CN109344524A - A kind of thin-slab structure reinforced bag sand well optimization method - Google Patents
A kind of thin-slab structure reinforced bag sand well optimization method Download PDFInfo
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Abstract
The present invention provides a kind of thin-slab structure reinforced bag sand well optimization method comprising following steps: S1, defining the height factors that design variable unit maturity is reinforcing rib, and carries out to design variable equidistant discrete；S2, local stress constraint condition is established based on Von mises yield criterion, global displacement constraint condition is established based on unified constraint function, the two-stage optimizing model of algorithm is established based on the thought that classification solves；S3, the finite element plate-girder discrete model that reinforcing rib is in M shape is established, each rebar element design variable is initialized, the initial configuration as optimization；S4, first order solution is carried out using linear search method, second level solution, as the reinforced bag sand well result of optimizing is carried out using Relative Difference Quotient Algorithm on the basis of first order optimum results.This method, which can be classified, solves local stress constraint and global displacement constraint, and the double optimization to reinforcing rib sectional dimension and distributing position may be implemented, finally obtain the Optimal Distribution form of reinforcing rib.
Description
Technical field
The present invention relates to a kind of thin-slab structure reinforced bag sand well optimization methods.
Background technique
Thin-slab structure is different from slab and membrane structure, refer to the ratio between plate face characteristic size and plate thickness between 5 to 100 one
Class formation form.Thin-slab structure is widely used structure lightened more demanding field in Aeronautics and Astronautics, automobile, ship etc.,
But it there is the disadvantages of structural strength is low, easily-deformable.Under normal circumstances, by arranging that reinforcing rib can be mentioned substantially in plate face
High structural behaviour, while less increasing construction weight.However common reinforcing rib design form is mostly to wait highly, at equal intervals
Orthogonal packing in length and breadth, such as " two " font, " well " font, " rice " font.Such design is overly conservative, although improving structure
Performance, but be easy to cause the waste of reinforcing rib material keeps structure weight gain larger, this with before meeting structural mechanical property requirement
It puts and realizes that the maximum light-weighted requirement of structure is runed counter to.
The optimization of thin-slab structure reinforced bag sand well is exactly to obtain meeting structural mechanical property requirement with least reinforcing rib material
Reinforced bag sand well form, existing reinforced bag sand well optimization method mainly include the following types:
The first is the optimization method based on material distributed model.Document " Chung J, Lee K.Optimal design
of rib structures using the topology optimization technique[J].Proceedings of
The Institution of Mechanical Engineers, 1997,211, Part C, 425-437. " utilizes density variable method
The optimum shape and optimal location problem of muscle are probed into, but the initial position of reinforcing rib is that rule of thumb guess is determined
, lack stringent theories integration.Document " Lam Y.C., Santhikumar S.Automated rib location and
optimization for plate structures[J].Structural Multidisciplinary
Optimization, 2003,25 (1): 35-45. " first optimizes substrate thickness with Varying-thickness method, then under manufacturing process limitation
Configuration is optimized to the width of reinforcing rib, height and spacing.Optimization method based on material distributed model be a kind of development compared with
Early thin-slab structure reinforced bag sand well optimization method, for thought source in non-individual body topological optimization, what is obtained is reinforcing rib
Substantially distributed areas cannot obtain clearly reinforcing rib layout, need just be obtained most according to designer's experience and subsequent processing
Whole reinforced bag sand well form.
Second is the optimization method based on equivalent perpendicular heterogeneous slab model.Document " Qiao Huiyun, Zhou Kemin multiplexing
Topological optimization grid [J] engineering mechanics under condition stress constraint, 2009,26 (6): thin plate reinforced structure is reduced to by 46-51 "
A kind of composite structure of grid and non-individual body enhances composite material model using orthotropic to simulate grid-non-individual body sheet
Structure relationship, using density of the beam at node and direction as design variable, according to Finite element analysis results, using fully stressed criterion
Method optimizes the cell structure under each either simplex condition.Optimization method based on equivalent perpendicular heterogeneous slab model, it is desirable that reinforcing rib
Density is sufficiently large and marshalling；Its equivalent process need by elasticity it is equivalent, plasticity is equivalent, dynamic equivalent, in the hope of it is each to
Some parameters of anisotropic hardened structure, process are more complicated；Therefore, this equivalent method has limitation, is not promoted.
The third is the optimization method based on plate-girder discrete model.Document " Zhang Shengdong, Yang Jungang, Zhang Weihong thin-slab structure
Evolutionary structural optimization method [J] modern Manufacturing Engineering of reinforcement layout design, 2009,04:5-9. " Evolutionary structural optimization
The reinforcement distribution problem of thin-slab structure is studied, grid dividing is carried out to thin plate with shell63 unit, uses beam188
Unit represents reinforcing rib, establishes plate-girder discrete model.The standard that strain energy level of sensitivity is gone or stayed as unit, by gradually
The lesser unit of sensitivity is deleted, optimal reinforced bag sand well is obtained.Optimization method based on plate-girder discrete model to reinforce
Adding or deleting for muscle is all evidence-based, and clearly reinforced bag sand well form can be obtained after optimizing, thus in recent years this
Class method is quickly grown, the main stream approach being increasingly becoming in thin-slab structure reinforced bag sand well optimization design.
