CN106126832A - A kind of composite laminated plate Multidisciplinary systems bilayer level optimization method - Google Patents

Abstract

The invention discloses a kind of composite laminated plate Multidisciplinary systems bilayer level optimization method.The method is first according to the loading characteristic of composite laminated plate, it is considered to the uncertain effect of composite material strength parameter in the case of finite sample, theoretical based on Multidisciplinary systems, it is established that composite laminated plate Multidisciplinary systems assessment models；Ground floor optimization uses simulated annealing to carry out composite laminated plate with thickness as variable, and strength reliability and local stiffness changed are the optimization of constraint.Second layer optimization consideration process constraint is with ply stacking-sequence as variable, and maximum intensity is that target is optimized, and is met the laying scheme base of technological requirement by foundation, uses genetic algorithm that laminate is carried out ply stacking-sequence optimization.Ensure that composite laminated plate meets engineering actual process level, compromise between security and economy while having higher reliability and less weight under condition of uncertainty.

Description

A kind of composite laminated plate Multidisciplinary systems bilayer level optimization method

Technical field

The present invention relates to the design optimizing field of laminated composite plate structures, particularly to a kind of composite layer Plywood Multidisciplinary systems bilayer level optimization method, the method considers that the Multidisciplinary systems under fibre strength condition of uncertainty is excellent Changing design problem, with under certain reliability requirement, the double-deck level reliability that the thickness of laminate accounts for process constraint is excellent Change design.

Background technology

The tool that composite is made up of on a macroscopic scale the different material physics of two or more and chemical method Having the material of new capability, the performance of general composite is better than the performance of its component material, and some performance is original component Material does not has, and composite improves the mechanical properties such as the rigidity of component material, intensity.

Composite is widely used in the fields such as Aero-Space, automobile, machinery because of its good characteristic.These fields are to material The safety of material has the highest requirement.Laminated plate structure is typical composite structure, its material properties, military service load Etc. there being the biggest uncertainty.Therefore the strength design of being determined by property can not accurately reflect its real safety, Laminated plate structure is carried out fail-safe analysis and is optimized be the most necessary by reliability design.

Currently, Chinese scholars and engineers and technicians are to the uncertainty analysis of composite laminated plate and design studies It is concentrated mainly on laminated plate structure fail-safe analysis based on Probability Statistics Theory and optimizes design, but managing based on probability statistics Opinion, for having strong dependence for large sample, limits its application in engineering reality.

In sum, the laminated composite plate structures fail-safe analysis based on non-probability theory framework is set up with excellent Change method for designing, and during optimizing, consider that the process constraint in composite preparation process has significant realistic meaning.

Summary of the invention

The technical problem to be solved in the present invention is: overcome the deficiencies in the prior art, is meeting structural reliability and technique about There is provided a kind of for composite laminated plate reliability bilayer level optimization method on the premise of bundle.The present invention takes into full account actual work The uncertain factor generally existed in Cheng Wenti, first does based on Tsai-Wu criterion and non-probabilistic strength-stress with propose Relate to the Multidisciplinary systems metric optimization constraint as Optimized model of theory, breakaway layer model is carried out reliability constraint Under laminate thickness optimization, carry out rounding according to process constraint afterwards, obtain the number of plies in each laying direction, according to the laying number of plies Set up the laying storehouse meeting process constraint, use genetic algorithm to carry out carrying out excellent with maximum intensity for target in the range of laying storehouse Change.

The technical solution used in the present invention is:

A kind of composite laminated plate Multidisciplinary systems bilayer level optimization method, implementation step is as follows:

Step one: build laminate breakaway layer model, in initial for composite laminated plate laying scheme, will there is identical paving The laying of layer angle carries out thickness and adds up, and will be converted into and have the breakaway layer model of [0 °, 45 ° ,-45 °, 90 °] by laminate；

Step 2: arrange laminated plate structure breakaway layer original depth H, calculates original state quality m, each during optimization The maximum iteration time of m value correspondence is L；

Step 3: optimize process iterations K=0；

Step 4: produce and meet solution H' less than quality m, according to the geometric properties of composite laminated plate, material properties And boundary condition, analyze based on composite laminated plate macromechanics, laminate is carried out stress and displacement d and current solves Solving of quality m', length a and width b in wherein the geometric properties of laminate includes laminate face；Material properties includes elasticity Constant and intensive parameter, elastic constant includes: 1 direction elastic modulus E₁, 2 direction elastic modulus Es₂, shear modulus G₁₂, Poisson's ratio υ, wherein 1 direction is fiber axial direction, and 2 directions are vertical fibers axial direction in laminate plane；Boundary condition include x and Y direction compressive load N_xAnd N_y；Intensive parameter is uncertain, compares X including longitudinal tensile strength_T, longitudinal compressive strength X_C, horizontal To hot strength Y_T, transverse compression intensity Y_C, in-plane shear strength S；

Step 5: according to step 2 stress situation, substitutes into Tsai-Wu tensor theories, calculates composite laminated plate Tsai- Wu index, the computing formula of Tsai-Wu intensity index is:

$t=F_1{\mathrm{\σ}}_1+F_2{\mathrm{\σ}}_2+F_{11}{\mathrm{\σ}}_1^2+2F_{12}{\mathrm{\σ}}_1{\mathrm{\σ}}_2+F_{22}{\mathrm{\σ}}_2^2+F_{66}{\mathrm{\σ}}_6^2$

