CN112052537A

CN112052537A - Bionic design optimization method for high-specific-stiffness structure

Info

Publication number: CN112052537A
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: 2020-12-08
Anticipated expiration: 2040-09-08
Also published as: CN112052537B

Abstract

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

Description

Bionic design optimization method for high-specific-stiffness structure

Technical Field

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

Background

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

Various high-efficiency space topological structures with excellent performance in nature provide an endless inspiration source for the optimization and innovation design of a mechanical high-specific-stiffness structure. The spatial topological configuration of the organism is the result of natural selection and life evolution for hundreds of millions of years, and fully embodies the trend of natural evolution: the best space configuration and the least material are used for bearing the maximum external force, namely the best structural efficiency, namely the highest specific rigidity.

Although there are many light and efficient structures in nature, the efficient load-bearing structure and the load-bearing mechanical properties and mechanisms thereof are greatly different. The bionic force distribution is limited by a specific natural environment of a bionic source, the mechanical adaptability of the biological topological structure is single, if the vein distribution is more suitable for bending moment load, the co-oriented bearing performance of the honeycomb structure is better, and the non-co-planar mechanical bearing performance is much poorer. The existing mechanical structure bionic design method is mostly oriented to a single bionic source, and the mechanical adaptability of the biological topological configuration of the single bionic source is single or the mechanical property is insufficient, so that the mechanical property of the final bionic design structure is insufficient.

Disclosure of Invention

The purpose of the invention is as follows: aiming at the problem that the mechanical structure bionic design method is mostly oriented to a single bionic source at present and the final bionic design structure bearing mechanical property is easy to have defects, the invention provides a high specific stiffness structure bionic optimization design method based on RMI (Relationship Mapping Inversion) and coupling element hybridization, seeks a biological high specific stiffness structure design biological high specific stiffness structure solution, solves the problem of biological high specific stiffness hybridization integration, realizes the high specific stiffness mechanical structure bionic optimization design under the biological high specific stiffness advantage performance integration, and makes up the defects of single bearing property and possible existence in the original single bionic source structure bionic optimization design.

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

(1) firstly, carrying out engineering-biological mapping by an R-M mapping principle, and solving a solution of a biological high-efficiency bearing structure of a high-specific stiffness structural design;

(2) analyzing a biological space topological configuration efficient bearing mechanism to obtain biological efficient bearing coupling elements and similar cells expressed based on an object element matrix, wherein the biological efficient bearing coupling elements and the similar cells are the essence of the biological space topological configuration;

(3) carrying out efficient bearing coupling element hybridization integration modeling based on physical element expansibility, and realizing integration of high specific stiffness superiority of different organisms through hybridization integration of a biological efficient bearing unit;

(4) and performing R-I inversion to use the hybrid coupling element as a mechanical element structure, and performing inversion mapping on the hybrid coupling element to a high-specific-stiffness mechanical structure by using a multi-objective structure optimization method based on an approximate element model and a mechanical structure design method based on an element structure.

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

(1.1) analyzing the design problem of mechanical high specific stiffness, and obtaining the original understanding of the biological invention by means of engineering contradiction transformation, contradictory operation domain description and contradiction elimination solution by means of a Biotriz conflict matrix;

(1.2) mapping an example library of a biological invention principle, and solving based on the biological invention principle to obtain a biological high-efficiency bearing structure;

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

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

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

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

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

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

in the formula (I), the compound is shown in the specification,

x' is the biological space topology, Co_iThe number of the ith coupling element contained in the biological space topological configuration is n, and the n is the total number of the contained biological high-efficiency bearing coupling elements; r_ijIs a biological high specific stiffness topological coupling element Co_iAnd Co_jWhen i ═ j, R_ijFor the biological high-efficiency bearing of the relationship of each part in the coupling element, R is equal to j when i ≠ j_ijThe mutual relation between topological coupling elements with high specific stiffness; cL is a borne load set, and cB is a boundary constraint set; co is a mixture of_iIs the ithTopological structure coupling element Co_iThe name of (a); r is_ijIs a biological high specific stiffness topological element coupling relation R_ijThe name of (a); o_ik、d_ikFor topological configuration of coupling element Co_iThe kth feature of (1) and its feature description; q. q.s_ijk、t_ijkIs R_ijThe kth feature of (1) and features thereof; m and p are Co_iAnd R_ijThe number of features involved.

In the step (2.2), the structure model of the quasi-cellular is as follows:

in the formula, ce_iFor the ith biological high-efficiency bearing type unit cell, R_ijIs a biological high specific stiffness topological coupling element Co_iAnd Co_jWhen i ═ j, R_ijThe relation of each part in the topological coupling element with high specific stiffness is shown in the specification, and R is_ijIs namely R_ii。

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

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

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

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

and (3.4) carrying out biological coupling element hybridization integration based on the matter element extension transformation of the gene coupling element to obtain a hybrid bionic source coupling element integrated with the high specific stiffness superiority performance of the bionic source organism, namely a hybrid bionic source space topological configuration.

The step (3.4) comprises the following steps:

(3.4.1) determining a solving formula of the spatial topological configuration of the hybrid bionic source based on the object element expansibility;

(3.4.2) constructing four basic extension transformations of the gene coupling element based on the object element extensibility to obtain all coupling element basic transformations of the bionic source biological high specific stiffness advantage performance integration problem;

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

(3.4.4) combining the necessary coupling element basic transformations to carry out combined transformation to obtain the basic de-transformation of the bionic source biological high specific stiffness advantage performance integration problem;

(3.4.5) compounding the basic de-transformation with other coupling element basic transformations, and constructing other de-transformations to obtain all de-transformation sets; said other coupler basic transforms are coupler basic transforms other than the necessary coupler basic transforms of step (3.4.3) of all the coupler basic transforms of step (3.4.2);

and (3.4.6) selecting evaluation elements to evaluate the hybrid coupling element de-transformation set, determining the optimal de-transformation, and obtaining the hybrid bionic source coupling element oriented to the advantage performance integration, namely the hybrid bionic source space topological configuration.