4th kind is the optimization method based on bionic structure model." Zhao Ling, Chen Wuyi, Ma Jianfeng are based on Wang Lianye to document
Machine tool beam reinforcing plate structure bionic optimization [J] the high-tech communication of arteries and veins distribution, 2008,18 (8): 806-810. " has studied Wang Lian
Vein be configured rule, and be applied to machine tool beam reinforced bag sand well design in.Due to biological evolution and natural selection
Effect, biological structure be adapt to environment " optimal " structure.The thought of bionic structure is introduced into thin-slab structure reinforced bag sand well
It can obtain preferable reinforced bag sand well form in optimization design, but this method is there is the selection of bionical prototype is relatively difficult,
The approximate construction that biomimetic features are biological prototypes is obtained, structure is complicated, is not easy the problems such as manufacturing.Although therefore this method theory
It is advanced, but development is also immature, and more scholars is needed to further investigate it.
The existing reinforced bag sand well optimization method of Comprehensive Correlation is it can be found that the optimization method based on plate-girder discrete model has
There is apparent advantage.However this kind of methods are greatly mostly from continuous variable topological optimization, it is difficult to solve and contain stress and displacement
The optimization problem of equal constraints.And in Optimum design of engineering structures, so that designed structure is met every structural behaviour index,
The constraint such as stress and displacement is just inevitably handled, the parsing mathematical tool that continuous variable topological optimization is dependent at this time is lost
Effect.In contrast, although discrete variable topological optimization the problem of there is Combinatorial Optimizations, it is not by objective function and constraint item
The limitation of part type, the problem of can solution containing the constraint of multiple and different types, engineering practical value is bigger.Therefore, attempt with
The method of discrete variable topological optimization carries out the new approaches that thin-slab structure reinforced bag sand well optimization design is the area research.
Summary of the invention
In order to overcome the drawbacks of the prior art, the present invention is based on plate-girder discrete models, from the angle of discrete variable topological optimization
Degree sets out, and proposes a kind of thin-slab structure reinforced bag sand well optimization method.
Specifically, the present invention provides a kind of thin-slab structure reinforced bag sand well optimization method comprising following steps:
S1, the height factors that design variable unit maturity is reinforcing rib are defined, and design variable is carried out equidistant discrete；
S2, local stress constraint condition is established based on Von mises yield criterion, is established based on unified constraint function whole
Displacement constraint establishes the two-stage optimizing model of algorithm based on the thought that classification solves；
S3, the finite element plate-girder discrete model that reinforcing rib is in M shape distribution is established, it will be at the beginning of each rebar element design variable
Beginningization, the initial configuration as optimization；
S4, first order solution is carried out using linear search method, relative mistake is used on the basis of first order optimum results
Commercial law carries out second level solution, the reinforced bag sand well form after being optimized.
Preferably, step S1 specifically includes the following steps:
S11, reinforcing rib width is set as definite value, using the height of reinforcing rib as optimization object, design variable is defined as
One factor of reinforcement height, and it is named as unit maturity, value range is a continuum [0,1], and 0 represents reinforcement
Unit is not present, and 1 represents rebar element growth and maturity, and median represents the different degrees of of rebar element growth, single by optimization
First maturity controls the size of reinforcement height and the going or staying of rebar element, the relationship of unit maturity and reinforcement height
It may be expressed as:
H (k)=HmX (k) (k=1,2 ..., Ne)
Wherein, H (k) is the height of k-th of rebar element；HmIt is the upper limit of reinforcement height；X (k) is k-th of reinforcement list
The unit maturity of member；Ne is rebar element sum in structure；
S12, discrete variable is converted by design variable, carried out in the continuous interval [0,1] of unit maturity etc.
Distance dissipates, and obtains the design variable value set of discretization, if the step-size in search in unit evolutionary process is d, then design variable
Value set are as follows:
X (k) ∈ 0, d, 2d ..., and 1 } (d=1/n, n ∈ N+)
Wherein, the value of step-size in search d represents the increment of design variable in each iterative process.
Preferably, step S2 comprising the following steps:
S21, the Materials Yield Limit in VonMises yield criterion is replaced with the proportional limit of material, makes structural material only
Linear elastic deformation occurs, and considers design safety factor (DSF), acquires allowable stress, and then construct local stress constraint condition；
S22, the displacement constraint of node each in structure is divided into operative constraint and inactivce constraints, ignores inactivce constraints, used
Multiple operative constraints are converted a constraint condition by unified constraint function, i.e., takes two norms to each operative constraint, and building is whole
Displacement constraint；
S23, classification solve stress and displacement two classes constraint, and the first order first solves local stress constraint, reduces design rapidly
Then on this basis the value range of variable carries out the fine solution of second level global displacement constraint.
Preferably, the expression formula that local stress constrains in step S21:
Wherein, σkIt is the equivalent stress of k-th of rebar element, σ1σ2σ3It is first principal stress, second principal stress, respectively
Three principal stresses；σpIt is the proportional limit of material；N is safety coefficient；[σ] is allowable stress.
Preferably, using unified constraint function building global displacement constraint in step S22, the specific method is as follows:
S221, note structure interior joint sum are Nn, and each modal displacement is δl, it is corresponding it is allowable displacement beThen each displacement constraint is divided into nothing according to whether each modal displacement meets corresponding displacement allowable
Effect constraint and operative constraint, if modal displacement is not more than displacement allowable, this is constrained to inactivce constraints；Permitted if modal displacement is greater than
With displacement, then this is constrained to operative constraint；
Wherein, Ni is the number of inactivce constraints；Nj is the number of operative constraint；
S222, the form that operative constraint is transformed into constraint function are as follows:
S223, two norms are taken to constraint function, obtain the expression formula of global displacement constraint are as follows:
The necessary and sufficient condition for meeting whole displacement constraints is Z (x)=0.
