CN103034766B - A kind of laying angular direction of definite Test of Laminate Composites and the method for thickness - Google Patents

Abstract

A kind of laying angular direction of definite Test of Laminate Composites and the method for thickness, step: (1) is set up Test of Laminate Composites and designed a model, discrete variable in model is converted into continuous variable, and the corresponding constraint of increase, generate several particles according to specific initialization scheme, the coordinate figure of each particle is a design; (2) recording the coordinate figure of each particle when initial is individual optimal case, and then obtains global optimum's design; (3) first utilize population method for designing to upgrade the position of particle, carry out different maximum iteration time Mathematical Plannings designs according to particle dissimilar; (4) obtain the potential design of new Test of Laminate Composites and upgrade individual and global optimum's design; (5) judge whether to meet the condition of convergence, if do not met and forward (3) to; (6) design using the laying direction after the laying thickness in global optimum's design and rounding as final Test of Laminate Composites.

Description

A kind of laying angular direction of definite Test of Laminate Composites and the method for thickness

Technical field

The present invention relates to composite optimized design method field, particularly a kind of particle swarm optimization and Mathematical Planning phaseIn conjunction with the laying angular direction of definite Test of Laminate Composites and the method for thickness.

Background technology

Test of Laminate Composites, by high strength, low-density fibrous material and matrix composition, has higher than traditional materialSpecific strength and specific modulus, be used widely at the industrial circle such as Aero-Space, automobile. But, because laminate is compoundMaterial has anisotropy, so close relations such as its performance and laying angles. In the time that labyrinth bears complex load,With respect to ordinary metallic material, its corresponding structural design also becomes more complicated. The modular design of Test of Laminate Composites becomesAmount is laying angle, laying thickness. Due to the restriction of processing technology, in laminate, the laying angle of each lamina generally can not be continuousValue, conventionally only selects the angle of several comparison rule, and as 0 °, 30 °, 45 ° etc., and the thickness of lamina generally can be continuouslyIn variable, choose. Therefore, the optimal design of Test of Laminate Composites belongs to hybrid optimization design, comprises continuous design variable(laying thickness), comprises again discrete design variable (laying angle). In addition, because Compound Material Engineering characteristic is very complicated, orderScalar functions and constraints are of a great variety, many times need to carry out global optimization. Current method for designing mainly contains based on micro-The method, enumerative technique, stochastic search methods and the heuristic search that divide, but because the computational efficiency of existing algorithm is too low,Therefore be not suitable for the Test of Laminate Composites design of multiple design variables.

Colony intelligence optimization method is the another kind of method of Test of Laminate Composites optimal design, colony intelligence optimization method excellentGesture is that its method for designing is simple, is easy to realize, and has certain of overall importance; But particle group optimizing method also exists calculatingAmount is large, restrain the shortcomings such as slow.

Adopt and based on markoff process, the optimizing characteristic of particle group optimizing method is analyzed, utilize semi analytical method to obtainTo the probability density distribution of particle one dimension design variable X in normed space under different inertia weight ω as shown in Figure 1Situation; Its analytical expression is:

$\mathrm{\ρ}\left(X_{i,d}\right(t\left)\right)=\frac{1}{a\left(\mathrm{\ω}\right)+|X_{i,d}{|}^{b\left(\mathrm{\ω}\right)}}/{\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}\frac{1}{a\left(\mathrm{\ω}\right)+|X{|}^{b\left(\mathrm{\ω}\right)}}dX---\left(1.a\right)$

In formula (1.a),

a(ω)＝0.4446+0.4555ω+1.675ω²-6.7103ω³+9.3196ω⁴

(1.b)

b(ω)＝1.7728+5.0184ω-6.3798ω²+4.052ω³-5.2016ω⁴

Above-mentioned normed space is to utilize the actual space of living in of particle to carry out the space that linear transformation obtains, and transformation for mula is:Mid_i,d(t) be the intermediate value of the coordinate of particle global optimum's point and individual optimum point, L_i,d(t) grainThe distance of sub-global optimum's point and individual optimum point.

Formula (1.a) is carried out to numerical integration, obtain particle one dimension standard design scheme X as shown in Figure 23 kinds of scopesThe probability density curve of the different inertia weight ω of lower correspondence; The above results shows from different perspectives, and particle is tool in optimizing processThere is the strong probability ergodic of concentrating; This strong ergodic causes population convergence slowly and can not escape locally optimal solutionReason;

Due to the Test of Laminate Composites method for designing based on Mathematical Planning and population Test of Laminate Composites design sideMethod all can be absorbed in locally optimal plan to some extent with different mechanism, and usually these designs can be brought a large amount of waves of materialExpense and bring certain unsafe factor; Therefore, existing Optimization Design is established for complicated Test of Laminate CompositesMeter problem is difficult to find the optimization design scheme (for example weight is the lightest, Buckling Critical Load maximum etc.) of Test of Laminate Composites,Even obtain a very poor design: waste a large amount of materials and even do not reach required application and safety requirements.

