CN108763778A - A kind of solid material and quasi-truss fine structure material integration Multidisciplinary systems Topology Optimization Method - Google Patents
A kind of solid material and quasi-truss fine structure material integration Multidisciplinary systems Topology Optimization Method Download PDFInfo
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Abstract
The invention discloses a kind of solid materials and quasi-truss fine structure material integration Multidisciplinary systems Topology Optimization Method.Realize the foundation of the bi-material layers interpolation model of solid material and quasi-truss fine structure material indirectly by the elastic constant of material；Elastic constant with material in the equivalent microcosmic point quasi-truss micro-structure of macroscopic aspect rigidity property is obtained by strain energy equivalent method；The uncertainty that Optimized model parameter is described with interval model, it is Multidisciplinary systems index to establish reliability displacement；Sensitivity of the reliability displacement to design variable is solved using adjoint vector method；Design variable is updated with MMA algorithms, iteration optimization is until obtain optimization design scheme.The present invention effectively realizes entity and quasi-truss fine structure material integrated design during carrying out OPTIMIZATION OF CONTINUUM STRUCTURES, influence of the uncertain parameters described with interval model to structural behaviour rationally is characterized, lightweight, security performance and the economy of structure are all effectively promoted.
Description
Technical field
The present invention relates to the topology optimization design field of Continuum Structure, more particularly to a kind of solid material and quasi-truss are micro-
The Continuum Structure Multidisciplinary systems Topology Optimization Method of structural material integrated design.
Background technology
Existing industrial products are almost all based on solid material design and manufacture, are based on more materials, are based particularly on reality
Body material and the industrial products of quasi-truss fine structure material integrated design are quite few.Although the industrial products based on solid material
Design and process it is relatively easy, but certain positions material property utilize and it is insufficient, occupy construction weight but do not send out
Wave enough effects.Such case shows particularly evident in aerospace field.Aerospace field is to the important requirement of structure
It is more harsh, because construction weight directly affects voyage, payload and economic performance of aircraft etc..In this environment
Under, it is necessary to the position at unessential position in structure, such as non-primary load bearing is replaced with other more efficient materials, quasi-truss is micro-
Structural material is exactly a kind of extraordinary material.It is all greatly reduced compared to solid material density and rigidity, particularly suitable Mr. Yu
A little inessential but essential positions, can give full play to the rigidity property of solid material and fine structure material, to real
Now preferable structure lightened design.With the rapid development of 3D printing technique in recent years, this bi-material layers design scheme just has
Preferable industry manufacture basis.
This bi-material layers design philosophy is incorporated in topology optimization design, can be achieved with providing satisfaction in conceptual phase
The configuration and material layout of the component of job requirement are designed with great reference significance, Neng Gouyou for industrial product structure
Effect reduces the difficulty of structure design and improves working efficiency.Since the material of structure is in production process its Young's modulus, shearing
The material properties such as modulus there is unavoidable dispersibility, and load for being subject in actual engineering-environment of structure etc. is outer
It always changes in factor, influencing these factors of the safety of structure should not ignore.From traditional design philosophy
Consider, structure can be avoided safety problem occur by increasing safety coefficient.However, the safety coefficient of structure design is increased, it will
Construction weight can be caused to greatly increase, economic benefit will substantially reduce, and not be one preferable for Flight Vehicle Design
Solution.Therefore, with Topology Optimization Method and theoretical research constantly make progress and the pole of computer computation ability
Big enhancing, uncertain Topology Optimization have obtained larger development.
It has been obtained for being applied successfully in topology optimization design based on the reliability Optimum Design of probabilistic model.But it is general
The complete probability distribution information for the uncertain parameter that rate reliability model needs is generally difficult to obtain in practice in engineering.Probability can
Very sensitive to probabilistic model parameter by property, the small error of probability data this may result in structural reliability and calculate the larger mistake of appearance
Difference.In many cases, though being unable to get the exact probability distributed data of uncertain parameter, the amplitude of parameter uncertainty or
Boundary is then easy to determining.Interval model is suitable for handling the parameter of this kind of unknown-but-bounded.Interval model description based on parameter,
It is proposed the concept of Continuum Structure Multidisciplinary systems topological optimization.