In formula:X_TIt is vertical To hot strength, X_CFor longitudinal compressive strength, Y_TFor transverse tensile strength, Y_CFor transverse compression intensity, F₁₂Characterize two-way direct stress Interaction, typically takeσ₁For fiber 1 direction stress, σ₂For fiber 2 direction stress, σ₆For shearing stress；

Step 6: utilize interval vector x ∈ x^I=(X_T,X_C,Y_T,Y_C,S,E₁,E₂,G₁₂,υ₁₂, P) rationally characterize uncertain bar The uncertainty of strength of materials parameter, elastic parameter and the external applied load in step one under part, wherein, longitudinal tensile strength X_T, vertical To compressive strength X_C, transverse tensile strength Y_T, transverse compression intensity Y_C, in-plane shear strength S, elastic parameter 1 direction elastic modelling quantity E₁, 2 direction elastic modulus Es₂, shear modulus G₁₂, Poisson's ratio υ and external applied load P can be expressed as interval variable；

Step 7: application Taylor Series Method, the response interval t of the maximum Tsai-Wu coefficient t of Analysis for Composite Laminated plate^IAnd position Move the interval d of d response^I；

Step 8: when Tsai-Wu coefficient t is more than 1, this layer by layer plywood lost efficacy, during less than 1, this plywood safety layer by layer, by Intensive parameter in composite laminated plate is interval variable, and therefore laminate maximum Tsai-Wu coefficient t is also an interval, i.e. Tsai-Wu intensity interval, then be with the ratio of whole siding-to-siding block length less than the siding-to-siding block length of 1 part in Tsai-Wu intensity interval This laminate reliabilityAssume that the maximum displacement that structure allows is [d], then laminate displacement interval d^IIn less than [d] part The ratio of shared overall siding-to-siding block length is the local stiffness changed of structure

Step 9: judge the local stiffness changed of laminated plate structure, whether strength reliability meets reliability constraint, if full Sufficient then carry out step 10, as being unsatisfactory for, then skip to step 11；

Step 10: if the increment Delta m ＜ 0 of quality, then accepting current H' is new explanation, and m=m', H=H', if be unsatisfactory for Then accept new solution according to Metropolis rule；

Step 11: K=K+1, and if K be not more than L, then skip to step 4；If K is ＞ L, then judge whether to meet Optimize stop criterion, if it is satisfied, then carry out step 12；As being unsatisfactory for, reduce m, and skip to step 3；

Step 12: the breakaway layer thickness that step 5 optimizes gained carries out rounding, each wing flapping after being optimized The number of plies；

Step 13: according to step 6 gained each laying number of plies, according to process constraint, generate the laying storehouse of material, laying Storehouse is included in the ply stacking-sequence scheme optimized under the gained laying number of plies and process constraint, and laying storehouse is encoded, each Individual coding stands one laying scheme；

Step 14: be target to the maximum with intensity level, ply stacking-sequence is optimized variable, on the basis in the laying storehouse of step 7 On set up genetic algorithm, carry out the optimization of ply stacking-sequence.

Further, the optimization of breakaway layer can be expressed as: under fibre strength condition of uncertainty, with laminate quality Little for target, the thickness of each layer is optimized design, can column be specifically:

Wherein,For each angle breakaway layer thickness, a, b are respectively laminated plate structure length and width；M is layer Plywood quality, is thickness H, length a, width b and the function of density p；P_sFor the reliability of laminate, it it is the super thickness of laminate Degree H, fibre strength x, length a, width b, 1 direction elastic modulus E₁, 2 direction elastic modulus Es₂, shear modulus G₁₂, Poisson's ratio υ Function；For the Design permissible value of strength reliability,For the Design permissible value of strength reliability,With The biggest, laminate reliability is the highest, and weight is the biggest；WithIt is respectively breakaway layer thickness during optimizing adaptable Minima and maximum, characterize the design space of optimization；

In described step one, the foundation of breakaway layer model can be expressed as:

I.e.In formula, H_0°, H_45°, H_-45°, H_90°Respectively lower 0 ° of original state, 45 ° ,-45 °, the breakaway layer thickness of 90 °, It is 0 °, 45 ° ,-45 °, the initial laying number of plies of 90 ° of layings, h represents the thickness in monolayer under laminate technological requirement, For the most initial breakaway layer thickness, subscript 0 represents original state.

Further, maximum iteration time L=1000 that in described step 2, each quality m is corresponding；

In described step 4, the Multidisciplinary systems of laminate is decided by that intensive parameter includes longitudinal tensile strength X_T, longitudinally Compressive strength X_C, transverse tensile strength Y_T, transverse compression intensity Y_C, in-plane shear strength S, elastic parameter 1 direction elastic modelling quantity E₁, 2 direction elastic modulus Es₂, shear modulus G₁₂, Poisson's ratio υ and the uncertainty of external applied load P.