Summary of the invention

Technology of the present invention deals with problems: overcome the deficiencies in the prior art, a kind of definite Test of Laminate Composites is providedThe method of laying angular direction and thickness obtains global optimum's Test of Laminate Composites structural design ginseng in reducing amount of calculationNumber.

The technology of the present invention solution: a kind of laying angular direction of definite Test of Laminate Composites and the method for thickness, baseIn Hybrid particle swarm optimization method and Mathematical Planning given layer plywood composite Materials Design method really, comprise the following steps:

(1) taking the laying angular direction of Test of Laminate Composites and thickness as design variable, with the matter of Test of Laminate CompositesAmount minimum or Buckling Critical Load are design object f (x to the maximum_C1,x_C2,...,x_Cd,x_D1,x_D2,...,x_Ds), multiple with laminateThe allowable stress of condensation material and the displacement of assigned position are constraints g_j(x_C1,x_C2,...,x_Cd,x_D1,x_D2,...,x_Ds)，jFor constraint numbering, the number of m representative constraint, set up the optimization row formula of Test of Laminate Composites design:

$\left\{\begin{array}{ccc}\min & f(x_{C1},x_{C2},...,x_{Cd},x_{D1},x_{D2},...,x_{Ds})& \\ s.t.& g_j(x_{C1},x_{C2},...,x_{Cd},x_{D1},x_{D2},...,x_{Ds})\≤0,& j=0,1,...,m\\ & x_{Cl}^L\≤x_{Cl}\≤x_{Cl}^U,l=1,2,...,d& \\ & x_{Di}\∈\left\{{\mathrm{qa}}_{Di}\right\},q=0,1,...,M_{Di},i=1,2,...,s& \end{array}\right.---\left(1\right);$

Wherein x_C1,x_C2,...,x_CdFor continuous variable, represent the thickness in monolayer of Test of Laminate Composites, d is continuous variableNumber; x_D1,x_D2,...,x_DsFor discrete variable, represent the laying angular direction of Test of Laminate Composites, what s was discrete variable is individualNumber; a_DiRepresent that laying angular direction chooses specification, M_DiFor x_DiThe multiple of specification is chosen in the maximum laying angular direction that can select;For lower bound and the upper bound of continuous design variable; { qa_Di}，q＝0,1,...,M_DiFor comprising x_DiSelectable laying angleDirection discrete set;

Then adopt continuous variable x_d1,x_d2,...,x_dsTo the discrete variable x in above-mentioned optimization row formula_D1,x_D2,...,x_DsReplace; In optimization row formula, introduce discrete variable constraint simultaneouslya_iFor at g_m+1In make x_diFinal optimization pass result meet the adjustment coefficient of discrete variable condition, a_i＝2π/a_Di, ε is predefined little value; ?End form becomes the continuous variable design row formula of Test of Laminate Composites:

$\left\{\begin{array}{ccc}\min & f(x_{C1},x_{C2},...,x_{Cd},x_{d1},x_{d2},...,x_{ds})& \\ s.t.& g_j(x_{C1},x_{C2},...,x_{Cd},x_{d1},x_{d2},...,x_{ds})\&le;0,& j=0,1,...,m\\ & g_{m+1}=\underset{i=1}{\overset{s}{\&Sigma;}}{(1-\cos (a_i{x}_{di}\left)\right)}^2<\mathrm{\&epsiv;}& \\ & x_{Cl}^L\&le;x_{Cl}\&le;x_{Cl}^U,l=1,2,...,d& \\ & 0\&le;x_{di}\&le;M_{Di}{a}_{Di},i=1,2,...,s& \end{array}\right.---\left(2\right);$

Then in the variable space surrounding at the bound of described design variable, generate N particle, in each particle, compriseThe position x of particle_iAnd speed v_iTwo state vectors, i represents the numbering of particle; The position x of particle_i＝(x_i,C1,x_i,C2,...,x_i,Cd,x_i,d1,x_i,d2,...,x_i,ds) be the vector of a design variable composition, the position of particle is potential optimal design,The position of each particle is a design; Each particle rapidity vector v_i＝(v_i,C1,v_i,C2,...,v_i,Cd,v_i,d1,v_i,d2,...,v_i,ds) represent the size of change in location when next update; Part particle position is equal on variable space leading diagonalEven generation, the position of other particle generates at random in the variable space, and the speed of all particles all generates at random;

Finally with described design object and constraints, to the original design scheme x of the N of an above generation particle_i′(0)，Adopt respectively Mathematical Planning method for designing to be no more than n₀Inferior optimal design, and by the design x obtaining_i(0) as grainThe preliminary design scheme of subgroup;