Uncertain parameter is described with interval model, and is applied to the actual topological optimization technology of engineering and is not yet received
Fully development and effectively application.Our work not only enriches bi-material layers topology optimization design research to a certain extent, but also
For considering that application of probabilistic Multidisciplinary systems topological optimization in engineering is of great significance.
Invention content
The technical problem to be solved by the present invention is to：Overcome the deficiencies of the prior art and provide a kind of solid material and quasi-truss
Fine structure material integration Multidisciplinary systems Topology Optimization Method.The present invention fully considers single material structure material in Practical Project
Expect that performance uses insufficient and generally existing uncertain factor, proposes solid material and quasi-truss fine structure material one
Change design scheme, with the constraints of the Multidisciplinary systems Measure Indexes of proposition model as an optimization, obtained optimization is set
It is more economical efficiently to count resultative construction more lightweight.
The technical solution adopted by the present invention：A kind of solid material and quasi-truss fine structure material integration Multidisciplinary systems
Topology Optimization Method, this method comprises the following steps：
The first step：Solid material and quasi-truss fine structure material are established based on traditional material interpolation model with penalty function
The bi-material layers interpolation model of integrated design：
Wherein ΨiFor the element stiffness matrix of i-th of unit, Ψ1,iFor the list with relevant i-th of the unit of solid material
First stiffness matrix, Ψ2,iFor the element stiffness matrix with relevant i-th of the unit of quasi-truss fine structure material；x1,iAnd x2,iRespectively
For design variable of i-th of unit in terms of solid material level and quasi-truss fine structure material；p(p>1) it is penalty factor.
Second step：Utilize anisotropic material (being equally applicable to isotropic material) elasticity modulus, modulus of shearing and pool
Pine is than totally 9 elastic constant E in all directionsi,x,Ei,y,Ei,z,νi,xy,νi,yz,νi,zx,Gi,xy,Gi,yz,Gi,zxIt realizes indirectly
The foundation of bi-material layers interpolation model：
Wherein Ωi=[Ei,x,Ei,y,Ei,z,νi,xy,νi,yz,νi,zx,Gi,xy,Gi,yz,Gi,zx]T, Ai=[Ei,x1,Ei,y1,
Ei,z1,νi,xy1,νi,yz1,νi,zx1,Gi,xy1,Gi,yz1,Gi,zx1]TAnd Bi=[Ei,x2,Ei,y2,Ei,z2,νi,xy2,νi,yz2,νi,zx2,
Gi,xy2,Gi,yz2,Gi,zx2]TThe fusion elastic constant vector of respectively i-th unit, the elastic constant vector sum class of solid material
The elastic constant vector of truss fine structure material.
Third walks：It is obtained and the material microstructure layer noodles purlin equivalent in macroscopic aspect rigidity property by strain energy equivalent method
The elastic constant of frame micro-structure.Different typical load modes and periodic boundary condition are applied to quasi-truss micro-structure unit cell, by
Finite element method obtains the Effective Elastic Properties of quasi-truss fine structure material：
Wherein E1,E2And E3For the elasticity modulus in three directions, G12,G23And G31For the modulus of shearing in three directions(p, q=1,2,3) is Poisson's ratio.
4th step：With the quality minimum of structure target as an optimization, the displacement of node is loaded as constraining using concentrfated load
It is as follows to establish topological optimization model for item：
Object function
Constraint function bv,r-bv,c≤ 0, v=1,2 ..., m
Ψ(Ψ1,i,Ψ2,i) b=F, i=1,2 ..., N
Wherein, M indicates the quality of structure, ρ1And ρ2The respectively density of solid material and quasi-truss fine structure material, ViFor
The volume of i-th of unit, N are the unit sum for optimizing region division, Ψ ∈ CN×NFor the global stiffness matrix of unit, b ∈ CN×1
For the overall displacements column vector of unit, F ∈ CN×1For General load column vector, bv,rIt is the actual displacement of i-th of displacement constraint point
Value, bv,cIt is the Admissible displacement value of i-th of displacement constraint, m is the number of displacement constraint, x1And x2For design variable lower threshold,WithFor threshold value of reaching the standard grade.
