CN112052537B

CN112052537B - High specific stiffness structure bionic design optimization method

Info

Publication number: CN112052537B
Application number: CN202010932826.7A
Authority: CN
Inventors: 杨勇; 彭漩; 朱其新; 曹自洋; 蒋全胜; 卢金斌; 张元晶; 刘威; 沈晔湖
Original assignee: Suzhou University of Science and Technology
Current assignee: Suzhou University of Science and Technology
Priority date: 2020-09-08
Filing date: 2020-09-08
Publication date: 2024-04-26
Anticipated expiration: 2040-09-08
Also published as: CN112052537A

Abstract

The invention discloses a high specific stiffness structure bionic design optimization method, which aims at solving the problem that the existing mechanical structure bionic design method is multi-faced to a single simulation source and is easy to cause defects of the bearing mechanical property of a final bionic design structure.

Description

High specific stiffness structure bionic design optimization method

Technical Field

The invention relates to the field of mechanical structure optimization design, in particular to a high specific stiffness structure bionic design optimization method.

Background

By adopting a bionics method and by means of a high-efficiency bearing configuration in organism space, the high-specific stiffness structure bionic optimization design is carried out on the mechanical structure, and the structure light-weight high-specific stiffness design is realized, so that the method is one of the important means for light-weight mechanical structure.

Various high-performance space topological structures with excellent performances in nature provide endless inspiration source for mechanical high-specific stiffness structure optimization innovation design. The spatial topological configuration of organisms is the result of hundreds of millions of years of natural selection and life evolution, and fully reflects the trend of natural evolution: the best spatial configuration and the least material are used to withstand the greatest external forces, i.e. the best structural efficiency, i.e. the highest specific stiffness.

Although there are many light and efficient structures in nature, the efficient bearing structures, bearing-mechanical properties and mechanisms are greatly different. Limited by the specific natural environment of the simulated source, the mechanical adaptability of the biological topological configuration is single, for example, the vein distribution is more suitable for bending moment load, the bearing performance of the honeycomb structure on the coplanar direction is better, and the mechanical bearing performance of the honeycomb structure on the non-coplanar direction is much worse. The prior mechanical structure bionic design method is more oriented to a single simulated source, and the mechanical adaptability of the biological topological configuration of the single simulated source is single or the mechanical property is insufficient, so that the bearing mechanical property of the final bionic design structure is insufficient.

Disclosure of Invention

The invention aims to: aiming at the problems that the prior mechanical structure bionic design method is multi-faced to a single simulation source and the bearing mechanical property of the final bionic design structure is easy to cause defects, the invention provides a high specific stiffness structure bionic optimization design method based on RMI (Relationship Mapping Inversion, relation-mapping-inversion) and coupling element hybridization, a biological high-efficiency bearing structure solution of mechanical high-specific stiffness structure design is sought, and the biological high-efficiency bearing coupling element hybridization integration problem is solved, so that the high specific stiffness mechanical structure bionic optimization design under the biological high-specific stiffness dominant performance integration is realized, and the defects of single bearing property and possible existence in the prior single bionic source structure bionic optimization design are overcome.

The technical scheme is as follows: a high specific stiffness structure bionic design optimization method comprises the following steps:

(1) Firstly, engineering-biological mapping is carried out through an R-M mapping principle, and solution solving of a biological high-efficiency bearing structure designed by a high-specific stiffness structure is carried out;

(2) The method comprises the steps of obtaining a biological high-efficiency bearing coupling element and a class cell based on the expression of an object element matrix through analysis of a biological space topological structure high-efficiency bearing mechanism, wherein the biological high-efficiency bearing coupling element and the class cell are essential in the biological space topological structure;

(3) Performing high-efficiency bearing coupling element hybridization integration modeling based on the extension of the physical element, and realizing the integration of the advantage performance of different biological bodies in terms of high specific stiffness through the hybridization integration of the biological high-efficiency bearing unit;

(4) The hybrid coupler is used as a mechanical element structure through R-I inversion, and the hybrid coupler is mapped to a mechanical structure with high specific stiffness through a multi-objective structure optimization method based on an approximate meta model and a mechanical structure design method based on a meta structure.

Further, the step (1) specifically includes the following:

The method comprises the steps of (1.1) analyzing a mechanical high specific stiffness design problem, and solving engineering contradictory transformation, contradictory operation domain description and contradictory elimination by means of Biotriz conflict matrixes to obtain biological invention original understanding;

(1.2) obtaining a biological efficient bearing structure based on the solution of the biological invention principle through mapping an example library of the biological invention principle;

and (1.3) carrying out similarity calculation and evaluation between the biological high-efficiency bearing configuration and the engineering design structure from the aspects of loading, boundary, structure and function based on the similarity principle.

If the similarity is lower than a preset threshold, re-mapping through the example library in the step (1.2), re-selecting the biological efficient bearing configuration, and repeating the step (1.3) until the similarity between the selected biological efficient bearing configuration and the engineering design structure is higher than the preset threshold, and performing the step (2); the preset threshold is not lower than 0.7, namely, when the calculated similarity value is higher than 70%, the similarity is considered to be higher.

Further, the step (2) specifically includes the following:

(2.1) constructing a biological structure topological coupling element mathematical model oriented to biological high-efficiency bearing performance to obtain biological high-efficiency bearing coupling elements;

and (2.2) performing biological space topological configuration process modeling based on biological cells to obtain the biological high-efficiency bearing cells.

In the step (2.1), the biological structure topological coupling element mathematical model facing the biological high-efficiency bearing performance is as follows:

In the method, in the process of the invention, X' is a biological space topological structure, co _i is the ith coupling element contained in the biological space topological structure, and n is the total number of the contained biological high-efficiency bearing coupling elements; r _ij is a relationship between the high specific stiffness topological coupling elements Co _i and Co _j, when i=j, R _ij is a relationship between each part in the bio-efficient bearing coupling element, and when i+.j, R _ij is a relationship between the high specific stiffness topological coupling elements; cL is the loaded set, cB is the boundary constraint set; co _i is the name of the i-th topologically configured coupler Co _i; r _ij is the name for a topological coupling relation R _ij with high specific stiffness; o _ik、d_ik is the kth feature and characterization of the topologically configured coupler Co _i; q _ijk、t_ijk is the kth feature of R _ij and its features; m and p are the number of features contained in Co _i and R _ij.

In the step (2.2), the structural model of the metamorphic cell is:

In the formula, ce _i is the i-th biological high-efficiency bearing type cell, R _ij is the relationship between the high-specific-stiffness topological coupler Co _i and Co _j, when i=j, R _ij is the relationship between all parts in the high-specific-stiffness topological coupler, and at the moment, R _ij is R _ii.