Preferably, in step S3, design variable initialization, which refers to, is set to the pole greater than zero for the initial value of design variable
Decimal, in this, as the initial configuration of optimization.
Preferably, in step S4, the reinforced bag sand well form after optimization includes rebar element sectional dimension and distributing position
Two parameters.
Preferably, establish finite element plate-girder discrete model in step S3 specifically includes the following steps:
S31, shell63 shell unit and beam188 beam element in ANSYS is selected to carry out finite element plate-girder discrete model
It establishes, grid dividing is carried out to substrate with shell unit, shell unit node is attached with beam element between any two, and being formed is in rice word
The reinforcement distribution form of shape；
S32, it is programmed using ANSYS Parametric Design Language APDL, realizes the parametric modeling of plate-girder discrete model,
Key step is as follows:
The modeling of a thin plate, and with shell63 to thin plate grid division, note Shell Finite Element node total number is N；
B chooses i-th of node, referred to as central node, generates key point Ki by node；
C chooses in the node of M shape distribution around node i, and sum is denoted as n；
D surroundings nodes sort from small to large by number, and successively generate corresponding key point Kj respectively；
E establishes straight line by key point Ki and Kj, with beam188 to straight line grid division；
F repeats step e, when j is greater than n, stops iteration；
G repeats step b~f, when i is greater than N, program determination；
Wherein, by adjusting grid dividing number in step a, the plate-girder discrete model of available different shape.
Preferably, step S4 specifically includes the following steps:
S41, by each rebar element design variable Xi(k) Optimized model is substituted into, corresponding unit equivalent stress is extracted, is checked
Whether each unit equivalent stress meets local stress constraint condition, if satisfied, then XiIt (k) is the optimal of the unit design variable
Value；If not satisfied, then design variable removes a value Xi+1(k), Optimized model is substituted into again and solve verifying, answer until meeting part
Until force constraint condition, the optimization solution of the algorithm first order is finally obtained are as follows:
X#={ X#(1),X#(2),…,X#(Ne)}；
S42, using the optimum results of the first order as the second level optimization in design variable value lower limit, the first order optimize
Afterwards on the basis of reinforced bag sand well form, using Relative Difference Quotient Algorithm, the second level Optimization Solution of algorithm is carried out.
Preferably, the key step that the algorithm first order solves are as follows:
Beam element sum is denoted as Ne in a plate-girder discrete model, and design variable step-size in search is set as d, and each beam element design becomes
The initial value X of amounti(k) it is set to 1e-5；
B applies load to plate-girder discrete model and freedom degree constrains；
The equivalent stress σ of each beam element is extracted in c static analysisk；
D checks whether the equivalent stress of each rebar element meets stress constraint, if σkGreater than allowable stress, and Xi(k) small
In 1, then design variable removes a value Xi+1(k)；Otherwise, design variable remains unchanged；
E repeats step c-d, carries out next round iteration；
F is respectively less than equal to the maximum of the equivalent stress of allowable stress or rebar element when the equivalent stress of all rebar elements
When value is greater than 1 greater than the unit maturity of allowable stress and the corresponding unit, iteration ends.
Preferably, the key step that the algorithm second level solves are as follows:
The global displacement that a calculates after first order optimization constrains Z1, if Z1=0, calculating terminates；
B chooses initial growth point, and number is denoted as Nc；
C selects t-th of initial growth point；
D selects the rebar element around growing point, and unit number is denoted as Et；
E allow around each rebar element evolve respectively, calculate corresponding global displacement constraint Z2.If Z2=0, knot is calculated
Otherwise beam calculates corresponding relative mistake quotient；
F makes that relative mistake quotient is negative and the smallest unit is grown, and then calculates global displacement again and constrains Z1, if Z1
=0, then calculating terminates；
H is made a living long point with another end node of rebar element after growing, if current growing point and a certain growing point weight before
Conjunction then stops growing, otherwise the repeatedly growth of step d-f progress next unit；
G repeats step c-h, grows since next initial growth point, if all to have carried out one verticillate for all initial growths point
Growth process then continues back and forth to be grown from first to a last initial growth dot cycle.
Compared with prior art, the invention has the following advantages:
This method, which can be classified, solves local stress constraint and global displacement constraint, may be implemented to reinforcing rib sectional dimension and
The double optimization of distribution form finally obtains the Optimal Distribution form of reinforcing rib.Based on the algorithm routine of ANSYS APDL language,
Have the characteristics that the degree of modularity is high, modification is simple, convenient for being solved the different structure and load working condition aiming at the problem that, has
Wide applicability.In addition, the thought of the algorithm can optimize the two and grind for topological optimization and thin-slab structure reinforced bag sand well
The development for studying carefully field provides certain theories integration.