Further, the mathematical model of the integration problem of the high specific stiffness superiority of the bionic source organism is as follows:

wherein Q represents the integration problem of the high specific rigidity superiority of the bionic source organism,

M_a，M_brespectively describing the object elements of the bionic sources a and b; n is a radical of_a，N_bIs its bionic source name; c. C_a，c_bThe bionic source is a space topological configuration of a bionic source a and a bionic source b; v. of_a，v_bThe bionic source has different high-efficiency bearing performances of the spatial topological configurations of the bionic sources a and b; m_xBionically derived elements formed for hybridizationDescription, M_x＝(N_x,c_x,v_x)，N_xFor the name of hybrid bionic source, c_xFor a hybrid bionic source spatial topology, v_xFor efficient load-bearing performance integration with space topology configurations of both bionic sources a and b, i.e. v_x＝v_a∩v_b(ii) a r is a conditional element and is the known biological space topological configuration of the bionic sources a and b, namely

The hybridization bionic source space topological configuration c_xThe solution of (A) is:

in the formula (I), the compound is shown in the specification,

known conditional matter elements formed for efficient carrying of gene coupling elements of known bionic sources, T_rcFor forward extension of the coupling element, T_rcBy four basic extension transformations

Compounding to obtain the compound, namely:

where k is { a, d, c or s },

adding/deleting conversion for coupler,

Is a replacement transformation of the coupling element,

For the decomposition/combination transformation of coupling elements,

For the coupler expansion/contraction transformation.

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

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

and (4.2) according to the optimized element structure, carrying out mechanical specific stiffness structural design by a mechanical structure design method based on the element structure.

Compared with the prior art, the invention has the following remarkable effects: according to the bionic optimization design method of the high specific stiffness structure based on RMI and coupling element hybridization, the bionic design of the high specific stiffness structure under the integration of the superior performance of biological high specific stiffness is realized by solving the problem of high-efficiency biological load-bearing coupling element hybridization integration, and the problems of single load-bearing performance, possible insufficient mechanical performance and the like in the bionic design of the original single bionic source structure are solved.

Drawings

FIG. 1 is a diagram of an example machine tool column and its web fill area;

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

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

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

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

FIG. 6(a) is a pillar model based on the hybrid coupler structure, and FIG. 6(b) is a pillar model based on the original to-be-improved coupler structure.

Detailed Description

The technical solution of the present invention is further explained with reference to the drawings and the embodiments.

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

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

Due to the high-efficiency bearing characteristic of the honeycomb structure, the honeycomb structure is widely applied to machinery, particularly to the filling design of the bionic rib plate with high specific stiffness of the machine tool structure shown in (a) in fig. 1. However, the honeycomb structure has better load-bearing performance in the co-planar direction, but has much poorer mechanical load-bearing performance in the non-co-planar direction, as shown in fig. 2 (a).

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

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

step 1, firstly, engineering-biological mapping is carried out through an R-M mapping principle, and a solution of a biological high-efficiency bearing structure of a high-specific stiffness structural design is solved.

And if S is the design requirement of the mechanical domain high specific stiffness structure, x is the mechanical high specific stiffness structure to be solved, F is the topological reconstruction of the unknown overall structure, and CON is 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 for high specific stiffness design requirements under load constraints.

Many highly efficient load bearing structures in nature offer numerous biobearing solutions for high specific stiffness mechanical structure designs. The biological high-efficiency bearing topological structure can be regarded as a structural self-adaptive generation type topological structure oriented to a natural loading environment of organisms through long-term evolution and environment adaptive screening. Thus, the adaptive generative topological configuration mathematical expression for a living being is:

x′＝{F′(S′,x′))|CON′(x′)＝0} (2)

in the formula: f' is a solving algorithm and represents a natural competitive selection process or a natural evolution process of organisms; s' the environment to be adapted by the organism is required to be loaded; x' is a high-efficiency bearing topological configuration generated by biological self-adaption; CON' is the restriction condition of the biological growth environment.

The method provides a biological topological configuration solution of a mechanical high specific stiffness structure based on relationship-mapping-inversion, and seeks an innovative solution of a mechanical design problem of high specific stiffness in a biological domain, so that

For mapping from a mechanical domain to a biological domain, a mapping inverse relationship structure R between a high specific stiffness design structure to be solved and a biological high-efficiency topological configuration is shown as a formula (3):

a schematic diagram of a mapping-inversion-relationship structure between a high specific stiffness design structure and a biological high-performance topological structure is shown in fig. 3, where ψ in fig. 3 is inversion from a biological domain to a mechanical domain, that is

The reverse process of (1) 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 is carried out

Decomposition is carried out as shown in formula (5):

in the formula (I), the compound is shown in the specification,

in order to map the BioTRIZ matrix,

in order to map the biological instance base,

for mapped complex product operations, Matrix_BtrizIs a BioTRIZ matrix, r_F、c_FDbase, the improved and degraded operation domains of the BioTRIZ matrix, respectively_BtrizExample library for the original understanding of the invention, m_ipFor the BioTRIZ biological invention understanding.

Step 1.1, analyzing the design problem of mechanical high specific stiffness, and obtaining the original understanding of the biological invention by means of a BioTRIZ matrix, namely, mapping the BioTRIZ matrix to perform engineering contradiction transformation, contradictory operation domain description and contradiction elimination solution.

BioTRIZ matrix table, which is shown in numerous references and is not described herein, uses 6 domains of material, structure, energy, information, space and time as the rows of the BioTRIZ matrix (improved domain r)_F) And column (corruption operation field c)_F) The inventive principle of 40 TRIZ is used as the matrix value. In the biological high-efficiency bearingIn the mapping process of the structure-loaded scheme, the improvement and deterioration of the engineering problem can be conflicted with the corresponding operation domain r_F、c_FThe six parameters are described and expressed, and the BioTRIZ invention principle special solution can be obtained through the BioTRIZ matrix element values corresponding to the rows and the columns of the BioTRIZ matrix table, and the solution is the biological original understanding m_ip。

As can be seen from the design analysis of the example, the structural design can be understood as follows: the maximum structural efficiency is achieved with the minimum use of structural materials. The method can be regarded as a conflict solving problem, the use of materials as less as possible is actually to optimize a mechanical structure or reduce the structural space, and the structure or the spatial operation domain of BioTRIZ is used for description; the maximum structural efficiency is to ensure the mechanical bearing performance of the mechanical structure and the like, and is described by the strength operation domain of BioTRIZ.

