Structural strength optimization method based on triangular fractal algorithm

Abstract

The invention discloses a structural strength optimization method based on a triangular fractal algorithm, and relates to the field of civil engineering structure optimization design, and the method comprises the following steps: I, setting geometric parameters and material parameters of an initial rod piece, and calculating a buckling critical load and specific strength of the initial rod piece; iI, geometric parameters and material parameters of the reinforced rod piece during first iteration are set, and the buckling critical load and the specific strength of the rod piece after iteration are calculated; iII, during each iteration, changing the radius of the added rod piece, calculating the maximum specific strength of the triangular fractal structure during each iteration, and recording the radius of the corresponding rod piece; the fractal structure generated after operation of multiple iterations can bear larger loads and has higher strength, the strength can be kept to be increased when the number of iterations is further increased, the structure is not prone to being damaged, the fractal structure generated after operation of multiple iterations can bear larger loads and has higher strength, and the fractal structure is not prone to being damaged when the number of iterations is further increased. And optimization of an engineering solution is facilitated.

Description

Technical Field

[0001] The present invention relates to the field of optimal design of civil engineering structures, and particularly to a structural strength optimization method based on a triangular fractal algorithm. Background Art

[0002] In recent years, fractal algorithms have received attention in structural optimization design. Through fractal algorithms, complex planar and three-dimensional structures can be constructed. Fractal structures have been used in the civil engineering industry. Under certain load conditions, fractal structures have advantages in efficiency compared to traditional non-fractal structures. The use of tetrahedron and octahedron fractal algorithms can increase the mass-to-strength ratio, enabling higher structural strength with less material, thus creating more robust structures and contributing to the establishment of new engineering solutions. However, existing technical solutions have deficiencies in structural strength optimization. When using tetrahedron and octahedron fractal algorithms, the structural strength does not continuously increase as the number of iterations increases. As the iteration progresses, the tetrahedron and octahedron fractal structures become more complex, the failure modes increase, the structure is damaged, and the strength decreases. It is necessary to avoid using such relatively complex structures to maintain the continuous increase of structural strength as the number of iterations increases and to prevent failure and damage. Summary of the Invention

[0003] The purpose of the present invention is to solve the defects existing in the prior art and provide a structural strength optimization method based on a triangular fractal algorithm.

[0004] The present invention provides 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 parameters and material parameters of the initial member, and calculate the buckling critical load and specific strength of the initial member;

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

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

[0008] Ⅳ. Determine whether the preset iteration optimization stop condition is reached. After the iteration stops, output the optimized geometric parameters of each member.

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

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

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

[0012]

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

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

[0015]

[0016]

[0017] In the formula, f represents the specific strength; 4 n represents the length of the reinforced rod at the n-th iteration, and its length is m0 represents the initial mass of the rod, which has the same meaning as m0 in formula (2); m n represents the mass of the rod at the n-th iteration, which has the same meaning as m n in formula (2).

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

[0019] S1.1: Set the radius increment. At the beginning of each iteration, by means of binary search, gradually adjust the radius of the newly added rod according to the preset radius increment, and update the moment of inertia of the cross-section of the rod after each adjustment;

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

[0021] As a further solution of the present invention, the specific steps of the specific strength after changing the radius of the rod 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 length of the initial rod; R0 represents the radius of the initial rod; R1 represents the radius of the rod after the first iteration; i represents the i-th iteration; j represents the total number of iterations.

[0024] As a further solution of the present invention, the iteration optimization stop condition in step Ⅳ is that in the first iteration, the iteration optimization stop condition is that the maximum specific strength of the triangular fractal structure is not greater than 1, and in non-first iterations, the stop iteration 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.

[0025] Advantages of the present invention:

[0026] Different from the structural rod without fractal that fails due to buckling under a small load, the fractal structure generated after multiple iterations can withstand a greater load 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 increase in the number of iterations in the fractal algorithms of tetrahedrons and octahedrons, and can maintain an increase in strength when the number of iterations further increases, and the structure is not easily damaged. At the same time, this optimization method is applicable to various materials, consumes less materials during the construction process, and has high construction efficiency. Therefore, adopting this method helps to optimize engineering solutions. Description of the drawings

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

[0028] Figure 1 It is a framework diagram of a structural strength optimization method based on the triangular fractal algorithm. Specific embodiments

[0029] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0030] Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0031] Embodiment. An embodiment of the present invention provides a structural strength optimization method based on a triangular fractal algorithm. Refer to Figure 1 , Figure 1 which is a framework diagram of a structural strength optimization method based on a triangular fractal algorithm provided by an embodiment of the present invention. The method includes the following steps:

[0032] Set the geometric parameters 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 member specifically include the length L, radius R, and effective length factor K of the member, where the effective length factor K is a constant, and the material parameters of the member include Young's modulus E and the moment of inertia J of the member cross-section.