Detailed description of the invention
Fig. 1 is a kind of technical schematic diagram of thin-slab structure reinforced bag sand well optimization method；
Fig. 2 is the connection procedure schematic diagram of shell63 shell unit Yu beam188 beam element；
Fig. 3 is the square plate stress analysis schematic diagram for being completely fixed plate face on one side by normal direction uniform load；
Fig. 4 a is the structural stress figure that static analysis is individually carried out to thin plate
Fig. 4 b is the displacement cloud atlas that static analysis is individually carried out to thin plate；
Fig. 5 a is the structural stress figure after first order optimization；
Fig. 5 b is the displacement cloud atlas after first order optimization；
Fig. 6 is the position distribution of initial growth point and succession number in the optimization process of the second level；
Fig. 7 a is the structural stress figure after the optimization of the second level；
Fig. 7 b is the displacement cloud atlas after the optimization of the second level；
Fig. 8 a is the structural stress figure for the thin plate reinforcement that " two " font is laid out under identical reinforcing rib quality；
Fig. 8 b is the displacement cloud atlas for the thin plate reinforcement that " two " font is laid out under identical reinforcing rib quality；
Fig. 9 a is the structural stress figure for the thin plate reinforcement that " well " font is laid out under identical reinforcing rib quality；
Fig. 9 b is the displacement cloud atlas for the thin plate reinforcement that " well " font is laid out under identical reinforcing rib quality；
Figure 10 a is the structural stress figure for the thin plate reinforcement that " rice " font is laid out under identical reinforcing rib quality；
Figure 10 b is the displacement cloud atlas for the thin plate reinforcement that " rice " font is laid out under identical reinforcing rib quality.
Specific embodiment
Below with reference to the attached drawing exemplary embodiment that the present invention will be described in detail, feature and aspect.It is identical attached in attached drawing
Icon note indicates element functionally identical or similar.Although the various aspects of embodiment are shown in the attached drawings, unless special
It does not point out, it is not necessary to attached drawing drawn to scale.
Specifically, the present invention provides a kind of thin-slab structure reinforced bag sand well optimization method, as shown in Figure 1 comprising following
Step:
Step 1: define design variable unit maturity as a factor of reinforcement height, and design variable is carried out etc.
Distance dissipates:
Since thin-slab structure is primarily subjected to normal load on face, by taking the reinforcing rib of rectangular section as an example, by the mechanics of materials
Knowledge is it is found that influence of the height to its bending resistant section coefficient of reinforcing rib is bigger, i.e., its is wide than increase for the height of increase reinforcing rib
Degree can more effectively enhancing structure performance.Therefore, reinforcing rib width is set as definite value, using the height of reinforcing rib as optimization pair
As design variable to be defined as to a factor of reinforcement height, and be named as " unit maturity ", value range is a company
Continuous section [0,1].The distribution optimization process of reinforcing rib is regarded as each rebar element from scratch, from small to large simultaneously
" gradually growing " process, 0, which represents rebar element, is not present, and 1 represents rebar element growth and maturity, and it is raw that median represents rebar element
Long is different degrees of, controls the size of reinforcement height and the going or staying of rebar element by optimization unit maturity.Unit
The relationship of maturity and reinforcement height may be expressed as:
H (k)=HmX (k) (k=1,2 ..., Ne) (1)
Wherein, H (k) is the height of k-th of rebar element；HmIt is the upper limit of reinforcement height；X (k) is k-th of reinforcement list
The unit maturity of member；Ne is rebar element sum in structure.
A factor of the unit maturity as reinforcement height, itself belongs to continuous variable.In order to by discrete variable
Sequence Two-Level Algorithm in Optimal Structure Designing handles multiple constraint problem, needs to convert discrete variable for design variable.I.e.
Progress is equidistant discrete in the continuous interval [0,1] of unit maturity, obtains the design variable value set of discretization, from
And convert the distribution optimization problem of reinforcing rib to the combination optimization problem of discrete variable.If the search in unit evolutionary process walks
A length of d, then the value set of design variable are as follows:
X (k) ∈ 0, d, 2d ..., and 1 } (d=1/n, n ∈ N+) (2)
The value of step-size in search d represents the increment of design variable in each iterative process, will have a direct impact on algorithm optimization
Solving precision, the distributional pattern for solving reinforcing rib after time and optimization.Theoretically speaking d value is smaller, then algorithm solving precision
Higher, the solution time is longer, and the distributional pattern of reinforcing rib is also closest to " optimal " form in ideal after optimization.
Step 2: local stress constraint condition being established based on Von mises yield criterion, is established based on unified constraint function
Global displacement constraint condition establishes the two-stage optimizing model of algorithm based on the thought that classification solves, specifically includes the following steps:
Step 201: in structural section optimization, handled problem is mostly statically indeterminate problem, generallys use static determinacyization vacation
If statically indeterminate structure is simplified to statically determinate structure, that is, think that the internal force distribution of unit is not influenced by element stiffness variation.It is based on
Constraint condition it is assumed that can be divided into locality constraint condition and globality (overall situation) constraint condition by this, wherein stress constraint
Belong to locality constraint condition, displacement constraint belongs to globality constraint condition.
For stress constraint, the stress of unit can be changed by changing the geometric dimension of rebar element, to make every
The stress of one rebar element all meets stress constraint condition.The expression formula of local stress constraint condition are as follows:
σk≤[σ]k(k=1,2 ..., Ne) (3)
Wherein, σkIt is the stress of k-th of rebar element, [σ]kBe the allowable stress of k-th of rebar element (under normal circumstances
The allowable stress of each rebar element is identical).
In structure optimization, usual stress constraint condition be in order to guarantee structural material do not occur Strength Failure (plasticity bend
Clothes or brittle fracture), therefore stress constraint condition can be established by strength theory.The present invention is in Von Mises yield criterion
On the basis of, the Materials Yield Limit in Von Mises yield criterion is replaced with the proportional limit of material, guarantees that structural material is only sent out
Raw linear elastic deformation, and consider design safety factor (DSF), certain stress surplus is reserved, the expression of final local stress constraint is obtained
Formula:
Wherein, σkIt is the equivalent stress of k-th of rebar element, σ1σ2σ3It is the first, second and third principal stress respectively；σpIt is material
Proportional limit；N is safety coefficient；[σ] is allowable stress.