Further, the step (3) specifically includes the following:

(3.1) constructing a mathematical model of the bionic source biological high specific stiffness dominant performance integration problem according to the definition description of the high-efficiency bearing dominant performance integration problem;

(3.2) solving the problem of integration of the high specific stiffness dominant performance of the bionic source organism based on the expansibility of the physical element to obtain a solution scheme of the problem of integration of the high specific stiffness dominant performance of the bionic source organism;

(3.3) evaluating the weight influence of each coupling element and coupling element characteristic facing the high specific stiffness dominant performance of the bionic source organism, extracting the coupling element and coupling element characteristic which have decisive action on the high specific stiffness dominant performance, and defining the coupling element and coupling element characteristic as gene coupling element and gene coupling element characteristic;

And (3.4) performing bio-coupling element hybridization integration based on the extension transformation of the genetic coupling element to obtain a hybridization simulated source coupling element integrated with the advantage of high specific stiffness of the bionic source organism, namely a hybridization bionic source space topology configuration.

Step (3.4) comprises the following contents:

(3.4.1) determining a solving formula of the hybrid bionic source space topology configuration based on the extension of the physical elements;

(3.4.2) constructing four basic extension transformations of the gene coupling element based on the extension of the element, and obtaining all basic transformation of the coupling element of the bionic source organism high specific stiffness advantage performance integration problem;

(3.4.3) performing feasibility screening on all the coupling element basic transformations, and further determining necessary coupling element basic transformations;

(3.4.4) compounding the necessary coupling element basic transformation to perform combination transformation to obtain basic transformation of the simulation source organism high specific stiffness advantage performance integration problem;

(3.4.5) compounding the basic de-transformation with other coupling element basic transformations, constructing other de-transformations, and obtaining all de-transformation sets; the other primitive transforms are primitive transforms other than the required primitive transforms described in step (3.4.3) in the total primitive transforms described in step (3.4.2);

And (3.4.6) selecting an evaluation element to evaluate the hybrid coupling element decoupling transformation set, and determining the optimal decoupling transformation to obtain the hybrid simulated source coupling element which is oriented to the dominant performance integration, namely the hybrid simulated source space topology configuration.

Further, the mathematical model of the bionic source biological high specific stiffness advantage performance integration problem is as follows:

Wherein Q represents the problem of integration of high specific stiffness dominant performance of the simulated biogenic organisms, M _a,M_b is the description of the physical elements of the bionic sources a and b respectively; n _a,N_b is the name of its bionic source; c _a,c_b is the spatial topological configuration of the bionic sources a and b; v _a,v_b is the different efficient bearing performance of the spatial topological configuration of the bionic sources a and b; m _x is the description of the material element of the imitative source formed by hybridization, M _x＝(N_x,c_x,v_x),N_x is the name of the hybridized bionic source, c _x is the spatial topological configuration of the hybridized bionic source, v _x is the high-efficiency bearing performance integration with the spatial topological configuration of the imitative source a and b, namely v _x＝v_a∩v_b; r is a conditional element, which is the biological space topological configuration of the known bionic sources a and b, namely/>

The solution formula of the hybridization simulated source space topology configuration c _x is as follows:

In the method, in the process of the invention, Is a known conditional element formed by coupling elements of known imitative source high-efficiency bearing genes, T _rc is forward extension transformation of the coupling elements, and T _rc is formed by four basic extension transformation/>Compounding to obtain the following components:

where k= { a, d, c or s }, Adding/deleting transforms to/from coupling elements,/>Substitution transformation for coupling element,/>Decomposing/combining transforms for coupling elements,/>Enlarging/reducing the transform for the coupler.

Further, the step (4) specifically includes the following:

(4.1) taking the hybrid simulated source coupling element obtained in the step (3) as a mechanical element structure, selecting a high specific stiffness performance measurement index of the element structure, and optimizing dimensional parameters of the element structure by means of a multi-objective optimization algorithm through constructing an approximate element model function between a design variable and a high specific stiffness performance evaluation index;

And (4.2) carrying out mechanical rigidity specific stiffness structural design according to the optimized meta structure by a mechanical structure design method based on the meta structure.

Compared with the prior art, the invention has the following remarkable effects: the high specific stiffness structure bionic optimization design method based on RMI and coupling element hybridization solves the problem of biological high-efficiency bearing coupling element hybridization integration, realizes the high specific stiffness structure bionic design under the integration of biological high specific stiffness dominant performance, and overcomes the problems that the bearing performance is single, the mechanical performance possibly has defects and the like in the original single simulated source structure bionic design.

Drawings

FIG. 1 is an example machine tool column and tendon fill area;

Fig. 2 (a) is a cellular high efficiency load bearing structure, and 2 (b) is a high efficiency load bearing structure of a human vertebra;

FIG. 3 is a schematic diagram of the mapping-inversion relationship between a mechanical high specific stiffness design structure and a bio-efficient bearing structure;

FIG. 4 is a solution process for the solution of coupled element hybridization;

FIG. 5 (a) is a three-dimensional finite element model of the original improved coupler, i.e., honeycomb coupler, and 5 (b) is a three-dimensional finite element model of hybrid coupler solution ①;

Fig. 6 (a) is a column model based on hybrid coupler structures, and 6 (b) is a column model based on original coupler structures to be improved.

Detailed Description

The technical scheme of the invention is further described below with reference to the accompanying drawings and examples.

In general, mechanical structure bionic design for a single bionic source has a mechanical property deficiency, and the mechanical property deficiency of the original bionic design structure can be made up by using the biological bearing topological configuration of another bionic source, so that two bionic sources are used for hybridization in the hybridization method example. If the design structure obtained by hybridization of the two bionic sources still has defects, other new bionic sources can be further borrowed on the basis, and the high-specific-stiffness mechanical structure bionic design can be further carried out by the method.

Fig. 1 shows a three-dimensional structure model of a machine tool column, wherein (a) is a design area of a rib plate inside a support structure at two sides, and (b) is a grid filling mode of a rib plate in an original design.

Due to the high-efficiency bearing characteristic of the honeycomb structure, the honeycomb structure is widely applied to mechanical filling design of the machine tool structure bionic rib plate with high specific stiffness, particularly as shown in (a) of fig. 1. But the bearing performance of the honeycomb structure on the coplanar direction is better, but the mechanical bearing performance of the non-coplanar direction is much worse, as shown in fig. 2 (a).

Therefore, based on the proposed high specific stiffness structure bionic design method based on RMI and coupling element hybridization, a solution of a biological high-efficiency bearing structure designed by a mechanical high specific stiffness structure is sought, and the biological high-efficiency bearing coupling element hybridization integration problem is solved, so that the high specific stiffness mechanical structure bionic optimization design under the biological high specific stiffness dominant performance integration is realized, and the problems of single bearing performance, possible defects and the like of the original single simulated source are overcome.

The invention relates to a high specific stiffness structure bionic design optimization method, which comprises the following steps:

Step 1, engineering-biological mapping is firstly carried out according to an R-M mapping principle, and solution solving of a biological high-efficiency bearing structure solution of high-specific stiffness structural design is carried out.