Further, in step 6, intensity uncertainty is characterized as:

$\begin{array}{c}{x}^U=(X_T^U,X_C^U,Y_T^U,Y_C^U,S^U,E_1^U,E_2^U,G_{12}^U,{\mathrm{\υ}}_{12}^U,P^U)\\ =(X_T^c+X_T^r,X_C^c+X_C^r,Y_T^c+Y_T^r,Y_C^c+Y_C^r,S^c+S^r,E_1^c+E_1^r,E_2^c+E_2^r,G_{12}^c+G_{12}^r,{\mathrm{\υ}}_{12}^c+{\mathrm{\υ}}_{12}^r,P^c+P^r)\end{array}$

$\begin{array}{c}{x}^L=(X_T^L,X_C^L,Y_T^L,Y_C^L,S^L,E_1^L,E_2^L,G_{12}^L,{\mathrm{\υ}}_{12}^L,P^L)\\ =(X_T^c-X_T^r,X_C^c-X_C^r,Y_T^c-Y_T^r,Y_C^c-Y_C^r,S^c-S^r,E_1^c-E_1^r,E_2^c-E_2^r,G_{12}^c-G_{12}^r,{\mathrm{\υ}}_{12}^c-{\mathrm{\υ}}_{12}^r,P^c-P^r)\end{array}$

Wherein, longitudinal tensile strength X_T, longitudinal compressive strength X_C, transverse tensile strength Y_T, transverse compression intensity Y_C, in face Shear strength S, 1 direction elastic modulus E₁, 2 direction elastic modulus Es₂, shear modulus G₁₂, Poisson's ratio υ and external applied load P uncertain Property can be expressed as interval variable, and subscript U represents the value upper bound of parameter, and subscript L represents the value lower bound of parameter, subscript c Representing central value, subscript r represents radius, x^IInterval for intensive parameter；

In described step 7, application Taylor Series Method solves the process in Tsai-Wu coefficient and displacement interval and is: it is poor to utilize Point-score tries to achieve Tsai-Wu coefficient and displacement derivative dt, the dd about uncertain variables x, then Tsai-Wu coefficient and the interval of displacement For:

$\left\{\begin{array}{c}{t}^L=t-abs\left(dt\right)*x^{\′}*0.3\\ t^U=t+abs\left(dt\right)*x^{\′}*0.3\\ d^L=d-abs\left(dd\right)*x^{\′}*0.3\\ d^U=d-abs\left(dd\right)*x^{\′}*0.3\end{array}\right.$

Wherein, subscript L represents interval lower bound, and subscript U represents the interval upper bound, and abs () represents the computing that takes absolute value, Dt is the Tsai-Wu coefficient derivative to each variable, and dd is the displacement derivative to each variable.

Further, in described step 8, the strength reliability P of structure_s ^tIt is calculated as follows:

Situation is 1.: if t^U＞ 1 and t^L＜ 1, then

$P_s^t=\frac{1-\left(t^L\right)}{\left(t^U\right)-\left(t^L\right)}$

Situation is 2.: if t^U≤ 1, then

$P_s^t=1$

Situation is 3.: if t^L>=1, then

$P_s^t=0$

In formula, P_siFor laminate breakaway layer reliability, t is Tsai-Wu coefficient, and subscript U represents the upper bound of range of variables, on Mark L represents the lower bound of range of variables, and n is the laying number of plies.

In described step 8, the rigidity reliability of structureIt is calculated as follows:

Situation is 1.: if d^U＞ 1 and d^L＜ 1, then

$P_s^d=\frac{\[d\]-\left(d^L\right)}{\left(d^U\right)-\left(d^L\right)}$

Situation is 2.: if d^U≤ 1, then

$P_s^d=1$

Situation is 3.: if d^L>=1, then

$P_s^d=0$

In formula,For laminate breakaway layer reliability, d is Tsai-Wu coefficient, and [d] is the maximum displacement that structure allows, on Mark U represents the upper bound of range of variables, and subscript L represents the lower bound of range of variables.

Further, in described step 9, Reliability Constraint is set toDescribed step 9 Middle composite laminated plate process constraint includes: avoid same direction laying to continue to exceed four layers；Adjacent two layers angle is less than 60°；Laminate surface is minimum wants one group ± 45 ° layers of lay.

Further, in described step 10, Metropolis rule is set to: accept new with probability exp (-Δ m/m) H'。

Further, described step 11 optimizes stop criterion to be set to: if residual error all ratios of adjacent continuous 3 times are little In 0.001.

Further, in described step 11, optimization gained thickness rounding being obtained all directions laying laying number can column For:

In formula, N_0°, N_45°, N_-45°, N_90°Representing 0 ° respectively, 45 ° ,-45 °, 90 ° optimize the layer after rounding according to ground floor Number, ceil () represents the computing that rounds up,For optimize after 0 ° of breakaway layer thickness,45 ° of super thickness after optimization Degree,-45 ° of breakaway layer thickness after optimization,90 ° of breakaway layer thickness after optimization.

Further, the ply stacking-sequence optimization in step 14 is designed as: under fibre strength condition of uncertainty, with layer The minimum target of plywood Tsai-Wu coefficient, is optimized design to laminate ply stacking-sequence, can column be specifically:

$\left\{\begin{array}{cc}min& t_{max}\\ s.t.& seq\∈\left\{seq\right\}\end{array}\right.$

In formula, t_maxFor the maximum of Tsai-Wu coefficient, seq represents ply stacking-sequence, and { seq} represents laying storehouse.

Present invention advantage compared with prior art is: the invention provides the new think of of composite reliability design Road, makes up and perfect tradition limitation based on probability theory reliability design approach.The constructed non-probability of laminate can By property measurement model and double-deck level optimization method, on the one hand can significantly reduce the dependency to sample information, the most permissible Take into full account the laminated composite plate structures strength reliability under intensity condition of uncertainty, can at laminated composite plate structures By, under property and technological requirement, being designed by optimization, laminate is carried out light-weight design, protect on the premise of increasing economic efficiency The exploitativeness of card prioritization scheme.