Step 202: for displacement constraint, the single displacement constraint by node each in structure being needed to combine, realized
The comprehensive of each nodal Displacement Constraint solves.The displacement of each node corresponds to a displacement constraint in structure, belongs to mostly about
Beam optimization problem.Using unified constraint function building global displacement constraint, the specific method is as follows:
Note structure interior joint sum is Nn, and each modal displacement is δl, it is corresponding it is allowable displacement beSo
Each displacement constraint is divided into inactivce constraints and operative constraint according to whether each modal displacement meets corresponding displacement allowable afterwards.
If modal displacement is not more than displacement allowable, this is constrained to inactivce constraints；Otherwise if modal displacement, greater than displacement allowable, this is about
Beam is operative constraint.
Wherein, Ni is the number of inactivce constraints；Nj is the number of operative constraint.
The form that operative constraint is transformed into constraint function is as follows:
Two norms are taken to constraint function again, obtain the expression formula of global displacement constraint are as follows:
The necessary and sufficient condition for meeting whole displacement constraints is Z (x)=0.The essence of global displacement constraint condition is exactly from feasible
Collection is outer a little to set out, search one by one iteration, and each modal displacement greater than displacement allowable is made gradually to level off to displacement allowable.
Step 203: establishing a kind of thin-slab structure reinforced bag sand well optimization method by target of reinforcing rib gross mass in structure
Mathematical model, principle is exactly that one group of numerical value is found in the value set of each rebar element unit maturity, and structure is made to exist
Under the premise of meeting local stress constraint and global displacement constraint, the gross mass of reinforcing rib is most light, this group of unit maturation degree
Value is exactly final optimization solution, and corresponding reinforcing rib size and distribution are exactly the reinforced bag sand well form after optimization.
Monotonicity based on constraint condition is assumed and classification solves thought and solves to above-mentioned mathematical model.The first order is first
Stress constraint is solved, then using its optimization solution as the value lower limit of design variable in the optimization of the second level.Due to stress constraint function
It is monotone decreasing about design variable, therefore in the solution procedure of the second level, stress constraint is to meet always, only needs list
Displacement constraint is solely solved, the resulting optimization solution in the second level that is to say the optimal solution for meeting and all constraining.
Step 3 establishes the finite element plate-girder discrete model that reinforcing rib is in the distribution of " rice " font, and each rebar element is designed and is become
Amount initialization, the initial configuration as optimization；
The shell63 shell unit and beam188 beam element selected in ANSYS carry out building for finite element plate-girder discrete model
It is vertical, i.e., grid dividing is carried out to substrate with shell unit, shell unit node is attached with beam element between any two, and being formed is in " rice "
The reinforcement distribution form of font.Fig. 2 is the connection procedure schematic diagram of shell63 shell unit Yu beam188 beam element.
Since there are two distinct types of units in structure, it is therefore desirable to consider the connection between different units, i.e., in fact
The coupling of existing cell node freedom degree, guarantees structure each point displacement coordination.Plate-girder discrete model central sill cell node and shell unit
Node is not overlapped, but it includes the situation in shell surface that the connection type of two kinds of units, which belongs to beam, therefore only need to be by beam element
Node bias certain distance is overlapped, i.e. common points with shell unit node, without setting up the displacement coordination equation at node.
It is programmed using ANSYS Parametric Design Language APDL (ANSYS Parameter Design Language),
Realize the parametric modeling of plate-girder discrete model.Key step is as follows:
The modeling of a thin plate, and with shell63 to thin plate grid division, note Shell Finite Element node total number is N；
B chooses i-th of node, referred to as central node, generates key point Ki by node；
C chooses in the node of " rice " font distribution around node i, and sum is denoted as n；
D surroundings nodes sort from small to large by number, and successively generate corresponding key point Kj respectively；
E establishes straight line by key point Ki and Kj, with beam188 to straight line grid division；
F repeats step e, when j is greater than n, stops iteration；
G repeats step b~f, when i is greater than N, program determination.
Wherein, by adjusting grid dividing number in step a, the plate-girder discrete model of available different shape.
Step 4 carries out first order solution using linear search method, using opposite on the basis of first order optimum results
Difference coefficient method carries out second level solution, the reinforced bag sand well form after being optimized.
Its basic thought of linear search method is, since first value of design variable, successively by design variable generation
Enter constraint condition, if constraint condition is unsatisfactory for, design variable removes a value, until meeting constraint condition.Specific to calculation
It is exactly by each rebar element design variable X in method first order solution procedurei(k) Optimized model is substituted into, corresponding unit etc. is extracted
Efficacy, checks whether each unit equivalent stress meets local stress constraint condition.If satisfied, then XiIt (k) is that the unit is set
Count the optimal value of variable；If not satisfied, then design variable removes a value Xi+1(k), Optimized model is substituted into again and solve verifying, directly
Until meeting local stress constraint condition.Finally obtain the optimization solution of the algorithm first order are as follows:
X#={ X#(1),X#(2),…,X#(Ne)} (8)
It is substantially exactly set composed by the optimal value of unit maturity when each rebar element meets local stress constraint.
The key step that the algorithm first order solves are as follows:
Beam element sum is denoted as Ne in a plate-girder discrete model, and design variable step-size in search is set as d, and each beam element design becomes
The initial value X of amounti(k) it is set to 1e-5；
B applies load to plate-girder discrete model and freedom degree constrains；
The equivalent stress σ of each beam element is extracted in c static analysisk；
D checks whether the equivalent stress of each rebar element meets stress constraint, if σkGreater than allowable stress, and Xi(k) small
In 1, then design variable removes a value Xi+1(k)；Otherwise, design variable remains unchanged；
E repeats step cd, carries out next round iteration；
F is respectively less than equal to the maximum of the equivalent stress of allowable stress or rebar element when the equivalent stress of all rebar elements
When value is greater than 1 greater than the unit maturity of allowable stress and the corresponding unit, iteration ends.
