CN102222150A - Full-stress structure topological optimization design method based on continuous phase step reference stress - Google Patents

Abstract

The invention relates to a fully-stress structure topological optimization design method based on continuous phase step reference stress, which comprises the following steps: hardening a material in a high-stress area of a structure and softening the material in a low-stress area of the structure; taking the reference stress which can continuously carry out phase step change as a judgment standard; and through two optimizing cycles of local optimization and overall optimization, avoiding a premature phenomenon in the optimizing process, thereby leading the stress distribution of the structure to be gradually optimized.

Description

Full stress structure method of topological optimization design based on continuous step Reference Stress

Technical field

The present invention relates to a kind of structure-design technique, particularly a kind of full stress structure method of topological optimization design based on continuous step Reference Stress.

Background technology

Structural Topology Optimization is meant seeks the optimum topological form that structured material distributes, with some performance of optimizing structure or the weight that alleviates structure.Structural Topology Optimization has developed more than 100 year, is divided into analytic method and numerical method substantially.Analytical method is used classical mathematical theory and is found the solution, and is not easy to directly use in engineering reality.In recent decades, because the widespread usage of computing machine in structure analysis impelled the fast development of structure optimization numerical method, it mainly is divided into two big classes: a class is size, shape and the topological optimization that can solve each class formation, but the unsatisfactory homogenization method (homogenization method) of counting yield and versatility; Another kind of is to be the enlightening optimized Algorithm of representative with progressive structure optimization method (evolutionary structural optimization), its feature is that distribution designs to structured material on the angle of macroscopic view, the counting yield height, versatility is good, can obtain approximate optimal solution.In engineering reality, approximate optimal solution is extensively adopted usually, so this class algorithm has bright development prospect.

The structural Topology Optimization method that the present invention proposes is based on " soft killing " technology (SKO:soft kill option), its ultimate principle is " to soften " material of low stress gradually, " sclerosis " heavily stressed material makes through the structural stress level after optimizing and becomes more even.It is proposed by German Karlsruhe research centre at first, and ultimate principle is as follows: putative structure is made up of different materials, the elastic modulus of each unit is changed the topological form of structure as parameter.The elastic modulus of material is defined as the function of temperature, and promptly along with the rising of temperature, elastic modulus diminishes, and material " is softened ", when material " soft " arrives to a certain degree, can think that material is deleted; Along with the reduction of temperature, the springform quantitative change of material is big simultaneously, and material is by " sclerosis ".Temperature TAnd elastic modulus EBetween relation can be assumed to be linear relationship, temperature does not herein have physical significance, only is the controller that the unitary elasticity modulus changes.

At present, the research to the SKO method both at home and abroad is divided into two kinds substantially, and the one, adopt with the method for volume fraction as the deletion criterion, the 2nd, with the method for Reference Stress as material deletion criterion.The former makes and optimizes the result and converge on target volume by repeatedly deleting certain volume, in each delete procedure with the stress value of volume fraction correspondence as deletion standard soft or hard formed material gradually.This method is because the stress value of volume fraction correspondence is asked for difficulty, computing length consuming time.The latter distributes and selects a Reference Stress by analyzing structural stress in the optimizing iterative process, if the stress of certain node greater than Reference Stress, then node temperature reduces, the elastic modulus of material increases, material is by " sclerosis "; Otherwise node temperature raises, and material " is softened ".The relevant stress of distribution of material in mean stress that the choosing of Reference Stress is generally structure etc. and the structure iterative process.This method Reference Stress is chosen simply, computing weak point consuming time.Yet different Reference Stress is bigger to optimizing result's influence, if the Reference Stress value is crossed conference and caused deletion, too small meeting causes searching process efficient low, even because of material can't continue deletion, causes the iteration premature convergence, can not get optimum solution.

Summary of the invention

The present invention be directed to the problem that present structural Topology Optimization exists, a kind of full stress structure method of topological optimization design based on continuous step Reference Stress has been proposed, two optimizing circulations by local optimal searching and global optimizing, avoid with Reference Stress as the deletion criterion the structural Topology Optimization method in precocious phenomenon, make the stress distribution of structure progressively become excellent.