Let S be the design requirement of the mechanical domain high specific stiffness structure, x be the mechanical high specific stiffness structure to be solved, F be the topology reconstruction of the unknown overall structure, CON be the structure loading constraint, the mechanical high specific stiffness design problem to be solved is described as

x＝{F(S,x)|CONS＝0} (1)

The above equation can be described as a structural design solution with high specific stiffness design requirements under load constraints.

Many high-efficiency load-bearing structures in nature offer numerous biological load-bearing solutions for high specific stiffness mechanical structural designs. The biological high-efficiency bearing topological structure can be regarded as a structural self-adaptive generation type topological structure facing the natural loading environment of the living beings through long-term evolution and environment adaptation screening. Thus, the adaptively generated topological mathematical expression of the organism is:

x′＝{F′(S′,x′))|CON′(x′)＝0} (2)

wherein: f' is a solution algorithm, and represents a natural object bidding or biological natural evolution process; s' the environment load requirement to which the organism needs to be adapted; x' is a biological self-adaptive generation high-efficiency bearing topological configuration; CON' is a biological growth environment constraint.

The biological topological configuration solving method based on the relation-mapping-inversion mechanical high-specific stiffness structure is provided, an innovative solution to the mechanical design problem of high-specific stiffness is sought in the biological domain, and the following steps are achievedFor mapping from a mechanical domain to a biological domain, the mapping inversion relation structure R between the high specific stiffness design structure to be solved and the biological high-efficiency topological configuration is represented by the formula (3):

The map-inversion-relation structure diagram between the high specific stiffness design structure and the biological high efficiency topological configuration is shown in fig. 3, wherein ψ in fig. 3 is inversion from biological domain to mechanical domain, namely The reverse process of (2) is:

in order to reduce the solving difficulty of the biological high-efficiency bearing structure scheme of the engineering problem in the biological domain, the mapping solving process of the biological high-efficiency bearing structure scheme of the engineering problem in the biological domain Decomposition is performed as shown in formula (5):

In the method, in the process of the invention, For BioTRIZ matrix mapping,/>Biological instance library mapping,/>For the mapped complex product operation, matrix _Btriz is BioTRIZ Matrix, r _F、c_F is BioTRIZ Matrix improvement operation domain and deterioration operation domain, dbase _Btriz is an example library of biological inventive understanding, and m _ip is BioTRIZ biological inventive understanding.

And 1.1, analyzing the design problem of high specific stiffness of the machinery, and solving the contradictory operation domain description and contradictory elimination of engineering contradictory conversion by means of BioTRIZ matrix, namely through BioTRIZ matrix mapping, so as to obtain the original understanding of the biological invention.

The BioTRIZ matrix table, which is not described here, has 6 operation fields of substance, structure, energy, information, space and time as rows (improvement operation field r _F) and columns (deterioration operation field c _F) of the BioTRIZ matrix and 40 TRIZ inventive principles as matrix values in numerous documents. In the mapping process of the biological high-efficiency bearing structure scheme, the improvement and deterioration conflict existing in the engineering problem can be expressed in a description mode by six parameters of a corresponding operation domain r _F、c_F, and the BioTRIZ principle special solution can be obtained through the BioTRIZ matrix element values corresponding to the row and the column of the BioTRIZ matrix table, and the solution is the biological original understanding m _ip.

As can be seen from the analysis of the design of this example, the structural design can be understood as follows: with minimal structural material usage, the maximum structural performance is exhibited. It can be seen as a conflict resolution problem, that as little material use as possible is actually optimizing the mechanical structure, also known as reducing the structural space, described by the structural or spatial operating domain of BioTRIZ; the maximum structural efficiency is to ensure the mechanical bearing performance of the mechanical structure and the like, and is described by a BioTRIZ strength operation domain.

The selection of the structural operation domain describes the former, so the problem can be expressed as BioTRIZ conflicts: the energy is improved, namely, the operation domain r _F is improved to be energy, and the structure is deteriorated, namely, the operation domain c _F is deteriorated to be structure. From the BioTRIZ collision matrix of BioTRIZ matrix table, we get the inventive principle solution number given from the biological point of view: 1,3,5,6, 25, 35, 36, 40. Each number represents a different inventive principle understanding, and inquiring about 40 inventive principles in TRIZ can obtain specific content corresponding to the inventive principles, for example, the inventive principle corresponding to the number 1 is understood as a segmentation principle.

And step 1.2, obtaining the biological high-efficiency bearing structure based on the biological invention principle through mapping an example library of the biological invention principle.

Biological instance library mapping further by means of the inventive principlesThe biological example is obtained by solving the principle of the invention. The biological example library mapping principle of the invention is as follows: the bionic cases which succeed in the past under the principle of the invention are stored in an example library in the description mode of the examples, and effective biological examples can be searched for in the subsequent searching mode to serve as starting points for solving the bionic design problem. The biological example library can be used for collecting typical biological function information corresponding to the innovation principle by searching related biological materials, documents and the like, and establishing a special biological example library; the general biological example library of the inventive principles in the existing literature (literature [1]Vincent J.F.V.,Bogatyreva O.,Pahl A.,etc.Putting Biology into TRIZ：A Database of Biological Effects[J].Creativity&Innovation Management,2005,14(1)：66-72.;, literature 2, jian Yanhui. Green innovative design method of combining bionics and TRIZ is applied to study [ D ]. Taiwan: university of success, 2013.) can also be used for query corresponding to the original understanding of the invention: 1,3,5,6, 25, 35, 36, 40.

And the bearing requirement of the non-coplanar mechanical property of the honeycomb and the bearing requirement of the upright column in the height direction are considered, and finally the human vertebra structure is selected as a biological example.

And 1.3, carrying out similarity calculation and evaluation between the biological high-efficiency bearing configuration and the engineering design structure from the aspects of loading, boundary, structure and function based on a similarity principle analysis method.

And if the similarity is lower, reselecting the biological high-efficiency bearing configuration through the example library mapping of the step 1.2, and repeating the step 1.3 until the similarity calculation evaluation between the selected biological high-efficiency bearing configuration and the engineering design structure is higher, and then performing the step 2.

From the aspects of loading, boundary constraint, structure and function, the similarity between the selected biological example and the designed upright post is evaluated, and the specific steps are as follows:

selecting similar elements as four elements of load, boundary constraint, structure and function, and defining a similar element set u:

Based on a similarity analysis method, defining a similarity Q between the human vertebra and the upright post:

wherein q (u _i)、β_i is the similarity of the ith similar element and its corresponding weight coefficient:

where the right side of the equation is the similarity scale and the left side is the degree of similarity corresponding to the similarity scale.