Accompanying drawing explanation

Fig. 1 is to the present invention is directed to composite laminated plate Multidisciplinary systems Optimizing Flow figure；

Fig. 2 is composite laminated plate load schematic；

Fig. 3 is Composite Laminated Panel scheme schematic diagram；

Fig. 4 is to the present invention is directed to fibre strength indeterminacy of calculation laminate monolayer reliability schematic diagram；

Fig. 5 be the present invention to laminate thickness optimization process reliability to iterations course curve；

Fig. 6 be the present invention to laminate thickness optimization process gross thickness to iterations course curve；

Fig. 7 be the present invention to laminate sequential optimization process Tsai-Wu coefficient to iterations course curve.

Detailed description of the invention

Below in conjunction with the accompanying drawings and specific embodiment further illustrates the present invention.

As it is shown in figure 1, the present invention proposes a kind of for composite laminated plate Multidisciplinary systems method for designing, including Following steps:

Step one: build laminate breakaway layer model, in initial for composite laminated plate laying scheme, will there is identical paving The laying of layer angle carries out thickness and adds up, and will be converted into and have the breakaway layer model of [0 °, 45 ° ,-45 °, 90 °] by laminate.Super The foundation of level layer model can be expressed as:

I.e.In formula, H_0°, H_45°, H_-45°, H_90°Respectively lower 0 ° of original state, 45 ° ,-45 °, the breakaway layer thickness of 90 °, It is 0 °, 45 ° ,-45 °, the initial laying number of plies of 90 ° of layings, h represents the thickness in monolayer under laminate technological requirement, For the most initial breakaway layer thickness, subscript 0 represents original state.

Step 2: arrange laminated plate structure breakaway layer original depth H, calculates original state quality m, each during optimization The maximum iteration time of m value correspondence is L, wherein L=1000；

Step 3: optimize process iterations K=0；

Step 4: produce and meet solution H' less than quality m.According to the geometric properties of composite laminated plate, material properties And boundary condition, analyze based on composite laminated plate macromechanics, laminate is carried out stress and displacement d and current solves Solving of quality m'.Length a and width b in wherein the geometric properties of laminate includes laminate face；Material properties includes elasticity Constant and intensive parameter, elastic constant includes: 1 direction elastic modulus E₁, 2 direction elastic modulus Es₂, shear modulus G₁₂, Poisson's ratio υ, wherein 1 direction is fiber axial direction, and 2 directions are vertical fibers axial direction in laminate plane；Boundary condition include x and Y direction compressive load N_xAnd N_y；Intensive parameter is uncertain, compares X including longitudinal tensile strength_T, longitudinal compressive strength X_C, horizontal To hot strength Y_T, transverse compression intensity Y_C, in-plane shear strength S；

Step 5: according to step 2 stress situation, substitutes into Tsai-Wu tensor theories, calculates composite laminated plate Tsai- Wu index.The computing formula of Tsai-Wu intensity index is:

$t=F_1{\mathrm{\σ}}_1+F_2{\mathrm{\σ}}_2+F_{11}{\mathrm{\σ}}_1^2+2F_{12}{\mathrm{\σ}}_1{\mathrm{\σ}}_2+F_{22}{\mathrm{\σ}}_2^2+F_{66}{\mathrm{\σ}}_6^2$

In formula:X_TIt is vertical To hot strength, X_CFor longitudinal compressive strength, Y_TFor transverse tensile strength, Y_CFor transverse compression intensity, F₁₂Characterize two-way direct stress Interaction, typically take

Step 6: utilize interval vector x ∈ x^I=(X_T,X_C,Y_T,Y_C,S,E₁,E₂,G₁₂,υ₁₂, P) rationally characterize uncertain bar The uncertainty of strength of materials parameter, elastic parameter and the external applied load in step one under part.Wherein, longitudinal tensile strength X_T, vertical To compressive strength X_C, transverse tensile strength Y_T, transverse compression intensity Y_C, in-plane shear strength S, elastic parameter 1 direction elastic modelling quantity E₁, 2 direction elastic modulus Es₂, shear modulus G₁₂, Poisson's ratio υ and external applied load P can be expressed as interval variable, subscript U represents The value upper bound of parameter, subscript L represents the value lower bound of parameter, and subscript c represents central value, and subscript r represents radius, x^IFor intensity Parameter is interval.Uncertainty is characterized as:

$\begin{array}{c}{x}^U=(X_T^U,X_C^U,Y_T^U,Y_C^U,S^U,E_1^U,E_2^U,G_{12}^U,{\mathrm{\υ}}_{12}^U,P^U)\\ =(X_T^c+X_T^r,X_C^c+X_C^r,Y_T^c+Y_T^r,Y_C^c+Y_C^r,S^c+S^r,E_1^c+E_1^r,E_2^c+E_2^r,G_{12}^c+G_{12}^r,{\mathrm{\υ}}_{12}^c+{\mathrm{\υ}}_{12}^r,P^c+P^r)\end{array}$

$\begin{array}{c}{x}^L=(X_T^L,X_C^L,Y_T^L,Y_C^L,S^L,E_1^L,E_2^L,G_{12}^L,{\mathrm{\υ}}_{12}^L,P^L)\\ =(X_T^c-X_T^r,X_C^c-X_C^r,Y_T^c-Y_T^r,Y_C^c-Y_C^r,S^c-S^r,E_1^c-E_1^r,E_2^c-E_2^r,G_{12}^c-G_{12}^r,{\mathrm{\υ}}_{12}^c-{\mathrm{\υ}}_{12}^r,P^c-P^r)\end{array};$