Technical scheme of the present invention is: a kind of full stress structure method of topological optimization design based on continuous step Reference Stress specifically comprises the steps:

1) sets up the mechanical model of structure, carry out finite element grid and divide.According to designing requirement design section is set, initialization design parameter and material parameter;

2) make cycle index I=1, J=1

3) carry out the linear static Finite Element Analysis of structure, extract node stress;

4) calculate continuous step Reference Stress σ ^{(i, j)} _Ref , computing formula is:

, wherein ζ ^{(i, j)} Be iIn the searching process of rank jThe weight coefficient of inferior iteration, σ ⁽ⁱ⁾ _Ave Be iThe mean stress of structure during the 1st iteration in the searching process of rank.Weight coefficient ζ ^{(i, j)} Computing formula is as follows:

, wherein ζ ₀ ⁽ⁱ⁾ Be iRank optimizing weight coefficient initial value, αBe constant, get 0.1, Δ ζBe the weight coefficient increment.The continuous step of being calculated by this formula of weight coefficient changes, but its maximal value must not surpass the weight coefficient upper limit of regulation ζ _Max

5) upgrade local temperature according to structure partial stress, formula is

,

Subscript in the formula i, jExpression the iIn the searching process of rank jInferior iteration, T _n ^{(i, j)} For iIn the searching process of rank jDuring inferior iteration nThe temperature of node; σ _n ^{(i, j-1)} Be iRank searching process J-During 1 iteration nThe stress of node; σ ^{(i, j)} _Ref Be iIn the searching process of rank jThe continuous step Reference Stress of inferior iteration is calculated by step 4); sBe step factor,

For according to iRank searching process J-Node temperature during 1 iteration T _n ^{(i, j-1)} The temperature reference value of determining ,Constant interval is (0,100): when T _n ^{(i, j-1)} Surpass at 100 o'clock, be forced to 100; When T _n ^{(i, j-1)} Less than 0 o'clock, be forced to 0; When T _n ^{(i, j-1)} In the time of between 0-100, then be T _n ^{(i, j-1)}

6) according to the elastic modulus of local temperature renewal local material, update method is: when T _n ^{(i, j)} In the time of between 0～100, linearity reduces elasticity modulus of materials with the rising of temperature; If T _n ^{(i, j)} ≤ 0, then E= E _Max , E _Max Be the elastic modulus of selected material, in order to the simulation solid area; When T _n ^{(i, j)} 〉=100 o'clock, then E= E _Min , E _Min For E _Max / 1000;

7) volume change of computation structure determines whether to reach local optimum, and the volume change of twice iteration is greater than given local volume tolerance before and after structure ε ₁The time, for not reaching the local optimum state, continue this local optimal searching, upgrade J=j+1,Return step 3); Otherwise be local optimum, this local optimal searching finishes, and carries out downwards;

8) upgrade I=i+1, J=1, return step 3), up to satisfying the global optimizing end condition, the volume change of promptly working as twice iteration in structure front and back is less than given global volume tolerance εThe time, then obtain final optimization result.

Beneficial effect of the present invention is: the full stress structure Topology Optimization Method that the present invention is based on continuous step Reference Stress, avoid the precocious phenomenon in designing as the structural Topology Optimization of deleting criterion, make the stress distribution of structure progressively become excellent with Reference Stress.

Description of drawings

Fig. 1 the present invention is based on algorithm flow block diagram in the full stress structure Topology Optimization Method of continuous step Reference Stress;

Fig. 2 the present invention is based on temperature and elastic modulus graph of a relation in the full stress structure Topology Optimization Method of continuous step Reference Stress;

Fig. 3 the present invention is based on weight coefficient in the full stress structure Topology Optimization Method of continuous step Reference Stress ζChange synoptic diagram;

Fig. 4 is subjected to the mechanical model of two face endogenetic processes for example 1 rectangle cantilever slab of the present invention;

Fig. 5 is subjected to the design result figure of the no continuous step Reference Stress method of two face endogenetic processes for example 1 rectangle cantilever slab of the present invention;

Fig. 6 is subjected to the present invention of two face endogenetic processes to propose the design result figure of method for example 1 rectangle cantilever slab of the present invention;

Fig. 7 is the mechanical model and the design result figure of example 2 arch bridge structure optimal design of the present invention.