(2) adopt FInite Element or analytic method to carry out mechanical analysis to Test of Laminate Composites, obtain laminate compoundThe stress of each laying of material and the displacement of assigned position; According to above mechanical analysis result, computation layer plywood composite woodThe design object gross weight of material or the functional value of maximum Critical Buckling Load and constraints; Then calculate each particle orderOffer of tender numerical value $L\left(x_i\right)=f\left(x_i\right)+(1+\mathrm{\&alpha;}|f\left(x_i\right)\left|\right)\left(\underset{j=1}{\overset{m+1}{\&Sigma;}}\right|max\left(0,g_j\left(x_i\right)\right)\left|\right),$ F () is the company of Test of Laminate CompositesDesign object in continuous Variational Design row formula, the inequality in the continuous variable design row formula that g () is Test of Laminate CompositesConstraint, α is penalty factor; Sort from small to large, select two particles of target function value minimum, record this two particlesTarget function value and position as the design gbest of global optimum₁(0)＝(gbest_1,C1(0),...,gbest_1,Cd(0),gbest_1,d1,...,gbest_1,ds) and overall Suboptimal Design scheme gbest (0)₂(0)＝(gbest_2,C1(0),...,gbest_2,Cd(0),gbest_2,d1,...,gbest_2,ds(0)), recording now N particle position is individual optimization design schemepbest_i(0)＝(pbest_i,C1(0),...,pbest_i,Cd(0),pbest_i,d1,...,pbest_i,ds(0))；

(3) choose during evolution gbest_1,pAnd gbest (k)_2,p(k) intermediate value is as nominal optimization design scheme, pRepresent any one dimension, k is the iterations having completed, and recycles the position x of current particle_iAnd speed v (k)_i(k), adopt grainSubgroup method for designing is evolved and is obtained the reposition x of particle the Position And Velocity of N particle_i' (k+1) with new speed v_i(k+1); The finally distance in normed space according to the particle after evolving $B_{i,p}(k+1)=abs\left(\frac{x_{i,p}^{\&prime;}(k+1)-\&lsqb;\left({\mathrm{gbest}}_{1,p}\right(k)+{\mathrm{gbest}}_{2,p}\left(k\right))/2+{\mathrm{pbest}}_{i,p}\left(k\right)\&rsqb;/2}{\left({\mathrm{gbest}}_{1,p}\right(k)+{\mathrm{gbest}}_{2,p}(k\left)\right)/2-{\mathrm{pbest}}_{i,p}\left(k\right)}\right)$ Particle is classified;Dissimilar with x according to particle_i' (k+1) be initial value, adopt the continuous variable of above-mentioned Test of Laminate Composites to establishMeter row formula, carries out the Mathematical Planning design of different maximum iteration time, by the Mathematical Planning side of design to Test of Laminate CompositesMethod obtains the reposition of N particle, i.e. the design x of N new Test of Laminate Composites_i(k+1)；

(4) first adopt the Test of Laminate Composites of FInite Element or the analytic method reposition representative to N particleDesign is carried out mechanical analysis, obtains the stress of each laying and the displacement of assigned position of Test of Laminate Composites, meterCalculate the design object of Test of Laminate Composites; Then calculate and finally obtain N the target function value L that particle is new by step (3)(x_i), this target function value is identical with step (2); The relatively fresh target functional value of N particle and the individual optimal design of recordThe target function value of scheme, if i new target function value of particle is better than the order of the individual optimization design scheme of i particleOffer of tender numerical value, is recorded as new individual optimization design scheme pbest by i particle position now_i(k+1); Finally by NIndividual particle sorts from small to large according to target function value, selects the first two minimum of a value; Comparison object functional value and the overall situation areThe relation of the target function value of excellent design and overall Suboptimal Design scheme, just replaces if less, by desired valueThe position of less particle is as the new design gbest of global optimum₁Or the inferior design gbest of global optimum (k+1)₂(k+1)；

(5), if the target function value of global optimum's design and overall Suboptimal Design scheme is quite approaching, stop meterCalculate, carry out step (6), otherwise the value that completes iterations is increased to one, return to step (3);

(6) change of the laying angular direction of Test of Laminate Composites will be represented in the variable of the global optimum's design obtainingValue rounding is to the specification at the laying angle of regulation, by the laying direction after the laying thickness in global optimum's design and roundingAs the design of final Test of Laminate Composites;

In described step (1), Mathematical Planning method for designing comprises that sequential quadratic programming method, sequence linear programming are based on ladderSpend theoretical method, specific implementation comprises that four step: a are according to the laying thickness of current Test of Laminate Composites and laying angle sideTo, obtain the stress of each laying and the displacement of assigned position of Test of Laminate Composites by carrying out mechanical analysis, totalWeight; B solves laying thickness and laying angular direction design variable to Test of Laminate Composites weight or Buckling Critical LoadObject function and the sensitivity of the value of constraint function; C adopts sequence double optimization method or sequence linear optimization method to carry outOptimize and analyze; Stop Mathematical Planning if d reaches the iterations of regulation, otherwise forward a to.

Described in described step (1), the original design scheme of part particle is defined on the diagonal of search volume, itsThe original design scheme of remaining particle generates at random in search volume, and step is as follows: get" [] " represents to round,If N≤a, getsI=1,2 ..., the original design scheme that N is population; If N > is a,GetI=1,2 ..., a is the original design scheme of a front a particle, and all the other N-a grainsThe original design scheme x of son_i' (0), i=a+1, a+2 ..., N generates at random in search volume, and the speed of all particles is allRandom generation. x_imin,x_imaxFor the bound of design variable.

Penalty factor α span in described step (2) is 20 to 1000.

N in described step (1)₀Get 15～20.

The present invention's advantage is compared with prior art: the invention provides the new of Test of Laminate Composites structural designThinking, comprehensive and made up Mathematical Planning method for designing and population method for designing advantage and deficiency separately, can significantly reduceTo the dependence of initial designs, more easily obtain global optimum's design effective precision that improves optimal solution, large-scale and complicatedIn problem, compared with traditional particle group optimizing method, optimization efficiency can improve 1 to 2 order of magnitude, greatly reduces laminate simultaneouslyThe weight of composite structure, improves performance and security.

Brief description of the drawings

Fig. 1 is particle one dimension standard design scheme X probability density distribution cloud atlas;

Fig. 2 is the probability density curve of particle standard design scheme X corresponding different inertia weight ω under 3 kinds of scopes;

Fig. 3 is that population initial value produces schematic diagram;

Fig. 4 is that population particle moves schematic diagram;

Fig. 5 is method realization flow figure of the present invention.

Detailed description of the invention

As shown in Figure 5, given layer plywood is multiple really to the present invention proposes a kind of Hybrid particle swarm optimization method and Mathematical PlanningCondensation material method for designing, comprises the following steps:

(1) taking the laying angular direction of Test of Laminate Composites and thickness as design variable, with the matter of Test of Laminate CompositesAmount minimum or maximum flexion critical load are design object f (x_C1,x_C2,...,x_Cd,x_D1,x_D2,...,x_Ds), multiple with laminateThe allowable stress of condensation material and the displacement of assigned position are constraints g_j(x_C1,x_C2,...,x_Cd,x_D1,x_D2,...,x_Ds)，jFor constraint numbering, the number of m representative constraint, constraint numbering, set up the optimization row formula of Test of Laminate Composites design:

$\left\{\begin{array}{ccc}\min & f(x_{C1},x_{C2},...,x_{Cd},x_{D1},x_{D2},...,x_{Ds})& \\ s.t.& g_j(x_{C1},x_{C2},...,x_{Cd},x_{D1},x_{D2},...,x_{Ds})\&le;0,& j=0,1,...,m\\ & x_{Cl}^L\&le;x_{Cl}\&le;x_{Cl}^U,l=1,2,...,d& \\ & x_{Di}\&Element;\left\{{\mathrm{qa}}_{Di}\right\},q=0,1,...,M_{Di},i=1,2,...,s& \end{array}\right.;$

Wherein x_C1,x_C2,...,x_CdFor continuous variable, represent the thickness in monolayer of Test of Laminate Composites, d is continuous variableNumber; x_D1,x_D2,...,x_DsFor discrete variable, represent the laying angular direction of Test of Laminate Composites, what s was discrete variable is individualNumber; a_DiRepresent that laying angular direction chooses specification, M_DiFor x_DiThe multiple of specification is chosen in the maximum laying angular direction that can select;For lower bound and the upper bound of continuous design variable; { qa_Di}，q＝0,1,...,M_DiFor comprising x_DiSelectable layingAngular direction discrete set;

Then adopt continuous variable x_d1,x_d2,...,x_dsTo the discrete variable x in above-mentioned optimization row formula_D1,x_D2,...,x_DsReplace; In optimization row formula, introduce discrete variable constraint simultaneouslya_iFor at g_m+1In make x_diFinal optimization pass result meet the adjustment coefficient of discrete variable condition, a_i＝2π/a_Di, ε is predefined little value; ?End form becomes the continuous variable design row formula of Test of Laminate Composites:

$\left\{\begin{array}{ccc}\min & f(x_{C1},x_{C2},...,x_{Cd},x_{d1},x_{d2},...,x_{ds})& \\ s.t.& g_j(x_{C1},x_{C2},...,x_{Cd},x_{d1},x_{d2},...,x_{ds})\&le;0,& j=0,1,...,m\\ & g_{m+1}=\underset{i=1}{\overset{s}{\&Sigma;}}{(1-\cos (a_i{x}_{di}\left)\right)}^2<\mathrm{\&epsiv;}& \\ & x_{Cl}^L\&le;x_{Cl}\&le;x_{Cl}^U,l=1,2,...,d& \\ & 0\&le;x_{di}\&le;M_{Di}{a}_{Di},i=1,2,...,s& \end{array}\right.$