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

[0035]

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

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

[0038]

[0039] In the formula, f represents the specific strength; 4 n represents the length of the reinforced member at the n-th iteration, and its length is m0 represents the initial member mass, which has the same meaning as m0 in formula (2); m n represents the mass of the member at the n-th iteration, which has the same meaning as m n in formula (2).

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

[0041] In each iteration, change the radius of the added rod, calculate the maximum specific strength of the triangular fractal structure in each iteration, and record the corresponding rod radius.

[0042] Specifically, set the radius increment. At the beginning of each iteration, use the binary search method to gradually adjust the radius of the newly added rod according to the preset radius increment. After each adjustment, update the moment of inertia of the rod's cross-section, recalculate the critical load of the reinforced structure through the buckling critical load formula, and calculate the total mass of the structure under the current reinforcement plan. Then, calculate the specific strength after changing the rod radius multiple times, compare the calculated specific strengths of each group, select the one with the maximum specific strength, and record the corresponding optimal radius value.

[0043] It should be further noted that the specific steps for calculating the specific strength after changing the rod radius are as follows:

[0044]

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

[0046] Judge whether the preset iteration optimization stop condition is reached. After the iteration stops, output the optimized geometric parameters of each rod.

[0047] In this embodiment, the iteration optimization stop condition is that in the first iteration, the maximum specific strength of the triangular fractal structure is not greater than 1, and in non-first iterations, the stop iteration 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.

[0048] The above has described an embodiment of the present invention in detail, but the content described is only a preferred embodiment of the present invention and cannot be considered as limiting the scope of implementation of the present invention. All equivalent changes and improvements made according to the scope of the present invention application should still fall within the scope covered by the patent of the present invention.

Claims

1. A structural strength optimization method based on a triangular fractal algorithm, characterized in that, It includes the following steps: Ⅰ. Set the geometric parameters and material parameters of the initial member, and calculate the buckling critical load and specific strength of the initial member; Ⅱ. Set the geometric parameters and material parameters of the reinforced member at the first iteration, and calculate the buckling critical load and specific strength of the member after iteration; Ⅲ. At each iteration, change the radius of the added member, calculate the maximum specific strength of the triangular fractal structure at each iteration, and record the corresponding member radius; Ⅳ. Determine whether the preset iteration optimization stop condition is reached. After the iteration stops, output the optimized geometric parameters of each member.

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

3. A structural strength optimization method based on a 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 represents the sectional moment of inertia of the rod at the y-th iteration, and the initial sectional moment of inertia is J0; R y represents the radius of the rod at the y-th iteration, and the initial rod radius is R0; P by represents the buckling critical load of the rod at the y-th iteration, and the initial buckling critical load is P b0 ; E represents the Young's modulus of the rod; K represents the effective length factor; L x represents the length of the rod, and the initial rod length is L0; m n represents the mass of the rod at the n-th iteration, and the initial rod mass is m0; ρ represents the density of the rod.

4. A structural strength optimization method based on a triangular fractal algorithm according to claim 3, characterized in that The specific calculation formula for the specific strength of the member described in step Ⅰ is as follows: (3) In the formula, f represents the specific strength; 4 n represents the length of the reinforced member at the n-th iteration, and its length is m0 represents the initial member mass, which is consistent with the meaning of m0 in formula (2); m n represents the mass of the member at the n-th round of iteration, which is consistent with the meaning of m n in formula (2).

5. A structural strength optimization method based on the triangular fractal algorithm according to claim 4, characterized in that The specific steps for changing the radius of the added member and calculating the maximum specific strength of the triangular fractal structure at each iteration described in step Ⅲ are as follows: S1.1: Set the radius increment. At the beginning of each iteration, use the binary search method to gradually adjust the radius of the newly added member according to the preset radius increment, and update the moment of inertia of the member after each adjustment; S1.2: Recalculate the critical load of the reinforced structure through the buckling critical load formula, and count the total mass of the structure under the current reinforcement plan. Then calculate the specific strength after changing the member radius multiple times, calculate the specific strength multiple times, compare the calculated specific strength of each group, select the one with the maximum specific strength, and record its corresponding optimal radius value.

6. A structural strength optimization method based on a triangular fractal algorithm according to claim 5, characterized in that The specific steps for the specific strength after changing the member radius described in S1.2 are as follows: In the formula, f′ represents the specific strength after changing the member radius; ρ represents the density of the member; L0 represents the length of the initial member; R0 represents the radius of the initial 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.

7. A structural strength optimization method based on the triangular fractal algorithm according to claim 1, characterized in that The iteration optimization stop condition described in step Ⅳ is that in the first iteration, the iteration optimization stop condition is that the maximum specific strength of the triangular fractal structure is not greater than 1, and in non-first iterations, the stop iteration condition is that the maximum specific strength of the fractal member is not greater than the maximum specific strength recorded up to the previous iteration.

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