Based on the analytic hierarchy process, determining importance degrees of four elements and listing a judgment matrix A of 4 similar elements:

Solving the maximum eigenvalue λ of the matrix and its corresponding eigenvector Λ, i.e. aΛ=λΛ, to obtain the maximum eigenvalue λ of 4, and the corresponding eigenvector Λ= [0.85,0.46,0.16,0.16]. And normalizing the eigenvector lambda to obtain the weight coefficient beta ₁、β₂、β₃、β₄ of the similar element as 0.521, 0.282, 0.099 and 0.099. And analyzing the similarity of the two similar elements, wherein q (u ₁)、 q(u₂)、q(u₃)、q(u₄) is 0.75, 0.5, 1 and 1. Substitution formula (7) eventually yields a similarity of 0.729 between the two.

The similarity of the two is higher, and finally the human body vertebra structure is determined to be a biological prototype integrated with the advantage performance of the honeycomb structure in high specific stiffness.

And 2, analyzing by a high-efficiency bearing mechanism of the biological space topological structure to obtain a biological high-efficiency bearing coupler and a cell-like cell based on the expression of the physical element matrix, wherein the biological high-efficiency bearing coupler and the cell-like cell are the essence of the biological high-specific stiffness topological structure.

And 2.1, constructing a biological structure topological coupling element mathematical model oriented to biological efficient bearing to obtain the biological efficient bearing coupling element.

The efficient bearing topological configuration under the influence of biological natural environment (loading boundary and the like) is written as follows from a systematic point of view based on conjugate theory:

The upper part of the device consists of two parts, The sum of the hard portion, the soft portion having a conjugated relationship with the hard portion, and the intermediate portion is a topological configuration corresponding to the biological load-bearing constraint. Where ha (x ') represents a hard portion of the bio-efficient load-bearing topology, so (x') represents a soft portion conjugated thereto, mid (x ') represents an intermediate portion, con (x') is a bio-load-bearing constraint (including load, boundary constraints, etc.).

Since the middle part is not involved in the topological conjugate analysis of the high specific stiffness of the living being, the middle part can be omitted in the formula (10). Hard ha (x ') refers to the interrelationship within and between the components of the bio-efficient topological structure, so (x').

In the formula (10), ha (x ') is a coupling element set of a biological efficient bearing topological configuration, and so (x') is a set of self-criterion and mutual criterion relations of high specific stiffness topological coupling elements; and writing con (x') as the set of loads to which the set of boundary constraints is subjected:

Namely:

Wherein: co _i is the ith coupling element contained in the high-efficiency bearing topological structure, and n is the total number of the biological high-specific stiffness topological coupling elements contained in the high-efficiency bearing topological structure; r _ij is a relationship between the high specific stiffness topological coupler Co _i and Co _j, R _ij is a relationship between each part in the high specific stiffness topological coupler when i=j, and R _ij is a relationship between the high specific stiffness topological couplers when i+.j; cL (x ') is the set of loads to be imposed and cB (x') is the set of boundary constraints.

The coupling elements of the high-efficiency bearing topological configuration are defined by the object element matrix, and the relationship of the biological high-specific stiffness topological coupling elements is defined by the relationship element matrix, so that the method can be obtained:

wherein: co _i is the name of the i-th topologically configured coupler Co _i; r _ij is the name for a topological coupling relation R _ij with high specific stiffness; o _ik,d_ik is the kth feature and characterization of the topologically configured coupler Co _i; q _ijk,t_ijk is the kth feature of R _ij and its features; m and p are the number of features contained in Co _i and R _ij.

Similarly, boundary constraint and load elements are defined by an element matrix, respectively, and therefore con (x') based on the element matrix is defined as follows:

Wherein cl and cb are names of the load element and the boundary element respectively, and ol, dl, ob and db are characteristics and characteristic descriptions of the load element and the boundary element respectively.

Substituting formulas (14) - (16) into formulas (12) (13) and then into formula (10) to obtain the coupled element mathematical model which is expressed based on the object element matrix-relation element matrix and faces to biological high-efficiency bearing performance under the influence of biological natural environment (loading boundary and the like) as follows

And 2.2, performing high-efficiency bearing topological configuration process modeling based on biological cells to obtain the biological high-efficiency bearing cells.

Some mechanical structures may be considered approximately as a whole or in part, as a combination of repeated arrays/permutations of a certain basic type of structure in space/plane, which is mechanically defined as a cellular structure/structure.

Similar cellular structures, such as a branched structure of a repeated array of blades in the plane thereof, also exist in the biological high-efficiency bearing topological configuration; an array-ordered near quadrilateral structure of dragonfly wings, and the like. The basic structural unit of the repetitive array/arrangement in space/plane in an organism is defined as a cell-like structure of a bio-efficient topological configuration.

And carrying out space complexity dimension reduction on the biological high-efficiency bearing topological structure, carrying out structure dimension reduction according to biological cells, and dividing the biological high-efficiency bearing topological structure into a cell-like structural layer, a sub cell-like structural layer and an integral target layer based on the principle of mechanical structure hierarchical analysis and a sub structure method.

Firstly, constructing a biological high-specific stiffness cell-like structural model by constructing a biological high-efficiency bearing:

wherein: ce _i is the ith bio-efficient bearer class cell. The analysis can be obtained:

(1) The biological cell structure model consists of a basic element-coupling element Co which affects the biological high-efficiency bearing performance and a coupling element self-criterion relation element matrix representation R. The constructed biological cell structure model ce fuses the biological high-efficiency bearing element matrix representation (biological high-efficiency bearing coupling element) and the relation element matrix representation (internal component mutual criterion relation) thereof, which form the basic composition of the biological high-efficiency bearing topological structure and reflect the basic form of the biological high-specific stiffness topological structure and the basic structure of the high-efficiency bearing.

(2) Unlike mechanically designed cell structures, the cell-like structure in a space-efficient load-bearing topology of an organism may be more than one.

(3) There is a correlation between the different cell-like structures ce _i and ce _j. Thus, based on the formula (18), a biological sub-class cell structure is further constructed, and the space construction rule describing different class cell structures is characterized by the sub-class cells.

The construction of a secondary cell structure model is shown as (19):

wherein: ce _ij is bio-efficient to carry sub-class cells.

The combination of formulas (19) and (17) can achieve a high-efficiency load-bearing configuration without introducing load and boundary descriptions of:

x′＝∩Ce_ij (20)

The construction process of formulas (18) - (20) models the process based on the high-efficiency bearing topology of the biological cell-like structure.

It should be noted that the biological cell structure ce shown in the formula (18) is composed of the coupling element Co and the coupling element self-criterion relationship element matrix representation R. In general, in the process of modeling the cell-like structure of the biological high-efficiency bearing by means of the formula (18), through the definition of characteristics such as shape, dimension, size, angle, density, distribution and the like in the coupling element Co, the complete definition of the cell-like structure of the biological high-efficiency bearing topological structure can be realized, the clear expression of the spatial topological structure of the cell-like structure can be realized, and the relation among the characteristics in the coupling element is defined without the need of defining the relation by the coupling element self-criterion relation element matrix R, so that redundant definition is performed. Thus, feature t _ii in the self-criterion relation of equation (18) R _ii may be left empty, and it is possible to:

It can be seen that ce _i is equivalent to Co _i if complete definition of the bio-efficient load topology cell-like structure can be achieved by feature definition in coupler Co. Therefore, the subsequent integration of the dominant performance of the biological high specific stiffness is realized by coupling element hybridization integration modeling (step 3) when the biological high specific stiffness bearing performance is hybridized.

