CN102637223B - Topological optimization design method on basis of pseudo-density sequencing and with consideration of draft manufacturing constraints - Google Patents
Topological optimization design method on basis of pseudo-density sequencing and with consideration of draft manufacturing constraints Download PDFInfo
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- CN102637223B CN102637223B CN201210071247.3A CN201210071247A CN102637223B CN 102637223 B CN102637223 B CN 102637223B CN 201210071247 A CN201210071247 A CN 201210071247A CN 102637223 B CN102637223 B CN 102637223B
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Abstract
The invention discloses a topological optimization design method on the basis of pseudo-density sequencing and with consideration of draft manufacturing constraints, which is used for realizing introducing draft manufacturing constraints in a topological optimization design of an irregular grid model. The technical scheme includes that the topological optimization design method includes sequencing the pseudo-densities of units on the same row in a draft direction again by the aid of a unit pseudo-density sequencing method; leading the pseudo-densities of the units to be distributed from large to small in the draft direction; and accordingly realizing draft constraint. By the aid of the method, design requirements of the draft constraints can be met without introducing a large quantity of constraints. The topological optimization design method solves the problems that a large quantity of constraint conditions are introduced into an existing method and a topological optimization process is not converged due to the excessive constraint conditions.
Description
Technical field
The present invention relates to a kind of method of topological optimization design, particularly a kind ofly based on pseudo-density, sort and consider the method for topological optimization design of withdrawing pattern manufacturing constraints.
Background technology
With reference to Fig. 1～3.In fields such as Aero-Space, automobile makings, there are a large amount of components of machine need to be with Mould Machining manufacture or sand casting, so need to consider withdrawing pattern problem.Mould withdrawing pattern is in order to guarantee mould product demoulding smoothly in the process of producing product; Sand casting withdrawing pattern is not destroy sand mold in order to take out wooden model from sand.The result of traditional Structural Topology Optimization Design, cannot create by the mode of Mould Machining or sand casting.Along with Topology Optimization Method is used widely in engineering, consider that the Topology Optimization Method of the various manufacturing constraints such as withdrawing pattern constraint meets the requirement of structural design more, so need to consider withdrawing pattern problem in topology optimization design.
Hinder several situations of withdrawing pattern: in structure, have cap holes 1, cap holes 1 hinders withdrawing pattern; The angle 2 of structure outward flange and withdrawing pattern parting/profile 4 is less than 90 degree, and angle 2 hinders withdrawing pattern.
With reference to Fig. 4.Document " Zhou M; Shyy YK; Thomas HL (2001) Topology optimization with manufacturing constraints.In:4th world congress of structural and multidisciplinary optimization, Dalian " discloses a kind of method of topological optimization design of considering withdrawing pattern manufacturing constraints.Document is introduced withdrawing pattern manufacturing constraints condition, and, in withdrawing pattern direction, the pseudo-density of topology optimization design variable meets constraint:
Wherein,
for the pseudo-density in the same unit listing 3 of withdrawing pattern direction.K is total columns of unit in withdrawing pattern direction.
Although the disclosed method of document is incorporated into withdrawing pattern manufacturing constraints in topology optimization design, the method has been introduced K and has been tied in topological optimization.If finite element model has K row in withdrawing pattern direction, just there is K to retrain and be introduced in during topological optimization solves.Shortcoming is: the method has been introduced a large amount of constraint condition, and the problem one of bringing due to a large amount of constraint condition of introducing is greatly to have increased topological optimization sensitivity to solve difficulty; The 2nd, constraint condition too much may cause process of topology optimization not restrain.
Summary of the invention
In prior art, there is the technical matters of introducing a large amount of constraints, the invention provides and a kind ofly based on pseudo-density, sort and consider the method for topological optimization design of withdrawing pattern manufacturing constraints, the method adopts the pseudo-density ranking method in unit, by the method, the pseudo-density in the unit of same row in withdrawing pattern direction is resequenced, make the descending distribution in withdrawing pattern direction of the pseudo-density in unit, thereby can realize withdrawing pattern constraint.This method can realize the designing requirement of withdrawing pattern constraint, but does not introduce a large amount of constraints.Can solve not convergence problem of the process of topology optimization introducing a large amount of constraint condition and too much cause due to constraint condition.