The former was described by selecting the structural operation domain, so the problem can be expressed as a biotiz conflict: improved energy, i.e. improved operating region r_FFor energy, the structure is deteriorated, i.e. the operation domain c is deteriorated_FIs a structure. According to the BioTRIZ conflict matrix of the BioTRIZ matrix table, the invention principle solution number given from the biology perspective is obtained: 1,3,5,6, 25, 35, 36, 40. Each number represents different original understanding, and specific contents corresponding to the inventive principles can be obtained by querying 40 inventive principles in the TRIZ, for example, the original understanding corresponding to the number 1 is a segmentation principle.

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

Biological instance library mapping further aided by inventive principles

The biological examples are obtained by solving the principle of the invention. The biological example library mapping principle of the invention principle is as follows: the bionic cases which are successful in the past under the principle of the invention are stored in an example library in an example description mode, and effective biological examples can be searched for as a starting point for solving the bionic design problem in a subsequent retrieval mode. The biological example base can be related by searchingBiological materials, documents and the like, and typical biological function information corresponding to the innovative principle is collected to establish a special biological example library; general biological example libraries that can also utilize 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.; document [2 ]]Simple swallow-glow, a green innovative design method using biological vocabulary combined with bionic and TRIZ [ D]Taiwan: university of success, 2013.), the query corresponds to the original understanding of the invention: examples of organisms under 1, 3, 5, 6, 25, 35, 36, 40.

Considering the bearing requirement that honeycomb non-coplanar mechanical properties are poor and the upright columns are not in the height direction, the structure of the human vertebra is finally selected as a biological example.

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

And if the similarity is low, reselecting the biological high-efficiency bearing configuration through the example library mapping in the step 1.2, repeating the step 1.3 until the similarity between the selected biological high-efficiency bearing configuration and the engineering design structure is calculated and evaluated to be high, and then performing the step 2.

From the perspective 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 loading, boundary constraint, structure and function, and defining a similar element set u:

based on a similarity analysis method, defining the similarity Q between the human vertebra and the upright column:

in the formula, q (u)_i)、β_iThe similarity of the ith similar element and the corresponding weight coefficient thereof. The 5 similarity scales and meanings that define similar elements are:

in the formula, the right side of the equation is the similarity scale, and the left side is the similarity corresponding to the similarity scale.

Based on the analytic hierarchy process, the importance of four elements is determined and a judgment matrix A of 4 similar elements is listed:

solving the maximum eigenvalue λ of the matrix and the corresponding eigenvector Λ, i.e., Λ ═ λ Λ, the maximum eigenvalue λ can be found to be 4, and the corresponding eigenvector Λ ═ 0.85,0.46,0.16]. Normalizing the feature vector Lambda into the weight coefficient beta of the similar elements₁、β₂、β₃、β₄0.521, 0.282, 0.099. Analyzing the similarity of the two similar elements, and taking q (u)₁)、 q(u₂)、q(u₃)、q(u₄) 0.75, 0.5, 1. The similarity between the two is 0.729 by substituting the formula (7).

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

And 2, analyzing a biological space topological configuration efficient bearing mechanism to obtain biological efficient bearing coupling elements and quasi-cells expressed based on the matter element matrix, wherein the biological efficient bearing coupling elements and the quasi-cells are the essence of the biological high specific stiffness topological configuration.

And 2.1, constructing a biological structure topological coupling element mathematical model facing the biological high-efficiency load to obtain the biological high-efficiency load coupling element.

Based on a conjugate theory, the efficient bearing topological configuration under the influence of the biological natural environment (loaded boundary and the like) is written as follows:

the above formula is composed of two parts,

the sum of the hard part, the soft part in conjugate relation with the hard part and the middle part of the hard part is the topological configuration corresponding to the biological bearing constraint. Where ha (x ') represents the stiff portion of the bio-efficient load-bearing topology, so (x') represents the soft portion conjugated thereto, mid (x ') represents the intermediate portion, and con (x') is the bio-load-bearing constraints (including the loads being borne, boundary constraints, etc.).

Since the intermediate portion is not involved in the topological conjugate analysis of high specific stiffness for living things, the intermediate portion can be omitted in equation (10). The hard portion ha (x ') refers to the components of the bio-efficient topology, so (x') the interrelationship within and between the components of the bio-efficient topology.

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

namely:

in the formula: co_iThe number of the ith coupling elements contained in the high-efficiency bearing topological configuration is n, and the n is the total number of the contained biological high-specific-stiffness topological coupling elements; r_ijIs a biological high specific stiffness topological coupling element Co_iAnd Co_jWhen i ═ j, R_ijFor the relationship of each part in the topological coupling element with high specific stiffness, R is equal to j when i ≠ j_ijThe mutual relation between topological coupling elements with high specific stiffness; cL (x ') is a borne load set, and cB (x') is a boundary constraint set.

The coupling element of the high-efficiency bearing topology configuration is defined by the element matrix, the relation of the biological high specific stiffness topology coupling element is defined by the relation element matrix, and the following can be obtained:

in the formula: co is a mixture of_iCoupling element Co for ith topological configuration_iThe name of (a); r is_ijIs a biological high specific stiffness topological element coupling relation R_ijThe name of (a); o_ik，d_ikFor topological configuration of coupling element Co_iThe kth feature of (1) and its feature description; q. q.s_ijk，t_ijkIs R_ijThe kth feature of (1) and features thereof; m and p are Co_iAnd R_ijThe number of features involved.

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

in the formula, cl and cb are the names of the load object element and the boundary object element respectively, and ol, dl, ob and db are the characteristics and the characteristic description of the load object element and the boundary object element respectively.