In special cases, if R _ii is not empty, the spatial position relationship between structural features in the coupling element Co _i in R _ii can be described, the new spatial structural features are added to Co _i to express, and by such transformation, R _ii can be emptied, so that the integration of the biological high specific stiffness dominant performance is realized through coupling element hybridization integration modeling according to the subsequent steps.

The following describes the procedure of step 2.1 and step 2.2 in detail with reference to specific examples:

As shown in fig. 2 (a), the honeycomb is composed of a series of hexagonal cylinder cells made of beeswax in a closely arranged structure called honeycomb structure. The honeycomb structure is a strict hexagonal cylinder, one end of the honeycomb structure is provided with a hexagonal opening, the other end of the honeycomb structure is provided with a closed hexagonal pyramid bottom, and the honeycomb structure consists of three identical diamonds.

The conjugated analysis of the honeycomb high-efficiency bearing structure can prove that the honeycomb hexagonal cylinder structure has the maximum strength/mass ratio, the whole structure is good in stability and not easy to deform, and the compressive capacity is outstanding, so that the honeycomb high-efficiency bearing structure x _e can be obtained, namely the honeycomb hexagonal cylinder coupling element Co ₁(x_e.

According to equation (14), co ₁(x_e) is defined based on the primitive matrix:

Wherein, the coupling element features: shape.

From the element matrix definition formula (22), the high-efficiency carrier coupler Co ₁(x_e) has already fully defined the cellular high-efficiency carrier configuration x _e, so the relationship element matrix R ₁₁(x_e) for coupling the internal generic relationship self-criteria between the internal parts of the coupler Co ₁(x_e) is defined as an empty relationship element matrix, i.e., R ₁₁(x_e) =Φ.

And since there is only one coupler Co ₁(x_e), its coupler mutual criterion R _ij(x_e) is a null relation element matrix, i.e., R _ij(x_e) =Φ.

Substituting the formula (22) into the formula (12) to obtain the hard part ha (x _e)＝Co₁(x_e) of the honeycomb high-efficiency bearing structure; substituting R _ij(x_e)、 R₁₁(x_e) into equation (13), a hard part so (x _e) of the cellular high efficiency load bearing structure can be obtained.

According to equation (16), the boundary constraint element cB _e and the load element cL _e are defined by the element matrix:

Substituting cB _e and cL _e into equation (16) gives con (x _e) expressed based on the matrix of the primitives, and Substituting cB _e、cL_e、ha(x_e)、so(x_e) into the formula (17) to obtain the coupling element mathematical model for the high-efficiency bearing performance.

Co ₁(x_e)、R₁₁(x_e) was substituted into formula (18) to obtain cell-like ce _e＝Co_1e.

The same analysis procedure is used for the high-efficiency bearing structure of the human vertebra. As shown in fig. 2 (b), the rib is an arc-shaped small bone, one end of which is connected to both sides of the vertebra of the trunk, the wall of the trunk is bent to the spreading surface, and the other end is in a meat-free state or connected to the sternum in the center of the chest. Similarly, the same analysis process as the cellular high-efficiency bearing is adopted, and finally, the coupling element Co ₁(x_r) of the rib high-efficiency bearing topological configuration x _r defined by the element matrix, the boundary constraint element cB _r and the load element cL _r can be obtained:

cL _r＝[cl_r load main height direction bearing ]

In formula (24), its coupling element features: shape.

Similarly, the human vertebra high-efficiency bearing structure R ₁₁(x_r)＝Φ,R_ij(x_r) =Φ, can be obtained according to formula (18): ce _r＝Co_1r.

According to the coupling element Co, the cell-like element ce, the coupling element self-criterion relation R ₁₁ and the mutual criterion relation R _ij of the high-efficiency bearing topological configuration of the honeycomb and the human rib, the process models based on the high-efficiency bearing topological configuration of the biological cell-like element can be obtained respectively by substituting the coupling element Co, the cell-like element ce, the coupling element self-criterion relation R ₁₁ and the mutual criterion relation R _ij into formulas (18) - (20).

Step 3, performing high-efficiency bearing coupling element hybridization integration modeling based on the expansibility of the physical element, and realizing integration of different biological high specific stiffness advantage performances through hybridization integration of biological high-efficiency bearing units;

and 3.1, constructing a mathematical model of the dominant performance integration problem according to the definition description of the efficient bearing dominant performance integration problem.

The advantageous performance integration problem can be described as: to realize the integration of high specific stiffness bearing performance by crossing species by high specific stiffness coupling element topological configuration of different organisms, the defect of the mechanical bearing performance of a single bionic topological configuration is overcome.

According to the description of the problems, based on the definition of the object element problem, an object element mathematical model of the high specific stiffness topological configuration dominant performance integration problem is established:

Assuming that the high-efficiency bearing space topological configuration of a certain imitative source a has the high-efficiency bearing performance; the other efficient load-bearing spatial topology of the simulated source b has a different efficient load-bearing performance than a. Based on the primitive matrix representation, the above description is defined as:

Wherein: m _a,M_b is the description of the physical elements of the bionic sources a and b respectively; n _a,N_b is the name of the bionic source; c _a,c_b is its spatial load-bearing topology; v _a,v_b is the high-efficiency bearing performance of different space topological configurations

Performance integration objective matter element: solving a target by defining a problem with the object element M _x:

M_x＝(N_x,c_x,v_x) (27)

Wherein: m _x is the description of the bio-element of the bio-source obtained by hybridization of the bio-source a and b; n _x is the name of the hybrid biomimetic source and can be considered to be known; c _x is the hybrid biomimetic source spatial topology, which is unknown to be solved; v _x is an integration of efficient load bearing properties with a spatial topology of both the simulated sources a and b, which is known, i.e

v_x＝v_a∩v_b (28)

Performance integration condition matter element: the known conditional physical element r is the high-efficiency bearing space topological configuration of the bionic sources a and b, namely M _a and M _b, and can be obtained by the following steps:

Mathematical model of dominant performance integration problem: the high specific stiffness bearing performance integration problem is marked as Q, and based on the conditional element definition of the formula (29) and the object element definitions of the formulas (27) and (28), the element mathematical model of the integration problem can be obtained by the comprehensive formula (26):

The compatibility function of the high specific stiffness structure load bearing performance integration problem Q described above is noted as K _r(M_x, which represents the degree of realisation of the hybrid simulation source M _x under known conditions of the element r.