Step 7: application Taylor Series Method, the response interval t of the maximum Tsai-Wu coefficient t of Analysis for Composite Laminated plate^IAnd position Move the interval d of d response^I.Application Taylor Series Method solves the process in Tsai-Wu coefficient and displacement interval: utilize calculus of finite differences Trying to achieve Tsai-Wu coefficient and displacement derivative dt, the dd about uncertain variables x, concrete behaviour is another uncertain variables.Then Tsai- The interval of Wu coefficient and displacement is:

$\left\{\begin{array}{c}{t}^L=t-abs\left(dt\right)*x^{\′}*0.3\\ t^U=t+abs\left(dt\right)*x^{\′}*0.3\\ d^L=d-abs\left(dd\right)*x^{\′}*0.3\\ d^U=d-abs\left(dd\right)*x^{\′}*0.3\end{array}\right.$

Wherein, subscript L represents interval lower bound, and subscript U represents the interval upper bound, and abs () represents the computing that takes absolute value, Dt is the Tsai-Wu coefficient derivative to each variable, and dd is the displacement derivative to each variable.

Step 8: when Tsai-Wu coefficient t is more than 1, this layer by layer plywood lost efficacy, during less than 1, this plywood safety layer by layer, by Intensive parameter in composite laminated plate is interval variable, and therefore laminate maximum Tsai-Wu coefficient t is also an interval, i.e. Tsai-Wu intensity interval, then be with the ratio of whole siding-to-siding block length less than the siding-to-siding block length of 1 part in Tsai-Wu intensity interval This laminate reliabilityAssume that the maximum displacement that structure allows is [d], then laminate displacement interval d^IIn less than [d] part The ratio of shared overall siding-to-siding block length is the local stiffness changed of structure

The strength reliability of structureIt is calculated as follows:

Situation is 1.: if t^U＞ 1 and t^L＜ 1, then

$P_s^t=\frac{1-\left(t^L\right)}{\left(t^U\right)-\left(t^L\right)}$

Situation is 2.: if t^U≤ 1, then

$P_s^t=1$

Situation is 3.: if t^L>=1, then

$P_s^t=0$

In formula, P_siFor laminate breakaway layer reliability, t is Tsai-Wu coefficient, and subscript U represents the upper bound of range of variables, on Mark L represents the lower bound of range of variables, and n is the laying number of plies.

The rigidity reliability of structureIt is calculated as follows:

Situation is 1.: if d^U＞ 1 and d^L＜ 1, then

$P_s^d=\frac{\[d\]-\left(d^L\right)}{\left(d^U\right)-\left(d^L\right)}$

Situation is 2.: if d^U≤ 1, then

$P_s^d=1$

Situation is 3.: if d^L>=1, then

$P_s^d=0$

In formula,For laminate breakaway layer reliability, d is Tsai-Wu coefficient, and [d] is the maximum displacement that structure allows, on Mark U represents the upper bound of range of variables, and subscript L represents the lower bound of range of variables；

Step 9: judge the local stiffness changed of laminated plate structure, whether strength reliability meets reliability constraint, if full Sufficient then carry out step 10, as being unsatisfactory for, then skip to step 11.Reliability Constraint is set to

Step 10: if the increment Delta m ＜ 0 of quality, then accepting current H' is new explanation, and m=m', H=H', if be unsatisfactory for Then accept new solution according to Metropolis rule.Metropolis rule is set to: accept new with probability exp (-Δ m/m) H'。

Step 11: K=K+1, and if K be not more than L, then skip to step 4；If fruit K ＞ L, then judge whether to meet Optimize stop criterion, if it is satisfied, then carry out step 12；As being unsatisfactory for, reduce m, and skip to step 3.Optimize and terminate standard Then it is set to: if residual error all ratios of adjacent continuous 3 times are less than 0.001；

Step 12: the breakaway layer thickness that step 5 optimizes gained carries out rounding, each wing flapping after being optimized The number of plies, to optimize gained thickness rounding obtain all directions laying laying number can column be:

In formula, N_0°, N_45°, N_-45°, N_90°Representing 0 ° respectively, 45 ° ,-45 °, 90 ° optimize the layer after rounding according to ground floor Number, ceil () represents the computing that rounds up；

Step 13: according to step 6 gained each laying number of plies, according to process constraint, generate the laying storehouse of material, laying Storehouse is included in the ply stacking-sequence scheme optimized under the gained laying number of plies and process constraint.And laying storehouse is encoded, each Individual coding stands one laying scheme.Composite laminated plate process constraint includes: avoid same direction laying to continue to exceed four Layer；Adjacent two layers angle is less than 60 °；Laminate surface is minimum wants one group ± 45 ° layers of lay.

Step 14: set up genetic algorithm on the basis of the laying storehouse of step 13, carries out the optimization of ply stacking-sequence.With The minimum target of laminate Tsai-Wu coefficient, is optimized design to laminate ply stacking-sequence, can column be specifically:

$\left\{\begin{array}{cc}min& t_{max}\\ s.t.& seq\∈\left\{seq\right\}\end{array}\right.$

In formula, t_maxFor the maximum of Tsai-Wu coefficient, seq represents ply stacking-sequence, and { seq} represents laying storehouse.