Substituting the formulas (14) to (16) into the formulas (12) and (13), and finally substituting the formula (10) to finally obtain a coupled element mathematical model expressed based on the object element matrix-relation element matrix and having efficient bearing performance towards the living beings under the influence of the natural environment of the living beings (such as a loaded boundary and the like) as

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

The whole or part of some mechanical structures can be approximately regarded as being formed by repeated array/arrangement combination of a certain basic type structure in space/plane, and the basic type structure is defined as a cellular structure/a meta-structure in the machine.

Similar cellular structures also exist in the biological high-efficiency bearing topological configuration, such as a branch structure of a repeated array of blades in the plane of the blade; a nearly quadrilateral structure of array ordering of dragonfly wings, etc. The basic structural units in a spatial/planar repeating array/arrangement in a living being are defined as cell-like structures in a bio-efficient topological configuration.

The method comprises the steps of carrying out space complexity dimension reduction on a 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 structure layer, a secondary cell-like structure layer and an integral target layer based on the principles of mechanical structure hierarchical analysis and a substructure method.

Firstly, constructing a biological high-efficiency bearing construction biological high specific stiffness cell structure model comprises the following steps:

in the formula: ce (ce)_iCarrying the quasi-cellular for the ith organism. Analysis can obtain:

(1) the biological cellular structure model consists of a basic element-coupling element Co which influences the high-efficiency bearing performance of organisms and a coupling element self-rule relation element matrix representation R. The constructed biological cellular structure model ce fuses biological efficient load-bearing matter element matrix representation (biological efficient load-bearing coupling element) and relation element matrix representation (mutual criterion relation of internal components), which form the basic composition of biological efficient load-bearing topological structure and reflect the basic form of biological high specific stiffness topological structure and the essential structure of efficient load-bearing.

(2) Unlike mechanically designed cellular structures, there may be more than one cell-like structure in a space-efficient load-bearing topology of a living being.

(3) Different class cellular structure ce_iAnd ce_jThere is a relationship between them. Therefore, on the basis of the formula (18), a biological secondary cell structure is further constructed, and the secondary cells are used for representing and describing different structural space construction rules of the secondary cells.

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

in the formula: ce_ijThe biology bears the secondary cells with high efficiency.

The high-efficiency load-bearing configuration without load introduction and boundary description can be obtained by combining the formula (19) and the formula (17):

x′＝∩Ce_ij (20)

the construction processes of equations (18) - (20) model the process based on the efficient load-bearing topological configuration of the biological cellular structure.

It should be noted that the biological cellular structure ce shown in formula (18) is formed by a coupling element Co and a coupling element self-calibration relation element matrix representation R. In general, in the process of modeling the cell-like structure of the bio-efficient load by means of the equation (18), through the definition of features 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 bio-efficient load-bearing topological structure can be realized, the clear expression of the spatial topological configuration of the cell-like structure can be realized, and the redundant definition is performed without defining the relationship among the features in the coupling element by the coupling element self-rule relationship element matrix R. Thus, the formula (18) R may be_iiFeature t in the self-rule relation of_iiAnd (5) emptying to obtain:

it can be seen that if the complete definition of the cellular structure of the bio-efficient load-bearing topological structure type can be realized through the feature definition in the coupled element Co, then ce_iEquivalent to Co_i. Therefore, the integration of the superior performance of the high specific stiffness of the organism is realized through coupling element hybridization integration modeling (step 3) when the high specific stiffness bearing performance of the organism is hybridized subsequently.

In special cases, if R_iiIf not, R may be substituted_iiMiddle coupling element Co_iSpatial positional relationships between internal structural features are described by being in Co_iAdding new spatial structural characteristics to express, and transforming R_iiAnd (5) emptying, so that integration of the high specific stiffness and superior performance of the organism is realized through coupling element hybridization integration modeling according to the subsequent steps.

The process of step 2.1 and step 2.2 is described in detail below with reference to specific examples:

as shown in fig. 2(a), the honeycomb is composed of a series of hexagonal cylindrical cells made of beeswax and arranged closely, and the structure formed by such hexagonal arrangement is called a honeycomb structure. The honeycomb structure is a strict hexagonal cylinder, one end of which is a hexagonal opening, and the other end is the bottom of a closed hexagonal pyramid, and the honeycomb structure consists of three same diamonds.

Conjugate analysis is carried out on the honeycomb high-efficiency bearing structure to obtain the honeycomb hexagonal cylinder structure which has the maximum strength/mass ratio, good stability of the whole structure, difficult deformation and outstanding pressure resistance, so that the honeycomb high-efficiency bearing structure x can be obtained_eThe number of the high-efficiency load-bearing coupling elements is only one, namely the honeycomb hexagonal cylinder coupling element Co₁(x_e)。

According to equation (14), Co is defined based on the matrix of object elements₁(x_e) Comprises the following steps:

in the formula, the coupling element is characterized in that: the wall thickness of the cylinder can be used respectively_e1……o_e5To indicate.

According to the object matrix definition formula (22), the high efficiency load coupling element Co₁(x_e) Has carried configuration x for cellular high efficiency_eAre fully defined and thus used for coupling element Co₁(x_e) Relation element matrix R of internal relation self-criterion between internal parts₁₁(x_e) Defined as a matrix of empty relational elements, i.e. R₁₁(x_e)＝Φ。

And because there is only one coupling element Co₁(x_e) So that its coupling element mutual standard R_ij(x_e) Is a null relational element matrix, i.e. R_ij(x_e)＝Φ。

The formula (22) is substituted into the formula (12), and the hard part ha (x) of the honeycomb high-efficiency bearing structure can be obtained_e)＝Co₁(x_e) (ii) a R is to be_ij(x_e)、 R₁₁(x_e) The hard part so (x) of the honeycomb high-efficiency bearing structure can be obtained by substituting the hard part (13)_e)。

According to the formula (16), the boundary constraint object elements cB are respectively defined by the object element matrix_eAnd a load cell cL_e：

C B is_eAnd cL_eSubstitution of formula (16) can result in con (x) expressed based on the matrix of object elements_e) And is and

c B is_e、cL_e、ha(x_e)、so(x_e) The coupling element mathematical model oriented to the efficient and effective bearing performance of the coupling element mathematical model can be obtained by substituting the formula (17).