Step 3.2, solving the integration problem based on the extension of the physical element to obtain a solution scheme of the dominant performance integration problem;

analysis shows that the load performance integration problem Q is an incompatibility problem, i.e., the compatibility function K _r(M_x) is smaller than zero.

To solve this incompatibility problem, the degree of realisation of the hybrid imitation-source topology element M _x under known conditions r is increased.

The primitive extension describes various possibilities of the thing change, so this incompatibility problem is solved based on the primitive extension, and the problem of the compatibility K _r(M_x) of Q is solved by performing primitive extension transformation on the hybrid simulated source topology primitive M _x and the known condition primitive r, as shown in the formula (31):

Wherein T _x is the extension transformation of the hybrid simulated source topology material element, and T _r is the extension transformation of the material element of the known condition material element.

The analysis can be obtained:

[1] of the three formulae (31), formula (III) The two-way extension transformation of the object element M _x and the conditional element r in the problem solving is carried out; k _r(T_xM_x) is the unidirectional extension transformation of the object element M _x to the conditional element r; /(I)The method is one-way extension transformation from a conditional object element R to a target object element R _x.

[2] The first two kinds of extension transformation comprise the inverse change of the object element M _x to the condition element r, and the third extension transformation is the forward extension transformation from the known condition to the solving target.

Based on the analysis in the step 3.1, the target object M _x includes the unknown hybridization simulation source space topology configuration c _x to be solved, so that a third forward extension transformation is selectedThe solution scheme is more convenient.

Step 3.3, evaluating the weight influence of each coupling element and the coupling element characteristic based on a fuzzy analytic hierarchy process, extracting the coupling element and the coupling element characteristic with the greatest decisive effect on the high specific stiffness dominant performance, namely the weight influence, and defining the coupling element and the coupling element characteristic as gene coupling element and gene coupling element characteristics;

The fuzzy analytic hierarchy process has been widely used, the technology is very mature, and when the influence of each coupling element weight is evaluated by the fuzzy analytic hierarchy process, the triangular fuzzy numbers M1-M9 are taken as 1-9, wherein [1,3,5,7,9] respectively represent the scales [ general, medium, strong and extremely strong ], and the rest intermediate numbers represent the intermediate scales. Selecting an initial comprehensive fuzzy evaluation matrix with the number of experts being 3 and finally integrating the influence of all coupling element characteristics obtained by three expert evaluations on the biological high-efficiency bearing performance, wherein the initial comprehensive fuzzy evaluation matrix is shown as a formula (32):

And (3) deblurring the formula (32) by means of a triangular deblurring function to obtain relative importance evaluation [1, 0] of the coupling element characteristics, and obtaining the gene coupling element characteristics of o _e1 as coupling element Co ₁(x_e).

Similarly, fuzzy chromatography analysis is carried out on each coupling element characteristic of Co ₁(x_r) according to the steps to obtain the influence weight of the coupling element characteristic of Co ₁(x_r) on the high-specific-stiffness bearing performance, so that the gene coupling element characteristic of Co ₁(x_r) is o _r1

Step 3.4, performing bio-coupling element hybridization integration based on the matter element extension transformation of the gene coupling element to obtain a hybridization simulated source coupling element integrated with the biological efficient bearing advantage performance, namely a hybridization simulated source space topology configuration:

step 3.4.1, determining a solving formula of the hybrid bionic source space topology configuration based on the expansibility of the physical elements;

From step 3.2, it can be derived from forward extension transformation To obtain the object element M _x, namely

M_x＝T_rr (33)

Based on the primitive theory, T _r can be written as the component of T _r＝(T_rN,T_rc,T_rv),T_rN、T_rc、T_rv to T _r.

The general formulas (26) (27) (28) (29) (33) can be obtained:

From step 3.1, the hybrid biomimetic source spatial topology c _x is known, v _x、N_x is known, i.e. the first and third equations in equation (34) are known. Thus, the destination primitive (33) to be solved based on the forward extension transform can be written as:

assuming that the gene coupler of the high-efficiency bearing space topology c _a、c_b is ce _aG、ce_bG, according to the definition of the gene coupler, ce _aG、ce_bG is the decisive part for the high-efficiency bearing space topology c _a、c_b, and c _a、c_b is replaced by ce _aG、ce_bG, where formula (35) can be further written as:

Using ce _aG、ce_bG as a component element, Multidimensional matter expression/>, which can be written as a combination thereofThus, equation (36) can be written as:

The above formula is the solving formula of the hybrid bionic source space topological configuration c _x.

From the above, it can be seen that the hybrid simulated source space topology c _x can be coupled by known conditionsObtained by forward extension transformation T _rc.

Based on the extension of the object element, the coupling element forward extension transformation T _rc is formed by basic transformationObtained by compounding, i.e

Where k= { a, d, c or s },Adding/deleting transforms to/from coupling elements,/>Substitution transformation for coupling element,/>Decomposing/combining transforms for coupling elements,/>Enlarging/reducing the transform for the coupler.

Because the honeycomb and rib high-efficiency bearing topological structures only contain one coupling element Co ₁(x_e) and Co ₁(x_r), the coupling element is the corresponding gene coupling element. Therefore, co ₁(x_e) and Co ₁(x_r) are used as gene coupling elements to be substituted into the formula (38) to obtainWhich represents coupling element/>, by known conditionsThe forward extension transformation T _rc can obtain the hybrid bionic source topology c _x of the hybrid bionic source.

Step 3.4.2, constructing four basic extension transformations of the gene coupling element based on the extension of the element, and obtaining the coupling element basic transformation of the dominant performance integration problem;

Coupling element addition transformation Expressed by formula (39):

based on the primitive scalability, the coupling element Co _q(Co_q＝[co o_q d_q) is subjected to a scalable transformation. After extension transformation, the coupler Co _q is added with the feature o _q0 and the corresponding feature d _q0. The coupling elements before and after transformation in the formula (39) have the additive relation of the object elements; and the inverse transformation in formula (39) Is an extensible pruning transformation of the coupling elements.

Coupling element substitution transformationRepresented by formula (40):

/>

In the formula, [ co o _h d_h]＝Co_h ] represents a post-transformation coupler. Based on the object divergence, the coupling element Co _q is subjected to divergence extension transformation, and the coupling element Co _q is extension replaced by Co _h. Before and after the substitution, the characteristic of the coupler is changed from o _q to o _h, the corresponding characteristic quantity is also changed from d _q to d _h.Co_q, and a divergent extension relationship exists between Co _h, and the transformation of reverse extension of the coupler Co _h to the coupler Co _q is that Is an inverse transform of (a). It should be noted that the permutation transformation cannot be arbitrarily transformed, but rather follows the principle of primitive extension of the coupling element.

