength after altering the member radius are as follows:

[0044]

[0045] In the formula, f′ represents the specific strength after changing the radius of the rod; ρ represents the density of the rod; L0 represents the initial length of the rod; R0 represents the initial radius of the rod; R1 represents the radius of the rod after the first iteration; i represents the i-th iteration; and j represents the total number of iterations.

[0046] Determine whether the preset iteration optimization stopping condition has been met. After the iteration stops, output the optimized geometric parameters of each member.

[0047] In this embodiment, the iteration optimization stopping condition is as follows: during the first iteration, the iteration optimization stopping condition is that the maximum specific strength of the triangular fractal structure is not greater than 1; during subsequent iterations, the iteration stopping condition is that the maximum specific strength of the fractal component is not greater than the maximum specific strength recorded up to the last iteration.

[0048] The foregoing has provided a detailed description of one embodiment of the present invention, but this description is merely a preferred embodiment and should not be construed as limiting the scope of the invention. All equivalent variations and modifications made within the scope of the claims of this invention should still fall within the patent coverage of this invention.

Claims

1. A structural strength optimization method based on a triangular fractal algorithm, characterized in that, Includes the following steps: Ⅰ. Set the geometric and material parameters of the initial members, and calculate the buckling critical load and specific strength of the initial members; II. Set the geometric and material parameters of the reinforced member in the first iteration, and calculate the critical buckling load and specific strength of the member after the iteration; III. During each iteration, change the radius of the added members, calculate the maximum specific strength of the triangular fractal structure during each iteration, and record the corresponding member radii; IV. Determine whether the preset iteration optimization stopping condition has been met. After the iteration stops, output the optimized geometric parameters of each member. The specific formula for calculating the specific strength of the member mentioned in step I is as follows: In the formula, f represents specific strength; P by This represents the buckling critical load of the member at the y-th iteration, with the initial buckling critical load being P. b0 ;4 n This represents the length of the reinforced member in the nth iteration, and its length is... Where L represents the length of the member; m0 represents the initial mass of the member, which has the same meaning as m0 in formula (2); m n This represents the mass of the rod in the nth iteration, and is related to m in formula (2). n The meaning is consistent; The specific steps for calculating the maximum specific strength of the triangular fractal structure in each iteration by changing the radius of the added rods in step III are as follows: S1.1: Set the radius increment. At the beginning of each iteration, the radius of the newly added members is gradually adjusted according to the preset radius increment using a binary search method, and the moment of inertia of the members is updated after each adjustment. S1.2: Recalculate the critical load of the reinforced structure using the buckling critical load formula, and count the total mass of the structure under the current reinforcement scheme. Calculate the specific strength after changing the member radius multiple times, compare the calculated specific strengths, select the one with the largest specific strength, and record its corresponding optimal radius value. The specific steps for changing the specific strength of the member after altering its radius, as described in S1.2, are as follows: In the formula, f′ represents the specific strength after changing the radius of the member; ρ represents the density of the member; L0 represents the initial length of the member; R0 represents the initial radius of the member; R1 represents the radius of the member after the first iteration; i represents the i-th iteration; j represents the total number of iterations; The iterative optimization stopping condition described in step IV is as follows: for the first iteration, the iterative optimization stopping condition is that the maximum specific strength of the triangular fractal structure is not greater than 1; for subsequent iterations, the iterative stopping condition is that the maximum specific strength of the fractal component is not greater than the maximum specific strength recorded up to the previous iteration.

2. The structural strength optimization method based on the triangular fractal algorithm according to claim 1, characterized in that, The geometric parameters of the rod mentioned in step I specifically include the rod's length L, radius R, and effective length factor K, where the effective length factor K is a constant; The material parameters of the rod include Young's modulus E and the moment of inertia J of the rod section.

3. The structural strength optimization method based on the triangular fractal algorithm according to claim 2, characterized in that, The specific calculation formula for the buckling critical load of the member described in step I is as follows: In the formula, J y R represents the moment of inertia of the member's cross section at the y-th iteration, with the initial moment of inertia being J0; y P represents the radius of the member in the y-th iteration, with the initial member radius being R0; by This represents the buckling critical load of the member at the y-th iteration, with the initial buckling critical load being P. b0 E represents the Young's modulus of the rod; K represents the effective length factor; L x This represents the length of the member, with an initial member length of L0; m n ρ represents the mass of the rod in the nth iteration, with the initial mass of the rod being m0; ρ represents the density of the rod.

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