Then in the variable space surrounding at the bound of described design variable, generate N particle, in each particle, compriseThe position x of particle_iAnd speed v_iTwo state vectors, i represents the numbering of particle; The position x of particle_i＝(x_i,C1,x_i,C2,...,x_i,Cd,x_i,d1,x_i,d2,...,x_i,ds) be the vector of a design variable composition, the position of particle is potential optimal design,The position of each particle is a design; Each particle rapidity vector v_i＝(v_i,C1,v_i,C2,...,v_i,Cd,v_i,d1,v_i,d2,...,v_i,ds) represent the size of change in location when next update; Part particle position is equal on variable space leading diagonalEven generation, the position of other particle generates at random in the variable space, and the speed of all particles all generates at random;

The original design scheme of part particle is defined on the diagonal of search volume as shown in Figure 3, and all the other particlesOriginal design scheme in search volume at random generate, specific implementation process is as follows: get" [] " represents to getThe number whole, D is design variable: the number d of continuous variable and the number s of discrete variable and, if N≤a getsI=1,2 ..., the original design scheme that N is population; If N > is a, getI=1,2 ..., a is the original design scheme of a front a particle, and all the other N-a particleOriginal design scheme x_i' (0), i=a+1, a+2 ..., N generates at random in search volume, and the speed of all particles is all randomGenerate; Because large-scale problem design space is compared with negligible amounts large and particle, adopt the method can obtain one as far as possible evenlyPreliminary design scheme;

Finally with described design object and constraints, for the original design scheme x of N particle of above generation_i′(0), adopt respectively Mathematical Planning method for designing to be no more than n₀Inferior optimal design, and by the design x obtaining_i(0) doFor the preliminary design scheme of population;

Mathematical Planning method for designing comprises sequential quadratic programming method, the method for sequence linear programming based on gradient theory,Specific implementation comprises that four step: a are according to the laying thickness of current Test of Laminate Composites and laying angular direction, by carrying out powerEpidemiological Analysis obtains the stress of each laying and the displacement of assigned position of Test of Laminate Composites, total weight; B solves layingThe design variables such as thickness and laying angular direction to the object function of Test of Laminate Composites weight or Critical Buckling Load withThe sensitivity of the value of constraint function; C adopts sequence double optimization method or sequence linear optimization method to be optimized analysis; D asThe iterations that fruit reaches regulation stops Mathematical Planning, otherwise forwards a to.

(2) adopt FInite Element or analytic method to carry out mechanical analysis to Test of Laminate Composites, obtain laminate compoundThe stress of each laying of material and the displacement of assigned position; According to above mechanical analysis result, computation layer plywood composite woodThe design object gross weight of material and the functional value of constraints; Then calculate each particle target function value $L\left(x_i\right)=f\left(x_i\right)+(1+\mathrm{\&alpha;}|f\left(x_i\right)\left|\right)\left(\underset{j=1}{\overset{m+1}{\&Sigma;}}\right|max\left(0,g_j\left(x_i\right)\right)\left|\right),$ The continuous variable that f () is Test of Laminate Composites is establishedDesign object in meter row formula, the inequality constraints in the continuous variable design row formula that g () is Test of Laminate Composites, α isPenalty factor; α (get 20～1000 all can, generally in program realizes, get 20) for penalty factor;

Sort from small to large, select two particles of target function value minimum, record this two particle object functionsValue and position are as the design gbest of global optimum₁(0)＝(gbest_1,C1(0),...,gbest_1,Cd(0),gbest_1,d1,...,gbest_1,ds) and overall Suboptimal Design scheme gbest (0)₂(0)＝(gbest_2,C1(0),...,gbest_2,Cd(0),gbest_2,d1,...,gbest_2,ds(0)), recording now N particle position is individual optimization design schemepbest_i(0)＝(pbest_i,C1(0),...,pbest_i,Cd(0),pbest_i,d1,...,pbest_i,ds(0))；

(3) choose during evolution first as shown in Figure 4 gbest_1,pAnd gbest (k)_2,p(k) intermediate value is as nameOptimization design scheme, p represents any one dimension, k is the iterations having completed, and recycles the position x of current particle_i(k) withSpeed v_i(k), adopt population method for designing to evolve and obtain the reposition x of particle the Position And Velocity of N particle_i'(k+ 1) with new speed v_i(k+1); Every one dimension speed and the design iterative formula of i particle are respectively:

v_i,p(k+1)＝ωv_i,p(k)+C₁(pbest_i,p(k)-x_i,p(k))+C₂[(gbest_1,p(k)+gbest_2,p(k))/2-x_i,p(k)]，

x′_i,p(k+1)＝x_i,p(k)+v_i,p(k+1)

Wherein, ω is inertia weight, describes particle previous generation speed to the impact when former generation speed; C₁、C₂Respectively interval[0,c₁]、[0,c₂] upper equally distributed random number, c₁And c₂For normal number, be called accelerated factor, c₁Regulate particle to fly to individualityThe step-length of optimization design scheme, c₂Regulate particle to fly to the step-length of global optimum's design, conventionally get c₁＝c₂＝2；

According to individual optimization design scheme pbest_iAnd the design gbest of Liang Ge global optimum (k)₁And gbest (k)₂(k), calculate respectively i the every one dimension design of particle x '_i,p(k+1) gauged distance B_i,p(k+1), get

$B_{i,p}(k+1)=abs\left(\frac{x_{i,p}^{\&prime;}(k+1)-{\mathrm{Mid}}_{i,p}\left(k\right)}{\left({\mathrm{gbest}}_{1,p}\right(k)+{\mathrm{gbest}}_{2,p}(k\left)\right)/2-{\mathrm{pbest}}_{i,p}\left(k\right)}\right),$

Wherein, Mid_i,p(k)＝[(gbest_1,p(k)+gbest_2,p(k))/2+pbest_i,p(k)]/2；

Distance B according to the particle after evolving in normed space_i,p(k+1) particle is classified, according to particle notOf the same type with x_i' (k+1) be initial value, adopt the continuous variable design row formula of above-mentioned Test of Laminate Composites, carry outThe Mathematical Planning of different maximum iteration time designs, and obtains the reposition of N particle by Mathematical Planning method for designing, NThe design x of new Test of Laminate Composites_i(k+1); Concrete grammar is as follows:

According to the gauged distance B of the every one dimension design of particle_i,p(k+1) size, establishes comprising Test of Laminate CompositesThe particle of meter scheme information is classified: 1. for any 1≤p≤D, all have B_i,p(k+1)≤1.5; 2. for any 1≤p≤, at least there is a B in D_i,p(k+1) > 4.5; 3. do not satisfy condition 1. and condition particle 2. simultaneously; For the 1. class particle,Do not process; For the 2. class particle, choose at random N_B(getting 5～10) individual particle, as preliminary design scheme, utilizes mathematics ruleDraw method for designing and respectively potential design corresponding to seed designs scheme is no more than to n₁(getting 15～20) inferior optimizationIteration; For the 3. class particle, choose at random wherein two particles and, as initial value, utilize Mathematical Planning method for designing respectively to grainPotential design corresponding to sub-design is no more than n₂(getting 6～10) inferior Optimized Iterative; Will be through above-mentioned mathematicsThe new seed designs scheme that planning and designing method obtains and other untreated seed designs schemes are expressed as x_i(k+1) design while, walking as k+1 after i particle evolution; Meanwhile, with the current design gbest of global optimum₁And gbest (k)₂(k) be initial value, utilize Mathematical Planning method for designing (as sequential quadratic programming method) respectively to seed designs sidePotential design corresponding to case is no more than n₃(getting 5～10) inferior Optimized Iterative, obtains new gbest₁(k) andgbest₂(k)；

(4) first adopt the Test of Laminate Composites of FInite Element or the analytic method reposition representative to N particleDesign is carried out mechanical analysis, obtains the stress of each laying and the displacement of assigned position of Test of Laminate Composites, meterCalculate the design object of Test of Laminate Composites; Then calculate and finally obtain N the target function value L that particle is new by step (3)(x_i), this target function value is identical with step (2); The relatively fresh target functional value of N particle and the individual optimal design of recordThe target function value of scheme, if i new target function value of particle is better than the order of the individual optimization design scheme of i particleOffer of tender numerical value, is recorded as new individual optimization design scheme pbest by i particle position now_i(k+1); Finally by NIndividual particle sorts from small to large according to target function value, selects the first two minimum of a value; Comparison object functional value and the overall situation areThe relation of the target function value of excellent design and overall Suboptimal Design scheme, just replaces if less, by desired valueThe position of less particle is as the new design gbest of global optimum₁Or the inferior design gbest of global optimum (k+1)₂(k+1)；

(5), if the target function value of global optimum's design and overall Suboptimal Design scheme is quite approaching, stop meterCalculate, carry out step (6), otherwise the value that completes iterations is increased to one, return to step (3);

Meeting one of following condition stops calculating: the 1. design gbest of gained global optimum₁And gbest (k+1)₂(k+ 1) the absolute error N continuous of object function₁Inferior (getting 3～5 times) meets | gbest₁(k+1)-gbest₂(k+1)|≤ε₁；②The object function gbest of gained global optimum design₁And gbest₂Relative error N continuous₂Inferior (getting 3～5 times) meets3. reach greatest iteration step number N_max; Wherein ε₁、ε₂> 0 is pre-determined receiptsHold back precision;

(6) the laying angular direction of Test of Laminate Composites will be represented in the variable in the global optimum's design obtainingVariate-value rounding is to the specification at the laying angle of regulation, by the laying side after the laying thickness in global optimum's design and roundingTo the design of the Test of Laminate Composites as final;

In sum, the present invention proposes a kind of new method of definite Test of Laminate Composites structural parameters. Of the present inventionInitialization procedure divides two stages to implement, and first produces predecessor group, and recycling Mathematical Planning method for designing is by predecessor groupGenerate primary group, and a part in predecessor group produces at random, another part produces according to specific rule; ShouldInitialization procedure is conducive to improve primary group's quality, reduces the dependence of searching process for initial value; Be different from markThe particle evolution process of quasi particle group optimizing method, has introduced mathematics rule in the process that the present invention evolves in population designDrawing method for designing, and the result of optimizing characteristic being analyzed based on markoff process, will enter through population method for designingThe particle of changing is divided into 3 classes, as described in step (3), utilizes respectively Mathematical Planning method for designing to carry out for the second time its designEvolve; Wherein, for the 2. the processing of class particle be conducive to make design to jump out local optimum design, find betterDesign; For the 3. the processing of class particle can bring into play the effect of first two processing simultaneously; And for design side of global optimumThe processing of case particle is conducive to add near the convergence rate of fast particle local optimum design; In addition, be different from standard grainSubgroup optimization method only records global optimum's design, and the present invention records Liang Ge global optimum design, and is enteringIn change process, choose their intermediate value and carry out iteration, this is conducive to strengthen the effect of global optimizing.

Non-elaborated part of the present invention belongs to techniques well known.

Below be only concrete steps of the present invention, protection scope of the present invention is not constituted any limitation; It can be expanded shouldFor Test of Laminate Composites optimal design field, all employing equivalents or equivalence are replaced and the technical scheme of formation, allWithin dropping on rights protection scope of the present invention.

Claims (5)

1. the laying angular direction of definite Test of Laminate Composites and a method for thickness, is characterized in that performing step is as follows:

(1) taking the laying angular direction of Test of Laminate Composites and thickness as design variable, with the quality of Test of Laminate CompositesLittle or Buckling Critical Load is design object f (x to the maximum_C1,x_C2,...,x_Cd,x_D1,x_D2,...,x_Ds), with laminate composite woodThe allowable stress of material and the displacement of assigned position are constraints g_j(x_C1,x_C2,...,x_Cd,x_D1,x_D2,...,x_Ds), j is for approximatelyBundle numbering, the number of m representative constraint, set up the optimization row formula of Test of Laminate Composites design:

Wherein x_C1,x_C2,...,x_CdFor continuous variable, represent the thickness in monolayer of Test of Laminate Composites, what d was continuous variable is individualNumber; x_D1,x_D2,...,x_DsFor discrete variable, represent the laying angular direction of Test of Laminate Composites, the number that s is discrete variable;a_DiRepresent that laying angular direction chooses specification, M_DiFor x_DiThe multiple of specification is chosen in the maximum laying angular direction that can select;For lower bound and the upper bound of continuous design variable; { qa_Di}，q=0,1,...,M_DiFor comprising x_DiSelectable laying angleDirection discrete set;

Then adopt continuous variable x_d1,x_d2,...,x_dsTo the discrete variable x in above-mentioned optimization row formula_D1,x_D2,...,x_DsEnterRow is replaced; In optimization row formula, introduce discrete variable constraint simultaneouslya_iFor at g_m+1In makex_diFinal optimization pass result meet the adjustment coefficient of discrete variable condition, a_i=2π/a_Di, ε is predefined little value; End formBecome the continuous variable design row formula of Test of Laminate Composites:

Then in the variable space surrounding at the bound of described design variable, generate N particle, in each particle, comprise particlePosition x_iAnd speed v_iTwo state vectors, i represents the numbering of particle; The position x of particle_i=(x_i,C1,x_i,C2,...,x_i,Cd,x_i,d1,x_i,d2,...,x_i,ds) be the vector of a design variable composition, the position of particle is potential optimal design, eachThe position of particle is a design; Each particle rapidity vector v_i=(v_i,C1,v_i,C2,...,v_i,Cd,v_i,d1,v_i,d2,...,v_i,ds) represent the size of change in location when next update; Part particle position is equal on variable space leading diagonalEven generation, the position of other particle generates at random in the variable space, and the speed of all particles all generates at random;

Finally with described design object and constraints, for the original design scheme x of N particle of above generation_i' (0), pointDo not adopt Mathematical Planning method for designing to be no more than n₀Inferior optimal design, and by the design x obtaining_i(0) as particleGroup's preliminary design scheme;