Coupling element decomposition transformationExpressed by formula (41):

In the method, in the process of the invention,

Based on the object element separability, the coupling element Co _q is subjected to extension decomposition transformation. Through extension decomposition transformation, the coupling element characteristics o _q are decomposed to obtain o '_q and o' _q, and the corresponding coupling element characteristic quantities are d '_q and d' _q. The coupling elements before and after transformation in the formula (41) have the object element separability relation; and the inverse transformation in the formula (41)Is an extensible combined transformation of the coupling elements.

Coupling element expansion transformationExpressed by formula (42):

Where the coupler feature o _qs is the product of feature o _q and feature o _s, and the corresponding coupler feature d _qs is the product of d _q and d _s. Based on the primitive integrality, the extension transformation is performed on the coupling element Co _q. After extension transformation, the coupling element characteristic o _q is extended to o _qs, and the corresponding coupling element characteristic quantity is changed from d _q to d _qs. The relation of the integrality of the object element exists between the coupling elements before and after the expansion transformation can be expanded. In particular, when o _s = e, then o _qs＝o_qe＝o_q, at which point the formula (42) coupler expands the transform Only the extensive transformations of feature magnitudes. Similarly, the inverse transformation in equation (42), i.e./>Is an extension-reduction transformation of the coupling element.

According to the definition of the basic transformation of the four coupling elements, the basic transformation of the gene coupling elements in the example is carried out, the basic transformation of the obtained gene coupling elements is shown in table 1, and the specific operation and schematic diagram of the transformation are given in table 1.

Table 1 four basic transformations of Gene coupler and its feasibility

Step 3.4.3, carrying out feasibility screening on the coupling element basic transformation, and further determining necessary coupling element basic transformation;

The basic transformations in table 1 were subjected to feasibility analysis, which is represented by the symbol ∈v in table 1, and x represents infeasibility. In table 1, the addition of new coupling features in the incremental transformation may be attempted, and there is no feasibility because there are no new features to refer to. However, the decomposition transformation can be developed, and the attempt to decompose each coupling element feature fails, so that the decomposition transformation is not feasible.

The basic transformations of the coupling elements in Table 1 are analyzed to determine the necessary basic transformations:

Analysis shows that The transformation realizes the removal of other non-genetic coupling element characteristics; /(I)The transformation pair feature o _e1 can extend and retract in the height direction so as to realize the matching of the coupling element height direction during the combination transformation; /(I)The array formed by transformation can form a coupling element Co ₁(x_e) protection wall together with the hierarchical structure, and the Co ₁(x_e) non-coplanar mechanical property defect is compensated by the Co ₁(x_r) hierarchical bearing performance advantage; /(I)Transformed to achieve spatial combination of coupling features. Thereby determining the above basic transformation as the necessary basic transformation.

Step 3.4.4, combining the necessary coupling element basic transformation to perform combination transformation, so as to obtain basic de-transformation of the dominant performance integration problem;

Substituting the requisite elementary transformations of the coupling elements into formula (38), and constructing an elementary solution transformation T ₀ of the dominant performance integration problem: The basic transformation process is shown in fig. 4, and the hybrid coupler solution obtained by the basic transformation is shown as a reference number ① in fig. 4.

Step 3.4.5, compounding the basic de-transformation with other coupling element basic transformations, constructing other de-transformations, and obtaining all de-transformation sets;

taking into account the transformations in Table 1 And/>The effect generated when two coupling elements are simultaneously expanded or contracted and transformed is counteracted, so that the selection/>Only the coupling element Co ₁(x_r) was subjected to the expansion/contraction transformation, and it can be seen from Table 1 that/>To expand the transformation,/>To reduce the transform.

Thus, the method can be further used for other basic transformations based on the basic de-transformationCombining to construct other deconfigurations: /(I)The transformation process of these deconvolutions is shown in fig. 4.

All the final hybrid couplers of the deconversion are known as the number ①-⑩. It should be noted that, inThe transformation can be performed in a hierarchical direction, an array direction and an array layer direction, so/>And/>The transformation yields three hybrid couplers ②③④ and ⑥⑦⑧, respectively.

In addition, it should be noted that due toThe transformation is that a plurality of honeycomb structures are arranged in the hierarchical structure, which are similar to the original coupling elements to be improved and the original honeycomb structure coupling elements, and the protection wall for improving the non-coplanar mechanical property of the coupling elements cannot be formed, so that the transformation/>And/>I.e., hybrid coupler solution ⑨⑩.

And 3.4.6, selecting an evaluation element to evaluate the hybrid coupling element deconversion set, and determining the optimal deconversion to be the hybrid simulated source coupling element for dominant performance integration, namely the hybrid simulated source space topology configuration.

Constructing a three-dimensional finite element model of the original coupling element to be improved, namely decoupling of honeycomb structure coupling elements and all hybrid coupling elements: during modeling, the side length of the hexagonal structure contained in all hybrid coupling elements is the same as that of the hexagonal structure of the coupling element to be improved, and the structural wall thickness is the same; the same boundary constraints apply: a bottom surface fixing constraint, the top surface applying an equal magnitude of pressure load F _y =200n (boundary constraint see fig. 5 (a)); all finite element model grids have the size of 5mm, hexahedral grids are adopted as the grid shapes, and the quality of the grids is controlled to be more than 0.97; all the hybridization coupling element models are made of the same material: carbon steel, material density 7800kg/m ³, elastic modulus 210GPa and Poisson's ratio 0.26.

Calculating to obtain the mass m ₀ = 1.702kg, the first-order frequency f ₀ = 210.13Hz and the maximum load deformation of the coupling element to be improved, namely the coupling element with the original honeycomb structure/>

The quality m, the first-order frequency f and the maximum deformation U _Fy of the hybrid coupler are selected as evaluation factors, and the merits of the decoupling sets ①-⑧ of the hybrid couplers are compared, as shown in Table 2.

TABLE 2 comparison of the goodness of the respective deconverted hybrid couplers

Δf/Δm= (f-f ₀)/(m-m₀) in Table 2,Which represent the ratio of deformation to the increase in frequency to the increase in mass, respectively. As can be seen from Table 2, Δf/Δm are both positive values and ΔU _Fy/Δm are both negative values, which indicate that the initial deformation of the hybrid coupler is reduced and the natural frequency is increased compared to the deformation of the coupler to be improved. In all the deconversion, the absolute value of the ratio of the maximum deformation reduction/frequency increase to the mass increase of the hybrid coupler element deconvolution ① is the maximum, which means that the coupling element hybridization integration efficiency is the highest, and the hybrid coupler element deconvolution ③ is the next. Therefore, the solution ① is selected as the optimal hybrid coupler solution.

The hybrid coupler solution ① is the hybrid simulated source high specific stiffness topological configuration c _x to be solved by the integration problem.

And 4, taking the hybrid coupler as a mechanical element structure through R-I inversion, and mapping the hybrid coupler to a mechanical structure with high specific stiffness through a multi-objective structure optimization method based on an approximate element model and a mechanical structure design method based on the element structure.