Embodiment

One, optimizing iterative process: in optimizing iterative process based on the full stress structure Topology Optimization Method of continuous step Reference Stress, need through multistage local optimal searching process, iteration is for several times all passed through in the optimizing of every rank, therefore comprises 2 iterative loop, as shown in Figure 1.The one, the local optimal searching circulation (among Fig. 1 jCirculate), the volume change of twice iteration is less than given local volume tolerance before and after structure ε ₁The time, think that structure reaches a local optimum state; The 2nd, the global optimizing circulation (among Fig. 1 iCirculation), when less than given global volume tolerance εThe time, then obtain final optimization result.

According to the ultimate principle of SKO method, with the controller of temperature as elasticity modulus of materials, its iterative formula is:

⑴

⑵

Subscript in the formula i, jExpression the iIn the searching process of rank jInferior iteration. T _n ^{(i, j)} For iIn the searching process of rank jDuring inferior iteration nThe temperature of node; σ _n ^{(i, j-1)} Be iRank searching process J-During 1 iteration nThe equivalent node stress of node; σ _Ref ^{(i, j)} Be iIn the local optimal searching process of rank jThe continuous step Reference Stress of inferior iteration; sBe step factor.

By formula ⑴ as can be known, if node nStress greater than Reference Stress, then node temperature reduces, the elastic modulus of material increases, material is by " sclerosis "; Otherwise node temperature raises, and material " is softened ". E _Max Be the elastic modulus of selected material, in order to the simulation solid area.When T _n ^{(i, j-1)} In the time of between 0～100, the relation between elastic modulus and the temperature satisfies linear relationship as shown in Figure 2.If T _n ^{(i, j-1)} ≤ 0, then E= E _Max When T _n ^{(i, j-1)} 〉=100 o'clock, then E= E _Min E _Min Very little, for E _Max / 1000.

Concrete steps of the present invention such as Fig. 1:

1. set up initial mechanical model, and definite design space, some has that the border of specific (special) requirements or face need keep and not as design section in the practical structures.

2. give structure and have as shown in Figure 2 material properties, and use the finite element discretization grid, impose restriction and load, T ₀ Be environment temperature.

3. carry out the linear static Finite Element Analysis of structure, extract node stress, calculate continuous step Reference Stress, wherein weight coefficient ζ ^{(i, j)} The weight coefficient upper limit that must not surpass regulation ζ _Max

4. the operation of " soft or hardization " unit of ⑴ ⑵ realization by formula.

When 5. not reaching local optimum, upgrade j, repeated for the 3. step, after reaching the local optimum structure, upgrade i, j, repeated for the 3. step again, up to satisfying stopping criterion for iteration mentioned above, termination of iterations.

Two, determining of continuous step Reference Stress: by above-mentioned searching process as can be known, whether the optimizing result is desirable, is decided by the selection of Reference Stress in the formula (1).The Reference Stress that the present invention proposes is that the mean stress of structure in the iterative process multiply by the weight coefficient that a continuous step changes, and computing formula is:

（3）

Wherein ζ ^{(i, j)} Be iIn the searching process of rank jThe weight coefficient of inferior iteration; Continuous step Reference Stress σ ^{(i, j)} _Ref Be with iThe 1st iteration mean stress in the searching process of rank σ ⁽ⁱ⁾ _Ave For radix multiply by a weight coefficient ζ ^{(i, j)} Obtain.Weight coefficient ζ ^{(i, j)} Computing formula is as follows:

⑷

Wherein ζ ₀ ⁽ⁱ⁾ Be iRank optimizing weight coefficient initial value; αBe constant, get 0.1; Δ ζBe the weight coefficient increment.The iRank weight coefficient initial value ζ ₀ ⁽ⁱ⁾ Be iThe weight coefficient of the last iteration in-1 rank searching process

, promptly

⑸

Because with respect to the variation of weight coefficient, the mean stress of structure is less in the variation of iterative process, the variation tendency and the weight coefficient basically identical of therefore continuous step Reference Stress.Weight coefficient ζ ^{(i, j)} Increase by rank along with the increase of optimizing exponent number, for the Changing Pattern of continuous step Reference Stress is described better, with ζ ₀ ⁽⁰⁾ =0.8, α=0.1, Δ ζ=0.05 is parameter, supposes respectively through 4 rank local optimal searching processes the variation of weight coefficient in the searching process to be described, the iterations of establishing the optimizing of every rank is 10.As shown in Figure 3, curve is divided into 5 zones. jWhen entering down single order local optimal searching process since 1 counting, iOn original basis, increase once, at the beginning of the optimizing of every rank, 10 Δ ζ α ^j With Δ ζJust equate that equation becomes ζ ^{(i, 1)} = ζ ₀ ⁽ⁱ⁾ = ζ ^(i-1) So the first step iteration of local optimal searching process equates that with the weight coefficient of the final step iteration of last single order local optimal searching process function is not undergone mutation.And along with the increase of iterations, 10 Δ ζ α ^j Decay to zero very soon, final weight coefficient ζ ^{(i, j)} Equal iRank weight coefficient initial value ζ ₀ ⁽ⁱ⁾ With the weight coefficient increment Δ ζSum.1,3,4, the weight coefficient in 5 these 4 zones all satisfies above-described hoisting way, and twice iteration of the 2nd regional process all reaches local optimum, illustrates that weight coefficient rises greatly inadequately, need to promote once more, just can enter down the single order searching process, this is the self-regulating process of weight coefficient.

Three. application examples: the method for designing that the present invention proposes can be carried out topology optimization design to various structures, with two design example validity of the present invention is described below.

1, is subjected to the cantilever slab topology optimization design of two face internal force

The length breadth ratio of cantilever slab as shown in Figure 4 is 2, and an end of plate is fixed, and is subjected to two vertically downward power PEffect finds that by stress Analysis on Structure stress value concentrates between [0.02,51.2].

The weight coefficient parameter is chosen the local volume tolerance by 2 kinds of schemes as shown in the table respectively ε ₁And volume tolerance εIt is as shown in the table.

Initial weight coefficient in the scheme 1 ζ ₀ ⁽⁰⁾ With the weight coefficient upper limit ζ _Max Equate, promptly adopt the SKO method of no continuous step Reference Stress, carry out topological optimization with 0.8 times of mean stress as reference stress all the time.Optimize back distribution of material such as Fig. 5 (a).The middle top left region material of structure is piled up, and finds after the stress analysis that the structural stress value concentrates between [0,51.5], does not have obvious improvement than the degree of uniformity of the stress level of initial model, optimizes the result and only obtains local optimum.Fig. 5 (b) is a volume index, the iterative process figure of the Reference Stress index after weight coefficient and the dimensionless.Weight coefficient and Reference Stress do not change with the increase of iterations as seen from the figure, and the volume of structure reduces with the increase of iterations, stop up to reaching volume tolerance, and final volume is 0.61 times of initial volume.

Scheme 2 has adopted the scheme of continuous step Reference Stress, and the initial weight coefficient is ζ ₀ ⁽⁰⁾ Be 0.5, the weight coefficient increment Δ ζBe 0.05, the weight coefficient upper limit ζ _Max Be 1.25.Optimize the back distribution of material shown in Fig. 6 (a), comparing with Fig. 5 (a) has more thin portion structure, finds after the stress analysis that the structural stress value concentrates between [17.2,51.5], the degree of uniformity of comparing stress level with scheme 1 increases, and obtains comparatively desirable approximate optimal solution.Fig. 6 (b) is the iterative process figure of performance index.The continuous step of weight coefficient rises and finally reaches the weight coefficient upper limit ζ _Max Reference Stress changes and the weight coefficient basically identical.Volume is along with the increase of iterations reduces always, finally is tending towards volume tolerance and stops.Compare with scheme 1, the final volume of structure becomes original 0.41 times, manys deletion 20% than scheme 1.

By this example as can be known, with respect to traditional Reference Stress obtaining value method, the method for the continuous step Reference Stress that the present invention proposes can be avoided the precocious phenomenon of searching process, and the optimization that obtains is sharpness of border as a result, and is rational in infrastructure, and stress level is more even.SHAPE \*?MERGEFORMAT

2, the topology optimization design of arch bridge

Arch bridge mechanical model shown in Fig. 7 (a) supposes that the distance to the bridge floor top is at the bottom of the bridge H, the radius-of-curvature of bridge floor is R, R/H=5, at the bottom of the bridge about two fixed ends, the bridge upper surface is subjected to uniformly distributed load P

Fig. 7 (b) is distribution of material figure after the arch bridge optimization, and Fig. 7 (c) is the variation diagram of performance parameter in the iterative process, the initial weight coefficient ζ ₀ ⁽⁰⁾Be 0.5, the weight coefficient increment Delta ζBe 0.12, finish that weight system promotes by rank, reaches through 195 iteration ζ _MaxAfter no longer increase, volume index increases along with iterations and tends to be steady gradually, reaches the overall volume tolerance at last and stops.Final volume is original 0.41, and the result who obtains is similar to actual arch bridge structure.

Claims (1)

1. the full stress structure method of topological optimization design based on continuous step Reference Stress is characterized in that, specifically comprises the steps:

1) sets up the mechanical model of structure, carry out finite element grid and divide, according to designing requirement design section is set, initialization design parameter and material parameter;

2) make cycle index I=1, J=1;

3) carry out the linear static Finite Element Analysis of structure, extract node stress;

4) calculate continuous step Reference Stress σ ^{(i, j)} _Ref , computing formula is:

, wherein ζ ^{(i, j)} Be iIn the searching process of rank jThe weight coefficient of inferior iteration, σ ⁽ⁱ⁾ _Ave Be iThe mean stress of structure during the 1st iteration in the searching process of rank, weight coefficient ζ ^{(i, j)} Computing formula is as follows:

, wherein ζ ₀ ⁽ⁱ⁾ Be iRank optimizing weight coefficient initial value, αBe constant, get 0.1, Δ ζBe the weight coefficient increment, the continuous step of being calculated by this formula of weight coefficient changes, and maximal value must not surpass the weight coefficient upper limit of regulation ζ _Max

5) upgrade local temperature according to structure partial stress, formula is

,

Subscript in the formula i, jExpression the iIn the searching process of rank jInferior iteration, T _n ^{(i, j)} For iIn the searching process of rank jDuring inferior iteration nThe temperature of node; σ _n ^{(i, j-1)} Be iRank searching process J-During 1 iteration nThe stress of node; σ ^{(i, j)} _Ref Be iIn the searching process of rank jThe continuous step Reference Stress of inferior iteration is calculated by step 4); sBe step factor,

For according to iRank searching process J-Node temperature during 1 iteration T _n ^{(i, j-1)} The temperature reference value of determining ,Constant interval is (0,100): when T _n ^{(i, j-1)} Surpass at 100 o'clock, be forced to 100; When T _n ^{(i, j-1)} Less than 0 o'clock, be forced to 0; When T _n ^{(i, j-1)} In the time of between 0-100, then be T _n ^{(i, j-1)}

6) according to the elastic modulus of local temperature renewal local material, update method is: when T _n ^{(i, j)} In the time of between 0～100, linearity reduces elasticity modulus of materials with the rising of temperature; If T _n ^{(i, j)} ≤ 0, then E= E _Max , E _Max Be the elastic modulus of selected material, in order to the simulation solid area; When T _n ^{(i, j)} 〉=100 o'clock, then E= E _Min , E _Min For E _Max / 1000;

7) volume change of computation structure determines whether to reach local optimum, and the volume change of twice iteration is greater than given local volume tolerance before and after structure ε ₁The time, for not reaching the local optimum state, continue this local optimal searching, upgrade J=j+1,Return step 3); Otherwise be local optimum, this local optimal searching finishes, and carries out downwards;

8) upgrade I=i+1, J=1, return step 3), up to satisfying the global optimizing end condition, the volume change of promptly working as twice iteration in structure front and back is less than given global volume tolerance εThe time, then obtain final optimization result.

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