CN101788425A - Method for determining separation and distribution of structural-member composite crack front stress intensity factors - Google Patents

Abstract

The invention relates to a method determining separation and distribution of structural-member composite crack front stress intensity factors. The method comprises the following steps: giving thermal load, surface force load and volume force load borne by a structural member, and a universal weighting function method basic equation for three-dimensional I, II, III composite crack problems under the independent or combined actions of the thermal load, the surface force load and the volume force load; dividing the crack front into random N-1 numbered subsections through N numbered nodes, and introducing a basic interpolation function Nj(s) and a partial variation function N'j(s) at each node j, thereby constructing a finite number of partial variation modes and interpolation modes; and then introducing 3 basic reference loads to solve the basic equation, thereby determining the numerical solution of the separation and distribution of composite stress intensity factors KI, KII and KIII. By utilizing the self consistency, the method can obtain the high-precision exact solution of the distribution of the three-dimensional crack front composite stress intensity factors KI, KII and KIII by constructing an iterative process.

Description

Definite method that a kind of structural-member composite crack front stress intensity factors separates and distributes

Technical field

The present invention relates to a kind of safety of structure analysis and evaluation field, especially a kind of structural-member composite crack front stress intensity factors K _I, K _IIAnd K _IIISeparation and they are along the definite method of the distribution of crack front and the method for designing of COMPUTER CALCULATION program.It is used in safety of structure evaluation process high precision and determine the stress strength factor K of three-dimensional composite crack front in the structural member expeditiously _I, K _IIAnd K _IIISeparation and they are along the distribution of crack front.

Work as stress strength factor K _I, K _IIAnd K _IIIDistribution determine after, just can determine the propagation direction of crackle under external load function, and compare with the fracture toughness Kc of material, determine the security of structural member; Perhaps, can be according to K _I, K _IIAnd K _IIIVariation range, carry out fatigue strength and check, determine fatigue lifetime.The actual execution efficient of this method can improve tens times and even hundreds of times than existing other method; Particularly for the situation of shock load, utilize existing other method to need stress intensity factor that several weeks and even several months just can finish to separate and they set the tasks along the distribution of crack front, utilize this method to time a few hours, to finish at several minutes.

Background technology

Common, by COMPUTER CALCULATION the stress intensity factor distribution of crack front in the structural member is determined that two kinds of methods are arranged.A kind of is the Elasticity direct method, needs earlier the body of being with crackle to be carried out Elasticity and calculates, and determines displacement field or stress field under the loading; According to the displacement field or the stress field of trying to achieve, carry out the calculating of stress strength factor K value in the each point place pointwise of crack front and determine then.The concrete method of determining of calculating has stress field singularity method, crack surface opening displacement method and J integral method etc.When calculating the stress intensity factor of composite crack front, need further to K with the J integral method _I, K _IIAnd K _IIISeparate.Existing K _I, K _IIAnd K _IIISeparation method reciprocation integral method and virtual crack closure methods etc. are arranged.The shortcoming of these methods is that efficient is low, particularly when load is time dependent variable load, need be to each time point, all to the body of band crackle carry out Elasticity calculate (such as, carrying out finite element method or boundary element method calculates), determine displacement field or stress field under this moment loading; Then according to this displacement field or stress field constantly, again at the each point place of crack front, by getting the limit, the method for asking the crack surface opening displacement or asking the J integration to separate then, the definite K of pointwise ground calculating _I, K _IIAnd K _IIIValue.To engineering problem, because the workload that each finite element method or boundary element method calculate is all bigger, so total efficiency is very low.Second method is based on the stress weight-function method of superposition principle, need earlier to not with the body of crackle carry out Elasticity calculate (such as, carry out finite element method or boundary element method and calculate), determine the stress field under the loading; Utilize superposition principle then, the negative value of the stress of being tried to achieve is put on the crack surface; Again according to the stress weight function on the crack surface of this cracks in body of having got well as calculated in advance, the integration of the product by power load above the crack surface and stress weight function is determined the K value at the each point place of crack front.Carry out the document of this method, generally this method is abbreviated as weight-function method.But in fact it only is applicable to the situation that the loading of face power is arranged on the crack surface, can not calculate definite to other load (such as temperature loading or body force load).And traditional weight-function method can only be applicable to the crack problem of simple I type, simple II type or simple III type, can not be applied to the calculating of the compound Mixed Mode Crack problem of I, II, III type.Therefore, weight-function method described in these documents should be called as the stress weight-function method or the face power weight-function method of single type crack problem definitely, can consider temperature loading, face power load and body force load simultaneously described in it and the present patent application, and be applicable to the general weight-function method difference of Mixed Mode Crack problem of Mixed Mode Crack problem.When load was time dependent variable load, the efficient of traditional single type crack problem stress weight-function method was also very low.Because also need not with the body of crackle, carry out repeatedly Elasticity calculate (such as, carry out finite element method or boundary element method and calculate), determine the stress field under each loading constantly, could determine the K value in this moment of each point place then by integral and calculating.

Common, the crack problem of the body that traditional single type crack problem stress weight-function method only is applied to geometric configuration fairly simple (maybe can do to simplify and handle) under simple I type (or simple II type, or simple III type) loading; During use, generally need obtain the approximate expression and the corresponding reference loading stress intensity factor value of the stress weight function at each point place on the crack surface earlier.And this point only does obtaining for the fairly simple situation of shape, and the situation for body profile or how much more complicated of crackle is difficult to accomplish.For the situation of geometric configuration more complicated, then need to use methods such as finite elements method of approximation, Stiffness Matrix derivative method and microtomy to determine weight function; Then, could pass through the integration of the product of face power load and weight function, ask the K value.Methods such as employed in this respect finite elements method of approximation, Stiffness Matrix derivative method and microtomy for three-dimensional cracks, only are suitable for finding the solution the problem of linear pattern crack front; For the problem (such as ellipse, semiellipse and part ellipse immerged crack or surface crack problem) of shaped form crack front, mathematical simulation result just is on duty mutually; Result of calculation shows that ratio of precision is lower.And these methods are for fairly simple load condition, and promptly stress intensity factor still can obtain comparatively satisfied result along the milder situation of the changes in distribution of crack front; But for the load condition of more complicated, promptly stress intensity factor is along the more violent situation of the changes in distribution of crack front, and error is just very big, and precision is very low, poor effect.

Low in order to solve in above these methods ubiquitous counting yield, and exist in the single type crack problem stress weight-function method be not suitable for temperature loading and body force load, for shaped form crack front problem, the mathematical simulation weak effect, problems such as precision is low, applicant has proposed a kind of technical method that is called the limited variational method in patent of invention " a kind of method for confirming stress intensity factor distribution on member crack tip " (patent No. ZL200610050685.6), be used for high precision and determine the distribution of the stress intensity factor of single type crack front expeditiously.But the related method of this patent can only be used for determining crackle under simple I type (or simple II type, or simple III type) loading, the K of crack front _I(or K _II, or K _III) distribution, can not be used for determining the K of crackle crack front under the compound complex load effect situation of I type, II type and III type _I, K _IIAnd K _IIIDistribution.

The shortcoming that prior art exists is: stress field singularity method in (1) Elasticity direct method and crack surface opening displacement method ask the efficient of stress strength factor K value low; (2) to add that the reciprocation integral method is carried out the efficient of stress intensity factor decouples computation low for the J integral method in the Elasticity direct method; (3) the J integral method in the Elasticity direct method adds that the virtual crack closure methods carries out that the efficient of stress intensity factor decouples computation is low, computational accuracy is low; (4) usually the used stress weight-function method based on superposition principle only is applicable to and crack problem under simple I type (or simple II type, or the simple III type) loading is not suitable for the compound Mixed Mode Crack problem of I type, II type and III type; (5) based on the stress weight-function method of superposition principle for time dependent variable load situation, counting yield is low, and is not suitable for temperature loading and body force load; (6) methods such as finite elements method of approximation, Stiffness Matrix derivative method and microtomy in the usually used stress weight-function method, for shaped form crack front problem, the mathematical simulation weak effect, precision is low; (7) methods such as finite elements method of approximation, Stiffness Matrix derivative method and microtomy in the usually used stress weight-function method, along the more violent situation of the changes in distribution of crack front, the error of calculation is big for stress intensity factor, and precision is low; (8) in stress weight-function method use based on superposition principle, be used as with reference to the corresponding of load and must know in advance with reference to the loading stress intensity factor, this is a prerequisite restrictive condition; (9) used technology only is applicable to simple I type (or simple II type among the patented technology ZL 200610050685.6, or simple III type) crack problem under the loading can not be used for finding the solution the K of crackle crack front under the compound complex load effect situation of I type, II type and III type _I, K _IIAnd K _IIISeparation and they are along Distribution calculation of crack front etc.

Summary of the invention

For the counting yield that overcomes existing method for confirming stress intensity factor distribution on member crack tip is low, mathematical simulation weak effect, precision are low, and the K that is not suitable for crackle crack front under the compound complex load effect situation of I type, II type and III type _I, K _IIAnd K _IIISeparation and they are along the deficiency of Distribution calculation of crack front etc., the invention provides definite method that a kind of structural-member composite crack front stress intensity factors separates and distributes, the high precision and the stress strength factor K of march line style three-dimensional cracks leading edge expeditiously _I, K _IIAnd K _IIISeparation and determine their distributions along crack front; And the counting yield height, mathematical simulation is effective, precision is high.