Mixing Co₁(x_e)、R₁₁(x_e) Substituted formula (18)) Obtaining the similar cellular ce_e＝Co_1e。

Similarly, the same analysis procedure is used for the human spinal high efficiency load bearing structure. As shown in fig. 2(b), the ribs are arc-shaped ossicles, one end of which is attached to both sides of the vertebra of the trunk, the road body wall is curved to the abduction plane, and the other end is in a fleshy state or attached to the sternum in the center of the chest. In the same way, by adopting the same analysis process as the honeycomb efficient bearing, the rib efficient bearing topological configuration x defined by the object element matrix can be finally obtained_rIs coupled element Co₁(x_r) And its boundary constraint object element cB_rAnd a load cell cL_r：

cL_r＝[cl_rLoad bearing mainly in height direction]

In the formula (24), the coupling element characteristic is as follows: the shape can be used_r1……o_r4To indicate.

Human vertebra high-efficient bearing structure R of the same reason₁₁(x_r)＝Φ，R_ij(x_r) Φ, obtainable from formula (18): ce (ce)_r＝Co_1r。

Coupling element Co, similar cell ce and coupling element self-alignment relation R according to the efficient bearing topological configuration of the honeycomb and the human body ribs₁₁Relation with mutual rule R_ijBy substituting equations (18) - (20), process models based on their efficient load-bearing topological configuration based on biological cells can be obtained respectively.

Step 3, carrying out efficient bearing coupling element hybridization integration modeling based on physical element expansibility, and realizing integration of high specific stiffness superiority performance of different organisms through hybridization integration of a biological efficient bearing unit;

and 3.1, constructing an advantage performance integration problem mathematical model according to the definition description of the efficient load bearing advantage performance integration problem.

This advantageous performance integration problem can be described as: the high specific stiffness coupling element topological structure cross-species hybridization of different organisms is intended to realize the integration of the high specific stiffness bearing performance and make up for the defects of the mechanical bearing performance of a single bionic topological structure.

According to the problem description, based on the definition of the matter element problem, establishing a matter element mathematical model of the high specific stiffness topological configuration advantage performance integration problem:

the efficient bearing space topological structure of a certain bionic source a is assumed to have the efficient bearing performance; the efficient bearing space topological configuration of the other bionic source b has efficient bearing performance different from a. Based on the expression of the element matrix, the above description is defined as:

in the formula: m_a，M_bRespectively describing the object elements of the bionic sources a and b; n is a radical of_a，N_bIs a bionic source name; c. C_a，c_bTo its space bearing topology; v. of_a，v_bHigh efficiency load bearing capability for different spatial topologies

Performance integration objective elements: with the object element M_xDefining a problem solving objective:

M_x＝(N_x,c_x,v_x) (27)

in the formula: m_xDescribing the object elements of the bionic source obtained by hybridizing the bionic source a and the bionic source b; n is a radical of_xThe name of the hybrid bionic source can be considered as known; c. C_xThe bionic source is a hybrid bionic source space topological configuration which is unknown and needs to be solved; v. of_xFor the integration of efficient load-bearing properties with a spatial topology of bionic origin a and b, it is known, i.e.

v_x＝v_a∩v_b (28)

Performance integration conditional physical element: the known conditional object element r is a high-efficiency bearing space topological configuration (M) of bionic sources a and b_aAnd M_bThe following can be obtained:

superiority performance integration problem mathematical model: taking the integration problem of the high specific stiffness bearing performance as Q, based on the condition object element definition of equation (29) and the object element definitions of equations (27) and (28), the mathematical model of the object elements of the integration problem can be obtained by integrating equation (26) as follows:

recording the compatibility function of the bearing performance integration problem Q of the high specific stiffness structure as K_r(M_x) Which means that the biomimetic source M is hybridized under a known condition r_xThe degree of implementation of (c).

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

the analysis shows that the bearing performance integration problem Q is an incompatibility problem, namely the compatibility function K_r(M_x) Is less than zero.

To solve this incompatibility problem, it is necessary to increase the hybridization bionic source topological structure M under the known condition r_xThe degree of implementation of (c).

The object topology describes the various possibilities of object change, so the incompatibility problem is solved based on the object topology, and the object M is constructed by the topology of the hybrid bionic source_xAnd performing object extension transformation on the known condition object r to solve the problem of the compatibility K of Q_r(M_x) Problem, as shown in equation (31):

in the formula，T_xFor the extension of the matter elements of the topological configuration of the hybrid bionic source, T_rThe method can be used for extension transformation of the matter elements under the known conditions.

Analysis can obtain:

[1]of the three formulae of formula (31), formula

Object element M in solving problem_xAnd bidirectional extension transformation of the condition matter element r; k_r(T_xM_x) For the purpose of thing M_xOne-way extension transformation to a condition object element r;

is a condition object R to a target object R_xThe one-way extension transformation of (1).

[2]The first two extension transformations include the target object M_xAnd (3) changing to the inverse direction of the condition object element r, and changing the third extension into a forward extension from the known condition to the solution target.

Based on the analysis in step 3.1, the target M_xComprises a hybridization bionic source space topological configuration c which is unknown to be solved_xThus, the third forward extension transform is selected

The solution is more convenient.