(2) adopt FInite Element or analytic method to carry out mechanical analysis to Test of Laminate Composites, obtain Test of Laminate CompositesThe stress of each laying and the displacement of assigned position; According to above mechanical analysis result, calculating Test of Laminate CompositesThe functional value of design object gross weight or maximum Critical Buckling Load and constraints; Then calculate each particle target letterNumerical valueF () is the continuous change of Test of Laminate CompositesDesign object in amount design row formula, the inequality constraints in the continuous variable design row formula that g () is Test of Laminate Composites,α is penalty factor; Sort from small to large, select two particles of target function value minimum, record the order of these two particlesOffer of tender numerical value and position are as the design gbest of global optimum₁(0)=(gbest_1,C1(0),...,gbest_1,Cd(0),gbest_1,d1,...,gbest_1,ds) and overall Suboptimal Design scheme gbest (0)₂(0)=(gbest_2,C1(0),...,gbest_2,Cd(0),gbest_2,d1,...,gbest_2,ds(0)), recording now N particle position is individual optimization design schemepbest_i(0)=(pbest_i,C1(0),...,pbest_i,Cd(0),pbest_i,d1,...,pbest_i,ds(0))；

(3) choose during evolution gbest_1,uAnd gbest (k)_2,p(k) intermediate value is as nominal optimization design scheme, p generationShow any one dimension, k is the iterations having completed, and recycles the position x of current particle_iAnd speed v (k)_i(k), adopt particleGroup design method is evolved and is obtained the reposition x ' of particle the Position And Velocity of N particle_i(k+1) with new speed v_i(k+1); The finally distance in normed space according to the particle after evolvingParticle is classified,Dissimilar with x ' according to particle_i(k+1) be initial value, adopt the continuous variable of above-mentioned Test of Laminate Composites to establishMeter row formula, carries out the Mathematical Planning design of different maximum iteration time, by the Mathematical Planning side of design to Test of Laminate CompositesMethod obtains the reposition of N particle, i.e. the design x of N new Test of Laminate Composites_i(k+1)；

(4) the Test of Laminate Composites design of employing FInite Element or the reposition representative of analytic method to N particleCarry out mechanical analysis, obtain the stress of each laying and the displacement of assigned position of Test of Laminate Composites, computation layer plywoodThe design object of composite; Then calculate by step (3) and finally obtain N the target function value L (x that particle is new_i), this targetFunctional value is identical with step (2); The relatively target letter of the fresh target functional value of N particle and the individual optimization design scheme of recordNumerical value, if i new target function value of particle is better than the target function value of the individual optimization design scheme of i particle,I particle position is now recorded as to new individual optimization design scheme pbest_i(k+1); Finally by N particle according toTarget function value sorts from small to large, selects the first two minimum of a value; Comparison object functional value and global optimum's designAnd the relation of the target function value of overall Suboptimal Design scheme, just replace if less, by particle less desired valuePosition as the new design gbest of global optimum₁Or the inferior design gbest of global optimum (k+1)₂(k+1)；

(5) if the target function value of global optimum's design and overall Suboptimal Design scheme is quite approaching, stop calculating, enterRow step (6), otherwise the value that completes iterations is increased to one, return to step (3);

(6) variate-value of the laying angular direction of Test of Laminate Composites will be represented in the variable of the global optimum's design obtainingRounding is to the specification at laying angle of regulation, using the laying direction after the laying thickness in global optimum's design and rounding asThe design of final Test of Laminate Composites, thus the laying angular direction of final Test of Laminate Composites and thick obtainedDegree.

2. the laying angular direction of a kind of definite Test of Laminate Composites according to claim 1 and the method for thickness, its spyLevy and be: in described step (1), Mathematical Planning method for designing comprises that sequential quadratic programming method, sequence linear programming are based on gradientTheoretical method, specific implementation comprises that four step: a. are according to the laying thickness of current Test of Laminate Composites and laying angle sideTo, obtain the stress of each laying and the displacement of assigned position of Test of Laminate Composites by carrying out mechanical analysis, totalWeight; B. solve laying thickness and laying angular direction design variable to critical year of Test of Laminate Composites weight or flexingThe sensitivity of the object function of lotus and the value of constraint function; C. adopt sequence double optimization method or sequence linear optimization method to enterRow optimization is analyzed; Stop Mathematical Planning if d. reach the iterations of regulation, otherwise forward a to.

3. the laying angular direction of a kind of definite Test of Laminate Composites according to claim 1 and the method for thickness, its spyLevy and be: described in described step (1), the original design scheme of part particle is defined on the diagonal of search volume, all the otherThe original design scheme of particle generates at random in search volume, and step is as follows: get" [] " represents to round, ifN≤a, getsI=1,2 ..., the original design scheme that N is population; If N > a, getsI=1,2 ..., a is the original design scheme of a front a particle, and all the other N-a particleOriginal design scheme x '_i(0), i=a+1, a+2 ..., N generates at random in search volume, and the speed of all particles is all randomGenerate x_imin,x_imaxFor the bound of design variable.

4. the laying angular direction of a kind of definite Test of Laminate Composites according to claim 1 and the method for thickness, its spyLevy and be: the penalty factor α span in described step (2) is 20 to 1000.

5. the laying angular direction of a kind of definite Test of Laminate Composites according to claim 1 and the method for thickness, its spyLevy and be: the n in described step (1)₀Get 15～20.