The technical solution adopted for the present invention to solve the technical problems is:

Definite method that a kind of structural-member composite crack front stress intensity factors separates and distributes may further comprise the steps:

1), thermal force, surface force load and the body force load that provides structural member and born, and at the independent compound general weight-function method fundamental equation of representing with variation type integral equation form of Mixed Mode Crack problem (challenge variation type integral equation) of three-dimensional I, II, III type under effect or the acting in conjunction of described three kinds of load, suc as formula (1):

Wherein, variation symbol δ _c(...) expression physical quantity (...) is about the inclined to one side variation of the single order of crack position; Promptly ought have only crack position to change, and other is not when changing, the first variation of respective physical amount (...); u ^(r), t ^(r)And K _I ^(r), K _II ^(r), K _III ^(r)Be respectively some displacement function, boundary forces function and I, II, III type stress intensity factor distribution functions of doing the time spent arbitrarily with reference to load (r); u ^(a), t ^(a), f ^(a), Θ ^(a)And K _I ^(a), K _II ^(a), K _III ^(a)Be respectively the required load of finding the solution (a) the boundary displacement function of doing the time spent, boundary forces function, body force function, Temperature Distribution function and along I, II, the III type stress intensity factor distribution function of crack front; E, v, H and α are respectively elastic modulus, Poisson ratio, equivalent elastic constant and the thermal expansivity of material, and Γ is a crack front, and s is the arc length along crack front; ∑ _t, ∑ _u, ∑ and V be respectively face power known boundaries, displacement known boundaries, body border and body volume; N is outer normal vector;

2), with N node, crack front is divided into any N-1 son section, at basic interpolation type function N of each node j place introducing _j(s) and a local variational function N ' _j(s), their formulas (2) that all satisfies condition:

$N_j\left(s_i\right)={\mathrm{\δ}}_{\mathrm{ij}}=\left\{\begin{array}{cc}1& (i=j)\\ 0& (i\≠j)\end{array}\right.,$

$\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{N}_j\left(s\right)=1$

3), select 3 kinds separate basic with reference to load r ₁, r ₂And r ₃, their I, II, III type are respectively K with reference to the loading stress intensity factor along the distribution function of crack front _I ^(r1), K _II ^(r2)And K _III ^(r3)Stress strength factor K with the unknown _I ^(a), K _II ^(a), K _III ^(a)Distribution function along crack front is expressed as formula (3) and formula (4):

$K_m^{\left(a\right)}={\mathrm{\Ψ}}_m\·K_m^{\left(r_m^0\right)},m=I,\mathrm{II},\mathrm{III}---\left(3\right)$

${\mathrm{\Ψ}}_m=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{A}_{\mathrm{mi}}{N}_i\left(s\right),m=I,\mathrm{II},\mathrm{III}---\left(4\right)$

Wherein,

M=I, II, III is respectively substantially with reference to load r ₁, r ₂And r ₃Pairing I, II and III type are with reference to the distribution function K of loading stress intensity factor along crack front _I ^(r1), K _II ^(r2)And K _III ^(r3)The approximate function that certain is suitable;

4), introduce the basic variation pattern δ of a macroscopic view at whole crack front _ca _s ⁰, suc as formula (5):

${\mathrm{\&delta;}}_{\mathrm{<figure-callout\; id="0"\; label="c\; a\; s"\; filenames="HSA00000031446000091.png,HSA00000031446000101.png"\; state="\{\{state\}\}">c</figure-callout>}}{a}_s^{}{}_0^{}=g\left(s\right)\&CenterDot;{\mathrm{\&delta;}}_{c}a---\left(5\right)$

Wherein, δ _cA is the variation of certain feature crack length a, and it is δ _ca _s ⁰Tolerance, g (s) is a zero dimension spread function;

5), introduce N local variation pattern at N node place, suc as formula (6):

$\mathrm{\&Delta;}{S}_j={\mathrm{\&delta;}}_c{a}_s^j=N_j^{\&prime;}\left(s\right){\mathrm{\&delta;}}_{\mathrm{<figure-callout\; id="0"\; label="c\; a\; s"\; filenames="HSA00000031446000091.png,HSA00000031446000101.png"\; state="\{\{state\}\}">c</figure-callout>}}{a}_s^{}{}_0^{},$ j＝1，2，…，N (6)

Wherein, N ' _j(s) be local variational function;

6), respectively for above-mentioned 3 kinds substantially with reference to load r ₁, r ₂And r ₃, and N local variation pattern δ _ca _s ^j, j=1,2 ..., N lists 3N equation, and the integration at accounting equation two ends, obtains about 3N undetermined coefficient A _MiSystem of linear equations, wherein, m=I, II, III, i=1,2 ..., N, formula (7):

j＝1，2，…，N， r＝r ₁，r ₂，r ₃ (7)

7), with system of equations (7) be rewritten as the equivalence matrix form equation, the Solving Linear program solution of utilizing computing machine then is about 3N unknowm coefficient A _MiSystem of equations (7), substitution formula then (4) and formula (3) just can obtain I, the II of crack front under the external load function, the separation value K of III type stress intensity factor _I ^(a), K _II ^(a), K _III ^(a)And they are along the numerical solution of the distribution situation of crack front.

As preferred a kind of scheme: in described step 7), system of equations (7) is rewritten as the matrix form equation I of equivalence again, suc as formula (8):

CA＝I (8)

Or

$\left[\begin{array}{ccc}{\mathrm{<figure-callout\; id="1"\; label="C\; ij"\; filenames="HSA00000031446000011.png,HSA00000031446000061.png"\; state="\{\{state\}\}">C</figure-callout>}}_{\mathrm{ij}}^{}& {\mathrm{<figure-callout\; id="1"\; label="C\; ij\; r"\; filenames="HSA00000031446000011.png,HSA00000031446000061.png"\; state="\{\{state\}\}">C</figure-callout>}}_{\mathrm{ij}r}^{1,\mathrm{II}}& {\mathrm{<figure-callout\; id="1"\; label="C\; ij\; r"\; filenames="HSA00000031446000011.png,HSA00000031446000061.png"\; state="\{\{state\}\}">C</figure-callout>}}_{\mathrm{ij}r}^{1,\mathrm{III}}\\ {\mathrm{<figure-callout\; id="2"\; label="C\; ij\; r"\; filenames="HSA00000031446000011.png,HSA00000031446000061.png"\; state="\{\{state\}\}">C</figure-callout>}}_{\mathrm{ij}r}^{2,I}& {\mathrm{<figure-callout\; id="2"\; label="C\; ij\; r"\; filenames="HSA00000031446000011.png,HSA00000031446000061.png"\; state="\{\{state\}\}">C</figure-callout>}}_{\mathrm{ij}r}^{2,\mathrm{II}}& {\mathrm{<figure-callout\; id="2"\; label="C\; ij\; r"\; filenames="HSA00000031446000011.png,HSA00000031446000061.png"\; state="\{\{state\}\}">C</figure-callout>}}_{\mathrm{ij}r}^{2,\mathrm{III}}\\ {\mathrm{<figure-callout\; id="3"\; label="C\; ij\; r"\; filenames="HSA00000031446000031.png,HSA00000031446000071.png"\; state="\{\{state\}\}">C</figure-callout>}}_{\mathrm{ij}r}^{3,I}& {\mathrm{<figure-callout\; id="3"\; label="C\; ij\; r"\; filenames="HSA00000031446000031.png,HSA00000031446000071.png"\; state="\{\{state\}\}">C</figure-callout>}}_{\mathrm{ij}r}^{3,\mathrm{II}}& {\mathrm{<figure-callout\; id="3"\; label="C\; ij\; r"\; filenames="HSA00000031446000031.png,HSA00000031446000071.png"\; state="\{\{state\}\}">C</figure-callout>}}_{\mathrm{ij}r}^{3,\mathrm{III}}\end{array}\right]\left\{\begin{array}{c}{A}_{I,i}\\ A_{\mathrm{II},i}\\ A_{\mathrm{III},i}\end{array}\right\}=\left\{\begin{array}{c}I({\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HSA00000031446000011.png,HSA00000031446000061.png"\; state="\{\{state\}\}">r</figure-callout>}}_1,\mathrm{\&Delta;}{S}_j)\\ I({\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA00000031446000011.png,HSA00000031446000061.png"\; state="\{\{state\}\}">r</figure-callout>}}_2,\mathrm{\&Delta;}{S}_j)\\ I({\mathrm{<figure-callout\; id="3"\; label="r"\; filenames="HSA00000031446000031.png,HSA00000031446000071.png"\; state="\{\{state\}\}">r</figure-callout>}}_3,\mathrm{\&Delta;}{S}_j)\end{array}\right\}---(8\text{'})$

Wherein, the subvector A of unknown number vector A to be asked _{M, i}, as the formula (9):

A _m，i＝[A _m，1?A _m，2…A _m，N] ^T，m＝I，II，III (9)

The submatrix C of the matrix of coefficients C of formula (8) left end _Ij ^{R, m}In coefficient C _Ij ^{R, m}, as the formula (10):

$C_{\mathrm{ij}}^{r,m}={\&Integral;}_{s_1}^{s_N}\frac{2}{H_{\mathrm{front}}^{\left(a\right)}}{N}_i\left(s\right)[K_m^{\left(r\right)}\&CenterDot;K_m^{\left({r_m}^0\right)}]N_j^{\&prime;}\left(s\right)g\left(s\right)\mathrm{ds},$ m＝I，II，r＝r ₁，r ₂，r ₃，i，j＝1，2，…，N

$C_{\mathrm{ij}}^{r,m}={\&Integral;}_{s_1}^{s_N}\frac{2(1+v_{\mathrm{front}}^{\left(a\right)})}{E_{\mathrm{front}}^{\left(a\right)}}{N}_i\left(s\right)[K_m^{\left(r\right)}\&CenterDot;K_m^{\left({r_m}^0\right)}]N_j^{\&prime;}\left(s\right)g\left(s\right)\mathrm{ds},$ m＝III，r＝r ₁，r ₂，r ₃，i，j＝1，2，…，N

(10)

Submatrix C _Ij ^{R, m}Correspond respectively to reference to load r=r ₁, r ₂, r ₃With crackle mode m=I, II, a subitem of III situation following formula (7) left end; Have 9 submatrixs, they all are narrow bandwidth diagonal form submatrix usually; Subvector I (r, the Δ S of the I vector of formula (8) right-hand member _j), r=r ₁, r ₂, r ₃Corresponding to the external applied load of formula (7) right-hand member and corresponding with reference to load r=r ₁, r ₂, r ₃At the virtual crack mode of extension

Under weight function

The integration of product; Coefficient value I wherein (r, Δ S _j), as the formula (11):

r＝r ₁，r ₂，r ₃，j＝1，2，…，N

(11)

System of equations (7) formula or (8) formula have 3N equation, 3N unknown undetermined coefficient; Find the solution about unknowm coefficient A _MiSystem of linear equations (7) formula or (8) formula; Substitution formula then (4) and formula (3) just can obtain I, the II of crack front under the external load function, the separation value K of III type stress intensity factor _I ^(a), K _II ^(a), K _III ^(a)And they are along the numerical solution of the distribution situation of crack front.