The value lower limit of design variable in being optimized using the optimum results of the first order as the second level, adds after first order optimization
On the basis of strengthening tendons distributional pattern, using Relative Difference Quotient Algorithm, the second level Optimization Solution of algorithm is carried out.
Relative mistake quotient is defined as design variable xiBy current value xi,kChange to next discrete value xi,k+1When, constraint function
Difference coefficient and objective function difference coefficient ratio.
The physical significance of relative mistake quotient is exactly the increment of the constraint function when objective function has unit increment.With minimum
It turns in the optimization design of target, generally to make target function value minimum while meeting constraint condition, this requires work as to set
Count variable xiBy current value xi,kChange to next discrete value xi,k+1When, objective function increases at least, while constraint function reduces most
It is more, i.e., using the smallest direction of relative mistake quotient as the direction of search, the discrete point of design variable is searched for one by one, is found every
The optimal value of one design variable, finally obtains the optimal solution of entire optimization problem.
By in algorithm optimization model objective function and global displacement constraint function substitute into opposite difference coefficient formula and can obtain:
The evolution and " growth " of rebar element are determined with the size of relative mistake quotient.As unit maturity xiBy current value
xi,kChange to next discrete value xi,k+1When, if its relative mistake quotient is negative value, illustrate that " growth " of the unit can reduce structure
Global displacement；If relative mistake quotient is nonnegative value, illustrates that " growth " of the unit cannot reduce and even increase structure
Global displacement, such unit needs to forbid its " growth ".Therefore, in the unit for waiting for " growing " at one group, relative mistake quotient
It is negative and the smallest unit contributes structure global displacement maximum, namely increase the unit maturity of the unit and can maximumlly subtract
Small structure global displacement, such unit need preferential " growth ".
The key step that the algorithm second level solves are as follows:
(1) global displacement after calculating first order optimization constrains Z1, if Z1=0, calculating terminates；
(2) initial growth point is chosen, number is denoted as Nc；
(3) t-th of initial growth point is selected；
(4) rebar element around growing point is selected, unit number is denoted as Et；
(5) allow around each rebar element evolve respectively, calculate corresponding global displacement constraint Z2.If Z2=0 is calculated
Terminate, otherwise, calculates corresponding relative mistake quotient；
(6) make relative mistake quotient be negative and the smallest unit carry out " growth ", then again calculate global displacement constraint Z1,
If Z1=0, calculating terminates；
(7) it is made a living long point with another end node of " growth " rebar element afterwards, if current growing point and a certain growth before
Point is overlapped and (forms closed loop), then stops " growing ", otherwise repeatedly " growth " of step (4)~(6) progress next unit；
(8) step (3)~(7) are repeated, since next initial growth point " growth ".If all initial growth points all carry out
One wheel " growth " process, then continuation back and forth carries out " growth " from first to a last initial growth dot cycle.
So far, a kind of its basic principle introduction of thin-slab structure reinforced bag sand well optimization method according to the present invention finishes,
Illustrate how the present invention applies in practice below with reference to specific example.
Example: the square thin plate being completely fixed on one side, side length 0.3m, plate thickness 0.008m, plate face are uniformly carried by normal direction
Lotus Q=40000N, material are 45 steel, elastic modulus E=206Gpa, Poisson's ratio 0.3, density 7850kg/m3, yield strength
For 246Mpa, proportional limit 205Mpa, stress safety coefficient is set as 2.5, and structure maximum distortion is no more than 0.5mm.
It can be obtained by known conditions, allowable stress 82Mpa, displacement (maximum distortion) allowable is 0.5mm.Fig. 3 is complete on one side
Square plate stress analysis schematic diagram of the complete fixed plate face by normal direction uniform load.
Static analysis individually is carried out to thin plate first, the maximum value for obtaining equivalent stress in structure is 164Mpa, perpendicular to
The maximum displacement of board direction is 4.368mm.Obviously it is unsatisfactory for design requirement, it is therefore desirable to the cloth on the back side of thin plate stress surface
Certain reinforcing rib is set, with enhancing structure mechanical property.Fig. 4 a is the structural stress figure that static analysis is individually carried out to thin plate, figure
4b is the displacement cloud atlas that static analysis is individually carried out to thin plate.
Corresponding finite element plate-girder discrete model is established, each rebar element design variable initial value is set to 1e-5, is designed
Variable step-size in search is taken as 1/8, and the first order for carrying out algorithm to upper example solves.The maximum value for obtaining equivalent stress in structure is
81.8Mpa, the maximum displacement perpendicular to board direction are 1.445mm, and reinforcing rib gross mass is 0.4664kg in structure at this time.It is excellent
Change result and although meet stress constraint requirement, but be unsatisfactory for displacement constraint requirement, it is therefore desirable to carry out algorithm on this basis
The second level solves.
The initial growth point that the node on restrained boundary optimizes as the second level is chosen, by the succession of initial growth point
Successively carry out " growth " process of reinforcing rib.It is 49Mpa that equivalent stress maximum value in structure is obtained after optimization, perpendicular to plate face side
To maximum displacement be 0.509mm, in allowable range of error, optimum results meet stress and displacement constraint requirement.Most terminate
Reinforcing rib gross mass is 1.312kg in structure, and thin plate quality is 5.652kg, and reinforcing rib quality accounts for about the 23.2% of thin plate quality.