5th step：By the uncertainty of interval model characterising parameter, it is Multidisciplinary systems index to establish reliability displacement.
Former Optimized model can be amended as follows using reliability displacement：
s.t.Lv≤ 0, v=1,2 ..., m
Wherein LvFor reliability displacement, work as Lv>There is b when 0v,r-bv,c>0, indicate that reliability is unsatisfactory for requiring；Work as Lv<Have when 0
bv,r-bv,c≤ 0, indicate that reliability is met the requirements.
6th step：According to the expression formula for the reliability displacement that the 5th step obtains, by compound function derivation law to design
Variable carries out derivation, and obtains sensitivity of the reliability displacement to design variable with adjoint vector method.
7th step：It is set using the reliability displacement difference pair obtained in the reliability displacement and the 6th step obtained in the 5th step
The sensitivity of meter variable, which substitutes into MMA algorithms, solves Multidisciplinary systems Optimized model, obtains new design variable.
8th step：Determine whether to meet convergence conditions, if being unsatisfactory for convergence conditions, by the iteration completed time
Number increases by 1, and returns to the 4th step；Otherwise, iterative process terminates.
The advantages of the present invention over the prior art are that：
The present invention provides a kind of solid materials and quasi-truss fine structure material integration Multidisciplinary systems topological optimization
Solid material and quasi-truss fine structure material are combined while applying to Structural Topology Optimization Design so that structure by method
The material at each position can give full play to its performance.It can in the case where structural behaviour does not reduce compared to single material structure
Realize that weight is lower, more efficient, economic performance is better.In addition, describing load condition, material properties and position with interval model
Move the uncertainty degree of the parameters such as cognition so that load-up condition etc. and the actual condition of structure are more nearly, structural material attribute
Influence of the dispersibility to structure safety is generated during material processing and manufacturing can also be fully considered, foundation with reliability
Displacement can not only improve the security performance of structure as Multidisciplinary systems measure of criterions standard, moreover it is possible to effectively reduce it is economical at
This.
Description of the drawings
Fig. 1 is solid material and quasi-truss fine structure material integration Multidisciplinary systems topological optimization flow chart；
Fig. 2 is macro micro-property equivalent schematic of the quasi-truss micro-structure under different unit cell types；
Fig. 3 is representative volume element periodic boundary condition schematic diagram；
Fig. 4 is that limiting condition plane and normed space interfere schematic diagram, wherein Fig. 4 (a) isFig. 4 (b) isFig. 4 (c) isFig. 4
(d) it isFig. 4 (e) isFig. 4 (f) is
Fig. 5 is that reliability displacement defines and calculates schematic diagram, wherein Fig. 5 (a) is the definition of reliability displacement symbol, Fig. 5
(b) it is the derivation of reliability displacement.
Specific implementation mode
Below in conjunction with the accompanying drawings and specific implementation mode further illustrates the present invention.
As shown in Figure 1, the present invention proposes a kind of solid material and the non-probability decision of quasi-truss fine structure material integration
Property Topology Optimization Method, includes the following steps：
(1) based on traditional, the material interpolation model with penalty function establishes solid material and quasi-truss fine structure material one
Change the bi-material layers interpolation model of design：
Wherein ΨiFor the element stiffness matrix of i-th of unit, Ψ1,iFor the list with relevant i-th of the unit of solid material
First stiffness matrix, Ψ2,iFor the element stiffness matrix with relevant i-th of the unit of quasi-truss fine structure material；x1,iAnd x2,iRespectively
For design variable of i-th of unit in terms of solid material level and quasi-truss fine structure material；p(p>1) it is penalty factor.