Or: in described step 7), system of equations (7) is rewritten as the matrix form equation II of equivalence again, suc as formula (12):

DB＝J (12)

Or

$\left[\begin{array}{cccc}{D}_{11}^{r,m}& D_{21}^{r,m}& ...& D_{N1}^{r,m}\\ D_{12}^{r,m}& D_{22}^{r,m}& ...& D_{N2}^{r,m}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ D_{1N}^{r,m}& D_{2N}^{r,m}& ...& D_{\mathrm{NN}}^{r,m}\end{array}\right]\left\{\begin{array}{c}{B}_{m,1}\\ B_{m,2}\\ .\\ .\\ .\\ B_{m,N}\end{array}\right..=\left\{\begin{array}{c}J(r,\mathrm{\&Delta;}{S}_1)\\ J(r,\mathrm{\&Delta;}{S}_2)\\ .\\ .\\ .\\ J(r,\mathrm{\&Delta;}{S}_N)\end{array}\right\}---(12\text{'})$

Wherein, the subvector B of unknown number vector B to be asked _{M, i}, as the formula (13):

B _m，i＝[A _I，i?A _II，i?A _III，i] ^T，i＝1，2，…，N (13)

The submatrix D of the matrix of coefficients D of formula (12) left end _Ij ^{R, m}In coefficient D _Ij ^{R, m}, as the formula (14):

$D_{\mathrm{ij}}^{r,m}={\&Integral;}_{s_1}^{s_N}\frac{2}{H_{\mathrm{front}}^{\left(a\right)}}{N}_i\left(s\right)[K_m^{\left(r\right)}\&CenterDot;K_m^{\left({r_m}^0\right)}]N_j^{\&prime;}\left(s\right)g\left(s\right)\mathrm{ds},$ m＝I，II，r＝r ₁，r ₂，r ₃，i，j＝1，2，…，N

$D_{\mathrm{ij}}^{r,m}={\&Integral;}_{s_1}^{s_N}\frac{2(1+v_{\mathrm{front}}^{\left(a\right)})}{E_{\mathrm{front}}^{\left(a\right)}}{N}_i\left(s\right)[K_m^{\left(r\right)}\&CenterDot;K_m^{\left({r_m}^0\right)}]N_j^{\&prime;}\left(s\right)g\left(s\right)\mathrm{ds},$ m＝III，r＝r ₁，r ₂，r ₃，i，j＝1，2，…，N

(14)

Submatrix D _Ij ^{R, m}Correspond respectively to the virtual crack mode of extension

J=1,2 ..., under the N with reference to load r=r ₁, r ₂, r ₃To crackle mode m=I, II, i the component B of III _{M, i}Contribution; Total N * N piece submatrix, every all is 3 * 3 matrixes; The overall coefficient matrix D is the block symmetric matrix of narrow bandwidth; Subvector J (r, the Δ S of the J vector of formula (12) right-hand member _j), j=1,2 ..., N is corresponding to the external applied load of formula (7) right-hand member and corresponding to load r=r ₁, r ₂, r ₃At the virtual crack mode of extension

Under weight function

The integration of product;

Coefficient value J wherein (r, Δ S _j), as the formula (15):

r＝r ₁，r ₂，r ₃，j＝1，2，…，N

(15)

System of equations (7) formula or (12) formula have 3N equation, 3N unknown undetermined coefficient; Find the solution about unknowm coefficient A _MiSystem of linear equations (7) formula or (12) formula; Substitution formula then (4) and formula (3) just can obtain I, the II of crack front under the external load function, the separation value K of III type stress intensity factor _I ^(a), K _II ^(a), K _III ^(a)And they are along the numerical solution of the distribution situation of crack front.

As preferred a kind of scheme, described definite method also comprises:

8), utilize self consistance of step 1) to step 7), promptly for basic with reference to load r ₁, r ₂And r ₃Self system of equations (7) is also set up the condition of such self sealing, finds the solution basic with reference to load r ₁, r ₂And r ₃The reference loading stress intensity factor distribution function K of crack front under the independent effect situation _I ^(r1), K _II ^(r2)And K _III ^(r3)To have very high-precision be the most accurate the most reasonable numerical solution corresponding to corresponding structure finite element discretization model in other words.Way is that step 1) to the external applied load (a) in the step 7) is taken as select in the step 3) basic with reference to load r respectively ₁, r ₂And r ₃The situation of independent effect, and be designated as external applied load (a ₁), (a ₂) and (a ₃); Then by reference loading stress intensity factor K _I ^(r1), K _II ^(r2)And K _III ^(r3)Certain group first approximation estimated value begin, calculate corresponding to external applied load (a by step 1) to step 7) earlier ₁), (a ₂) and (a ₃), promptly with reference to load r ₁, r ₂And r ₃I, II, III type stress strength factor K under the independent effect situation _m ^(a1), K _m ^(a2)And K _m ⁽³⁾, m=I, II, III; Utilize following formula (16) to try to achieve new reference loading stress intensity factor distribution function K then _I ^(r1), K _II ^(r2)And K _III ^(r3)More accurate approximate evaluation value (K _I ^(r1)) ^New, (K _II ^(r2)) ^New(K _III ^(r3)) ^New:

${\left(K_I^{\left(r1\right)}\right)}^{\mathrm{new}}=\sqrt{K_I^{\left(r1\right)}{K}_I^{\left(a1\right)}}$

${\left(K_{\mathrm{II}}^{\left(r2\right)}\right)}^{\mathrm{new}}=\sqrt{K_{\mathrm{II}}^{\left(r2\right)}{K}_{\mathrm{II}}^{\left(a2\right)}}---\left(16\right)$

${\left(K_{\mathrm{III}}^{\left(r3\right)}\right)}^{\mathrm{new}}=\sqrt{K_{\mathrm{III}}^{\left(r3\right)}{K}_{\mathrm{III}}^{\left(a3\right)}}$

9) carry out above-mentioned steps 3, repeatedly) to step 7) and step 8), form an iterative process, obtain with reference to loading stress intensity factor K _I ^(r1), K _II ^(r2)And K _III ^(r3)A sequence (K of approximate evaluation value _I ^(r1)) ^New, (K _II ^(r2)) ^New(K _III ^(r3)) ^NewAnd corresponding external applied load (a ₁), (a ₂) and (a ₃) I, II, III type stress strength factor K under the effect situation separately _m ^(a1), K _m ^(a2)And K _m ^(a3)A sequence of calculated value, m=I wherein, II, III; According to the levels of precision of first run approximate evaluation value in the iterative process, through some iterative computation of taking turns, sequence (K _I ^(r1)) ^New, (K _II ^(r2)) ^New(K _III ^(r3)) ^NewJust can converge on one group of stable value, this convergency value (K _I ^(r1)) ^New, (K _II ^(r2)) ^New(K _III ^(r3)) ^NewAnd corresponding K _m ^(a1), K _m ^(a2)And K _m ^(a3), m=I, II, the calculated value of III are exactly with reference to loading stress intensity factor distribution function K _I ^(r1), K _II ^(r2)And K _III ^(r3)And K _m ^(a1), K _m ^(a2)And K _m ^(a3), m=I, II, III to have very high-precision be the most accurate the most reasonable numerical solution corresponding to corresponding structure finite element discretization model in other words.

Further, described definite method also comprises:

10), with the new reference loading stress intensity factor K that is tried to achieve in the step 9) _I ^(r1), K _II ^(r2)And K _III ^(r3)To have very high-precision be the most accurate the most reasonable numerical solution, corresponding weight function corresponding to corresponding structure finite element discretization model in other words

R=r ₁, r ₂, r ₃And the direct substitution formula of other thermal force, surface force load and body force load (7), only the simple integral of the product by external applied load and weight function is calculated and solving equation group again, do not need to carry out again the finite element analysis computation of trouble, just can be with high counting yield, try to achieve other I, II, separation value K of III type stress intensity factor of the crack front under thermal force, surface force load and body force load (a) the effect situation arbitrarily _I ^(a), K _II ^(a), K _III ^(a)And they are separated along the suitable more accurate numerical that has of the distribution situation of crack front.