Fig. 5 a is the structural stress figure after first order optimization；Fig. 5 b is the displacement cloud atlas after first order optimization；Fig. 6 is that the second level optimized
The position distribution of initial growth point and succession number in journey；Fig. 7 a is the structural stress figure after the optimization of the second level；Fig. 7 b is
Displacement cloud atlas after the optimization of the second level.
Traditional " two " font, " well " font, " rice " font distribution form are pressed respectively with the reinforcing rib material of phase homogenous quantities
The distribution design for carrying out reinforcing rib, compares and analyzes the mechanical property of the thin plate reinforced structure of various distribution forms.Fig. 8 a
It is the structural stress figure for the thin plate reinforcement that " two " font is laid out under identical reinforcing rib quality；Fig. 8 b is under identical reinforcing rib quality
The displacement cloud atlas of the thin plate reinforcement of " two " font layout；Fig. 9 a is the thin plate reinforcement that " well " font is laid out under identical reinforcing rib quality
Structural stress figure；Fig. 9 b is the displacement cloud atlas for the thin plate reinforcement that " well " font is laid out under identical reinforcing rib quality；Figure 10 a is phase
With the structural stress figure for the thin plate reinforcement that " rice " font under reinforcing rib quality is laid out；Figure 10 b is under identical reinforcing rib quality " rice "
The displacement cloud atlas of the thin plate reinforcement of font layout.
The thin plate reinforced structure mechanical property comparison of different distribution forms under the identical reinforcing rib quality of table 1
As can be seen from Table 1, reinforced with identical reinforcing rib quality by three of the above tradition reinforcing rib distribution form
Muscle distribution designs resulting result and stress and displacement constraint requirement is not satisfied, so that it is thin to have proved one kind according to the present invention
Hardened structure reinforced bag sand well optimization method can effectively deal with thin-slab structure reinforced bag sand well optimization problem and can realize the light of structure
Quantization.
Finally, it should be noted that above-described embodiments are merely to illustrate the technical scheme, rather than to it
Limitation；Although the present invention is described in detail referring to the foregoing embodiments, those skilled in the art should understand that:
It can still modify to technical solution documented by previous embodiment, or to part of or all technical features into
Row equivalent replacement；And these modifications or substitutions, it does not separate the essence of the corresponding technical solution various embodiments of the present invention technical side
The range of case.
Claims (10)
1. a kind of thin-slab structure reinforced bag sand well optimization method, it is characterised in that: itself the following steps are included:
S1, the height factors that design variable unit maturity is reinforcing rib are defined, design variable is carried out equidistant discrete；
S2, local stress constraint condition is established based on Von mises yield criterion, global displacement is established based on unified constraint function
Constraint condition establishes the two-stage optimizing model of algorithm based on the thought that classification solves；
S3, the finite element plate-girder discrete model that reinforcing rib is in M shape is established, each rebar element design variable is initialized, as
The initial configuration of optimization；
S4, first order solution is carried out using linear search method, Relative Difference Quotient Algorithm is used on the basis of first order optimum results
Second level solution is carried out, the reinforced bag sand well form of optimizing is obtained.
2. thin-slab structure reinforced bag sand well optimization method according to claim 1, it is characterised in that: step S1 is specifically included
Following steps:
S11, reinforcing rib width is set as definite value, using the height of reinforcing rib as optimization object, design variable is defined as reinforcing
The height factors of muscle, and it is named as unit maturity, value range is a continuum [0,1], and 0, which represents rebar element, does not give birth to
Long, 1 represents rebar element growth and maturity, and median represents the differing maturity of rebar element growth, mature by optimization unit
Degree controls the height of reinforcing rib and the going or staying of rebar element, and the relationship of unit maturity and reinforcement height may be expressed as:
H (k)=HmX (k) (k=1,2 ..., Ne)
Wherein, H (k) is the height of k-th of rebar element；HmIt is the upper limit of reinforcement height；X (k) is k-th of rebar element
Unit maturity；Ne is rebar element sum in structure；
S12, discrete variable is converted by design variable, it is equidistant discrete to continuous interval [0, the 1] progress of unit maturity,
The design variable value set of discretization is obtained, if the step-size in search in unit evolutionary process is d, then the value collection of design variable
It is combined into:
X (k) ∈ 0, d, 2d ..., and 1 } (d=1/n, n ∈ N+)
Wherein, the value of step-size in search d represents the increment of design variable in each iterative process.
3. thin-slab structure reinforced bag sand well optimization method according to claim 1, it is characterised in that: step S2 specifically includes
Following steps:
S21, the Materials Yield Limit in VonMises yield criterion is replaced with the proportional limit of material, occurs that structural material only
Linear elastic deformation, and consider design safety factor (DSF), allowable stress is acquired, and then construct local stress constraint condition；
S22, the displacement constraint of node each in structure is divided into operative constraint and inactivce constraints, ignores inactivce constraints, using unified
Multiple operative constraints are converted a constraint condition by constraint function, i.e., takes two norms to each operative constraint, constructs global displacement
Constraint condition；
S23, classification solve stress and displacement two classes constraint, and the first order first solves local stress constraint, reduces design variable rapidly
Value range, then on this basis, carry out the constraint of second level global displacement fine solution.
