CN106126773A - A kind of intensity prediction method containing uncertain parameter composite laminated plate lost efficacy based on whole layer - Google Patents

Abstract

The invention discloses a kind of intensity prediction method containing uncertain parameter composite laminated plate lost efficacy based on whole layer, step: (1) tests, it is thus achieved that lamina mechanical property distribution characteristic parameter and numerical value analog sample point according to Compound Material Engineering；(2) start the cycle over, utilize stiffness matrix and laying angle, calculate lamina conversion stiffness matrix；(3) according to the laminate form of the composition, the stretching of computation layer plywood, coupling and bending stiffness；(4) based on constitutive equation computation layer plywood strain in middle plane and lamina principal stress；(5) principal stress is substituted into failure criteria and calculates strength ratio, by minimum strength than corresponding lamina performance degradation；(6) step (2)～(5) is repeated, until strength ratio calculates less than 1 stopping, the whole layer failure intensity of output；(7) repeat step (2)～(6), until loop ends, obtain laminate intensity distribution range.The present invention can effectively predict the whole layer failure intensity distribution characteristics containing uncertain parameter laminate.

Description

A kind of intensity containing uncertain parameter composite laminated plate based on whole layer inefficacy is pre- Survey method

Technical field

The present invention relates to the research of composite laminated plate layer at end failure intensity Forecasting Methodology, particularly to one based on end The intensity prediction method containing uncertain parameter composite laminated plate that layer lost efficacy, it is considered to laminate mechanical property parameters the most true Qualitative and based on the laminate strength distributing information under whole layer failure damage theory determination, including the upper bound and lower bound, to ensure The correctness of Laminate Strength of Composites prediction and effectiveness, also established theory for laminate layer at end strength reliability optimization Basis.

Background technology

Composite laminated plate have light weight, specific strength high and can the advantage such as free design, have been widely used in recent years In automobile, machinery, Aero-Space and military field.Its structure and damage and failure law etc. are studied, has powerful Practical meaning in engineering.On the one hand, the intensity behavior of composite laminated plate is by component material, interfacial property, laminate structures, load The impact of the many factors such as lotus, environment and restriction, inevitably comprise many uncertain factors so that the intensity of composite It is difficult to by a kind of clear and definite relation.Therefore, develop a kind of method that can predict composite material strength to be just particularly important.Separately On the one hand, composite structure form, military service load and use environment are the most considerably complicated, the impact of composite initial imperfection and damage Hinder the development in astride hierarchy structure, spread, propagate and ultimately result in the material damage mechanism complexity with structural failure.Therefore, How to set up the test of composite effective performance to characterize and appraisement system, develop high-precision Prediction theory and method, graduated from old-type opera school Learn rational composite structure failure criteria, the reliability of quantitative evaluation composite structure and safety, be composite wood The important topic that material worker faces.

For composite research from before experimentation to theoretical property simulate, the intensity analysis of composite is also Attention and numerous studies by domestic and international scientific research personnel.Intensity about laminate has two kinds of basic consideration methods.First The method of kind is thought: any damage layer of laminate, then it is assumed that laminate destroys, and referred to as initiation layer destroys and supposes.Another kind is examined Worry is: after in laminate, certain monolayer destroys, laminate can also continue to undertake load, only after all monolayers destroy, Assert that laminate destroys, referred to as end layer is destroyed and is supposed.For most of engineering structures, the destruction of monolayer is not result in knot The inefficacy of structure itself, therefore, prediction of strength and the whole layer failure analysis of carrying out laminated composite plate structures are design composite woods The key issue that must solve during material structure, be safe, apply the premise of composite economically.In this respect, relevant grind Study carefully existing.It is emphasized, however, that such: the failure analysis of composite layer at end intensity does not consider that uncertain mechanics is joined The impact of number, the failure intensity therefore obtained tends not to fully characterize the strength characteristics of laminated plate structure, and then limits layer Board structure range of application and effectiveness.Therefore, the mechanical property parameters how considering composite is uncertain, based on The whole damage layer set up is theoretical, and it is a good problem to study that laminated plate structure intensity is given reasonably prediction.

For the whole layer failure intensity of accurate prediction interval plywood, consider the impact of uncertain mechanical property parameters, profit simultaneously With non-statistical measure, uncertain mechanical property parameters is rationally measured, and then utilize Monte Carlo simulation method Provide the distribution characteristics of the whole layer failure intensity of laminate based on whole layer failure damage theory, be that one realizes layer simply and effectively The method that board structure intensity is accurately predicted.

Summary of the invention

The technical problem to be solved in the present invention is: the reasonable assumption lost efficacy based on laminate damage layer at end, it is considered to composite wood The impact that the uncertain mechanics parameter of bed of material plywood exists, utilizes the Monte simple and effective feature of Carlo simulation method, for In Aerospace Engineering, the intensity of laminated composite plate structures is accurately predicted and lost efficacy decision problem, it is provided that a kind of simple effectively The intensity prediction method containing uncertain parameter composite laminated plate lost efficacy based on whole layer.