(2) anisotropic material (being equally applicable to isotropic material) elasticity modulus, modulus of shearing and Poisson's ratio are utilized
Totally 9 elastic constant E in all directionsi,x,Ei,y,Ei,z,νi,xy,νi,yz,νi,zx,Gi,xy,Gi,yz,Gi,zxDouble materials are realized indirectly
Expect the foundation of interpolation model：
Wherein Ωi=[Ei,x,Ei,y,Ei,z,νi,xy,νi,yz,νi,zx,Gi,xy,Gi,yz,Gi,zx]T, Ai=[Ei,x1,Ei,y1,
Ei,z1,νi,xy1,νi,yz1,νi,zx1,Gi,xy1,Gi,yz1,Gi,zx1]TAnd Bi=[Ei,x2,Ei,y2,Ei,z2,νi,xy2,νi,yz2,νi,zx2,
Gi,xy2,Gi,yz2,Gi,zx2]TThe fusion elastic constant vector of respectively i-th unit, the elastic constant vector sum class of solid material
The elastic constant vector of truss fine structure material.
(3) it is obtained by strain energy equivalent method micro- in the equivalent microcosmic point quasi-truss of macroscopic aspect rigidity property with material
The elastic constant of structure.Different typical load modes and periodic boundary condition are applied to quasi-truss micro-structure unit cell, by limited
First method solves to obtain the Effective Elastic Properties of quasi-truss fine structure material：
When only there are two (as shown in Figure 3) when node, the harmony of boundary node deformation on each boundary of representative volume element
Met, the representative volume element that a unit cell is constituted only is needed to can be obtained by the Equivalent Elasticity for meeting required precision at this time
Energy.Macroscopical line strain is considered successivelyAnd shear strainThen periodic boundary equation is as follows：
WhereinIt is preset macro-strain vector；X, Y and Z indicate representative volume element three
The displacement in a direction；Arbitrary point on subscript A1, A2, B1, B2, C1, C2 representative volume element surface；S indicates the length of side of representative volume element.
In the volume V of representative volume elementRVEOn homogenized after mean stressAnd mean strainIt is represented by：
The equivalent strain energy of material is：
Strain energy in representative volume element is：
Volume integral can be turned to by Gauss integration by surface integral：
Wherein SRVEFor the outer surface of representative volume element, n is the outer normal vector of unit, is had on the outer surface：
Bringing formula (8) into formula (7) can obtain：
By introducing generalized Hooke law, may further obtain：
Wherein E1,E2And E3For the elasticity modulus in three directions, G12,G23And G31For the modulus of shearing in three directions,For Poisson's ratio.By applying suitable loading method and periodic boundary condition, generation to representative volume element
The equivalent elastic modulus E of table volume elements (or quasi-truss fine structure material)1,E2,E3,ν12,ν23,ν31,G12,G23, G31It can be by having
Finite element analysis obtains.
(4) with the quality minimum of structure, target, the displacement for loading node using concentrfated load are built as constraint item as an optimization
Vertical topological optimization model is as follows：
Object function
Constraint function bv,r-bv,c≤ 0, v=1,2 ..., m
Ψ(Ψ1,i,Ψ2,i) b=F, i=1,2 ..., N
Wherein, M indicates the quality of structure, ρ1And ρ2The respectively density of solid material and quasi-truss fine structure material, ViFor
The volume of i-th of unit, N are the unit sum for optimizing region division, Ψ ∈ CN×NFor the global stiffness matrix of unit, b ∈ CN×1
For the overall displacements column vector of unit, F ∈ CN×1For General load column vector, bv,rIt is the actual displacement of i-th of displacement constraint point
Value, bv,cIt is the Admissible displacement value of i-th of displacement constraint, m is the number of displacement constraint, x1And x2For design variable lower threshold,WithFor threshold value of reaching the standard grade.