As preferred another scheme, described definite method also comprises:

11) it is separate basic with reference to load r as 3 kinds in the step 3), directly to choose complex load operating mode to be asked ₁, r ₂And r ₃In one or more with reference to load, execution in step 1 then) to step 7), and execution in step 8) to the iterative computation of step 9), obtain K _I ^(r1), K _II ^(r2)And K _III ^(r3)A sequence (K of approximate evaluation value _I ^(r1)) ^New, (K _II ^(r2)) ^New(K _III ^(r3)) ^NewAnd corresponding external applied load (a ₁), (a ₂) and (a ₃), promptly comprise the reference load r of complex load operating mode to be found the solution ₁, r ₂And r ₃I, II, III type stress strength factor K under the independent effect situation _m ^(a1), K _m ^(a2)And K _m ^(a3), m=I, II, a sequence of the calculated value of III; By sequence (K _I ^(r1)) ^New, (K _II ^(r2)) ^New(K _III ^(r3)) ^NewConvergency value and corresponding K _m ^(a1), K _m ^(a2)And K _m ^(a3), m=I, II, the calculated value of III obtains I, II, III type stress strength factor K under the complex load effect situation to be asked _I, K _IIAnd K _IIISeparation and K _I, K _IIAnd K _IIIAlong the very high-precision accurate numerical solution of having of crack front distribution function.This numerical solution will be considered to rational and the most accurate numerical solution for complex load operating mode of being found the solution and used concrete structure finite element discretization model.This a kind of manner of execution has the extra high characteristics of computational accuracy.

Or: described definite method also comprises:

12), in the calculation stages in early stage, at random choose earlier 3 kinds of separate loading situations as 3 kinds in the step 3) substantially with reference to load r ₁, r ₂And r ₃, execution in step 1 then) and to step 7), and execution in step 8) to the iterative computation of step 9), obtain K _I ^(r1), K _II ^(r2)And K _III ^(r3)A sequence (K of approximate evaluation value _I ^(r1)) ^New, (K _II ^(r2)) ^New(K _III ^(r3)) ^NewAnd corresponding external applied load (a ₁), (a ₂) and (a ₃) I, II, III type stress strength factor K under the effect situation separately _m ^(a1), K _m ^(a2)And K _m ^(a3), m=I, II, a sequence of the calculated value of III; By sequence (K _I ^(r1)) ^New, (K _II ^(r2)) ^New(K _III ^(r3)) ^NewConvergency value and corresponding K _m ^(a1), K _m ^(a2)And K _m ^(a3), m=I, II, the calculated value of III obtains with reference to loading stress intensity factor K _I ^(r1), K _II ^(r2)And K _III ^(r3)Along the very high-precision accurate numerical solution of having of crack front distribution function; Then, in the later stage calculation stages, complex load that again will be to be asked (a) affacts on the body, and the K that has determined above utilizing _I ^(r1), K _II ^(r2)And K _III ^(r3)Have very high-precision exact solution and a corresponding weight function

R=r ₁, r ₂, r ₃Substitution, execution in step (10), the only integration of the product by load and weight function and the method for solving equation group are again tried to achieve I, II, III type stress strength factor K under complex load (a) the effect situation expeditiously _I ^(a), K _II ^(a), K _III ^(a)Separation value and they are along the quite high-precision accurate numerical solution of having of crack front distribution function.It is high especially and have characteristics of degree of precision that this a kind of manner of execution has counting yield.

Further again, described basic interpolation type function N _i(s) and local variational function N ' _j(s) be taken as identical function; Also can be taken as different functions.

Further, described basic interpolation type function N _i(s) and local variational function N ' _j(s), be taken as the linear function of linear model, need N branch.

Or, described basic interpolation type function N _i(s) and local variational function N ' _j(s), be taken as secondary or above (L time) function of secondary of higher modes, need N=LM+1 branch, M is a positive integer.

Principle of work of the present invention is: a kind ofly utilize limited special local variation pattern and special interpolation method, find the solution the compound general weight-function method fundamental equation (integral equation that contains variation of Mixed Mode Crack problem of three-dimensional I, II, III type under independent effect of thermal force, surface force load and body force load or the acting in conjunction situation approx, be called challenge variation type integral equation) brand-new type numerical value determine method, we are referred to as the limited variational method of challenge; Be used for high precision, find the solution thermal force, surface force load and body force load separately three-dimensional I, II, III composite crack front stress intensity factors K under effect or the acting in conjunction situation expeditiously _I, K _IIAnd K _IIISeparation problem, and determine their distribution function K along crack front _I ^(a), K _II ^(a)And K _III ^(a)Numerical solution.The technical scheme main points are to set up the general weight-function method fundamental equation of three-dimensional I, II, III Mixed Mode Crack problem (challenge variation type integral equation) under independent effect of thermal force, surface force load and body force load or the acting in conjunction situation; The variation territory of macroscopic view is divided into limited sub-variation territory; Based on this discrete cutting apart, construct special basic interpolation type function and special local variational function simultaneously; Then, utilize these basic interpolation type functions to unknown variable (thermal force, surface force load and body force load separately three-dimensional I, II under effect or the acting in conjunction situation, III composite crack front stress intensity factors along the distribution function K of crack front _I ^(a), K _II ^(a)And K _III ^(a)) carry out the discretize interpolation processing; Simultaneously, introduce the basic variation pattern that is defined on whole macroscopical variation territory, and utilize local variational function structure and produce limited local variation pattern; Select again 3 kinds separate basic with reference to load r=r ₁, r ₂, r ₃, to limited (N) local variation pattern Δ S of such generation _j, (j=1,2 ..., N), fundamental equation (challenge variation type integral equation) is carried out integral and calculating, form the system of linear equations with better calculated performance of a uniqueness that contains 3N unknown quantity and 3N equation; In order to find the solution this system of equations, next system of equations is rewritten as the matrix form I or the form II (formula (8) or formula (12)) of equivalence, utilize computing machine this system of equations of Solving Linear program solution again; Find the solution this system of linear equations, try to achieve 3N unknown quantity undetermined, then the K that introduces previously of substitution _I ^(a), K _II ^(a)And K _III ^(a)Discrete interpolation expression formula, try to achieve K _I ^(a), K _II ^(a)And K _III ^(a)Like this, just realized K _I ^(a), K _II ^(a)And K _III ^(a)Separation, and determined unknown variable K _I ^(a), K _II ^(a)And K _III ^(a)Distribution along macroscopical variation territory (crack front).In addition, utilize self consistance of said method, can set up a convergent iterative process, utilize the method for iteration directly try to achieve any with reference to three-dimensional I, II under load (thermal force, surface force load or body force load) the effect situation, III type stress intensity factor along crack front distribution function K _I ^(r), K _II ^(r)And K _III ^(r)The most accurate the most reasonable numerical solution.Therefore, utilize self consistance of this method, directly the applied stress intensity factor is separated still to unknown arbitrarily with reference to load r=r ₁, r ₂, r ₃, all that implement in this method are calculated, thereby have avoided the condition precedent restriction that must know in advance about reference loading stress intensity factor in the common stress weight-function method.With the top reference loading stress intensity factor distribution function K that tries to achieve _I ^(r1), K _II ^(r2)And K _III ^(r3)The most accurate the most reasonable numerical solution system of equations that forms previously of substitution once more, just can high precision, determine other I, II, separation value K of III type stress intensity factor of the crack front under thermal force, surface force load and body force load (a) the effect situation arbitrarily expeditiously _I ^(a), K _II ^(a), K _III ^(a)And they are along the numerical solution of the distribution situation of crack front.

Work as stress strength factor K _I, K _IIAnd K _IIIDistribution determine after, just can determine the propagation direction of crackle under external load function, and compare with the fracture toughness Kc of material, determine the security of structural member; Perhaps, can be according to K _I, K _IIAnd K _IIIVariation range, carry out fatigue strength and check, determine fatigue lifetime.The actual execution efficient of this method can improve tens times and even hundreds of times than existing other method; Particularly for the situation of shock load, utilize existing other method to need stress intensity factor that several weeks and even several months just can finish to separate and they set the tasks along the distribution of crack front, utilize this method to time a few hours, to finish at several minutes.

With respect to prior art, beneficial effect of the present invention mainly shows:

(1), provided the complex object that contains crackle under complex load (can comprise thermal force, surface force load and body force load and combination thereof) effect, the compound stress strength factor K of crack front _I, K _IIAnd K _IIIA kind of novel efficient and high-precision decouples computation determine method, and K _I, K _IIAnd K _IIIMethod is determined in efficient and high-precision calculating along the numerical solution of crack front distribution function.Specific implementation method has two kinds of selections.First kind of selection is execution in step 11), this manner of execution has high computational accuracy.Second kind of selection is execution in step 12), this manner of execution has high counting yield and very high computational accuracy.

(2), this method is not only applicable to the simple crack problem of simple I type, simple II type or simple III type, more goes for the Mixed Mode Crack problem of the compound complexity of I type, II type and III type, is used for finding the solution the stress strength factor K of composite crack front _I, K _IIAnd K _IIISeparation and they are along the numerical solution of the distribution function of crack front.

(3), in the implementation of this method, any one stress intensity factor is separated still to unknown complex load (can comprise thermal force, surface force load and body force load and combination thereof) can be selected to basic with reference to load as in the computation process, that is to say, common based on the prerequisite restrictive condition that must know in advance about reference loading stress intensity factor in the stress weight-function method of superposition principle, not limited by such condition precedent, can at random select according to calculating needs with reference to load.Such as, when the computational accuracy requirement of needs is high especially, can select with reference to load according to foregoing first kind of manner of execution; When the counting yield requirement of needs is high especially, can select with reference to load according to foregoing second kind of manner of execution.