Embodiment:

In order to understand the feature of this invention and the suitability actual to engineering thereof more fully, the present invention is directed to such as Fig. 2 institute Tensile load N in the bearing plane of the surrounding freely-supported shown_xAnd N_yAnd pressure P outside face₀Laminate carry out optimization based on reliability and set Meter.Laminate ply sequence is [0/45/-45/90]_4s.Laminate face inside dimension is a × b=(20*12.5) cm², lamina Thickness is 0.125mm, and therefore laminate total thickness is 0.125mm × 32=4mm.It is strong that table 1 gives Rectangular Plate Structure in embodiment The unascertained information of degree parameter, table 2 gives Rectangular Plate Structure elastic parameter and the uncertain letter of external applied load in embodiment Breath.

Table 1

Table 2

This embodiment uses, and reliability applies Tsai-Wu interval strength reliability as shown in Figure 4 to try to achieve, shadow region in figure Domain representation laminate safety, its ratio with whole interval is the reliability of lamina, strength reliability Design permissible valueIt is set to 0.95, rigidity RELIABILITY DESIGN allowable valueBeing set to 0.95, Fig. 5 and Fig. 6 gives object function peace treaty Bundle function iteration course curve, Fig. 5 gives laminate reliably along with the variation tendency of Optimized Iterative number of times, along with thickness Reduction, strength reliability does not reduce, and local stiffness changed then has 1 to be reduced to 0.95001, slightly larger than reliability allowable value 0.95, laminate gross thickness is reduced to 5.88 as can be seen from Figure 6, loss of weight 26.5%.Through rounding, 0 °, 45 ° ,-45 °, 90 ° The number of plies is respectively 3, and 3,3,4, loss of weight 25% after rounding.

According to optimizing the gained number of plies, set up laying storehouse and utilize genetic algorithm to be optimized.Fig. 7 gives sequential optimization mistake The iteration course curve of Tsai-Wu coefficient in journey, finally in [45 ,-45,0,0 ,-45,90 ,-45,0,45,90,90,90,45]_s Tsai-Wu coefficient minima 0.278388 is obtained under laying.

In sum, the present invention proposes a kind of composite laminated plate Multidisciplinary systems method for designing.First, according to Laminate physical dimension, elastic parameter, the computation layer plywood stress such as laying information；Secondly, by the uncertain letter of fibre strength Breath introduces Tsai-Wu strength theory, it is achieved the calculating of Tsai-Wu coefficient interval upper and lower bound；Manage according to Tsai-Wu intensity Opinion, in conjunction with the reliability of non-probability interference technique computation layer plywood；Then, turn to target with light weight, complete with laminate reliable Property for constraint, for Multidisciplinary systems optimization that each layer thickness is variable design, reach to meet the laminate of reliability requirement The target of light-weight design；Finally light-weight design result is carried out rounding, and laminate is carried out ply stacking-sequence optimization.

Below it is only the concrete steps of the present invention, protection scope of the present invention is not constituted any limitation；Its expansible should Replace for the optimization design field containing uncertain composite laminated plate, all employing equivalents or equivalence and formed Technical scheme, within the scope of all falling within rights protection of the present invention.

Non-elaborated part of the present invention belongs to the known technology of those skilled in the art.

Claims (10)

1. a composite laminated plate Multidisciplinary systems bilayer level optimization method, it is characterised in that realize step as follows:

Step one: build laminate breakaway layer model, in initial for composite laminated plate laying scheme, will there is identical wing flapping The laying of degree carries out thickness and adds up, and will be converted into and have the breakaway layer model of [0 °, 45 ° ,-45 °, 90 °] by laminate；

Step 2: arrange laminated plate structure breakaway layer original depth H, calculates original state quality m, each m value during optimization Corresponding maximum iteration time is L；

Step 3: optimize process iterations K=0；

Step 4: produce and meet less than solution H' of quality m, according to the geometric properties of composite laminated plate, material properties and Boundary condition, analyzes based on composite laminated plate macromechanics, and laminate carries out stress and displacement d and the current quality solved M' solves, length a and width b in wherein the geometric properties of laminate includes laminate face；Material properties includes elastic constant And intensive parameter, elastic constant includes: 1 direction elastic modulus E₁, 2 direction elastic modulus Es₂, shear modulus G₁₂, Poisson's ratio υ, its In 1 direction be fiber axial direction, 2 directions are vertical fibers axial direction in laminate plane；Boundary condition includes x and y side To compressive load N_xAnd N_y；Intensive parameter is uncertain, compares X including longitudinal tensile strength_T, longitudinal compressive strength X_C, laterally draw Stretch intensity Y_T, transverse compression intensity Y_C, in-plane shear strength S；

Step 5: according to step 2 stress situation, substitutes into Tsai-Wu tensor theories, calculates composite laminated plate Tsai-Wu and refers to Mark, the computing formula of Tsai-Wu intensity index is:

$t=F_1{\mathrm{\σ}}_1+F_2{\mathrm{\σ}}_2+F_{11}{\mathrm{\σ}}_1^2+2F_{12}{\mathrm{\σ}}_1{\mathrm{\σ}}_2+F_{22}{\mathrm{\σ}}_2^2+F_{66}{\mathrm{\σ}}_6^2$

In formula:X_TFor longitudinally drawing Stretch intensity, X_CFor longitudinal compressive strength, Y_TFor transverse tensile strength, Y_CFor transverse compression intensity, F₁₂Characterize the phase of two-way direct stress Interaction, typically takesσ₁For fiber 1 direction stress, σ₂For fiber 2 direction stress, σ₆For shearing stress；