(5) by the uncertainty of interval model characterising parameter, it is Multidisciplinary systems index to establish reliability displacement：
The uncertainty of consideration material properties, external applied load and safe displacement, due to the equation of static equilibriumIt is
Linear equation can acquire constrained displacement by interval parameter fix point methodBound.It willWrite as the shape of intervl mathematics
Formula：
Whereinb v,rWithRespectivelyLower bound and the upper bound.Formula (11) is linear equation, then by interval parameter fix point method
It can obtain：
WhereinT=m+k indicates global stiffness matrix
The sum of number k (k=1) and external applied load number m；G indicates different global stiffness matrix and external applied load fixed point combination；wv=1 or
2, wv=1 indicates to take the lower bound of parameter, wv=2 indicate to take the upper bound of parameter, i.e.,(Ψ-1)2=Ψ -1,
By displacement constraint node actual displacement bv,rWith safe displacement bv,cIt can define limit state equation：
And limiting condition plane：
By interval mathematical theory, following normed space can be obtained：
Wherein △ bv,rWith △ bv,cRespectively belong to standard sectionWithVariable；WithRespectivelyNominal value and section radius,With
RespectivelyNominal value and section radius.When meeting interference conditionWithWhen, limit state function P will be in normed space
It is divided into two parts, i.e. P (bv,c,bv,rThe part of) >=0 is security domain, P (bv,c,bv,r)<0 part is failure domain (such as Fig. 4 institutes
Show).Formula (15), which is substituted into formula (14), to be obtained：
And：
Without loss of generality, △ b are enabledv,c=1, △ bv,r=-1 can obtain：
By formula (20) and the area of security domain and normed space than the Multidisciplinary systems index of definition, can obtain：
As actual displacement section is different with the interference state in safe displacement section, security domain and failure domain in normed space
State it is also different.Correspondingly, the expression formula of reliability index includes 6 kinds of situations altogether, is a piecewise function：
Since the optimization algorithm based on gradient requires reliability index to have good continuity and differentiability to call
MMA algorithms have complete gradient information when solving grand designs variable, but work as Rv=1 and RvWhen=0, partial derivativeWithTotal is 0.At this point, MMA algorithms cannot be completed to optimize.In order to solve this problem, it is proposed that reliability displacement is as new
Multidisciplinary systems index Lv.Reliability displacement LvIt is defined as each Optimized Iterative face defined in formula (20) in the process
Between more corresponding than the obtained practical reliability limiting condition plane of product and the corresponding limiting condition plane of target reliability away from
From the two planes parallel i.e. expression formula in normed space differs a constant (as shown in Figure 5).Work as LvWhen≤0, Rv≥Rc
I.e. reliability is met the requirements.By the distance between two planes calculation formula, the expression formula of reliability distance can be obtained：
Thus Optimized model may be modified such that：
(6) expression formula of the reliability displacement obtained according to the 5th step, by compound function derivation law to design variable
Derivation is carried out, and sensitivity of the reliability displacement to design variable is obtained with adjoint vector method.
Reliability index LvTo design variable xe,i(i=1,2 ..., N, e=1,2) ask local derviation that can obtain：
It can be obtained by formula (22)：
And：
In order to avoid directly calculatingWith(xe,i, i=1,2 ..., N) huge calculation amount, proposition it is adjoint
Vector method can well solve this problem.Establish following Lagrange's equation：
Wherein ζv(v=1,2 ..., m) is the adjoint vector about static balancing equation.Due toObviouslySo formula (26) asks local derviation that can obtain design variable：
In order to avoid calculatingDifficulty, enableIt can obtain：
It can be seen that formula (28) in form with static balancing equationSo in order to acquire adjoint vector ζv
(v=1,2 ..., m) only can apply specific loading, that is, load vectors f at corresponding loading nodev=[0,0 ...,
1,…,0]TIt is obtained by FEM calculation.