The technical solution used in the present invention is: a kind of based on whole layer inefficacy containing uncertain parameter composite laminated plate Intensity prediction method, it is achieved step is as follows:

The first step: according to Composite Layer mechanical property test, including longitudinal stretching test, cross tensile test with And the mechanical property parameters finite data sample point that inplane shear test obtains, refer specifically to longitudinal stretching elastic modulus E₁, laterally Tensile modulus of elasticity E₂, Poisson's ratio v₁₂And shear modulus G₁₂, form matrixWherein x₁ (1),x₁(2),…x_mP () is test data, m is the number of lamina mechanics parameter, and p is the number of each parameter sample data； Utilize non-statistical measure ash topology degree or information entropy theory that finite sample data carry out screening assessment, go forward side by side column criterion not Degree of certainty is evaluated, and obtains the uncertain distribution characterization parameter of mechanical property parameters, the upper boundAnd lower boundX；And then it is random the most raw Become Monte Carlo simulation data sample point X_i, i=1,2 ..., n, n are total number of sample point, and total number n of sample is 10⁵~ 10⁷；

Second step: the Composite Layer mechanical property Monte Carlo simulation data sample obtained based on the first step Point X_i, i=1,2 ..., n, start the cycle over, make i=1, select mechanical property sample number strong point X_i, utilize two dimension stiffness matrix [Q] And laminate laying angle, θ_l, l=1,2 ..., N, calculate the conversion stiffness matrix of every layer of laminaWherein N is laminate Total laying number；

Wherein change stiffness matrixConcrete calculation as follows:

${\[\stackrel{\‾}{Q}\]}_l={\[T\]}_l^{-1}\[Q\]{\[{\[T\]}_l^{-1}\]}^T$

In formula, [T] is coordinate conversion matrix, the inverse operation of upper table-1 representing matrix, the transposition of upper table T representing matrix.[T] Expansion be:

$\[T\]=\left[\begin{array}{ccc}{\cos }^2\mathrm{\θ}& {\sin }^2\mathrm{\θ}& 2\sin \mathrm{\θ}\cos \mathrm{\θ}\\ {\sin }^2\mathrm{\θ}& {\cos }^2\mathrm{\θ}& -2\sin \mathrm{\θ}\cos \mathrm{\θ}\\ -\sin \mathrm{\θ}\cos \mathrm{\θ}& \sin \mathrm{\θ}\cos \mathrm{\θ}& {\cos }^2\mathrm{\θ}-{\sin }^2\mathrm{\θ}\end{array}\right]$

3rd step: the conversion stiffness matrix obtained based on second stepAnd eachComposition shape according to laminate Formula, the tensible rigidity matrix [A] of computation layer plywood, Coupling stiffness matrix [B] and bending stiffness matrix [D], it may be assumed that

$A_{ij}=\underset{k=1}{\overset{N}{\Σ}}{\left({\stackrel{\‾}{Q}}_{ij}\right)}_k(z_k-z_{k-1}),B_{ij}=\frac{1}{2}\underset{k=1}{\overset{N}{\Σ}}{\left({\stackrel{\‾}{Q}}_{ij}\right)}_k(z_k^2-z_{k-1}^2),D_{ij}=\frac{1}{3}\underset{k=1}{\overset{N}{\Σ}}{\left({\stackrel{\‾}{Q}}_{ij}\right)}_k(z_k^3-z_{k-1}^3)$

A in formula_ij,B_ij,D_ijIt is respectively tensible rigidity matrix, Coupling stiffness matrix and corresponding firm of bending stiffness matrix Degree coefficient；Represent the conversion stiffness coefficient of kth layer lamina, z_kFor coordinate, z on each thickness in monolayer_k-1For each thickness in monolayer Lower coordinate；

4th step: tensible rigidity matrix [A], Coupling stiffness matrix [B] and the bending stiffness square obtained based on the 3rd step Battle array [D], utilizes constitutive equationIt is calculated:

$\left(\begin{array}{c}{\mathrm{\ϵ}}^0\\ K\end{array}\right)=\left(\begin{array}{cc}a& b\\ b& d\end{array}\right)\left(\begin{array}{c}N\\ M\end{array}\right)$

N=[N in formula_x N_y N_xy]^ΤIt is to make a concerted effort in unit width face, wherein N_xAnd N_yIt is respectively laminate x direction and y side To pulling force or pressure, N_xyFor shearing force；M=[M_x M_y M_xy]^ΤFor unit width moment of flexure and moment of torsion, wherein M_xAnd M_yIt is respectively Around y direction and the moment of flexure in x direction, M_xyFor moment of torsion；It is strain in middle plane, whereinWithIt is respectively x direction Middle face stretching strain with y direction or compressive strain,For middle shear strain；K=[K_x K_y K_xy]^ΤIt is middle the rate of curving and distortion Rate, wherein K_xAnd K_yIt is respectively the middle face rate of curving around y direction and x direction, K_xyFor middle twisting coefficient, and then in computation layer plywood The strain of arbitrary monolayer, principal strain and principal stress；In laminate, the strain of arbitrary monolayer, principal strain and principal stress solved Journey mode is as follows:

Arbitrary monolayer strain in laminate:

$\left(\begin{array}{c}{\mathrm{\ϵ}}_x\\ {\mathrm{\ϵ}}_y\\ {\mathrm{\γ}}_{xy}\end{array}\right)=\left(\begin{array}{c}{\mathrm{\ϵ}}_x^0\\ {\mathrm{\ϵ}}_y^0\\ {\mathrm{\γ}}_{xy}^0\end{array}\right)+z\left(\begin{array}{c}{K}_x\\ K_y\\ K_{xy}\end{array}\right)$

Arbitrary monolayer principal strain in laminate:

$\left(\begin{array}{c}{\mathrm{\ϵ}}_1\\ {\mathrm{\ϵ}}_2\\ {\mathrm{\γ}}_{12}\end{array}\right)={\[{\[T\]}^{-1}\]}^T\left(\begin{array}{c}{\mathrm{\ϵ}}_x\\ {\mathrm{\ϵ}}_y\\ {\mathrm{\γ}}_{xy}\end{array}\right)$

Arbitrary monolayer principal stress in laminate:

$\left(\begin{array}{c}{\mathrm{\σ}}_1\\ {\mathrm{\σ}}_2\\ {\mathrm{\τ}}_{12}\end{array}\right)=\[Q\]\left(\begin{array}{c}{\mathrm{\ϵ}}_1\\ {\mathrm{\ϵ}}_2\\ {\mathrm{\γ}}_{12}\end{array}\right)$

5th step: each monolayer principal stress the 4th step obtained substitutes in Failure Analysis of Composite Materials criterion, answers including maximum Power criterion, Tsai-Wu criterion, Tsai-Hill criterion and Hoffman criterion, calculate every layer of corresponding damage index and strong Degree compares R_l, l=1,2 ..., N, compares R by minimum strength_minCorresponding lamina performance is degenerated；The tool of lamina performance degradation Body mode refers to: when there is matrix destruction or failure by shear, make E₂=0, G₁₂=0, but E₁Keep constant, wherein E₁For longitudinally drawing Stretch elastic modelling quantity, E₂For cross directional stretch elastic modelling quantity, G₁₂For modulus of shearing；When there is fibrous fracture, E₁=0, E₂=0, G₁₂ =0.

6th step: the minimum strength obtained for the 5th step compares R_min, it is judged that whether minimum strength ratio is less than 1, if the least In 1, then external applied load amplifies R_minTimes, repeat step 2～step 5, stop until minimum strength calculates than less than 1, determine whole layer Failure intensity F_i；Wherein strength ratio is a lateral magnifying power.If strength ratio R is equal to l, the most now destroy.If R =2, then safety coefficient is 2, it is meant that when load is increased to present twice, destroys and just can occur.This method for Judge that composite failure very quickly effectively, can make load increment increase with fast speed.

7th step: judge that cycle-index i, whether equal to n, if being not equal to n, then i=i+1, repeats step 2～step Six, if equal to n, then output layer plywood failure intensity distribution, calculating terminates, and completes containing uncertain parameter composite The whole layer failure intensity prediction of laminate.Wherein laminate failure intensity distribution refers to the upper bound of failure intensityAnd lower boundF, That is:

$\stackrel{\‾}{F}=max\{F_1,F_2,...,F_n\},\underset{\‾}{F}=min\{F_1,F_2,...,F_n\}$

In formula, max and min represents and takes maximum and take minimum operation, wherein F₁,F₂,…,F_nBe respectively the 1st time, second Secondary ..., n-th circulation obtained by whole layer failure intensity.

The principle of the present invention is:

The present invention takes into full account in Practical Project laminated composite plate structures mechanics parameter inevitably uncertain, Lost efficacy as theoretical basis with whole damage layer, with non-probabilistic measurement method valid metric reasonable to mechanical property test data, solved Laminate stress and Strength Failure index, and then to laminate performance degradation, finally realize the most pre-of laminate layer at end intensity Survey.Acquired results is possible not only to reach certain accuracy and confidence, and convenience of calculation, it is simple to research design personnel understand and Accept.

Present invention advantage compared with prior art is:

The present invention is directed to Aero-Space laminated composite plate structures provide one and can consider uncertain mechanics parameter shadow The method of the whole layer failure intensity prediction rung, on the premise of keeping whole layer failure damage theory hypothesis effectively to apply, utilizes non- The correlation test data of uncertain mechanics parameter are characterized by probability metrics method, Monte Carlo simulation method are applied In the whole layer theory of failure of laminate.The Laminate Strength Predictions method set up, not only ensure that the effective of prediction of strength Property and reasonability, and consider uncertain mechanics parameter to whole layer intensity effect.Answering containing uncertain mechanical property parameters During the whole layer prediction of strength of condensation material laminated plate structure, the impact of uncertain parameter can be taken into full account, guaranteeing structural strength Computational accuracy and credibility it is greatly improved on the premise of prediction process is simple and practical.

Accompanying drawing explanation

Fig. 1 is the stream of the intensity prediction method containing uncertain parameter composite laminated plate that the present invention lost efficacy based on whole layer Cheng Tu；

Fig. 2 is the schematic diagram by loads in plane composite laminated plate in the present invention；

Fig. 3 is the longitudinal stretching elastic modulus E in the present invention₁With cross directional stretch elastic modulus E₂Determine about ash topology degree Distribution schematic diagram；

Fig. 4 is Poisson's ratio v in the present invention₁₂Shear modulus G in dough-making powder₁₂The distribution determined about ash topology degree is shown It is intended to.

Detailed description of the invention

Below in conjunction with the accompanying drawings and detailed description of the invention further illustrates the present invention.

As it is shown in figure 1, the present invention propose a kind of based on whole layer lost efficacy containing uncertain parameter composite laminated plate Intensity prediction method, comprises the following steps:

(1) according to Composite Layer mechanical property test, including longitudinal stretching test, cross tensile test and face Interior shearing test obtains mechanical property parameters longitudinal stretching elastic modulus E₁, cross directional stretch elastic modulus E₂, Poisson's ratio v₁₂And Shear modulus G₁₂Finite data sample point, constitute matrixWherein x₁(1),x₁(2),… x_mP () is test data, m is the number of lamina mechanics parameter, is 4 herein；P is the number of each parameter sample data；Profit With the non-statistical measure of ash topology degree, information entropy theory, finite sample data are carried out screening assessment, go forward side by side column criterion not Degree of certainty is evaluated；

Wherein ash topology degree is by effective for a certain mechanical property parameters measurement data sequence { x_j(i), i=1,2 ..., p} is from little New sequence is become to longer spreadAnd the new sequence after one-accumulate generates:

$\begin{array}{c}\{x_j^{\left(1\right)}\left(i\right),i=1,2,\mathrm{...},p\}=\left(x_j^{\left(1\right)}\right(1\left){,}_j^{\left(1\right)}\right(2),\mathrm{...}{,}_j^{\left(1\right)}(p\left)\right)\\ =\left(x_j^{\left(0\right)}\right(1),x_j^{\left(0\right)}(1)+x_j^{\left(0\right)}(2),\mathrm{...},x_j^{\left(0\right)}(1)+x_j^{\left(0\right)}(2)+\mathrm{...}+x_j^{\left(0\right)}(p\left)\right)\end{array}$

Definition

$\left\{\begin{array}{c}{\mathrm{\Δ}}_j\left(k\right)=\frac{x_j^{\left(1\right)}\left(p\right)}{p}k-x_j^{\left(1\right)}\left(k\right)\\ {\mathrm{\Δ}}_{j\max }=\max ({\mathrm{\Δ}}_j\left(1\right),{\mathrm{\Δ}}_j\left(2\right),\mathrm{......},{\mathrm{\Δ}}_j\left(p\right))\\ s_j=c\frac{{\mathrm{\Δ}}_{j\max }}{p}\end{array}\right.$

Wherein, c is Lycoperdon polymorphum Vitt constant factor, it is considered that be 2.5.Max represents and takes maximum operation.s_jIt is to comment based on Lycoperdon polymorphum Vitt The estimated value of the mechanical property parameters Uncertainty of valency.IfSo intervalRecognized For being the estimation interval of this mechanical property parameters actual value, k is uncertainty spreading coefficient, typically takes 3.Repeat above-mentioned gray scale reason Opinion, obtains all uncertain estimation interval of the mechanical property parameters of lamina, i.e. has the upper bound and lower bound to be respectively as follows:

$\stackrel{\‾}{X}={\[{\stackrel{\‾}{x}}_1+{\mathrm{ks}}_1,{\stackrel{\‾}{x}}_2+{\mathrm{ks}}_2,{\stackrel{\‾}{x}}_3+{\mathrm{ks}}_3,{\stackrel{\‾}{x}}_4+{\mathrm{ks}}_4\]}^T$

$\underset{\‾}{X}={\[{\stackrel{\‾}{x}}_1-{\mathrm{ks}}_1,{\stackrel{\‾}{x}}_2-{\mathrm{ks}}_2,{\stackrel{\‾}{x}}_3-{\mathrm{ks}}_3,{\stackrel{\‾}{x}}_4-{\mathrm{ks}}_4\]}^T$

Wherein x₁,x₂,x₃,x₄Laminate represents mechanical property parameters E respectively₁,E₂,v₁₂,G₁₂.According to obtaining mechanical property The Lower and upper bounds of parameter, utilizes MATLAB directly random uniformly generation Monte Carlo simulation data sample point X_i, i=1, 2 ..., n, n are total number of sample point, and total number n of sample is 10⁵～10⁷；

(2) the Composite Layer mechanical property Monte Carlo simulation data sample obtained obtained based on the first step This some X_i, i=1,2 ..., n, proceed by Monte Carlo simulation.Start the cycle over, make i=1, now select mechanical property sample Notebook data point X_i, utilize two dimension stiffness matrix [Q] and laminate laying angle, θ_l, l=1,2 ..., N, calculate every layer of lamina Conversion stiffness matrixWherein two dimension stiffness matrix [Q] and mechanical property sample number strong point X_iRelation as follows:

$\[Q\]=\left[\begin{array}{ccc}{Q}_{11}& Q_{12}& 0\\ Q_{12}& Q_{22}& 0\\ 0& 0& Q_{66}\end{array}\right],X_i={\left[\begin{array}{cccc}{x}_{1i}& x_{2i}& x_{3i}& x_{4i}\end{array}\right]}^T={\left[\begin{array}{cccc}{E}_1& E_2& v_{12}& G_{12}\end{array}\right]}^T$

WhereinQ₁₂=v₁₂Q₂₂,Q₆₆=G₁₂,Conversion stiffness matrix 'sConcrete calculation as follows:

${\[\stackrel{\‾}{Q}\]}_l={\[T\]}_l^{-1}\[Q\]{\[{\[T\]}_l^{-1}\]}^T$

In formula, [T] is coordinate conversion matrix, the inverse operation of upper table-1 representing matrix, the transposition of upper table T representing matrix.[T] With the relational expression of laying angle, θ it is:

$\[T\]=\left[\begin{array}{ccc}{\cos }^2\mathrm{\θ}& {\sin }^2\mathrm{\θ}& 2\sin \mathrm{\θ}\cos \mathrm{\θ}\\ {\sin }^2\mathrm{\θ}& {\cos }^2\mathrm{\θ}& -2\sin \mathrm{\θ}\cos \mathrm{\θ}\\ -\sin \mathrm{\θ}\cos \mathrm{\θ}& \sin \mathrm{\θ}\cos \mathrm{\θ}& {\cos }^2\mathrm{\θ}-{\sin }^2\mathrm{\θ}\end{array}\right]$

(3) the conversion stiffness matrix obtained based on second stepUnderstand its eachFor:

${\stackrel{\‾}{Q}}_{11}=m^4{Q}_{11}+2m^2{n}^2(Q_{12}+2Q_{66})+n^4{Q}_{22}$

${\stackrel{\‾}{Q}}_{12}=m^2{n}^2(Q_{11}+Q_{22}-4Q_{66})+(m^4+n^4)Q_{12}$

${\stackrel{\‾}{Q}}_{22}=n^4{Q}_{11}+2m^2{n}^2(Q_{12}+2Q_{66})+m^4{Q}_{22}$

${\stackrel{\‾}{Q}}_{16}=m^{3}n(Q_{11}-Q_{12})+{\mathrm{mn}}^3(Q_{12}-Q_{22})-2mn(m^2-n^2)Q_{66}$

${\stackrel{\‾}{Q}}_{26}={\mathrm{mn}}^3(Q_{11}-Q_{12})+m^{3}n(Q_{12}-Q_{22})+2mn(m^2-n^2)Q_{66}$

${\stackrel{\‾}{Q}}_{66}=m^2{n}^2(Q_{11}+Q_{22}-2Q_{12}-2Q_{66})+(m^4+n^4)Q_{66}$

Here, there is m=cos θ, n=sin θ.According to the form of the composition of laminate, refer to laying angle and overlay thickness, calculate The tensible rigidity matrix [A] of laminate, Coupling stiffness matrix [B] and bending stiffness matrix [D], it may be assumed that

$A_{ij}=\∫{\stackrel{\‾}{Q}}_{ij}dz=\underset{k=1}{\overset{N}{\Σ}}{\left({\stackrel{\‾}{Q}}_{ij}\right)}_k(z_k-z_{k-1})$

$B_{ij}=\∫{\stackrel{\‾}{Q}}_{ij}zdz=\frac{1}{2}\underset{k=1}{\overset{N}{\Σ}}{\left({\stackrel{\‾}{Q}}_{ij}\right)}_k(z_k^2-z_{k-1}^2)$

$D_{ij}=\∫{\stackrel{\‾}{Q}}_{ij}{z}^{2}dz=\frac{1}{3}\underset{k=1}{\overset{N}{\Σ}}{\left({\stackrel{\‾}{Q}}_{ij}\right)}_k(z_k^3-z_{k-1}^3)$

A in formula_ij,B_ij,D_ijIt is respectively tensible rigidity matrix, Coupling stiffness matrix and corresponding firm of bending stiffness matrix Degree coefficient；When laminate is symmetrical laying, there is B_ij=0；Represent the conversion stiffness coefficient of kth layer lamina, z_kFor respectively Coordinate on thickness in monolayer, z_k-1For coordinate under each thickness in monolayer；

(4) tensible rigidity matrix [A], Coupling stiffness matrix [B] and the bending stiffness matrix obtained based on the 3rd step [D], utilizes constitutive equationIt is calculated:

$\left(\begin{array}{c}{\mathrm{\ϵ}}^0\\ K\end{array}\right)=\left(\begin{array}{cc}a& b\\ b& d\end{array}\right)\left(\begin{array}{c}N\\ M\end{array}\right)$

N=[N in formula_x N_y N_xy]^ΤIt is to make a concerted effort in unit width face, wherein N_xAnd N_yIt is respectively laminate x direction and y side To pulling force or pressure, N_xyFor shearing force；M=[M_x M_y M_xy]^ΤFor unit width moment of flexure and moment of torsion, wherein M_xAnd M_yIt is respectively Around y direction and the moment of flexure in x direction, M_xyFor moment of torsion；It is strain in middle plane, whereinWithIt is respectively x side To with the middle face stretching strain in y direction or compressive strain,For middle shear strain；K=[K_x K_y K_xy]^ΤIt is middle the rate of curving and distortion Rate, wherein K_xAnd K_yIt is respectively the middle face rate of curving around y direction and x direction, K_xyFor middle twisting coefficient.If Analysis of Symmetric Laminated Plates, Then have:

N=A ε⁰, M=DK

ε⁰=aN, K=dM

And then the strain of arbitrary monolayer, principal strain and principal stress in computation layer plywood；Arbitrary monolayer strain in laminate, The solution procedure mode of principal strain and principal stress is as follows:

Arbitrary monolayer strain in laminate:

$\left(\begin{array}{c}{\mathrm{\ϵ}}_x\\ {\mathrm{\ϵ}}_y\\ {\mathrm{\γ}}_{xy}\end{array}\right)=\left(\begin{array}{c}{\mathrm{\ϵ}}_x^0\\ {\mathrm{\ϵ}}_y^0\\ {\mathrm{\γ}}_{xy}^0\end{array}\right)+z\left(\begin{array}{c}{K}_x\\ K_y\\ K_{xy}\end{array}\right)$

Arbitrary monolayer principal strain in laminate:

$\left(\begin{array}{c}{\mathrm{\ϵ}}_1\\ {\mathrm{\ϵ}}_2\\ {\mathrm{\γ}}_{12}\end{array}\right)={\[{\[T\]}^{-1}\]}^T\left(\begin{array}{c}{\mathrm{\ϵ}}_x\\ {\mathrm{\ϵ}}_y\\ {\mathrm{\γ}}_{xy}\end{array}\right)$

Arbitrary monolayer principal stress in laminate:

$\left(\begin{array}{c}{\mathrm{\σ}}_1\\ {\mathrm{\σ}}_2\\ {\mathrm{\τ}}_{12}\end{array}\right)=\[Q\]\left(\begin{array}{c}{\mathrm{\ϵ}}_1\\ {\mathrm{\ϵ}}_2\\ {\mathrm{\γ}}_{12}\end{array}\right)$

(5) each monolayer principal stress [σ that the 4th step is obtained₁ σ₂ τ₁₂]^ΤSubstitute in Failure Analysis of Composite Materials criterion, including Maximum stress criterion, Tsai-Wu criterion, Tsai-Hill criterion and Hoffman criterion, calculate every layer of corresponding damage index； Wherein Tsai-Wu criterion refer to material do not occur destroy condition be:

$F.I.=F_1{\mathrm{\&sigma;}}_1+F_2{\mathrm{\&sigma;}}_2+F_{11}{\mathrm{\&sigma;}}_1^2+F_{22}{\mathrm{\&sigma;}}_2^2+F_{66}{\mathrm{\&tau;}}_{12}^2+2F_{12}{\mathrm{\&sigma;}}_1{\mathrm{\&sigma;}}_2<1$

In formula X_t,X_cIt is respectively longitudinal stretching, compressive ultimate strength；Y_t,Y_cIt is respectively cross directional stretch, compressive ultimate strength；S is inplane shear Ultimate strength.F.I. it is damage index.In order to use Failure Analysis of Composite Materials criterion more easily, introduce strength ratio R, should by maximum Power state substitutes into be had:I.e. have:

$F_1{\mathrm{R\&sigma;}}_1+F_2{\mathrm{R\&sigma;}}_2+F_{11}{R}^2{\mathrm{\&sigma;}}_1^2+F_{22}{R}^2{\mathrm{\&sigma;}}_2^2+F_{66}{R}^2{\mathrm{\&tau;}}_{12}^2+2F_{12}{R}^2{\mathrm{\&sigma;}}_1{\mathrm{\&sigma;}}_2=1$

OrderB=F₁σ₁+F₂σ₂, then have strength ratio R to be:

$R=\frac{-b+\sqrt{b^2+4a}}{2a}$

Minimum strength in every layer of strength ratio is compared R_minCorresponding lamina performance is degenerated；Lamina performance degradation Concrete mode refers to: when there is matrix destruction or failure by shear, make E₂=0, G₁₂=0, but E₁Keep constant, wherein E₁For longitudinal direction Tensile modulus of elasticity, E₂For cross directional stretch elastic modelling quantity, G₁₂For modulus of shearing；When there is fibrous fracture, E₁=0, E₂=0, G₁₂=0.

(6) in the every layer of strength ratio obtained for the 5th step, minimum strength compares R_min, it is judged that whether minimum strength ratio is less than 1, If not less than 1, then external applied load amplifies R_minTimes, repeat step 2～step 5, to the composite laminated plate after performance degradation Carry out intensity iterative, stop until minimum strength calculates than less than 1, determine whole layer failure intensity F_i:

F_i=R_min(1)·R_min(2)…R_min(k)·F₀

R in formula_min(1),R_min(2),…,R_minK () is the minimum strength ratio in iterative process more than 1, k is corresponding number. F₀For the initial external applied load applied.Wherein strength ratio is a lateral magnifying power.If strength ratio R is equal to l, the most now occur Destroy.If R=2, then safety coefficient is 2, it is meant that when load is increased to present twice, destroys and just can occur.This The method of kind is for judging that composite failure very quickly effectively, can make load increment increase with fast speed.

(7) judge that cycle-index i, whether equal to n, if being not equal to n, then has cycle-index i=i+1, repeat step 2～ Step 6, the distribution character carrying out laminate layer at end failure intensity solves, if equal to n, then output is containing uncertain mechanics parameter Laminate failure intensity distribution, calculating terminates, and completes the whole layer containing uncertain parameter composite laminated plate and lost efficacy strong Degree prediction.Wherein laminate failure intensity distribution refers to the upper bound of failure intensityAnd lower boundF, it may be assumed that

$\stackrel{\&OverBar;}{F}=max\{F_1,F_2,...,F_n\},\underset{\&OverBar;}{F}=min\{F_1,F_2,...,F_n\}$

In formula, max and min represents and takes maximum and take minimum operation, wherein F₁,F₂,…,F_nBe respectively the 1st time, second Secondary ..., n-th circulation obtained by whole layer failure intensity.

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 Show by tensile load N in face_xAnalysis of Symmetric Laminated Plates carry out whole layer prediction of strength.The material of this laminate is T300/QY8911, It is as shown in the table for 14 groups of mechanical property parameters test datas.The lamina thickness of this laminate is 0.125mm, and layering type is [0/ 45/-45/90]_s.Laminate strength character parameter is X_t=1500MPa, X_c=1200MPa, Y_t=50MPa, Y_c=250MPa, S =70MPa.

Based on whole layer theory of failure it is assumed that by means of programming software MATLAB, it is considered to the uncertain shadow of mechanical property parameters Ring, be predicted analyzing to laminate layer at the end intensity of composite.Wherein, Failure Analysis of Composite Materials criterion considers to use Tasi- Wu criterion, and do not consider the uncertainty analysis of strength character parameter.The uncertain employing non-statistical tolerance side of mechanical property parameters Method gray scale theoretical appraisal.T300/QY8911 mechanical property parameters test data is as shown in the table:

Table 1 T300/QY8911 mechanical property parameters test data

The mechanics parameter utilizing ash topology degree to determine is listed in Table 2, the distribution of the uncertain assessment result of mechanical property parameters Scope schematic diagram is as shown in Figure 3, Figure 4:

The uncertain assessment of table 2 Composite Layer

Composite laminated plate layer at the end failure intensity distribution obtained is as follows:

Table 3 composite laminated plate layer at end failure intensity distribution (N)

This embodiment completes the whole layer prediction of strength containing uncertain parameter composite laminated plate by MATLAB.Propose Method can effectively consider the existence of uncertain mechanical property parameters, and Monte Carlo simulation method calculates simple, it is simple to Understand, ensureing to calculate rational while, calculate convenient credible.

In sum, the present invention proposes a kind of strong containing uncertain parameter composite laminated plate lost efficacy based on whole layer Degree Forecasting Methodology.First, test the finite sample data determined according to composite materials property, utilize ash topology degree, information The non-statistical measure of entropy theory, obtains the reasonable uncertain tolerance interval of lamina mechanical property, and then random uniformly product The numerical point of raw Monte Carlo simulation；Mechanical property parameters numerical simulation point obtained by utilization, in conjunction with two dimension stiffness matrix And coordinate conversion matrix, calculate the conversion stiffness matrix of lamina；It is then based on laminate tensible rigidity, coupling stiffness and bending Rigidity Calculation formula and constitutive equation, strain that computation layer plywood is each layer and stress；Stress is substituted into Failure Analysis of Composite Materials accurate Then carry out the calculating of invalid principle and strength ratio, i.e. based on whole layer theory of failure, the intensity of composite laminated plate is carried out pre- Survey.Finally, utilize Monte Carlo method for numerical simulation, solve the distribution of whole layer intensity.

Below it is only the concrete steps of the present invention, protection scope of the present invention is not constituted any limitation；All employing is equal to The technical scheme that conversion or equivalence are replaced and formed, 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 (8)

1. the intensity prediction method containing uncertain parameter composite laminated plate lost efficacy based on whole layer, it is characterised in that real Existing step is as follows:

The first step: the mechanical property parameters finite data sample point obtained according to Composite Layer mechanical property test, shape Become matrixWherein x₁(1),x₁(2),…x_mP () is test data, m is lamina mechanics The number of parameter, p is the number of each parameter sample data；Utilize non-statistical measure that finite sample data are screened Assessment, obtains the uncertain distribution characterization parameter of mechanical property parameters, the upper boundAnd lower boundX；And then uniformly generate Monte at random Carlo simulation data sample point X_i, i=1,2 ..., n, n are total number of sample point；

Second step: the Composite Layer mechanical property Monte Carlo simulation data sample point X obtained based on the first step_i,i =1,2 ..., n, start the cycle over, make i=1, select mechanical property sample number strong point X_i, utilize two dimension stiffness matrix [Q] and lamination Plate laying angle, θ_l, l=1,2 ..., N, calculate the conversion stiffness matrix of every layer of laminaWherein N is total paving of laminate The number of plies；

3rd step: the conversion stiffness matrix obtained based on second stepAnd eachAccording to the form of the composition of laminate, meter Calculate the tensible rigidity matrix [A] of laminate, Coupling stiffness matrix [B] and bending stiffness matrix [D], it may be assumed that

$A_{ij}=\underset{k=1}{\overset{N}{\&Sigma;}}{\left({\stackrel{\&OverBar;}{Q}}_{ij}\right)}_k(z_k-z_{k-1}),B_{ij}=\frac{1}{2}\underset{k=1}{\overset{N}{\&Sigma;}}{\left({\stackrel{\&OverBar;}{Q}}_{ij}\right)}_k(z_k^2-z_{k-1}^2),D_{ij}=\frac{1}{3}\underset{k=1}{\overset{N}{\&Sigma;}}{\left({\stackrel{\&OverBar;}{Q}}_{ij}\right)}_k(z_k^3-z_{k-1}^3)$

A in formula_ij,B_ij,D_ijIt is respectively the rigidity system that tensible rigidity matrix, Coupling stiffness matrix and bending stiffness matrix are corresponding Number；Represent the conversion stiffness coefficient of kth layer lamina, z_kFor coordinate, z on each thickness in monolayer_k-1For sitting under each thickness in monolayer Mark；

4th step: tensible rigidity matrix [A], Coupling stiffness matrix [B] and the bending stiffness matrix obtained based on the 3rd step [D], utilizes constitutive equationIt is calculated:

$\left(\begin{array}{c}{\mathrm{\&epsiv;}}^0\\ K\end{array}\right)=\left(\begin{array}{cc}a& b\\ b& d\end{array}\right)\left(\begin{array}{c}N\\ M\end{array}\right)$

N=[N in formula_x N_y N_xy]^TIt is to make a concerted effort in unit width face, wherein N_xAnd N_yIt is respectively drawing of laminate x direction and y direction Power or pressure, N_xyFor shearing force；M=[M_x M_y M_xy]^TFor unit width moment of flexure and moment of torsion, wherein M_xAnd M_yIt is respectively around y direction With the moment of flexure in x direction, M_xyFor moment of torsion；It is strain in middle plane, whereinWithIt is respectively x direction and y direction The stretching strain of middle face or compressive strain,For middle shear strain；K=[K_x K_y K_xy]^TIt is middle the rate of curving and twisting coefficient, wherein K_x And K_yIt is respectively the middle face rate of curving around y direction and x direction, K_xyFor middle twisting coefficient, and then arbitrary monolayer in computation layer plywood Strain, principal strain and principal stress；

5th step: each monolayer principal stress the 4th step obtained substitutes in Failure Analysis of Composite Materials criterion, calculates every layer of correspondence Damage index and strength ratio R_l, l=1,2 ..., N, compares R by minimum strength_minCorresponding lamina performance is degenerated；

6th step: the minimum strength obtained for the 5th step compares R_min, it is judged that whether minimum strength is than less than 1, if not less than 1, Then external applied load amplifies R_minTimes, repeat second step～the 5th step, stop until minimum strength calculates than less than 1, determine that whole layer lost efficacy Intensity F_i；

7th step: judge that cycle-index i, whether equal to n, if being not equal to n, then i=i+1, repeats second step～the 6th step, as Fruit is equal to n, then output layer plywood failure intensity distribution, and calculating terminates, and completes containing uncertain parameter composite laminated The whole layer failure intensity prediction of plate.

A kind of intensity containing uncertain parameter composite laminated plate based on whole layer inefficacy the most according to claim 1 is pre- Survey method, it is characterised in that: the lamina mechanical property test in the described first step refers to longitudinal stretching test, cross tensile test And inplane shear test；Mechanical property parameters refers to longitudinal stretching elastic modulus E₁, cross directional stretch elastic modulus E₂, Poisson's ratio v₁₂ And shear modulus G₁₂；Non-statistical measure refers to ash topology degree, information entropy theory.

A kind of intensity containing uncertain parameter composite laminated plate based on whole layer inefficacy the most according to claim 1 is pre- Survey method, it is characterised in that: total number n of sample in the described first step is 10⁵～10⁷。

A kind of intensity containing uncertain parameter composite laminated plate based on whole layer inefficacy the most according to claim 1 is pre- Survey method, it is characterised in that: the conversion stiffness matrix in described second stepConcrete calculation as follows:

${\&lsqb;\stackrel{\&OverBar;}{Q}\&rsqb;}_l={\&lsqb;T\&rsqb;}_l^{-1}\&lsqb;Q\&rsqb;{\&lsqb;{\&lsqb;T\&rsqb;}_l^{-1}\&rsqb;}^T$

In formula, [T] is coordinate conversion matrix, the inverse operation of upper table-1 representing matrix, the transposition of upper table T representing matrix, the exhibition of [T] Open type is:

$\&lsqb;T\&rsqb;=\left[\begin{array}{ccc}{\cos }^2\mathrm{\&theta;}& {\sin }^2\mathrm{\&theta;}& 2\sin \mathrm{\&theta;}\cos \mathrm{\&theta;}\\ {\sin }^2\mathrm{\&theta;}& {\cos }^2\mathrm{\&theta;}& -2\sin \mathrm{\&theta;}\cos \mathrm{\&theta;}\\ -\sin \mathrm{\&theta;}\cos \mathrm{\&theta;}& \sin \mathrm{\&theta;}\cos \mathrm{\&theta;}& {\cos }^2\mathrm{\&theta;}-{\sin }^2\mathrm{\&theta;}\end{array}\right].$

A kind of intensity containing uncertain parameter composite laminated plate based on whole layer inefficacy the most according to claim 1 is pre- Survey method, it is characterised in that: in the laminate in described 4th step, the strain of arbitrary monolayer, principal strain and principal stress solved Journey mode is as follows:

Arbitrary monolayer strain in laminate:

$\left(\begin{array}{c}{\mathrm{\&epsiv;}}_x\\ {\mathrm{\&epsiv;}}_y\\ {\mathrm{\&gamma;}}_{xy}\end{array}\right)=\left(\begin{array}{c}{\mathrm{\&epsiv;}}_x^0\\ {\mathrm{\&epsiv;}}_y^0\\ {\mathrm{\&gamma;}}_{xy}^0\end{array}\right)+z\left(\begin{array}{c}{K}_x\\ K_y\\ K_{xy}\end{array}\right)$

Arbitrary monolayer principal strain in laminate:

$\left(\begin{array}{c}{\mathrm{\&epsiv;}}_1\\ {\mathrm{\&epsiv;}}_2\\ {\mathrm{\&gamma;}}_{12}\end{array}\right)={\&lsqb;{\&lsqb;T\&rsqb;}^{-1}\&rsqb;}^T\left(\begin{array}{c}{\mathrm{\&epsiv;}}_x\\ {\mathrm{\&epsiv;}}_y\\ {\mathrm{\&gamma;}}_{xy}\end{array}\right)$

Arbitrary monolayer principal stress in laminate:

$\left(\begin{array}{c}{\mathrm{\&sigma;}}_1\\ {\mathrm{\&sigma;}}_2\\ {\mathrm{\&tau;}}_{12}\end{array}\right)=\&lsqb;Q\&rsqb;\left(\begin{array}{c}{\mathrm{\&epsiv;}}_1\\ {\mathrm{\&epsiv;}}_2\\ {\mathrm{\&gamma;}}_{12}\end{array}\right).$

A kind of intensity containing uncertain parameter composite laminated plate based on whole layer inefficacy the most according to claim 1 is pre- Survey method, it is characterised in that: the Failure Analysis of Composite Materials criterion in described 5th step include maximum stress criterion, Tsai-Wu criterion, Tsai-Hill criterion and Hoffman criterion.

A kind of intensity containing uncertain parameter composite laminated plate based on whole layer inefficacy the most according to claim 1 is pre- Survey method, it is characterised in that: the concrete mode of the lamina performance degradation in described 5th step refers to: destroys when there is matrix or cuts Cut through bad time, make E₂=0, G₁₂=0, but E₁Keep constant, wherein E₁For longitudinal stretching elastic modelling quantity, E₂Elastic for cross directional stretch Modulus, G₁₂For modulus of shearing；When there is fibrous fracture, E₁=0, E₂=0, G₁₂=0.

A kind of intensity containing uncertain parameter composite laminated plate based on whole layer inefficacy the most according to claim 1 is pre- Survey method, it is characterised in that: the laminate failure intensity distribution in described 7th step refers to the upper bound of failure intensityUnder with BoundaryF, it may be assumed that

$\stackrel{\&OverBar;}{F}=max\{F_1,F_2,...,F_n\},\underset{\&OverBar;}{F}=min\{F_1,F_2,...,F_n\}$

In formula, max and min represents and takes maximum and take minimum operation, wherein F₁,F₂,…,F_nBe respectively the 1st time, second Secondary ..., n-th circulation obtained by whole layer failure intensity.