Step 6: utilize interval vector x ∈ x^I=(X_T,X_C,Y_T,Y_C,S,E₁,E₂,G₁₂,υ₁₂, P) rationally characterize under condition of uncertainty The uncertainty of strength of materials parameter, elastic parameter and external applied load in step one, wherein, longitudinal tensile strength X_T, longitudinally pressure Contracting intensity X_C, transverse tensile strength Y_T, transverse compression intensity Y_C, in-plane shear strength S, elastic parameter 1 direction elastic modulus E₁、2 Direction elastic modulus E₂, shear modulus G₁₂, Poisson's ratio υ and external applied load P can be expressed as interval variable；

Step 7: application Taylor Series Method, the response interval t of the maximum Tsai-Wu coefficient t of Analysis for Composite Laminated plate^IAnd displacement d rings The interval d answered^I；

Step 8: when Tsai-Wu coefficient t is more than 1, this layer by layer plywood lost efficacy, during less than 1, this plywood safety layer by layer, due to multiple The intensive parameter of condensation material laminate is interval variable, and therefore laminate maximum Tsai-Wu coefficient t is also an interval, i.e. Tsai- Wu intensity interval, then be this lamination less than the siding-to-siding block length of 1 part with the ratio of whole siding-to-siding block length in Tsai-Wu intensity interval Plate reliabilityAssume that the maximum displacement that structure allows is [d], then laminate displacement interval d^IIn shared whole less than [d] part The ratio of body siding-to-siding block length is the local stiffness changed of structure

Step 9: judge the local stiffness changed of laminated plate structure, whether strength reliability meets reliability constraint, if met, Carry out step 10, as being unsatisfactory for, then skip to step 11；

Step 10: if the increment Delta m ＜ 0 of quality, then accepting current H' is new explanation, m=m', H=H', if be unsatisfactory for, by New solution is accepted according to Metropolis rule；

Step 11: K=K+1, and if K be not more than L, then skip to step 4；If K is ＞ L, then judge whether to meet optimization Stop criterion, if it is satisfied, then carry out step 12；As being unsatisfactory for, reduce m, and skip to step 3；

Step 12: the breakaway layer thickness that step 5 optimizes gained carries out rounding, the layer of each wing flapping after being optimized Number；

Step 13: according to step 6 gained each laying number of plies, according to process constraint, generate the laying storehouse of material, in laying storehouse Being included in the ply stacking-sequence scheme optimized under the gained laying number of plies and process constraint, and encode laying storehouse, each is compiled Code represents a kind of laying scheme；

Step 14: be target to the maximum with intensity level, ply stacking-sequence is optimized variable, builds on the basis of the laying storehouse of step 7 Vertical genetic algorithm, carries out the optimization of ply stacking-sequence.

A kind of composite laminated plate Multidisciplinary systems optimization method the most according to claim 1, it is characterised in that: super The optimization of level layer can be expressed as: under fibre strength condition of uncertainty, with the minimum target of laminate quality, the thickness to each layer Degree is optimized design, can column be specifically:

Wherein,For each angle breakaway layer thickness, a, b are respectively laminated plate structure length and width；M is laminate Quality, is thickness H, length a, width b and the function of density p；P_sFor the reliability of laminate, it is the super layer thickness H of laminate, Fibre strength x, length a, width b, 1 direction elastic modulus E₁, 2 direction elastic modulus Es₂, shear modulus G₁₂, the letter of Poisson's ratio υ Number；For the Design permissible value of strength reliability,For the Design permissible value of strength reliability,WithIt is the biggest, Laminate reliability is the highest, and weight is the biggest；WithIt is respectively the adaptable minimum of breakaway layer thickness during optimizing Value and maximum, characterize the design space of optimization；

In described step one, the foundation of breakaway layer model can be expressed as:

I.e.In formula, H_0°, H_45°, H_-45°, H_90°Respectively lower 0 ° of original state, 45 ° ,-45 °, the breakaway layer thickness of 90 °, It is 0 °, 45 ° ,-45 °, the initial laying number of plies of 90 ° of layings, h represents the thickness in monolayer under laminate technological requirement, For the most initial breakaway layer thickness, subscript 0 represents original state.

A kind of composite laminated plate Multidisciplinary systems optimization method the most according to claim 1, it is characterised in that: institute State maximum iteration time L=1000 that in step 2, each quality m is corresponding；

In described step 4, the Multidisciplinary systems of laminate is decided by that intensive parameter includes longitudinal tensile strength X_T, longitudinal compression Intensity X_C, transverse tensile strength Y_T, transverse compression intensity Y_C, in-plane shear strength S, elastic parameter 1 direction elastic modulus E₁, 2 sides To elastic modulus E₂, shear modulus G₁₂, Poisson's ratio υ and the uncertainty of external applied load P.