By ζvSubstitution formula (27) can obtain sensitivity of the bound to design variable of actual displacement：
External applied load vector F is constant in Optimized Iterative process, soThen formula (29) can be further derived as：
Formula (1) is substituted intoIt can obtain：
Formula (31), which is substituted into formula (29), again to obtain：
So far, by formula (23)-(25) and formula (32), reliability index LvTo design variable xe,iSensitivity can be complete
Whole Efficient Solution.
(7) design is become using the reliability displacement difference obtained in the reliability displacement and the 6th step obtained in the 5th step
The sensitivity of amount is substituted into MMA algorithms and is solved to Multidisciplinary systems Optimized model, obtains new design variable.
(8) determine whether to meet convergence conditions, if being unsatisfactory for convergence conditions, the iterations completed are increased
Add 1, and returns to the 4th step；Otherwise, iterative process terminates.
In conclusion the present invention proposes a kind of solid material and quasi-truss fine structure material integration Multidisciplinary systems
Topology Optimization Method.Realize the bi-material layers interpolation of solid material and quasi-truss fine structure material indirectly by the elastic constant of material
The foundation of model；It is obtained by strain energy equivalent method micro- in the equivalent microcosmic point quasi-truss of macroscopic aspect rigidity property with material
The elastic constant of structure；The uncertainty that Optimized model parameter is described with interval model, it is that non-probability can to establish reliability displacement
By property index；Sensitivity of the reliability displacement to design variable is solved using adjoint vector method；Design is updated with MMA algorithms to become
Amount, iteration optimization is until obtain optimization design scheme.
The specific steps that the above is only the present invention, are not limited in any way protection scope of the present invention；Its is expansible to answer
It is all to be formed using equivalent transformation or equivalent replacement for the Topology Optimization Design of Continuum Structures field under displacement constraint
Technical solution is all fallen within rights protection scope of the present invention.
Part of that present invention that are not described in detail belong to the well-known technology of those skilled in the art.
Claims (6)
1. a kind of solid material and quasi-truss fine structure material integration Multidisciplinary systems Topology Optimization Method, feature exist
In steps are as follows for realization：
The first step：Solid material and quasi-truss fine structure material one are established based on traditional material interpolation model with penalty function
Change the bi-material layers interpolation model of design：
Wherein ΨiFor the element stiffness matrix of i-th of unit, Ψ1,iFor the element stiffness with relevant i-th of the unit of solid material
Matrix, Ψ2,iFor the element stiffness matrix with relevant i-th of the unit of quasi-truss fine structure material；x1,iAnd x2,iRespectively i-th
Design variable of a unit in terms of solid material level and quasi-truss fine structure material；p(p>1) it is penalty factor；
Second step：Using the elasticity modulus of anisotropic material or isotropic material, modulus of shearing and Poisson's ratio each
Totally 9 elastic constant E in directioni,x,Ei,y,Ei,z,νi,xy,νi,yz,νi,zx,Gi,xy,Gi,yz,Gi,zxBi-material layers interpolation is realized indirectly
The foundation of model：
Wherein Ωi=[Ei,x,Ei,y,Ei,z,νi,xy,νi,yz,νi,zx,Gi,xy,Gi,yz,Gi,zx]T, Ai=[Ei,x1,Ei,y1,Ei,z1,
νi,xy1,νi,yz1,νi,zx1,Gi,xy1,Gi,yz1,Gi,zx1]TAnd Bi=[Ei,x2,Ei,y2,Ei,z2,νi,xy2,νi,yz2,νi,zx2,Gi,xy2,
Gi,yz2,Gi,zx2]TThe fusion elastic constant vector of respectively i-th unit, the elastic constant vector sum quasi-truss of solid material are micro-
The elastic constant vector of structural material；
Third walks：It is obtained by strain energy equivalent method micro- in the equivalent microcosmic point quasi-truss of macroscopic aspect rigidity property with material
The elastic constant of structure applies different typical load modes and periodic boundary condition, by limited to quasi-truss micro-structure unit cell
First method solves to obtain the Effective Elastic Properties of quasi-truss fine structure material：
Wherein E1,E2And E3For the elasticity modulus in three directions, G12,G23And G31For the modulus of shearing in three directions,For Poisson's ratio；
4th step：With the quality minimum of structure, target, the displacement for loading node using concentrfated load are built as constraint item as an optimization
Vertical topological optimization model is as follows：
Object function
Constraint function bv,r-bv,c≤ 0, v=1,2 ..., m
Ψ(Ψ1,i,Ψ2,i) b=F, i=1,2 ..., N
Wherein, M indicates the quality of structure, ρ1And ρ2The respectively density of solid material and quasi-truss fine structure material, ViIt is i-th
The volume of a unit, N are the unit sum for optimizing region division, Ψ ∈ CN×NFor the global stiffness matrix of unit, b ∈ CN×1For
The overall displacements column vector of unit, F ∈ CN×1For General load column vector, bv,rIt is the actual displacement value of i-th of displacement constraint point,
bv,cIt is the Admissible displacement value of i-th of displacement constraint, m is the number of displacement constraint, x1And x2For design variable lower threshold,WithFor threshold value of reaching the standard grade；
5th step：By the uncertainty of interval model characterising parameter, it is Multidisciplinary systems index to establish reliability displacement, is utilized
Former Optimized model can be amended as follows by reliability displacement：
s.t.Lv≤ 0, v=1,2 ..., m
Wherein LvFor reliability displacement, work as Lv>There is b when 0v,r-bv,c>0, indicate that reliability is unsatisfactory for requiring；Work as Lv<There is b when 0v,r-
bv,c≤ 0, indicate that reliability is met the requirements；
6th step：According to the expression formula for the reliability displacement that the 5th step obtains, by compound function derivation law to design variable
Derivation is carried out, and sensitivity of the reliability displacement to design variable is obtained with adjoint vector method；
7th step：Design is become using the reliability displacement difference obtained in the reliability displacement and the 6th step obtained in the 5th step
The sensitivity of amount is substituted into MMA algorithms and is solved to Multidisciplinary systems Optimized model, obtains new design variable；
8th step：Determine whether to meet convergence conditions, if being unsatisfactory for convergence conditions, the iterations completed are increased
Add 1, and returns to the 4th step；Otherwise, iterative process terminates.
2. a kind of solid material according to claim 1 and quasi-truss fine structure material integration Multidisciplinary systems topology
Optimization method, it is characterised in that：Solid material and the micro- knot of quasi-truss are established based on traditional material interpolation model with penalty function
The bi-material layers interpolation model of structure material integrated design.
3. a kind of solid material according to claim 1 and quasi-truss fine structure material integration Multidisciplinary systems topology
Optimization method, it is characterised in that：Utilize the elasticity modulus of anisotropic material or isotropic material, modulus of shearing and Poisson
Than totally 9 elastic constant E in all directionsi,x,Ei,y,Ei,z,νi,xy,νi,yz,νi,zx,Gi,xy,Gi,yz,Gi,zxIt realizes indirectly double
The foundation of material interpolation model.
4. a kind of solid material according to claim 1 and quasi-truss fine structure material integration Multidisciplinary systems topology
Optimization method, it is characterised in that：It is obtained and the material microstructure layer equivalent in macroscopic aspect rigidity property by strain energy equivalent method
The elastic constant of noodles truss micro-structure.
5. a kind of solid material according to claim 1 and quasi-truss fine structure material integration Multidisciplinary systems topology
Optimization method, it is characterised in that：It is Multidisciplinary systems index to establish reliability displacement, and is built by Multidisciplinary systems index
Vertical Multidisciplinary systems topological optimization model.
6. a kind of solid material according to claim 1 and quasi-truss fine structure material integration Multidisciplinary systems topology
Optimization method, it is characterised in that：Sensitivity of the reliability displacement to design variable is solved using adjoint vector method.
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