(4), has very high computational accuracy.Because have good numerical evaluation performance according to the resulting system of linear equations of this method.Such as, as the basic interpolation type function N that chooses _i(s) and local variational function N ' _jWhen (s) all being taken as the once linear function, the overall coefficient Matrix C among the matrix form equation I has strong diagonally dominant three diagonal angles symmetry submatrix C by 6 _Ij ^{R, m}Form; Perhaps, the overall coefficient matrix D among the matrix form equation II is that to have strong diagonally dominant half-band width be 6 arrowband matrix of coefficients, and diagonal element is generally big number.As the basic interpolation type function N that chooses _i(s) and local variational function N ' _jWhen (s) all being taken as quadratic function, the overall coefficient Matrix C among the matrix form equation I has strong diagonally dominant five diagonal angles symmetry submatrix C by 6 _Ij ^{R, m}Form; Perhaps, the overall coefficient matrix D among the matrix form equation II is that to have strong diagonally dominant half-band width be 9 arrowband matrix of coefficients, and diagonal element also is big number usually.Therefore because with reference to loading stress intensity factor distribution function K _I ^(r1), K _II ^(r2)And K _III ^(r3)Estimate that (such as the intersection point place on crack front and body surface) can not strictly set up the local error that is produced and only can the result of calculation at adjacent several somes place be exerted an influence at the partial points place for inaccurate local error that is produced and fundamental equation, can the result of calculation at some place far away not exerted an influence, promptly local error can not be extended at a distance and go.

(5), for the time dependent problem of load, such as impacting for thermal shock, surface force or the situation of body force shock load, or for other stress strength factor K _I, K _IIAnd K _IIIThe time dependent situation that distributes has high definite efficient.For these situations, can exempt in the past direct Elasticity method or based in the stress weight-function method of superposition principle the analysis on Stress Field or the displacement field analytical calculation of the repeated multiple times that must carry out, directly utilize the integration of the product of load and general weight function to determine whole crack front stress intensity factors K _I, K _IIAnd K _IIIDistribution over time, simplify deterministic process greatly, raise the efficiency greatly.The actual execution efficient of the limited variational method of challenge can improve tens times and even hundreds of times than existing other method; Particularly for the situation of shock load, the stress intensity factor of utilizing existing other method to need several weeks and even several months just can finish is separated and distribution sets the tasks, and utilizes this method to finish to time a few hours at several minutes.

(6), for some concrete problems, can introduce the local variation pattern and the basic interpolation type function of infinite a plurality of linear independences.Therefore, along crack front complex situations jumpy, this method has good numerical simulation ability and very high precision for stress intensity factor.We can reasonably cut apart macroscopical variation territory according to the specific requirement of the concrete condition and the precision of particular problem; Change violent place in stress intensity factor, cut-point can be closeer; Change milder place in stress intensity factor, cut-point can be more sparse; Except the function of linear model, than higher place, can also introduce secondary or the more basic interpolation type function and the local variational function of high reps pattern in accuracy requirement.Like this, just can adjust concrete computation scheme neatly, thereby reach higher precision according to the concrete condition of particular problem.

(7), this method is not only applicable to the surface force load on the crack surface, and is applicable to the situation of temperature loading, non-crack surface face power load and body force load.For all these load, can utilize fundamental equation, the integration of the product by load and general weight function is directly determined the distribution of stress intensity factor.

(8), this method is not subjected to the restriction of geometric condition complicacy.For the situation of body profile or how much more complicated of crackle, do not need to obtain the analytical expression or the approximate expression of weight function, can directly utilize the displacement field of finite element method or boundary element method to separate, come evaluation to separate the general weight function of form; Then, utilize fundamental equation, the integration of the product by load and general weight function directly carries out stress strength factor K _I, K _IIAnd K _IIISeparation and they are along the calculation of devising a stratagem really of the distribution situation of crack front.

(9), for the three-dimensional cracks problem of shaped form crack front (such as oval, semiellipse and part ellipse immerged crack or surface crack problem), have good numerical simulation and find the solution ability, can obtain very high precision.

Description of drawings

Fig. 1 represents that a kind of structural-member composite crack front stress intensity factors separates and the flow process of definite method of distribution.

Fig. 2 represents that a kind of structural-member composite crack front stress intensity factors separates and first kind of manner of execution (high precision execution pattern) flow process of definite method of distribution.

Fig. 3 represents that a kind of structural-member composite crack front stress intensity factors separates and second kind of manner of execution (highly-efficient implementation pattern) flow process of definite method of distribution.

Fig. 4 represents basic variation pattern δ _ca _s ⁰With local variation pattern δ _ca _s ^j(is example with the linear model) and relation each other.Wherein, crack front represents crack front.

Fig. 5 represents local variational function and basic interpolation type function N _j(s) building method of (linear model).

Fig. 6 represents local variational function and basic interpolation type function N _j(s) building method of (quadratic modes).

Fig. 7 represents local variational function and basic interpolation type function N _j(s) building method of (L pattern is example with 3 patterns).

Fig. 8 represents two ends Z semiellipse surface crack crack front stress intensity factors K under the effect of crack surface power in fixed flat planar of embodiment 2 _I, K _IIAnd K _IIIThe separation and the first kind of manner of execution (high precision execution pattern) determined that distribute thereof are determined the result.In the marginal data wherein, KI represents K _I, KII represents K _II, KIII represents K _IIIR1 represents the situation of crack surface pressure effect, r2 represents along the situation of directions X effect crack surface shearing action, r3 represents along the situation of Y directive effect crack surface shearing action, FVM represents with method of the present invention to be the result of calculation of the limited variational method of challenge, COD represents the result of calculation with crack surface opening displacement method, and J represents the result of calculation with the J-integral method, and K represents to carry out the result of calculation that the K value is separated with the reciprocation integral method; Semi-elliptical surface crack in a plate fixed at two ends along Z direction represents along semiellipse surface crack in the fixing flat board in Z direction two ends, a represents the degree of depth of semiellipse surface crack, the thickness of T display plate, c are represented the length of semiellipse surface crack.

Fig. 9 represents two ends Z semiellipse surface crack crack front stress intensity factors K under plate surface pressing and temperature loading effect in fixed flat planar of embodiment 3 _I, K _IIAnd K _IIIThe separation and the second kind of manner of execution (highly-efficient implementation pattern) determined that distribute thereof are determined the result.In the marginal data wherein, KI represents K _I, KII represents K _II, KIII represents K _IIIP4 represents the situation of the front surface effect well-distributed pressure of whole plate, the front surface of four quadrants up and down of p5 display plate acts on the situation of staggered well-distributed pressure respectively, p6 only represents the situation at the front surface effect well-distributed pressure of the first half of plate, p7 represents the situation of the thermal force effect that whole plate even action temperature descends, FVM represents with method of the present invention to be the result of calculation of the limited variational method of challenge, and COD represents the result of calculation with crack surface opening displacement method; Semi-elliptical surface crack in a plate fixed attwo ends along Z direction represents along semiellipse surface crack in the fixing flat board in Z direction two ends, a represents the degree of depth of semiellipse surface crack, the thickness of T display plate, c are represented the length of semiellipse surface crack.

Figure 10 represents that two ends Z semiellipse surface crack in fixed flat planar of embodiment 4 acts under the situation of thermal shock and compression shock (pressure-bearing thermal shock) crack front stress intensity factors K simultaneously at the part surface of plate _I, K _IIAnd K _IIIDefinite result of the time dependent time history that distributes.Wherein, M represents the nondimensional stress intensity factor amplification coefficient corresponding with stress strength factor K, and Figure 10 (a) represents K _IDefinite result of the time dependent time history that distributes, Figure 10 (b) represents K _IIDefinite result of the time dependent time history that distributes, Figure 10 (c) represents K _IIIDefinite result of the time dependent time history that distributes; Semi-elliptical surface crackin a plate fixed at two ends along Z direction represents along semiellipse surface crack in the fixing flat board in Z direction two ends, a represents the degree of depth of semiellipse surface crack, the thickness of T display plate, c represents the length of semiellipse surface crack, and pressurized thermal shock on patial ofthe plate surface represents that part plate surface stands the pressure-bearing thermal shock.

Embodiment

Below in conjunction with accompanying drawing the present invention is further described.

Embodiment 1

With reference to Fig. 1, Fig. 4, Fig. 5, Fig. 6, Fig. 7, definite method that a kind of structural-member composite crack front stress intensity factors separates and distributes, this method mainly may further comprise the steps (referring to accompanying drawing 1):

1), thermal force, surface force load and the body force load that provides structural member and born, and at the independent compound general weight-function method fundamental equation of representing with variation type integral equation form of Mixed Mode Crack problem (challenge variation type integral equation) of three-dimensional I, II, III type under effect or the acting in conjunction of described three kinds of load, as the formula (1);

2), with N node, crack front is divided into any N-1 son section, at basic interpolation type function N of each node j place introducing _j(s) and a local variational function N ' _j(s), their formulas (2) that all satisfies condition;

3), select 3 kinds separate basic with reference to load r ₁, r ₂And r ₃, their I, II, III type are respectively K with reference to the loading stress intensity factor along the distribution function of crack front _I ^(r1), K _II ^(r2)And K _III ^(r3)Stress strength factor K with the unknown _I ^(a), K _II ^(a), K _III ^(a)Distribution function along crack front is expressed as formula (3) and formula (4).Wherein, be without loss of generality, M=I, II, III can be taken as constant 1 or other is not 0 suitable distribution function entirely;

4), introduce the basic variation pattern δ of a macroscopic view at whole crack front _ca _s ⁰, suc as formula (5).Wherein, δ _cA is the variation of certain feature crack length a, and it is δ _ca _s ⁰Tolerance, g (s) is a zero dimension spread function;

5), introduce N local variation pattern at N node place, suc as formula (6).Wherein, N ' _j(s) be local variational function;

6), respectively for above-mentioned 3 kinds substantially with reference to load r ₁, r ₂And r ₃, and N local variation pattern δ _ca _s ^j, list 3N equation, and the integration at accounting equation two ends, obtain about 3N undetermined coefficient A _Mi, m=I, II, III, i=1,2 ..., the system of linear equations of N is suc as formula (7);

7), for solving equation group formula (7), it can be rewritten as again the matrix form equation I of equivalence, suc as formula (8), coefficient wherein is suc as formula (perhaps it being rewritten as again the matrix form equation II of equivalence shown in (9), formula (10) and the formula (11), suc as formula (12), coefficient wherein is suc as formula shown in (13), formula (14) and the formula (15)); System of equations (7) formula or

(8) total 3N equation of formula or (12) formula, 3N unknown undetermined coefficient.Find the solution about unknowm coefficient A _MiSystem of linear equations, substitution formula then (4) and formula (3) just can obtain I, the II of crack front under the external load function, the separation value K of III type stress intensity factor _I ^(a), K _II ^(a), K _III ^(a)And they are along the numerical solution of the distribution situation of crack front.

8), utilize self consistance of this method, promptly formula (1) is also set up such condition for reference load itself, can directly utilize the program of working out to step 7) according to step 1), finds the solution basic with reference to load r ₁, r ₂And r ₃The reference loading stress intensity factor distribution function K of crack front under the independent effect situation _I ^(r1), K _II ^(r2)And K _III ^(r3)Have a very high-precision accurate numerical solution.Way is that step 1) to the external applied load (a) in the step 7) is taken as select in the step 3) basic with reference to load r respectively ₁, r ₂And r ₃The situation of independent effect, and be designated as external applied load (a ₁), (a ₂) and (a ₃).Then by reference loading stress intensity factor K _I ^(r1), K _II ^(r2)And K _III ^(r3)Certain group first approximation estimated value begin (first run approximate evaluation value can be set arbitrarily), earlier by step 1) to step

7) calculate corresponding to external applied load (a ₁), (a ₂) and (a ₃) (promptly with reference to load r ₁, r ₂And r ₃) I, II, III type stress strength factor K under the effect situation separately _m ^(a1), K _m ^(a2)And K _m ^(a3), m=I, II, III utilizes formula (16) to try to achieve new reference loading stress intensity factor distribution function K then _I ^(r1), K _II ^(r2)And K _III ^(r3)More accurate approximate evaluation value (K _I ^(r1)) ^New, (K _II ^(r2)) ^New(K _III ^(r3)) ^New

9) carry out above-mentioned steps 3, repeatedly) to step 7) and step 8), form an iterative process, just can obtain with reference to loading stress intensity factor K _I ^(r1), K _II ^(r2)And K _III ^(r3)A sequence (K of approximate evaluation value _I ^(r1)) ^New, (K _II ^(r2)) ^New(K _III ^(r3)) ^NewAnd corresponding external applied load (a ₁), (a ₂) and (a ₃) (promptly with reference to load r ₁, r ₂And r ₃) I, II, III type stress strength factor K under the effect situation separately _m ^(a1), K _m ^(a2)And K _m ^(a3), m=I, II, a sequence of the calculated value of III.According to the levels of precision of first run approximate evaluation value in the iterative process, through some the wheel (general only need 1 to take turns, 2 take turns or 3 take turns about) iterative computation, sequence (K _I ^(r1)) ^New, (K _II ^(r2)) ^New(K _III ^(r3)) ^NewJust converge on one group of stable value.This convergency value (K _I ^(r1)) ^New, (K _II ^(r2)) ^New(K _III ^(r3)) ^NewAnd corresponding K _m ^(a1), K _m ^(a2)And K _m ^(a3), m=I, II, the calculated value of III are exactly with reference to loading stress intensity factor distribution function K _I ^(r1), K _II ^(r2)And K _III ^(r3)And K _m ^(a1), K _m ^(a2)And K _m ^(a3), m=I, II, III has a very high-precision accurate numerical solution.

The new reference loading stress intensity factor K that 10), will in step 9), be tried to achieve _I ^(r1), K _II ^(r2)And K _III ^(r3)Accurate numerical solution, corresponding weight function

R=r ₁, r ₂, r ₃And the direct substitution formula of thermal force, surface force load and body force load (7), again solving equation group can further be tried to achieve other I, II, separation value K of III type stress intensity factor of the crack front under thermal force, surface force load and body force load (a) the effect situation arbitrarily _I ^(a), K _II ^(a), K _III ^(a)And they are along the numerical solution of the distribution situation of crack front.

For secondary and local variational function more than the secondary and basic interpolation type function N _j(s) structure, the node sum need satisfy the requirement of corresponding number of times, such as: for secondary, N is odd number 2M+1; For L time, N is LM+1; Wherein M is a positive integer.

Embodiment 2

With reference to Fig. 1, Fig. 2, Fig. 4, Fig. 5, Fig. 6, Fig. 7, Fig. 8, according to definite method of embodiment 1 described structural-member composite crack front stress intensity factors separation and distribution, to two ends Z semiellipse surface crack crack front stress intensity factors K under the effect of 3 kinds of crack surface power in fixed flat planar _I, K _IIAnd K _IIISeparate and distribution, determine according to first kind of manner of execution (high precision execution pattern) shown in Figure 2.Fig. 8 represents depth ratio a/T=0.5, and form is than the semiellipse surface crack of a/c=0.5, under three kinds of loading situations such as crack surface well-distributed pressure, the uniform shearing of directions X crack surface and the uniform shearing of Y direction crack surface up and down, and the stress strength factor K of crack front _I, K _IIAnd K _IIISeparating resulting and they are along the distribution situation of crack front.Wherein, M is the zero dimension stress intensity factor, and φ is the position (parameter angle) of crack front.In the mark, suffix _ FVM represents to use definite result of this method, and all the other postfix notations use other different programs and other method to calculate the reasonable definite result of resulting a part of result of calculation.Except the intersection point place of crackle and body Free Surface and near, the error between the reasonable definite result of definite result of this method and other result of calculation is less than 1%.

Embodiment 3

With reference to Fig. 1, Fig. 3, Fig. 4, Fig. 5, Fig. 6, Fig. 7, Fig. 9, according to definite method of embodiment 1 described structural-member composite crack front stress intensity factors separation and distribution, to two ends Z semiellipse surface crack crack front stress intensity factors K under several plate surface pressings and temperature loading effect in fixed flat planar _I, K _IIAnd K _IIISeparate and distribution, determine according to second kind of manner of execution (highly-efficient implementation pattern) shown in Figure 3.Fig. 9 represents depth ratio a/T=0.5, form is than the semiellipse surface crack of a/c=0.5, under four kinds of loading situations of degradation under plate front surface well-distributed pressure, the staggered well-distributed pressure of plate front surface, first half plate surface well-distributed pressure and the full plate uniform temperature, the stress strength factor K of crack front _I, K _IIAnd K _IIISeparating resulting and they are along the distribution situation of crack front.Wherein, make 3 kinds of load in the use-case 2 as reference load, and utilize the example 2 determined evaluation works of implementing this highly-efficient implementation pattern with reference to the very high-precision exact value of having of loading stress intensity factor.M is the zero dimension stress intensity factor, and φ is the position (parameter angle) of crack front.In the mark, suffix _ FVM represents definite result of this method, and suffix _ COD represents definite result of using crack surface opening displacement method to calculate.Except the intersection point place of crackle and body Free Surface and near, the error between definite result of definite result of this method and crack surface opening displacement method is less than 1.9%.

Embodiment 4

With reference to Fig. 1, Fig. 2, Fig. 3, Fig. 4, Fig. 5, Fig. 6, Fig. 7, Figure 10 (a), Figure 10 (b), Figure 10 (c), definite method according to embodiment 1 described structural-member composite crack front stress intensity factors separation and distribution, to two ends Z in fixed flat planar the semiellipse surface crack on part plate surface (first half 1/4 surface of plate) stand under the synergy situation of thermal shock and compression shock whole crack front stress intensity factors K _I, K _IIAnd K _IIIThe time dependent time history of distribution, determine.Figure 10 represents depth ratio a/T=0.5, and form is than the semiellipse surface crack of a/c=0.5, and (first half 1/4 surface of plate) stands under the synergy situation of thermal shock and compression shock whole crack front stress intensity factors K on part plate surface _I, K _IIAnd K _IIIThe time dependent time history of distribution, wherein, Figure 10 (a) represents K _IThe time dependent time history of distribution, Figure 10 (b) represents K _IIThe time dependent time history of distribution, Figure 10 (c) represents K _IIIThe time dependent time history of distribution.Wherein, make 3 kinds of load in the use-case 2 as reference load, and utilize the example 2 determined evaluation works of implementing this highly-efficient implementation pattern with reference to the very high-precision exact value of having of loading stress intensity factor.M _I, M _IIAnd M _IIIBe respectively the zero dimension stress intensity factor of I, II and III type, φ is the position (parameter angle) of crack front, and t is the time.The crack front stress intensity factors K of 60 time points in the impact process _I, K _IIAnd K _IIIDistribution determine.If utilize existing Elasticity direct method or stress weight-function method or reciprocation integral method to determine, need to carry out 60 finite element analysis computation and 60 secondary stress intensity factors respectively and calculate.But utilize technology of the present invention to determine, then only need carry out altogether 1 general weight function and with reference to the loading stress intensity factor calculate and 1 shock load situation under the stress intensity factor integral and calculating, total efficiency has improved tens times; And precision is also come highly than the method for front.If further, need carry out 10 kinds of safety of structure evaluations under the impact condition, then utilize existing Elasticity direct method or stress weight-function method or reciprocation integral method to determine the distribution of crack front stress intensity factors, need to carry out 600 finite element analysis computation and 600 secondary stress intensity factors respectively and calculate; Amount of calculation is big must to be difficult to bear on engineering.But utilize technology of the present invention to determine, then only need carry out altogether 1 general weight function and with reference to the loading stress intensity factor calculate and 10 shock load situations under the stress intensity factor integral and calculating, can finish in a short period of time, it is higher always to calculate efficient.Because this problem determines that with existing other method required amount of calculation is too big, not seeing other people as yet has the bibliographical information that this problem is carried out so detailed definite result.