3.3, aiming at the high specific stiffness advantage performance of the bionic source organism, evaluating the weight influence of each coupling element and the coupling element characteristics based on a fuzzy analytic hierarchy process, extracting the coupling element and the coupling element characteristics which have the most decisive effect on the high specific stiffness advantage performance, namely the maximum weight influence, and defining the coupling element and the coupling element characteristics as gene coupling elements and gene coupling element characteristics;

fuzzy analytic hierarchy process is widely used, the technology is mature and is not described herein, when fuzzy analytic hierarchy process is used to evaluate the influence of each couple weight, triangular fuzzy numbers M1-M9 are taken as 1-9, and [1, 3, 5, 7, 9] respectively represent scales [ general, medium, strong ], while the rest intermediate numbers represent the intermediate scales. Selecting an initial comprehensive fuzzy evaluation matrix with the expert number of 3, and finally integrating the influence of each coupling element characteristic on the biological high-efficiency bearing performance obtained by evaluation of three experts, wherein the initial comprehensive fuzzy evaluation matrix is shown as a formula (32):

defuzzifying the formula (32) by a triangular defuzzification function to obtain the evaluation [1, 0, 0 ] of the relative importance of the coupling element characteristics]Can obtain o_e1Is a coupling element Co₁(x_e) The gene signature of (1).

Similarly, the above steps are carried out on Co₁(x_r) The influence weight of each coupling element characteristic on the high specific stiffness bearing performance is analyzed by fuzzy chromatography, and the characteristic of the gene coupling element is o_r1

And 3.4, carrying out biological coupling element hybridization integration based on the matter element extension transformation of the gene coupling element to obtain a hybridization bionic source coupling element integrated with the biological high-efficiency bearing advantageous performance, namely a hybridization bionic source space topological configuration:

step 3.4.1, determining a solving formula of the spatial topological configuration of the hybrid bionic source based on the object element expansibility;

according to step 3.2, the extension transformation can be performed according to the forward extension

To obtain a target object M_xI.e. by

M_x＝T_rr (33)

Based on the theory of matter elements, T_rCan be written as T_r＝(T_rN,T_rc,T_rv)，T_rN、T_rc、T_rvIs T_rThe component (c).

The comprehensive formulas (26), (27), (28), (29) and (33) can obtain:

known from step 3.1, hybridization of biomimetic source spatial topological configuration c_xIs unknown, v_x、N_xIt is known that the first and third equations in equation (34) are known. Therefore, the target object element formula (33) to be solved based on the forward extension transformation can be written as:

assuming efficient bearer space topology c_a、c_bThe genetic element of (2) is ce_aG、ce_bGAccording to the definition of genetic elements, ce_aG、ce_bGRespectively a pair of efficient bearing space topological structures c_a、c_bOf the decisive part, in order to ce_aG、ce_bGReplacement c_a、c_bEquation (35) can be further written as:

will ce_aG、ce_bGAs a matter-separating element, the material is,

can be written as multi-dimensional matter element expression combined by the same

Thus, equation (36) can be written as:

the above formula is the spatial topological configuration c of the hybridization bionic source_xThe solution of (1).

From the above formula, the spatial topological configuration c of the hybrid bionic source_xCan be coupled by means of known conditions

By forward extension transformation T_rcThus obtaining the product.

Based on the object element expansibility, the coupling element forward extension transformation T_rcBy basic transformation

Are compounded to obtain

Where k is { a, d, c or s },

adding/deleting conversion for coupler,

Is a replacement transformation of the coupling element,

For the decomposition/combination transformation of coupling elements,

For the coupler expansion/contraction transformation.

Because the honeycomb and rib high-efficiency bearing topological structures only contain one coupling element Co₁(x_e) And Co₁(x_r) The element is the corresponding gene element. Thus mixing Co₁(x_e) And Co₁(x_r) As a gene coupling element, substituting into formula (38)

Which represents the coupling element passing through a known condition

Forward extension transformation T_rcCan obtain the topological configuration c of the hybrid bionic source_x。

Step 3.4.2, constructing four basic extension transformations of the gene coupling element based on the object element extensibility to obtain the basic transformation of the coupling element with the advantage performance integration problem;

coupling element adding transformation

Represented by formula (39):

based on the expandability of the object element, the counter-coupling element Co_q(Co_q＝[co o_q d_q]) Performing extension increase transformation. After extension and transformation, the coupling element Co_qIncrease the characteristic o_q0And its corresponding characteristic quantity d_q0. The coupling elements before and after transformation in the formula (39) have an additive relation of object elements; and the inverse transformation in the formula (39) is

The inverse transform of (2) is an exploitable subtractive transform of the coupler.

Element permutation transformation

Represented by formula (40):

wherein, [ co ] o_h d_h]＝Co_hAnd represents a transform post-coupling element. Based on divergence of object element, counter-coupling element Co_qPerforming divergence extension transformation to couple element Co_qSubstitution by Co_h. Before and after the permutation, the coupling element is characterized by_qIs changed into o_hThe corresponding characteristic quantity is also represented by d_qIs changed into d_h。Co_qAnd Co_hThere is divergence and extension relationship between them, and the coupling element Co_hReverse extension substitution as coupler element Co_qIs changed by

And (4) inverse transforming. It should be noted that the permutation transformation cannot be arbitrarily transformed, and the principle of object element expansibility of the coupled elements is followed.

Coupled component decomposition transform

Expressed by formula (41):

in the formula (I), the compound is shown in the specification,

based on object separability, counter coupling element Co_qAnd performing extension decomposition transformation. By extensive decomposition transformation, the characteristic o of the element_qDecomposed to obtain o'_qAnd o ″)_qAnd the corresponding coupling element characteristic quantity is d'_qAnd d ″)_q. The separability relationship of the object elements exists between the coupling elements before and after transformation in the formula (41); and the inverse transformation in the formula (41) is

The inverse transform of (2) is an extendible combinatorial transform of the coupler.

Coupling element expansion transformation

Expressed by formula (42):

in the formula, the coupling element characteristic o_qsIs characterized by o_qAnd the characteristic o_sThe product of (2), the corresponding element characteristic quantity d_qsIs d_qAnd d_sThe product of (a). Based on the integrability of the object element, the coupling element Co_qAnd performing extension and expansion transformation. After extensive transformation, the characteristic o of the coupling element_qEnlarged to o_qsThe corresponding coupling element characteristic quantity is represented by d_qIs changed into d_qs. The integrable relation of object elements exists between the coupling elements before and after expansion transformation. In particular, when o_sE, then o_qs＝o_qe＝o_qThe time-type (42) coupler expansion transformation

Only extension-wise transformations of the characteristic magnitudes. Similarly, the inverse transformation in equation (42) is

The inverse transform of (2) is an extension-wise reduction transform of the coupling element.