4. thin-slab structure reinforced bag sand well optimization method according to claim 3, it is characterised in that: part in step S21
The expression formula of stress constraint:
Wherein, σkIt is the equivalent stress of k-th of rebar element, σ1σ2σ3It is that first principal stress, second principal stress, third master answer respectively
Power；σpIt is the proportional limit of material；N is safety coefficient；[σ] is allowable stress.
5. thin-slab structure reinforced bag sand well optimization method according to claim 3, it is characterised in that: used in step S22
Unified constraint function building global displacement constraint, the specific method is as follows:
The finite element model interior joint sum that S221, note are not added with the thin-slab structure of reinforcing rib is Nn, and each modal displacement is δl, right
The displacement allowable answered isThen whether corresponding displacement allowable is met for each displacement according to each modal displacement
Constraint condition is divided into inactivce constraints and operative constraint, if modal displacement is not more than displacement allowable, this is constrained to inactivce constraints；If
Modal displacement is greater than displacement allowable, then this is constrained to operative constraint；
Wherein, Ni is the number of inactivce constraints；Nj is the number of operative constraint；
S222, the form that operative constraint is transformed into constraint function are as follows:
S223, two norms are taken to constraint function, obtain the expression formula of global displacement constraint are as follows:
The necessary and sufficient condition for meeting whole displacement constraints is Z (x)=0.
6. thin-slab structure reinforced bag sand well optimization method according to claim 1, it is characterised in that: in step S4, optimization
Reinforced bag sand well form afterwards includes two parameters of rebar element sectional dimension and distributing position.
7. thin-slab structure reinforced bag sand well optimization method according to claim 6, it is characterised in that: establishing in step S3 has
Limit first plate-girder discrete model specifically includes the following steps:
S31, shell63 shell unit and beam188 beam element in ANSYS is selected to carry out building for finite element plate-girder discrete model
It is vertical, grid dividing is carried out to substrate with shell unit, shell unit node is attached with beam element between any two, forms M shape
Reinforce distributional pattern；
S32, it is programmed using ANSYS Parametric Design Language APDL, realizes the parametric modeling of plate-girder discrete model, mainly
Steps are as follows:
The modeling of a thin plate, and with the plate unit shell63 in ANSYS to thin plate grid division, note Shell Finite Element node total number is N；
B chooses i-th of node, referred to as central node, generates key point Ki by node；
C chooses in the node of M shape distribution around node i, and sum is denoted as n；
D surroundings nodes sort from small to large by number, and sequentially generate corresponding key point Kj；
E establishes straight line by key point Ki and Kj, with beam element beam188 to straight line grid division；
F repeats step e, when j is greater than n, stops iteration；
G repeats step b~f, when i is greater than N, program determination；
Wherein, by adjusting grid dividing number in step a, the plate-girder discrete model of available different shape.
8. thin-slab structure reinforced bag sand well optimization method according to claim 1, it is characterised in that: step S4 is specifically included
Following steps:
S41, by each rebar element design variable Xi(k) Optimized model is substituted into, corresponding unit equivalent stress is extracted, checks each list
Whether first equivalent stress meets local stress constraint condition, if satisfied, then Xi(k) be the unit design variable optimal value；
If not satisfied, then design variable removes a value Xi+1(k), Optimized model is substituted into again and solve verifying, until meeting local stress about
Until beam condition, the optimization solution of the algorithm first order is finally obtained are as follows:
X#={ X#(1),X#(2),…,X#(Ne)}；
S42, using the optimum results of the first order as the second level optimization in design variable value lower limit, the first order optimization after plus
On the basis of strengthening tendons distributing position, using Relative Difference Quotient Algorithm, the second level Optimization Solution of algorithm is carried out.
9. thin-slab structure reinforced bag sand well optimization method according to claim 8, it is characterised in that: the algorithm first order solves
Key step are as follows:
Beam element sum is denoted as Ne in a plate-girder discrete model, and design variable step-size in search is set as d, each beam element design variable
Initial value Xi(k) it is set to 1e-5；
B applies load to plate-girder discrete model and freedom degree constrains；
The equivalent stress σ of each beam element is extracted in c static analysisk；
D checks whether the equivalent stress of each rebar element meets stress constraint, if σkGreater than allowable stress, and Xi(k) less than 1,
Then design variable removes a value Xi+1(k)；Otherwise, design variable remains unchanged；
E repeats step c-d, carries out next round iteration；
F is big when the maximum value that the equivalent stress of all rebar elements is respectively less than the equivalent stress for being equal to allowable stress or rebar element
When the unit maturity of allowable stress and corresponding unit is not less than 1, iteration ends.
10. thin-slab structure reinforced bag sand well optimization method according to claim 9, it is characterised in that: ask the algorithm second level
The key step of solution are as follows:
The global displacement that a calculates after first order optimization constrains Z1, if Z1=0, calculating terminates；
B chooses initial growth point, and number is denoted as Nc；
C selects t-th of initial growth point；
D selects the rebar element around growing point, and unit number is denoted as Et；
E allow around each rebar element evolve respectively, calculate corresponding global displacement constraint Z2.If Z2=0, calculating terminates,
Otherwise, corresponding relative mistake quotient is calculated；
F makes that relative mistake quotient is negative and the smallest unit is grown, and then calculates global displacement again and constrains Z1, if Z1=0,
Then calculating terminates；
H is made a living long point with another end node of rebar element after growing, if current growing point with if a certain growing point is overlapped before
It stops growing, otherwise the repeatedly growth of step d-f progress next unit；
G repeats step c-h, grows since next initial growth point, grows if all initial growths point has all carried out a wheel
Journey then continues back and forth to be grown from first to a last initial growth dot cycle.
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