Claims (9)

1. a structural-member composite crack front stress intensity factors definite method of separating and distributing, it is characterized in that: described definite method may further comprise the steps:

1), thermal force, surface force load and the body force load that provides structural member and born, and at the independent compound general weight-function method fundamental equation of representing with variation type integral equation form of Mixed Mode Crack problem of three-dimensional I, II, III type under effect or the acting in conjunction of described three kinds of load, be challenge variation type integral equation, suc as formula (1):

Wherein, variation symbol δ _c(...) expression physical quantity (...) is about the inclined to one side variation of the single order of crack position; Promptly ought have only crack position to change, and other is not when changing, the first variation of respective physical amount (...); u ^(r), t ^(r)And K _I( ^R), K _II ^(r), K _III ^(r)Be respectively some displacement function, boundary forces function and I, II, III type stress intensity factor distribution functions of doing the time spent arbitrarily with reference to load (r); u ^(a), t ^(a), f ^(a), Θ ^(a)And K _I ^(a), K _II ^(a), K _III ^(a)Be respectively the required load of finding the solution (a) the boundary displacement function of doing the time spent, boundary forces function, body force function, Temperature Distribution function and along I, II, the III type stress intensity factor distribution function of crack front; E, v, H and α are respectively elastic modulus, Poisson ratio, equivalent elastic constant and the thermal expansivity of material; Γ is a crack front, and s is the arc length along crack front; ∑ _t, ∑ _u, ∑ and V be respectively face power known boundaries, displacement known boundaries, body border and body volume; N is outer normal vector;

2), with N node, crack front is divided into any N-1 son section, at basic interpolation type function N of each node j place introducing _j(s) and a local variational function N ' _j(s), their formulas (2) that all satisfies condition:

$N_j\left(s_i\right)={\mathrm{\&delta;}}_{\mathrm{ij}}=\left\{\begin{array}{cc}1& (i=j)\\ 0& (i\&NotEqual;j)\end{array}\right.,$

(2)

$\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{N}_j\left(s\right)=1$

3), select 3 kinds separate basic with reference to load r ₁, r ₂And r ₃, their I, II, III type are respectively K with reference to the loading stress intensity factor along the distribution function of crack front _I ^(r1), K _II ^(r2)And K _III ^(r3)Stress strength factor K with the unknown _I ^(a), K _II ^(a), K _III ^(a)Distribution function along crack front is expressed as formula (3) and formula (4):

$K_m^{\left(a\right)}={\mathrm{\&Psi;}}_m\&CenterDot;K_m^{\left(r_m^0\right)},$ m＝I，II，III (3)

${\mathrm{\&Psi;}}_m=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{A}_{\mathrm{mi}}{N}_i\left(s\right),$ m＝I，II，III (4)

Wherein,

M=I, II, III is respectively substantially with reference to load r ₁, r ₂And r ₃Pairing I, II and III type are with reference to the distribution function K of loading stress intensity factor along crack front _I ^(r1), K _II ^(r2)And K _III ^(r3)Certain basic distribution function;

4), introduce the basic variation pattern δ of a macroscopic view at whole crack front _ca _s ⁰, suc as formula (5):

${\mathrm{\&delta;}}_c{a}_s^0=g\left(s\right)\&CenterDot;{\mathrm{\&delta;}}_{c}a---\left(5\right)$

Wherein, δ _cA is the variation of certain feature crack length a, and it is δ _ca _s ⁰Tolerance, g (s) is a zero dimension spread function;

5), introduce N local variation pattern at N node place, suc as formula (6):

$\mathrm{\&Delta;}{S}_j={\mathrm{\&delta;}}_c{a}_s^j={N^{\&prime;}}_j\left(s\right){\mathrm{\&delta;}}_c{a}_s^0,$ j＝1，2，…，N (6)

Wherein, N ' _j(s) be local variational function;

6), respectively for above-mentioned 3 kinds substantially with reference to load r ₁, r ₂And r ₃, and N local variation pattern δ _ca _s ^j, list 3N equation, and the integration at accounting equation two ends, obtain about 3N undetermined coefficient A _MiSystem of linear equations, wherein, m=I, II, III, i=1,2 ..., N, formula (7):

j＝1，2，…，N，r＝r ₁，r ₂，r ₃ (7)

7), with system of equations (7) be rewritten as the equivalence matrix form equation, the Solving Linear program solution of utilizing computing machine then is about 3N unknowm coefficient A _MiSystem of equations (7), substitution formula then (4) and formula (3) just can obtain I, the II of crack front under the external load function, the separation value K of III type stress intensity factor _I ^(a), K _II ^(a), K _III ^(a)And they are along the numerical solution of the distribution situation of crack front.

2. definite method that a kind of structural-member composite crack front stress intensity factors as claimed in claim 1 separates and distributes is characterized in that: in described step 7), system of equations (7) is rewritten as the matrix form equation I of equivalence again, suc as formula (8):

CA＝I (8)

Or

$\left[\begin{array}{ccc}{C}_{\mathrm{ij}}^{r1,I}& C_{\mathrm{ij}}^{r1,\mathrm{II}}& C_{\mathrm{ij}}^{r1,\mathrm{III}}\\ C_{\mathrm{ij}}^{r2,I}& C_{\mathrm{ij}}^{r2,\mathrm{II}}& C_{\mathrm{ij}}^{r2,\mathrm{III}}\\ C_{\mathrm{ij}}^{r3,I}& C_{\mathrm{ij}}^{r3.\mathrm{II}}& C_{\mathrm{ij}}^{r3,\mathrm{III}}\end{array}\right]\left\{\begin{array}{c}{A}_{I,i}\\ A_{\mathrm{II},i}\\ A_{\mathrm{III},i}\end{array}\right\}=\left\{\begin{array}{c}I(r_1,\mathrm{\&Delta;}{S}_j)\\ I(r_2,\mathrm{\&Delta;}{S}_j)\\ I(r_3,\mathrm{\&Delta;}{S}_j)\end{array}\right\}---\left(8^{,}\right)$

Wherein, the subvector A of unknown number vector A to be asked _{M, i}, as the formula (9):

A _m，i＝[A _m，1?A _m，2…A _m，N] ^T，m＝I，II，III (9)

The submatrix C of the matrix of coefficients C of formula (8) left end _Ij ^{R, m}In coefficient C _Ij ^{R, m}, as the formula (10):

$C_{\mathrm{ij}}^{r,m}={\&Integral;}_{s_1}^{s_N}\frac{2}{H_{\mathrm{front}}^{\left(a\right)}}{N}_i\left(s\right)[K_m^{\left(r\right)}\&CenterDot;K_m^{\left({r_m}^0\right)}]{N^{\&prime;}}_j\left(s\right)g\left(s\right)\mathrm{ds},$ m＝I，II，r＝r ₁，r ₂，r ₃，i，j＝1，2，…，N

$C_{\mathrm{ij}}^{r,m}={\&Integral;}_{s_1}^{s_N}\frac{2(1+v_{\mathrm{front}}^{\left(a\right)})}{E_{\mathrm{front}}^{\left(a\right)}}{N}_i\left(s\right)[K_m^{\left(r\right)}\&CenterDot;K_m^{\left({r_m}^0\right)}]{N^{\&prime;}}_j\left(s\right)g\left(s\right)\mathrm{ds},$ m＝III，r＝r ₁，r ₂，r ₃，i，j＝1，2，…，N(10)

Submatrix C _Ij ^{R, m}Correspond respectively to reference to load r=r ₁, r ₂, r ₃With crackle mode m=I, II, a subitem of III situation following formula (7) left end; Subvector I (r, the Δ S of the I vector of formula (8) right-hand member _j), r=r ₁, r ₂, r ₃Corresponding to the external applied load of formula (7) right-hand member and corresponding with reference to load r=r ₁, r ₂, r ₃At the virtual crack mode of extension

Under weight function

The integration of product; Coefficient value I wherein (r, Δ S _j), as the formula (11):

r＝r ₁，r ₂，r ₃，j＝1，2，…，N(11)

System of equations (7) formula or (8) formula have 3N equation, 3N unknown undetermined coefficient; Find the solution about unknowm coefficient A _MiSystem of linear equations (7) formula or (8) formula; Substitution formula then (4) and formula (3).