The basic transformation of the gene coupling element in the example is performed according to the four coupling element basic transformation definitions, and the obtained basic transformation of the gene coupling element 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 elements and their feasibility

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

the basic transformations in table 1 were analyzed for feasibility, where in table 1 the symbols v are feasible and x is not feasible. In table 1, the extension transformation attempts to add new coupler features, since no new features are referenced, it is not feasible. The extensive decomposition transformation fails to attempt to decompose the coupler characteristics, and therefore it is not feasible.

Analyzing the basic transformation of the coupling element in the table 1, determining the necessary basic transformation:

can be analyzed to know

The transformation realizes the removal of other non-genetic coupling element characteristics;

transformation pair feature o_e1Extension and contraction can be carried out in the height direction to realize matching of the height direction of the coupling element during combination transformation;

the array formed by transformation can form a coupling element Co together with the hierarchical structure₁(x_e) Protective walls with Co₁(x_r) Co is compensated by the advantage of level bearing performance₁(x_e) Non-coplanar mechanical property defects;

transformed to achieve spatial combination of the dipole characteristics. Thereby determining the basic transformations necessary for the above basic transformations.

Step 3.4.4, the necessary coupling element basic transformation is compounded to carry out combined transformation, and the basic de-transformation of the advantage performance integration problem is obtained;

the essential coupling elements are substantially transformed (38) to form the basic solution T of the advantageous performance integration problem₀：

The basic transformation process is shown in FIG. 4, and the hybrid coupler obtained by the basic de-transformation is shown by the number (r) in FIG. 4.

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

considering the transformations in Table 1

And

the effect generated when two coupling elements are simultaneously expanded or reduced is offset, so that the selection is made

Only the coupling element Co₁(x_r) Performing scaling transformation, and is clear from Table 1

In order to expand the transformation, the transformation is expanded,

to reduce the transform.

Therefore, the method can be further transformed with other basic transformations on the basis of the basic solution transformation

Other solution transforms are constructed in combination:

the transformation process of these de-transformations is shown in fig. 4.

The cross coupling element obtained by all the deconversion is shown in code (r-R). It should be noted that

The conversion can be performed by reducing the hierarchy, reducing the array, and reducing the array hierarchy simultaneously, so that

And

three kinds of cross coupling elements are obtained through transformation, and the cross coupling elements are the fourth cross coupling element and the sixth cross coupling element.

In addition, it should be noted that the reason is that

The transformation makes the hierarchical structure have a plurality of honeycomb structures, which are similar to the original coupling elements to be improved and the original honeycomb structure coupling elements and can not form a protective wall for improving the non-coplanar mechanical property of the original honeycomb structure coupling elements, so that the transformation is omitted

And

namely, cross coupling and uncoupling and ninthly.

And 3.4.6, selecting evaluation elements to evaluate the hybrid coupling element de-transformation set, wherein the determined optimal de-transformation is the hybrid bionic source coupling element oriented to the dominant property integration, namely the hybrid bionic source space topological configuration.

Constructing a three-dimensional finite element model of the original coupling element to be improved, namely the honeycomb structure coupling element and all hybrid coupling elements: during modeling, the side length of the hexagonal structure in all the 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 are applied: the bottom surface is fixedly restrained, and the top surface applies pressure loads F with equal magnitude_y200N (see fig. 5(a) for boundary constraint); the grid size of all finite element models is 5mm, the grid shape adopts hexahedral grids, and the quality of the control grids is more than 0.97; all the hybridization element models are made of the same material: carbon steel, material density 7800kg/m³Elastic modulus 210GPa and Poisson's ratio 0.26.

Calculating to obtain the mass m of the coupling element to be improved, namely the coupling element of the original honeycomb structure₀1.702kg, first order frequency f₀Maximum loaded deformation at 210.13Hz

Selecting the mass m, the first-order frequency f and the maximum deformation U of the hybrid coupling element_FyFor evaluating the elements, the advantages and disadvantages of the cross coupling element deconversion sets are compared and shown in table 2.

TABLE 2 comparison of superiority and inferiority of each of the deconverted hybrid pairs

In Table 2,. DELTA.f/. DELTA.m ═ f-f₀)/(m-m₀)、

Each of which isRepresenting the ratio of distortion to frequency increase to mass increase. As can be seen from Table 2, Δ f/Δ m are positive values, Δ U_FyThe values of/. DELTA.m are negative, which means 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 solution transformation, the absolute value of the ratio of the maximum deformation reduction amount/frequency increase amount to the mass increase of the cross coupling element solution is the largest, which indicates that the cross coupling integration efficiency of the cross coupling element is the highest, and then the cross coupling element solution is obtained. Therefore, the solution (i) is selected as the optimal hybrid element solution.

The cross coupling element solution is the cross bionic source high specific rigidity topological configuration c to be solved by the integration problem_x。

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

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

And selecting a mechanical element structure and biological cells as inversion media, and using the optimal hybrid coupling element as the mechanical element structure. Further performing element structure parameter optimization based on the approximate element model, as shown in fig. 5, selecting the side length, the thicknesses of two side walls, the thicknesses of upper and lower walls and the thickness of the inner hexagon of the mechanical element structure as design variables, and defining the variables as v₁、v₂、v₃、v₄V is known from its structure₃＝v₄. Selecting bearing deformation U according to main loading working condition_Mx、U_Mz、U_FyAnd the first order frequency f is used as the load-bearing performance index

Show, order

Order to

Is a mass m of the element structure, i.e.

Considering the design fill area size in the example, the variable v is set₁Has a value range of [90mm, 140mm]. Variable v₂、v₃Has a value range of [7mm, 12mm]. With the help of an experiment design module of Workbench software, adopting a Latin hypercube experiment design method and adopting a center composite design method for sampling to obtain 25 groups of sample design points, and calculating the variable value v of the sample design point_iCorresponding performance index

Some of the sample data points are shown in table 3.