The technical solution adopted for the present invention to solve the technical problems is: a kind of based on pseudo-density, sort and consider be characterized in the method for topological optimization design of withdrawing pattern manufacturing constraints comprising the following steps:
(a) by the cad model of structure, set up finite element model, definition load and boundary condition.
(b) set up Topological optimization model:
find?X＝(x
1，x
2，K，x
n)
minΦ(X)
s.t.KU＝F
Wherein, X is the pseudo-intensity vector in unit in design domain; N is design variable number; The objective function that Φ (X) is topological optimization; K is finite element model global stiffness matrix; F is node equivalent load vectors; U is node global displacement vector; G
j(X) be j constraint function;
it is the upper limit of j constraint function; J is the quantity of constraint.
(c) the pseudo-density (x to the unit in same row 3 in withdrawing pattern direction
p, x
q... x
w)
k, k=1 ..., K rearrangement meets the pseudo-density in the same unit listing in withdrawing pattern direction
relation, unit from the parting/profile 4 of withdrawing pattern more away from, its pseudo-density value is less.Wherein k is the k row of model in withdrawing pattern direction, and K is the total columns in withdrawing pattern direction.
(d) model is carried out to a finite element analysis; By optimizing sensitivity analysis, try to achieve the sensitivity of objective function and constraint condition, choose certain optimized algorithm and be optimized design, result is optimized.
The invention has the beneficial effects as follows: by introducing the pseudo-density ranking method in a kind of unit, can not increase under the prerequisite of topology optimization design constraint, by the pseudo-density in unit, resequence, withdrawing pattern constraint is incorporated in topology optimization design.For the two-dimentional cantilever beam structure in embodiment, application the inventive method is optimized design, does not increase any constraint; And method in application reference document needs to increase by 25 constraints (model in embodiment has 25 row in withdrawing pattern direction), the constraint condition increasing is:
Below in conjunction with drawings and Examples, the present invention is elaborated.
Accompanying drawing explanation
Fig. 1 is the structural representation that can manufacture by Mould Machining or sand casting in background technology.
Fig. 2 is the structural representation that cannot manufacture by Mould Machining or sand casting in background technology.
Fig. 3 is the structural representation that cannot manufacture by Mould Machining or sand casting in background technology.
Fig. 4 is the schematic diagram that the disclosed method of background technology document is introduced withdrawing pattern constraint.
Fig. 5 is the stress model of the inventive method.
Fig. 6 is the topology optimization design result that background technology does not add withdrawing pattern constraint.
Fig. 7 is the topology optimization design result that the inventive method is introduced withdrawing pattern constraint.
In figure, 1-hole; 2-angle; 3-is the unit in same row in withdrawing pattern direction; 4-parting/profile.
Embodiment
With reference to Fig. 5～7.Take two-dimentional semi-girder topology optimization design as example explanation the present invention.Two dimension semi-girder is of a size of long 500mm, high 100mm.Semi-girder left side is complete fixing; Base angle, right side is subject to concentrated force load F=100N vertically upward.Design cantilever beam structure, makes its rigidity maximum, and volume fraction is 60% to the maximum.Withdrawing pattern direction is for vertically upward.Method step is as follows:
The present invention proposes a kind of method of topological optimization design of considering withdrawing pattern manufacturing constraints, comprise following three key links:
(a) finite element modeling.
Cad model by structure is set up finite element model.Load is that base angle, right side is subject to concentrated force load F=100N vertically upward; Boundary condition is that semi-girder left side is complete fixing.
(b) set up Topological optimization model
find?X＝(x
1，x
2，K，x
n)
minΦ(X)
s.t.KU＝F
G(X)-0.6≤0
Wherein, X is design variable---the pseudo-intensity vector in unit in design domain; N is design variable number; Φ (X) is objective function; K is finite element model global stiffness matrix; F is node equivalent load vectors; U is node global displacement vector; The volume fraction that G (X) is finite element model.
(c) the pseudo-density sequence in unit and renewal.
To being positioned at the pseudo-density (x in the same unit listing in withdrawing pattern direction
p, x
q... x
w)
k, k=1 ..., K rearrangement meets the pseudo-density in the same unit listing in withdrawing pattern direction
relation, unit far from the parting/profile 4 of withdrawing pattern more away from, its pseudo-density value is less.Wherein k is the k row of model in withdrawing pattern direction, and K is the total columns in withdrawing pattern direction.
(d) finite element analysis and Optimization Solution.
By finite element soft Ansys, model is carried out to a finite element analysis; By structure optimization platform Boss-Quattro, be optimized sensitivity analysis again, try to achieve the sensitivity of objective function and constraint condition, choose gradient optimal method GCMMA (Globally Convergent Method of Moving Asymptotes) optimized algorithm and be optimized design, result is optimized.
By optimum results, can be found out, consider the modelling result of withdrawing pattern constraint, can in withdrawing pattern direction, by withdrawing pattern, cast and create.Do not have the design result of withdrawing pattern constraint cannot cast and create by withdrawing pattern because there is sealing cavity centre.And the Topological optimization model that the present invention sets up does not increase the number of constraint.
Claims (1)
1. based on pseudo-density, sort and consider and it is characterized in that the method for topological optimization design of withdrawing pattern manufacturing constraints comprising the following steps:
(a) by the cad model of structure, set up finite element model, definition load and boundary condition;
(b) set up Topological optimization model:
find?X＝(x
1,x
2,...，x
n)
min?Φ(X)
s.t.?KU＝F
Wherein, X is the pseudo-intensity vector in unit in design domain; N is design variable number; The objective function that Φ (X) is topological optimization; K is finite element model global stiffness matrix; F is node equivalent load vectors; U is node global displacement vector; G
j(X) be j constraint function;
it is the upper limit of j constraint function; J is the quantity of constraint;
(c) to the pseudo-density (x of the unit in same row (3) in withdrawing pattern direction
p, x
q... x
w)
k, k=1 ..., K rearrangement, make the pseudo-density in the same unit listing in withdrawing pattern direction, meet (
k=1 ..., the relation of K, far away away from the parting/profile (4) of withdrawing pattern, its pseudo-density value is less; Wherein k is the k row of model in withdrawing pattern direction, and K is the total columns in withdrawing pattern direction;
(d) model is carried out to a finite element analysis; By optimizing sensitivity analysis, try to achieve the sensitivity of objective function and constraint condition, choose gradient optimal method GCMMA optimized algorithm and be optimized design, result is optimized.
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| CN103207940B (en) * | 2013-04-23 | 2015-07-22 | 西北工业大学 | Topology optimization design method for cyclic symmetry cylindrical grid structure |
| CN103336870B (en) * | 2013-07-05 | 2016-01-20 | 西北工业大学 | Consider the wing spar Structural Topology Optimization Design method that nail carries |
| CN103425830B (en) * | 2013-08-06 | 2017-02-08 | 西北工业大学 | Structural topological optimization method based on multi-point displacement coordination constraint |
| CN109002598B (en) * | 2018-06-29 | 2020-09-18 | 华中科技大学 | Self-supporting microstructure topology optimization method considering overhanging angle and minimum size constraint |
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| CN101609479A (en) * | 2009-06-23 | 2009-12-23 | 北京理工大学 | A kind of optimal design method for trajectory robust |
| CN101923590A (en) * | 2010-08-16 | 2010-12-22 | 北京理工大学 | High-efficiency Latin hypercube experimental design method |
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| zhou M, etc.Topology optimization with manufacturering constraints.《Proceeding of the Fourth World Congress of structural and multidisciplinary optimization》.2001, |
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