3. definite method that a kind of structural-member composite crack front stress intensity factors as claimed in claim 1 separates and distributes is characterized in that: in described step 7), system of equations (7) is rewritten as the matrix form equation II of equivalence again, suc as formula (12):

DB＝J (12)

Or

$\left[\begin{array}{cccc}{D}_{11}^{r,m}& D_{21}^{r,m}& ...& D_{N1}^{r,m}\\ D_{12}^{r,m}& D_{22}^{r,m}& ...& D_{N2}^{r,m}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ D_{1N}^{r,m}& D_{2N}^{r,m}& ...& D_{\mathrm{NN}}^{r,m}\end{array}\right]\left\{\begin{array}{c}{B}_{m,1}\\ B_{m,2}\\ .\\ .\\ .\\ B_{m,N}\end{array}\right\}=\left\{\begin{array}{c}J(r,\mathrm{\&Delta;}{S}_1)\\ J(r,\mathrm{\&Delta;}{S}_2)\\ .\\ .\\ .\\ J(r,\mathrm{\&Delta;}{S}_N)\end{array}\right\}---\left({12}^{,}\right)$

Wherein, the subvector B of unknown number vector B to be asked _{M, i}, as the formula (13):

B _m，i＝[A _I，i?A _II，i?A _III，i] ^T，i＝1，2，…，N (13)

The submatrix D of the matrix of coefficients D of formula (12) left end _Ij ^{R, m}In coefficient D _Ij ^{R, m}, as the formula (14):

$D_{\mathrm{ij}}^{r,m}={\&Integral;}_{s_1}^{s_N}\frac{2}{H_{\mathrm{front}}^{\left(a\right)}}{N}_i\left(s\right)[K_m^{\left(r\right)}\&CenterDot;K_m^{\left({r_m}^0\right)}]{N^{\&prime;}}_j\left(s\right)g\left(s\right)\mathrm{ds},$ m＝I，II，r＝r ₁，r ₂，r ₃，i，j＝1，2，…，N

$D_{\mathrm{ij}}^{r,m}={\&Integral;}_{s_1}^{s_N}\frac{2(1+v_{\mathrm{front}}^{\left(a\right)})}{E_{\mathrm{front}}^{\left(a\right)}}{N}_i\left(s\right)[K_m^{\left(r\right)}\&CenterDot;K_m^{\left({r_m}^0\right)}]{N^{\&prime;}}_j\left(s\right)g\left(s\right)\mathrm{ds},$ m＝III，r＝r ₁，r ₂，r ₃，i，j＝1，2，…，N(14)

Submatrix D _Ij ^{R, m}Correspond respectively to the virtual crack mode of extension J=1,2 ..., under the N with reference to load r=r ₁, r ₂, r ₃To crackle mode m=I, II, i the component B of III _{M, i}Contribution; Total N * N piece submatrix, every all is 3 * 3 matrixes; The overall coefficient matrix D is the block symmetric matrix of narrow bandwidth; Subvector J (r, the Δ S of the J vector of formula (12) right-hand member _j), j=1,2 ..., N is corresponding to the external applied load of formula (7) right-hand member and corresponding to load r=r ₁, r ₂, r ₃At the virtual crack mode of extension Under weight function The integration of product; Coefficient value wherein, as the formula (15):

r＝r ₁，r ₂，r ₃，j＝1，2，…，N(15)

System of equations (7) formula or (12) formula have 3N equation, 3N unknown undetermined coefficient; Find the solution about unknowm coefficient A _MiSystem of linear equations (7) formula or (12) formula; Substitution formula then (4) and formula (3).

4. as definite method of described a kind of structural-member composite crack front stress intensity factors separation of one of claim 1-3 and distribution, it is characterized in that: described definite method also comprises:

8), step 1) to the external applied load (a) in the step 7) is taken as select in the step 3) basic respectively with reference to load r ₁, r ₂And r ₃The situation of independent effect, and be designated as external applied load (a ₁), (a ₂) and (a ₃); Then by reference loading stress intensity factor K _I ^(r1), K _II ^(r2)And K _III ^(r3)Certain group first approximation estimated value begin, calculate corresponding to external applied load (a by step 1) to step 7) earlier ₁), (a ₂) and (a ₃), promptly with reference to load r ₁, r ₂And r ₃I, II, III type stress strength factor K under the independent effect situation _m ^(a1), K _m ^(a2)And K _m ^(a3), m=I, II, III utilizes following formula (16) to try to achieve new reference loading stress intensity factor distribution function K then _I ^(r1), K _II ^(r2)And K _III ^(r3)More accurate approximate evaluation value (K _I ^(r1)) ^New, (K _II ^(r2)) ^New(K _III ^(r3)) ^New:

${\left(K_I^{\left(r1\right)}\right)}^{\mathrm{new}}=\sqrt{K_I^{\left(r1\right)}{K}_I^{\left(a1\right)}}$

${\left(K_{\mathrm{II}}^{\left(r2\right)}\right)}^{\mathrm{new}}=\sqrt{K_{\mathrm{II}}^{\left(r2\right)}{K}_{\mathrm{II}}^{\left(a2\right)}}---\left(16\right)$

${\left(K_{\mathrm{III}}^{\left(r3\right)}\right)}^{\mathrm{new}}=\sqrt{K_{\mathrm{III}}^{\left(r3\right)}{K}_{\mathrm{III}}^{\left(a3\right)}}$

9) carry out above-mentioned steps 3, repeatedly) to step 7) and step 8), form an iterative process, obtain with reference to loading stress intensity factor K _I ^(r1), K _II ^(r2)And K _III ^(r3)A sequence (K of approximate evaluation value _I ^(r1)) ^New, (K _II ^(r2)) ^New(K _III ^(r3)) ^NewAnd corresponding external applied load (a ₁), (a ₂) and (a ₃) I, II, III type stress strength factor K under the effect situation separately _m ^(a1), K _m ^(a2)And K _m ^(a3)A sequence of calculated value, m=I wherein, II, III; According to the levels of precision of first run approximate evaluation value in the iterative process, through some iterative computation of taking turns, sequence (K _I ^(r1)) ^New, (K _II ^(r2)) ^New(K _III ^(r3)) ^NewJust converge on one group of stable value, this convergency value (K _I ^(r1)) ^New, (K _II ^(r2)) ^New(K _III ^(r3)) ^NewAnd corresponding K _m ^(a1), K _m ^(a2)And K _m ^(a3), m=I, II, the calculated value of III are exactly with reference to loading stress intensity factor distribution function K _I ^(r1), K _II ^(r2)And K _III ^(r3)And K _m ^(a1), K _m ^(a2)And K _m ^(a3), m=I, II, III to have very high-precision be the most accurate the most reasonable numerical solution corresponding to corresponding structure finite element discretization model in other words.

5. definite method that a kind of structural-member composite crack front stress intensity factors as claimed in claim 4 separates and distributes, it is characterized in that: described definite method also comprises:

10) it is separate basic with reference to load r as 3 kinds in the step 3), directly to choose complex load operating mode to be asked ₁, r ₂And r ₃In one or more with reference to load, execution in step 1 then) to step 7), and execution in step 8) to the iterative computation of step 9), obtain K _I ^(r1), K _II ^(r2)And K _III ^(r3)A sequence (K of approximate evaluation value _I ^(r1)) ^New, (K _II ^(r2)) ^New(K _III ^(r3)) ^NewAnd corresponding external applied load (a ₁), (a ₂) and (a ₃), promptly comprise the reference load r of complex load operating mode to be found the solution ₁, r ₂And r ₃I, II, III type stress strength factor K under the independent effect situation _m ^(a1), K _m ^(a2)And K _m ^(a3), m=I, II, a sequence of the calculated value of III; By sequence (K _I ^(r1)) ^New, (K _II ^(r2)) ^New(K _III ^(r3)) ^NewConvergency value and corresponding K _m ^(a1), K _m ^(a2)And K _m ^(a3), m=I, II, the calculated value of III obtains I, II, III type stress strength factor K under the complex load effect situation to be asked _I, K _IIAnd K _IIISeparation and K _I, K _IIAnd K _IIIAlong the very high-precision accurate numerical solution of having of crack front distribution function.

6. definite method that a kind of structural-member composite crack front stress intensity factors as claimed in claim 5 separates and distributes, it is characterized in that: described definite method also comprises:

11), in the calculation stages in early stage, choose arbitrarily earlier 3 kinds of separate loading situations as 3 kinds in the step 3) substantially with reference to load r ₁, r ₂And r ₃, execution in step 1 then) and to step 7), and execution in step 8) to the iterative computation of step 9), obtain K _I ^(r1), K _II ^(r2)And K _III ^(r3)A sequence (K of approximate evaluation value _I ^(r1)) ^New, (K _II ^(r2)) ^New(K _III ^(r3)) ^NewAnd corresponding external applied load (a ₁), (a ₂) and (a ₃) I, II, III type stress strength factor K under the effect situation separately _m ^(a1), K _m ^(a2)And K _m ^(a3), m=I, II, a sequence of the calculated value of III; By sequence (K _I ^(r1)) ^New, (K _II ^(r2)) ^New(K _III ^(R3)) ^NewConvergency value and corresponding K _m ^(a1), K _m ^(a2)And K _m ^(a3), m=I, II, the calculated value of III obtains with reference to loading stress intensity factor K _I ^(r1), K _II ^(r2)And K _III ^(r3)Along the very high-precision accurate numerical solution of having of crack front distribution function; Then, in the later stage calculation stages, complicated external applied loads (a) such as thermal force that again will be to be asked, surface force load and body force load affact on the body, and the K that has determined above utilizing _I ^(r1), K _II ^(r2)And K _III ^(r3)Have very high-precision exact solution and a corresponding weight function

Substitution, only the simple integral of the product by external applied load and weight function is calculated and solving equation group again, do not need to carry out again the finite element analysis computation of trouble, just can be with high counting yield, try to achieve other I, II, separation value K of III type stress intensity factor of the crack front under thermal force, surface force load and body force load (a) the effect situation arbitrarily _I ^(a), K _II ^(a), K _III ^(a)And they are separated along the suitable more accurate numerical that has of the distribution situation of crack front.

7. definite method of separating and distributing as the described a kind of structural-member composite crack front stress intensity factors of one of claim 1-3 is characterized in that: described basic interpolation type function N _i(s) and local variational function N ' _j(s) be taken as identical function or different functions.

8. definite method of separating and distributing as the described a kind of structural-member composite crack front stress intensity factors of one of claim 1-3 is characterized in that: described basic interpolation type function N _i(s) and local variational function N ' _j(s), be taken as the linear function of linear model, N branch arranged.

9. definite method of separating and distributing as the described a kind of structural-member composite crack front stress intensity factors of one of claim 1-3 is characterized in that: described basic interpolation type function N _i(s) and local variational function N ' _j(s), be taken as the secondary of higher modes or secondary with superior function, need N=LM+1 branch, L is the number of times of function, and M is a positive integer.

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