A kind of composite laminated plate Multidisciplinary systems optimization method the most according to claim 1, it is characterised in that: step In rapid six, intensity uncertainty is characterized as:

$\begin{array}{c}{x}^U=(X_T^U,X_C^U,Y_T^U,Y_C^U,S^U,E_1^U,E_2^U,G_{12}^U,{\mathrm{\υ}}_{12}^U,P^U)\\ =(X_T^c+X_T^r,X_C^c+X_C^r,Y_T^c+Y_T^r,Y_C^c+Y_C^r,S^c+S^r,E_1^c+E_1^r,E_2^c+E_2^r,G_{12}^c+G_{12}^r,{\mathrm{\υ}}_{12}^c+{\mathrm{\υ}}_{12}^r,P^c+P^r)\end{array}$

$\begin{array}{c}{x}^L=(X_T^L,X_C^L,Y_T^L,Y_C^L,S^L,E_1^L,E_2^L,G_{12}^L,{\mathrm{\υ}}_{12}^L,P^L)\\ =(X_T^c-X_T^r,X_C^c-X_C^r,Y_T^c-Y_T^r,Y_C^c-Y_C^r,S^c-S^r,E_1^c-E_1^r,E_2^c-E_2^r,G_{12}^c-G_{12}^r,{\mathrm{\υ}}_{12}^c-{\mathrm{\υ}}_{12}^r,P^c-P^r)\end{array}$

Wherein, longitudinal tensile strength X_T, longitudinal compressive strength X_C, transverse tensile strength Y_T, transverse compression intensity Y_C, inplane shear is strong Degree S, 1 direction elastic modulus E₁, 2 direction elastic modulus Es₂, shear modulus G₁₂, the uncertainty of Poisson's ratio υ and external applied load P can be divided Not being expressed as interval variable, subscript U represents the value upper bound of parameter, and subscript L represents the value lower bound of parameter, during subscript c represents Center value, subscript r represents radius, x^IInterval for intensive parameter；

In described step 7, application Taylor Series Method solves the process in Tsai-Wu coefficient and displacement interval and is: utilize calculus of finite differences Try to achieve Tsai-Wu coefficient and displacement derivative dt, the dd about uncertain variables x, then the interval of Tsai-Wu coefficient and displacement is:

$\left\{\begin{array}{c}{t}^L=t-abs\left(dt\right)*x^{\′}*0.3\\ t^U=t+abs\left(dt\right)*x^{\′}*0.3\\ d^L=d-abs\left(dd\right)*x^{\′}*0.3\\ d^U=d-abs\left(dd\right)*x^{\′}*0.3\end{array}\right.$

Wherein, subscript L represents interval lower bound, and subscript U represents the interval upper bound, and abs () represents the computing that takes absolute value, and dt is The Tsai-Wu coefficient derivative to each variable, dd is the displacement derivative to each variable.

Laminated plate structure Multidisciplinary systems method for designing the most according to claim 1, it is characterised in that: described step 8 In, the strength reliability of structureIt is calculated as follows:

Situation is 1.: if t^U＞ 1 and t^L＜ 1, then

$P_s^t=\frac{1-\left(t^L\right)}{\left(t^U\right)-\left(t^L\right)}$

Situation is 2.: if t^U≤ 1, then

$P_s^t=1$

Situation is 3.: if t^L>=1, then

$P_s^t=0$

In formula, P_siFor laminate breakaway layer reliability, t is Tsai-Wu coefficient, and subscript U represents the upper bound of range of variables, subscript L Representing the lower bound of range of variables, n is the laying number of plies.

In described step 8, the rigidity reliability of structureIt is calculated as follows:

Situation is 1.: if d^U＞ 1 and d^L＜ 1, then

$P_s^d=\frac{\[d\]-\left(d^L\right)}{\left(d^U\right)-\left(d^L\right)}$

Situation is 2.: if d^U≤ 1, then

$P_s^d=1$

Situation is 3.: if d^L>=1, then

$P_s^d=0$

In formula,For laminate breakaway layer reliability, d is Tsai-Wu coefficient, and [d] is the maximum displacement that structure allows, subscript U Representing the upper bound of range of variables, subscript L represents the lower bound of range of variables.

A kind of composite laminated plate Multidisciplinary systems optimization method the most according to claim 1, it is characterised in that: institute State Reliability Constraint in step 9 to be set toComposite laminated plate work in described step 9 Skill constraint includes: avoid same direction laying to continue to exceed four layers；Adjacent two layers angle is less than 60 °；Laminate surface is minimum Want one group ± 45 ° layers of lay.

A kind of composite laminated plate Multidisciplinary systems optimization method the most according to claim 1, it is characterised in that: institute State Metropolis rule in step 10 to be set to: accept new H' with probability exp (-Δ m/m).

A kind of composite laminated plate Multidisciplinary systems optimization method the most according to claim 1, it is characterised in that: institute State and step 11 optimizes stop criterion be set to: if residual error all ratios of adjacent continuous 3 times are less than 0.001.

A kind of composite laminated plate Multidisciplinary systems optimization method the most according to claim 1, it is characterised in that: institute State in step 11 and to optimization gained thickness rounding acquisition all directions laying laying number can column be:

In formula, N_0°, N_45°, N_-45°, N_90°Representing 0 ° respectively, 45 ° ,-45 °, 90 ° optimize the number of plies after rounding according to ground floor, Ceil () represents the computing that rounds up,For optimize after 0 ° of breakaway layer thickness,45 ° of breakaway layer thickness after optimization,-45 ° of breakaway layer thickness after optimization,90 ° of breakaway layer thickness after optimization.

A kind of composite laminated plate Multidisciplinary systems optimization method the most according to claim 1, it is characterised in that: Ply stacking-sequence optimization in step 14 is designed as: under fibre strength condition of uncertainty, with laminate Tsai-Wu coefficient Little for target, laminate ply stacking-sequence is optimized design, can column be specifically:

$\left\{\begin{array}{cc}min& t_{max}\\ s.t.& seq\∈\left\{seq\right\}\end{array}\right.$

In formula, t_maxFor the maximum of Tsai-Wu coefficient, seq represents ply stacking-sequence, and { seq} represents laying storehouse.