Table 3 sample points of some experimental designs and their corresponding performance indexes

Based on the 25 groups of design samples, by means of an approximate model module of Workbench software, a Kriging meta model is selected as an approximate model, and the bearing performance index can be obtained

And element structure design variable v_iApproximate meta-model relationship function between. Based on these relational function models, at a first order frequency

Maximum simultaneous load deflection

Minimum is an optimization target, and the optimization constraint condition is quality

Less than the initial mass i.e

Using multi-target genetic algorithms

Solving to obtain the optimal value of the design variable as follows: v. of₁＝91.20mm，v₂＝9.50mm，v₃＝9.73mm。

And 4.2, according to the optimized element structure, designing a mechanical stiffness-specific stiffness structure by a mechanical structure design method based on the element structure.

The mechanical element structure design method is widely applied in the field of mechanical design, and is not described herein any more. And (3) carrying out element structure filling on the example design area shown in the figure 1 based on the element structure after the structural parameter optimization, and obtaining an example machine tool column three-dimensional model shown in the figure 6 (a). For comparison, a three-dimensional model based on the mechanical element structure filling of the original element to be improved, i.e., the honeycomb-structured element, is established as shown in fig. 6 (b).

The overall maximum deformation, mass, first order natural frequency of the example columns under different design scenarios are calculated and shown in table 4.

TABLE 4 comparison of different design schemes for column structures

As can be seen from table 4, in the scheme 1, the pillar structure is biomimetically designed based on the original to-be-improved coupling element, i.e. the honeycomb coupling element structure, the mass of the pillar structure is reduced by 9.2% compared with the original pillar structure design, the first-order natural frequency is increased by 12.3%, but the overall maximum deformation of the pillar structure is increased by 6.6%, which is very disadvantageous for the structural load. The natural frequency of the structure is simultaneously influenced by the mass of the structure and the rigidity of the structure, and under the condition that other conditions are not changed, the natural frequency of the structure can be increased when the mass of the structure is reduced. Therefore, reasonable conjecture shows that: the improvement of the first-order frequency of the design scheme 1 is greatly derived from the reduction of the self structural mass, but not the improvement of the self rigidity; so design 1 shows the phenomenon that the first order frequency of the system is increased and the maximum distortion of the whole system is obviously increased.

Scheme 2 is a column design based on a hybrid coupler element structure. As can be seen from table 4, the mass of case 2 is reduced by almost 3.2% compared to the initial design, but the loaded deformation is significantly reduced by 17.2% and the first order natural frequency is increased by 24.8%. It can be concluded that the significant reduction of the structure load deflection and the significant increase of the natural frequency are both caused by the increase of the stiffness of the structure design itself, not the change of the structure mass. This is clearly different from scheme 1. In addition, compared with the scheme 1, the working condition loaded total deformation of the scheme 2 is reduced by 22.4%, but the first-order natural frequency is increased by 11.2%.

In conclusion, the column design based on the hybrid coupler element structure in the scheme 2 is optimal. The correctness of the proposed inventive method is verified.

Claims

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

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

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

4. The bionic design optimization method for the structure with high specific stiffness according to claim 3, wherein in the step (2.1), the topological element-coupling mathematical model of the biological structure for the efficient biological load-bearing performance is as follows:

in the formula (I), the compound is shown in the specification,

x' is the biological space topology, Co_iThe number of the ith coupling element contained in the biological space topological configuration is n, and the n is the total number of the contained biological high-efficiency bearing coupling elements; r_ijIs a biological high specific stiffness topological coupling element Co_iAnd Co_jWhen i ═ j, R_ijFor the biological high-efficiency bearing of the relationship of each part in the coupling element, R is equal to j when i ≠ j_ijThe mutual relation between topological coupling elements with high specific stiffness; cL is a borne load set, and cB is a boundary constraint set; co is a mixture of_iCoupling element Co for ith topological configuration_iThe name of (a); r is_ijIs a biological high specific stiffness topological element coupling relation R_ijThe name of (a); o_ik、d_ikFor topological configuration of coupling element Co_iThe kth feature of (1) and its feature description; q. q.s_ijk、t_ijkIs R_ijThe kth feature of (1) and features thereof; m and p are Co_iAnd R_ijThe number of features involved.

5. The bionic design optimization method for the structure with high specific stiffness according to claim 3, wherein in the step (2.2), the structural model of the quasi-cellular is as follows:

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

7. The bionic design optimization method for the structure with high specific stiffness according to claim 6, wherein the step (3.4) comprises the following steps:

8. The bionic design optimization method of the high-specific-stiffness structure according to claim 6 or 7, wherein the mathematical model of the bionic source biological high-specific-stiffness advantage performance integration problem is as follows:

M_a，M_brespectively describing the object elements of the bionic sources a and b; n is a radical of_a，N_bIs its bionic source name; c. C_a，c_bThe bionic source is a space topological configuration of a bionic source a and a bionic source b; v. of_a，v_bThe bionic source has different high-efficiency bearing performances of the spatial topological configurations of the bionic sources a and b; m_xDescription of the bionic origin formed for the hybridization, M_x＝(N_x,c_x,v_x)，N_xFor the name of hybrid bionic source, c_xFor a hybrid bionic source spatial topology, v_xFor efficient load-bearing performance integration with space topology configurations of both bionic sources a and b, i.e. v_x＝v_a∩v_b(ii) a r is a conditional element and is the known biological space topological configuration of the bionic sources a and b, namely

9. The aspect ratio of claim 8The bionic design optimization method of the rigid structure is characterized in that the hybridization bionic source space topological configuration c_xThe solution of (A) is:

in the formula (I), the compound is shown in the specification,

Compounding to obtain the compound, namely:

where k is { a, d, c or s },

adding/deleting conversion for coupler,

Is a replacement transformation of the coupling element,

For the decomposition/combination transformation of coupling elements,

For the coupler expansion/contraction transformation.

10. The bionic design optimization method for the structure with high specific stiffness as claimed in claim 3, wherein the step (4) specifically comprises the following steps: