CN110188498A - A kind of optimal Non-design Space division methods based on topological optimization density variable method - Google Patents
A kind of optimal Non-design Space division methods based on topological optimization density variable method Download PDFInfo
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- CN110188498A CN110188498A CN201910483869.9A CN201910483869A CN110188498A CN 110188498 A CN110188498 A CN 110188498A CN 201910483869 A CN201910483869 A CN 201910483869A CN 110188498 A CN110188498 A CN 110188498A
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Abstract
The invention discloses a kind of based on topological optimization density variable method and using minimum mass as the optimal Non-design Space division methods of optimization aim, pass through the judgement of the topological optimization result under different Non-design Space volumes, to which the range where shortening Non-design Space volume step by step obtains most light mechanical structure, mechanical structure topological optimization globally optimal solution has been obtained.The present invention can be suitable for the division of the optimal Non-design Space of most of mechanical structure, be directly realized by from prototype structure to final topology structure, improve topological optimization efficiency, shorten the time of optimization design.
Description
Technical field
It is specially a kind of based on the optimal non-of topological optimization density variable method the present invention relates to mechanical structure topological optimization field
Design space division methods.
Background technique
With being constantly progressive for current science and technology, the continuous improvement of industrial level, Advanced Manufacturing Technology constantly occurs,
Such as 3D printing technique etc. so that the mechanical structure obtained originally by conventional machining process have bigger optimization space and
Machinability.The topological optimization of mechanical structure mainly first divides Non-design Space and design space, and it is excellent then to carry out topology
Change.There are many current design space division methods, such as rule of thumb carries out division design space, utilizes the model split of response
Design space.But these design space division modes, which hardly result in optimal design space, makes mechanical structure after topological optimization
Quality reach most light.
Summary of the invention
The optimal Non-design Space division methods based on topological optimization density variable method that the purpose of the present invention is to provide a kind of,
To solve the problems mentioned in the above background technology.
The present invention is based on the optimal Non-design Space division methods of topological optimization density variable method, include the following steps:
(1) it determines the volume change range of threedimensional model Non-design Space, defines Non-design Space volume minimum change αmin,
The material of selected structure and its determining material property, including Poisson's ratio, elasticity modulus, yield strength；
(2) parameter and design variable used in initialization calculating process are defined, initial when carrying out topological optimization non-sets
The volume for counting space is V1, the knots modification of volume is α when topological optimizationt, the number of j expression Non-design Space stereomutation, z table
Show that the design space knots modification of setting changes the upper limit value of number, defines initial designs variable
xi=1；
(3) it determines the boundary condition of structure, applies the constraint such as load, according to the size of current Non-design Space volume, set to non-
It counts space and carries out continuous body unit finite element analysis, obtain Displacement of elemental node ui, element stress σi, element stiffness matrix ki；
(4) design variable is updated to after topological optimization in the quality explicit expression of structure, is calculated, while carrying out sensitive
The analysis of degree；
(5) it is compared with the preceding quality being once calculated, if the two absolute value of the difference charge >=β, the number of iterations k=
k+1；
(6) step (3), (4), (5) are repeated, if the two absolute value of the difference charge < β, terminates iteration；
(7) V is enabledj+1=Vj+αt, j=j+1, and step (2), (3), (4), (5), (6) are repeated until Vj+1≥Vmax, obtain multiple groups
Mass M under different Non-design Space volumesj；
(8) work as Vj+1VmaxWhen, t=t+1 is enabled, while exporting Mmin=min { MjAnd Non-design Space volume corresponding to it
Vj, export Vj-1、Vj+1And its corresponding Mj-1、Mj+1, enable V1=Vj-1, Vmax=Vj+1, repeat step (2), (3), (4), (5),
(6),(7)；
(9) as t >=z, in volume VjLeft and right nearby selects two bulking value V respectivelyj+b、Vj-b, repeat step (3), (4),
(5), (6) obtain the mass M under two Non-design Space volumesj+b、Mj-b, and with
MjIt is compared, if Mj-bCompared with MjSmall, then selection is in section [Vj-1, Vj] in find the volume of optimal Non-design Space, together
Reason, if Mj+bCompared with MjSmall, then selection is in section [Vj, Vj+1] in find the volume of optimal Non-design Space；
(10) the intermediate product value V in above-mentioned section is takenaAs the volume of Non-design Space, step (3), (4), (5), (6) are repeated,
Obtain Ma, and and MjCompare, if MaGreater than Mj, then enabling the section of optimal Non-design Space volume is [Va, Vj], similarly, if MaIt is small
In Mj, repeat step (9), obtain the section of new optimal Non-design Space volume；
(11) step (9), (10) are repeated, until Ma≤Ma+bAnd Ma≥Ma-b, export Ma、VaAnd as optimal Non-design Space body
The minimum mass obtained after long-pending and structural Topology Optimization.
The beneficial effects of the present invention are: using Ku Enkate condition carries out solution calculating to the mathematical model established,
Obtain reliable design variable iterative formula and sensitivity；By the judgement and circulation of multiple topological optimization, can obtain
The globally optimal solution of Non-design Space；Judgement by dichotomy and to monotonicity near median reduces and calculates the time
And the number of iterations, improve computational efficiency.
Detailed description of the invention
Fig. 1 is optimal Non-design Space division methods general flow chart of the invention.
Fig. 2 is optimal Non-design Space division methods flow chart 1 of the invention.
Fig. 3 is optimal Non-design Space division methods flow chart 2 of the invention.
Fig. 4 is the X-Y scheme of example selected by the present invention.
Fig. 5 is topological structure of the example selected by the present invention when Non-design Space volume is 0.
Fig. 6 is topological structure of the example selected by the present invention when Non-design Space volume is optimal.
Fig. 7 is MATALAB subprogram screenshot in example implementation process selected by the present invention.
Specific embodiment
Below by using the division of the optimal Non-design Space of the topological optimization of a simple cantilever beam as example, and then to hair
Bright patent is described further.
It is illustrated in fig. 4 shown below the 2 d plane picture for cantilever beam, long 75mm, wide 25mm, high 25mm, Poisson's ratio 0.33, material
Expect density p0=2760kg/m3, left end is fixed, applies concentrfated load F=1N at its lower right corner, retain structure upper surface.
In the description of the present invention, it is to be understood that, term " on ", "lower", "front", "rear", "left", "right" etc. indicate
Orientation or positional relationship be based on the orientation or positional relationship shown in the drawings, be merely for convenience of description the present invention and simplification retouch
It states, rather than the device or element of indication or suggestion meaning must have a particular orientation, be constructed and operated in a specific orientation,
Therefore it is not considered as limiting the invention.
It is using SIMP interpolation method founding mathematical modelsMultiplied using Lagrange
Sub- method and Ku Enkate condition carry out explicit solution to above-mentioned model, have obtained design variable xiIterative formula beThe explicit expression of M isDefine cantilever
The upper surface of beam is reservation face, and Non-design Space maximum volume is 7500mm3, minimum value 1500mm3, it is empty to define non-design
Between volume characterization parameter be Non-design Space high h, definition size of mesh opening is 1mm, changes non-design by the size of change h
The volume in space, wherein 0≤h≤5,
α1=1, i.e. h changes 1mm every time, since cantilever beam structure is simple, so defining z=1.By simple in MATALAB
Programming complete above-mentioned steps, obtained the smallest topological structure of quality under optimal Non-design Space, Fig. 5 show non-set
Topological optimization when spatial volume is 0 is counted as a result, Fig. 6 show the topological optimization result under optimal Non-design Space.Output is most
Excellent h value is h=1mm, i.e., the volume of optimal Non-design Space is 2020mm3。
Claims (4)
1. the optimal Non-design Space division methods based on a kind of topological optimization density variable method, it is characterised in that including following steps
It is rapid:
(1) it determines the volume change range of threedimensional model Non-design Space, defines Non-design Space volume minimum change,
The material of selected structure and its determining material property, including Poisson's ratio, elasticity modulus, yield strength；
(2) parameter and design variable used in initialization calculating process are defined:
The volume of initial Non-design Space when-progress topological optimization；
The knots modification of volume when-topological optimization；
The number of-Non-design Space stereomutation；
The design space knots modification of-setting changes the upper limit value of number；
- definition initial designs variable is 1；
(3) it determines the boundary condition of structure, applies the constraint such as load, according to the size of current Non-design Space volume, set to non-
It counts space and carries out continuous body unit finite element analysis, obtain Displacement of elemental node, element stress, element stiffness matrix；
(4) design variable is updated to after topological optimization in the quality explicit expression of structure, is calculated, while carrying out sensitive
The analysis of degree；
(5) it is compared with the preceding quality being once calculated, if the two absolute value of the difference, then the number of iterations；
(6) step (3), (4), (5) are repeated, if the two absolute value of the difference, then iteration is terminated；
(7) it enables,, and repeat step (2), (3), (4), (5), (6) until,
Obtain the quality under multiple groups difference Non-design Space volume；
(8) whenWhen, it enables, export simultaneouslyAnd it is non-corresponding to it
Design space volume, output、And its it is corresponding、, enable,,
Repeat step (2), (3), (4), (5), (6), (7)；
(9) whenWhen, in volumeLeft and right nearby selects two bulking values respectively、, repetition step (3),
(4), (5), (6), obtain the quality under two Non-design Space volumes、, and withIt is compared, if
Compared withSmall, then selection is in sectionThe middle volume for finding optimal Non-design Space, similarly, ifCompared withIt is small,
Then selection is in sectionThe middle volume for finding optimal Non-design Space；
(10) the intermediate product value in above-mentioned section is takenAs the volume of Non-design Space, step (3), (4), (5), (6) are repeated,
It obtains, and withCompare, ifIt is greater than, then the section of optimal Non-design Space volume is enabled to be, similarly,
IfIt is less than, repeat step (9), obtain the section of new optimal Non-design Space volume；
(11) step (9), (10) are repeated, untilAnd, output、And as optimal
The minimum mass obtained after Non-design Space volume and structural Topology Optimization.
2. step (1) according to claim 1, it is characterised in that。
3. step (2) according to claim 1, it is characterised in that、、Initial value is 1.
4. step (4) according to claim 1, it is characterised in that can be according to engineering reality for the explicit expression of quality
Border carries out solution calculating using topological optimization SIMP interpolation method.
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| CN110704912A (en) * | 2019-09-19 | 2020-01-17 | 北京航空航天大学 | Method for topological optimization of bridge bracket arm structure under stress constraint |
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| CN103335091A (en) * | 2013-07-08 | 2013-10-02 | 北京汽车股份有限公司 | Method for optimizing automobile speed reducer shell structure |
| CN104077434A (en) * | 2014-06-09 | 2014-10-01 | 国家超级计算深圳中心(深圳云计算中心) | CAE (Computer Aided Engineering) analysis based product structure optimization method and system |
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