And 4.1, taking the hybrid simulated source coupling element obtained in the step 3 as a mechanical element structure, selecting a high specific stiffness performance measurement index of the element structure, and optimizing the dimension parameter of the element structure by means of a multi-objective optimization algorithm through constructing an approximate element model function between a design variable and a high specific stiffness performance evaluation index.

And selecting a mechanical element structure and biological element cells as inversion media, and taking the optimal hybrid element solution ① as the mechanical element structure. Further, the meta-structure parameter optimization based on the approximate meta-model is performed, as shown in fig. 5, the inner hexagonal side length, the wall thickness at two sides, the upper wall thickness and the lower wall thickness of the mechanical meta-structure are selected as design variables, the design variables are defined as variables v ₁、v₂、v₃、v₄, and v ₃＝v₄ is known according to the structure of the design variables. According to the main load condition, selecting the load deformation U _Mx、U_Mz、U_Fy and the first-order frequency f as the load performance indexRepresentation, order/>Let/>For meta-structure mass m, i.e./>Considering the size of the filling area designed in the example, the value range of the variable v ₁ is set to be 90mm,140 mm. The variable v ₂、v₃ has a value in the range of 7mm,12 mm. By means of an experimental design module of Workbench software, a Latin hypercube experimental design method is adopted, a central composite design method is adopted for sampling, 25 groups of sample design points are obtained, and a performance index corresponding to a variable value v _i of the sample design points is calculatedWherein a portion of the sample data points are shown in table 3.

TABLE 3 sample points of partial experimental design and corresponding performance metrics

/>

Based on the 25 groups of design samples, a Kriging meta-model is selected as an approximate model by means of an approximate model module of Workbench software, so that a bearing performance index can be obtainedAnd meta-model relation functions between the meta-structure design variables v _i. Based on the relation function models, the method uses first-order frequency/>Maximum simultaneous load bearing deformation/>Minimum is an optimization target, and the optimization constraint condition is mass/>Less than the initial mass, i.e./>Using multi-objective genetic algorithms

Solving to obtain the optimal value of the design variable as follows: v ₁＝91.20mm,v₂＝9.50mm,v₃ = 9.73mm.

And 4.2, carrying out mechanical rigidity specific stiffness structural design according to the optimized meta structure by a mechanical structure design method based on the meta structure.

The mechanical element structure design method is widely applied in the field of mechanical design and is not repeated here. Based on the meta-structure after the structural parameter optimization, filling the meta-structure into the example design area shown in fig. 1, and obtaining an example machine tool column three-dimensional model as shown in fig. 6 (a). For comparison, a three-dimensional model based on mechanical element structure filling of the original element to be improved, namely the honeycomb structure element is established as shown in fig. 6 (b).

The overall maximum deformation, mass and first-order natural frequency of the example upright post under different design schemes are calculated and obtained as shown in table 4.

Table 4 comparison of different designs of column structures

As can be seen from table 4, in the scheme 1, the pillar structure is designed based on the original element to be improved, i.e. the honeycomb element structure, the mass is reduced by 9.2% compared with the original pillar structure, the first-order natural frequency is increased by 12.3%, but the overall maximum deformation is increased by 6.6%, which is very unfavorable for structural load. The natural frequency of the structure is affected by both the mass of the structure and the rigidity of the structure itself, and in other cases, the natural frequency of the structure increases as the mass of the structure decreases. Reasonable speculation can therefore be seen: the first-order frequency improvement of design 1 is largely derived from the reduction of its own structural mass, rather than the improvement of its own stiffness; design 1 only shows a phenomenon that the first-order frequency of the system increases and the overall maximum deformation is significantly increased.

Scheme 2 is a column design based on hybrid coupler element structure. From table 4, the mass of scheme 2 was reduced by 3.2% with little change compared to the original design, but the deformation under load was significantly reduced by 17.2%, and the first order natural frequency was increased by 24.8%. It can be inferred that the significant reduction in the deformation under load of the structure, and the significant increase in the natural frequency, are all brought about to a great extent by the increase in the rigidity of the structural design itself, rather than by the variation in its structural mass. This is clearly different from scheme 1. In addition, the overall deformation under load of scheme 2 is reduced by 22.4% compared to scheme 1, but the first order natural frequency is increased by 11.2%.

In summary, it can be seen that the column design based on the hybrid coupler structure in scheme 2 is optimal. The correctness of the proposed inventive method is verified.

Claims

1. The bionic design optimization method for the high specific stiffness structure is characterized by comprising the following steps of:

The step (3) comprises the following specific contents:

(3.4) performing bio-element coupling hybridization integration based on the element extension transformation of the gene coupling element to obtain a hybridization simulated source coupling element integrated with the advantage performance of high specific stiffness of the bionic source organism, namely a hybridization bionic source space topology configuration;

Step (3.4) comprises the following contents:

(3.4.6) selecting an evaluation element to evaluate the hybrid coupling element decoupling transformation set, and determining the optimal decoupling transformation to obtain a hybrid simulated source coupling element which is oriented to dominant performance integration, namely a hybrid simulated source space topology configuration;

the mathematical model for simulating the high specific stiffness dominant performance integration problem of the biogenic organisms is as follows:

The description of the physical elements of the bionic sources a and b respectively; n _a,N_b is the name of its bionic source; c _a,c_b is the spatial topological configuration of the bionic sources a and b; v _a,v_b is the different efficient bearing performance of the spatial topological configuration of the bionic sources a and b; m _x is the description of the material element of the imitative source formed by hybridization, M _x＝(N_x,c_x,v_x),N_x is the name of the hybridized bionic source, c _x is the spatial topological configuration of the hybridized bionic source, v _x is the high-efficiency bearing performance integration with the spatial topological configuration of the imitative source a and b, namely v _x＝v_aIv_b; r is a conditional element, which is the biological space topological configuration of the known bionic sources a and b, namely/>

where k= { a, d, c or s }, Adding/deleting transforms to/from coupling elements,/>Substitution transformation for coupling element,/>Decomposing/combining transforms for coupling elements,/>Enlarging/reducing the transformation for the coupling element;

2. The high specific stiffness structure bionic design optimizing method according to claim 1, wherein the step (1) specifically comprises the following steps:

(1.3) based on the similarity principle, carrying out similarity calculation and evaluation between the biological high-efficiency bearing configuration and the engineering design structure from the aspects of loading, boundary, structure and function;

3. The high specific stiffness structure bionic design optimizing method according to claim 1, wherein the step (2) specifically comprises the following steps:

4. The method for designing and optimizing a high specific stiffness structure according to claim 3, wherein in the step (2.1), the biological structure topological coupling mathematical model facing the biological high-efficiency bearing performance is:

5. The method of optimizing a high specific stiffness structural bionic design according to claim 3, wherein in the step (2.2), the structural model of the cell-like is:

6. The high specific stiffness structure bionic design optimizing method of claim 3, wherein the step (4) specifically comprises the following steps: