CN106096134A - A kind of Structural Metallic Fatigue fail-safe analysis based on damage mechanics and Optimization Design - Google Patents

Abstract

The invention discloses a metal structure fatigue reliability analysis and optimal design method based on damage mechanics. This method first aims at the key metal structures that are prone to fatigue, uses interval vectors to measure the uncertainty of structure, material and damage parameters, establishes parametric geometric and finite element models, and combines interval finite element and damage mechanics finite element analysis methods to calculate fatigue Life interval range; further use the non-probability interval interference theory to realize the fatigue reliability analysis of the structure; finally, take the structure size as the design variable, the reliability as the constraint condition, and the structure weight as the objective function to realize the complete optimization iterative process through the global optimization algorithm, and output the algorithm The searched optimal design variable results are used as the final structural optimization design scheme. The reliability analysis and optimization method established by the invention overcomes the sensitivity of the scheme itself to the design parameters, and can minimize the importance and meet the requirements of fatigue reliability when the structure meets the bearing conditions, so the design scheme is more economical and reasonable.

Description

Fatigue reliability analysis and optimal design of a metal structure based on damage mechanics method

technical field

The present invention relates to the field of fatigue fracture and damage mechanics, in particular to a method for fatigue reliability analysis and optimal design of metal structures based on damage mechanics. Under the fatigue life reliability analysis and optimal design. The invention can provide reference for anti-fatigue design of engineering structures.

Background technique

Among the various failure forms of structures, fatigue is one of the most important causes of structural failure, and it is also the most important factor to be considered in structural reliability tests. In many cases, fatigue damage can have catastrophic consequences for people. For example, in 1952, the first jet Comet airliner was put into use after more than 300 hours of test flight. In 1954, it suddenly crashed and fell into the Mediterranean Sea during the flight. It was identified that it was caused by the fatigue damage of the pressure cabin. Relevant documents point out that "since the 1980s, there have been an average of 100 major accidents of machine crashes and fatalities caused by metal fatigue fractures per year." It can be seen that the fatigue analysis of the structure is of great significance.

When using the finite element method of damage mechanics for fatigue analysis, the main steps include determination of load, determination of damage evolution equation and fitting of damage parameters. However, in the calculation process, various factors affecting fatigue performance are not taken into account, such as the fluctuation of load level, structural size effect, surface finish, surface treatment process, temperature and hot and humid environment, and stress concentration. These factors can be viewed as the effects of material and structural uncertainties on the scatter of fatigue life. In the conventional optimization process, the loads, structural parameters and design requirements of the structure are all treated as deterministic forms. However, the results obtained by the design are often inconsistent with the actual situation, and the scheme itself is very sensitive to the design parameters. With the development of uncertain structural analysis methods, the design concept of reliability optimization gradually replaces the traditional deterministic optimization and becomes an inevitable trend of future engineering design.

Combining damage mechanics finite element and interval finite element, establishing an optimization model that meets the reliability index needs to know the range of load history, the range of structural geometric parameters and damage parameters, and the range of changes in related material performance parameters. Firstly, the stress-strain response is calculated according to the load and geometric structure, and then the fatigue life variation range is obtained by applying the damage model to the material properties. Then, the non-probabilistic reliability analysis is performed with the given life design conditions and the calculated life range, and finally the structural optimization is realized. Compared with the traditional method based on the test, the finite element fatigue reliability calculation can provide the life distribution of the parts, which can reduce the number of test prototypes, shorten the product development cycle, and then reduce the development cost, which will greatly improve the design efficiency. Therefore, the content of the present invention has significant practical significance.

Contents of the invention

The technical problem to be solved by the present invention is to overcome the deficiencies of the prior art and provide a fatigue reliability analysis and optimal design method for metal structures based on damage mechanics. The present invention fully considers the ubiquitous uncertainty factors in practical engineering problems, analyzes the uncertainty propagation problem with the proposed non-probability interval vertex method, establishes the reliability index according to the non-probability interval interference model, and obtains the optimal design through optimization algorithm search Program.

The technical solution adopted in the present invention is: a method for fatigue reliability analysis and optimal design of metal structures based on damage mechanics, and the realization steps are as follows:

Step 1: According to the geometric characteristics of the engineering structure, optimize the design for the length l of the rod, the thickness B of the plate, the diameter D of the opening or the connecting shaft at the key position prone to fatigue, and the variable is recorded as x =(x ₁ ,x ₂ ,…x _n ), where x _i represents any geometric feature information, and the structure size is allowed to fluctuate within a certain range, that is, x _i ∈[xi _min ,xi _max ], i=1,2 ,...,n, the value of each group of design variables corresponds to a design scheme, and each size information is given an initial design value;

The second step: use the interval vector f=(f ₁ ,f ₂ ,…f _m ) to reasonably represent the uncertain information of the structural parameters. Here, the upper and lower bounds of the uncertain parameter f _i , i=1,2,…,m Values can be expressed as:

${\mathrm{<span\; class="notranslate">\; f</span>}}^{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; f</span>}}^{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>$

Among them, the superscript U represents the upper bound of the value of the parameter, the superscript L represents the lower bound of the value of the parameter, the superscript c represents the central value of the parameter, and the superscript r represents the radius of the parameter;

The third step: establish the geometric model of the structure, realize the automatic generation of the model when the design variable changes within the feasible range during the geometric modeling, and use the CAD software macro recording to complete the geometric parametric modeling based on the design variable. Further associate the CAD model with the CAE analysis software, realize parametric grid division, unit attribute assignment, material attribute assignment, and boundary condition setting based on the finite element software. According to the selected design variables, complete the update of the entire set of parametric models;

Step 4: Select the damage evolution model, query the fatigue test value of the standard specimen according to the material of the optimized structure, and fit the parameters of the damage evolution equation. The general damage evolution equation can be expressed as follows:

$\frac{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; D.</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}{{\mathrm{<span\; class="notranslate">\; E.</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}}\frac{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; m</span>}}}{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; )</span>}^{\frac{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; m</span>}}}$

Among them, D is the scalar damage degree varying between 0 and 1, E is the elastic modulus, N is the fatigue life, σ _max is the unit equivalent stress, σ _th is the stress threshold, β and m are the fitting Damage parameters. Considering σ _max and N as points on the SN curve, σ _th is the fatigue limit stress intensity, and the damage degree D is integrated from 0 to 1, then the damage evolution equation can be expressed as:

${<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; m</span>}}\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; E.</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}$

In the above formula, only the damage parameters β and m are unknown quantities, let α=E ^m /β((3/2)m+1) take the logarithm on both sides and then take the residual Can be expressed as:

Then the n points on the S-N curve can be selected to obtain the corresponding damage parameters with the minimum residual error;

Step 5: Use finite element secondary development to write damage mechanics finite element method program. When the damage degree of the unit with the largest relative damage degree accumulates to 1, the structural fatigue damage is judged, and the structural fatigue life N and quality M are extracted;

Step 6: Combining the non-probabilistic uncertain vertex propagation analysis method with the finite element of damage mechanics, and substituting the interval uncertain variable into the structural fatigue finite element analysis to obtain the upper and lower bounds of fatigue life, expressed as N and The vertex propagation analysis method can be expressed as:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\underset{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; ,</span>\underset{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; ,</span>\underset{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\underset{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; ,</span>\underset{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; \&CenterDot;</span>\\ <span\; class="notranslate">\; \&CenterDot;</span>\\ <span\; class="notranslate">\; \&CenterDot;</span>\\ {\mathrm{<span\; class="notranslate">\; u</span>}}_{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}<span\; class="notranslate">\; )</span>\end{array}\right.$

in, Respectively represent the combined values of vertices of uncertain variables, f _i and represent the lower and upper bounds of uncertain variables, respectively;

Step 7: Establish the fatigue reliability analysis index based on the structural non-probabilistic reliability model based on interval variables, and its interference interval can be expressed as:

${\mathrm{<span\; class="notranslate">\; N</span>}}^{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; \&lsqb;</span>\underset{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; \&rsqb;</span>$

${\mathrm{<span\; class="notranslate">\; S</span>}}^{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; \&lsqb;</span>\underset{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; \&rsqb;</span>$

Among them, f _i ^I represents the interval range of the i-th uncertain variable, N ^I represents the life interval calculated by finite element calculation with uncertain damage mechanics, and S ^I represents the design fatigue life range of the structure, which is determined by the service capacity of the structure The value of the interval planning is obtained. Taking M(R,S)=NS=0 for the limit state plane, the non-probabilistic collective failure degree defined by the interference model can be expressed as:

Among them, F _reliability represents fatigue reliability, δ _N and δ _S represent the normalized space of calculated life and design life respectively δ _N ＝(NN ^c )/N ^r and δ _S ＝(SS ^c )/S ^r , and S _{safety domain} represents The area of the safety zone, S _total represents the total area;

Step 8: Taking the reliability as the constraint condition and the weight as the optimization target, construct the fatigue life optimization design model of the engineering structure for the design variables. The complete optimization iterative process is realized with the global optimization algorithm until the algorithm termination criterion is satisfied, that is, convergence is achieved during the global optimization, and the optimal design variable results searched by the algorithm are output as the final structural optimization design scheme.

Wherein, the structure size in the first step is allowed to fluctuate within a certain range, which generally depends on engineering experience and project cost, and the size cannot change the geometric characteristics of the structure.

Wherein, in the second step, using interval vectors to represent the uncertainty of structural parameters can also be expressed as:

f＝[f ^L ,f ^U ]＝[f ^c -f ^r ,f ^c +f ^r ]

＝f ^c +f ^r [-1,1]

＝f ^c +f ^r ×e

Among them, the uncertain parameter f _i , i=1,2,...,m can represent the structure size, material elastic modulus, density, load and damage parameters of the damage evolution equation, etc. e∈Ξ ^m , Ξ ^m is defined as the set of m-dimensional vectors whose elements are contained in [-1,1], the symbol "×" is defined as the operator for multiplying the corresponding elements of two vectors, and the product is still of dimension vector of m.

Wherein, the least square method of damage parameter fitting in the fourth step can be applied to any metal damage evolution equation, and the selection of damage evolution equation is generally based on the connection form and load condition of the structure.

Wherein, when performing damage mechanics finite element analysis in the fifth step, the initial damage degree of all elements should be set to zero, and the calculated unit Vonmises stress should be used as the maximum equivalent stress of the element under external load. During the calculation process, the damage degree of superimposed elements is continuously accumulated, and when the damage degree of any unit is judged to be 1, the structure is considered to have fatigue damage.

Among them, in the sixth step, the vertex method of interval propagation analysis is introduced, and the upper and lower limits of the vertex of the uncertain parameter are selected for non-probabilistic uncertainty propagation analysis. When the vertex method is introduced for propagation analysis, it must be ensured that the researched problem is monotonous According to the finite element analysis of damage mechanics, the fatigue life increases monotonically with the increase of the number of iterations.

Among them, in the seventh step, the fatigue non-probabilistic reliability index is defined, and the ratio of the volume of the structural safety domain to the total volume of the basic interval variable domain is used as the structural reliability measurement to realize the non-probabilistic reliability analysis and optimal design of the constraints .

The advantage of the present invention compared with prior art is:

(1), the present invention perfects the research on the uncertainty of damage mechanics, and establishes the non-probability interval reliability analysis theory of damage mechanics calculation fatigue life.

(2) The present invention realizes the anti-fatigue optimization design of the engineering structure through the global optimization algorithm, which can provide guidance and reference for design, and save engineering structure design and test costs.

(3) The present invention not only considers the uncertainty of the material parameters, but also considers the uncertainty of the damage model, the research on the fatigue dispersion is more refined, and the degree of influence of the structural parameters on the fatigue life is reasonably expressed.

(4) The non-probability interval vertex analysis method used in the present invention can be aimed at all damage evolution models, and it is more convenient to analyze the uncertainty propagation problem than the traditional probability method that requires explicit expressions.

Description of drawings

Fig. 1 is the flow chart of the present invention for the fatigue reliability analysis and optimal design method of metal structures based on damage mechanics;

Fig. 2 is the flowchart of the present invention about damage parameter fitting;

Fig. 3 is a schematic diagram of the non-probability interference model of the present invention;

Fig. 4 is a schematic diagram of the normalized space of the present invention for the lifetime reliability model, wherein Fig. 4(a) is a critical state, and Fig. 4(b) is an interference region;

Fig. 5 is a schematic diagram of the initial design size and structure of the orifice-containing plate in the embodiment of the present invention;

Fig. 6 is a schematic diagram of an optimized structure in the Isight software in an embodiment of the present invention;

Fig. 7 is a 1/4 finite element model diagram of a panel in an embodiment of the present invention;

Fig. 8 is an iterative convergence curve of the optimization process of the embodiment of the present invention.

detailed description

The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

As shown in Figure 1, the present invention proposes a metal structure fatigue reliability analysis and optimal design method based on damage mechanics, including the following steps:

(1) According to the geometric characteristics of the engineering structure, optimize the design for the key positions prone to fatigue, such as the length l of the rod, the thickness B of the plate, the diameter D of the opening or the connecting shaft, etc., and the variable is recorded as x = (x ₁ ,x ₂ ,…x _n ), where _xi represents any geometric feature information. Generally speaking, the structure size is allowed to fluctuate within a certain range, that is, x _i ∈ [ _ximin , _ximax ], i=1,2,…,n, and the value of each set of design variables corresponds to a design scheme, Each size information is given the initial design value;

(2) Use the interval vector f=(f ₁ ,f ₂ ,…f _m ) to reasonably represent the uncertain information of the structural parameters, here the value of the upper and lower bound intervals of the uncertain parameter f _i , i=1,2,…,m It can be expressed as:

${\mathrm{<span\; class="notranslate">\; f</span>}}^{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; f</span>}}^{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>$

Among them, the superscript U represents the upper bound of the value of the parameter, the superscript L represents the lower bound of the value of the parameter, the superscript c represents the central value of the parameter, and the superscript r represents the radius of the parameter;

(3) The geometric model of the structure is established, and the model is automatically generated when the design variable changes within the feasible range during geometric modeling. The geometric parametric modeling based on the design variable can be completed by using CAD software macro recording. Further associate the CAD model with the CAE analysis software, realize parametric grid division, unit attribute assignment, material attribute assignment, and boundary condition setting based on the finite element software. According to the selected design variables, complete the update of the entire set of parametric models;

(4) The damage evolution model is selected, and the parameters of the damage evolution equation are fitted by querying the fatigue test values of the standard specimen according to the material of the optimized structure. The general damage evolution equation can be expressed as follows:

$\frac{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; D.</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}{{\mathrm{<span\; class="notranslate">\; E.</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}}\frac{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; m</span>}}}{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; )</span>}^{\frac{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; m</span>}}}$

Among them, D is the scalar damage degree varying between 0 and 1, E is the elastic modulus, N is the fatigue life, σ _max is the unit equivalent stress, σ _th is the stress threshold, β and m are the fitting Damage parameters. Considering σ _max and N as points on the SN curve, σ _th is the fatigue limit stress intensity, and the damage degree D is integrated from 0 to 1, then the damage evolution equation can be expressed as:

${<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; m</span>}}\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; E.</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}$

In the above formula, only the damage parameters β and m are unknown quantities, let α=E ^m /β((3/2)m+1) take the logarithm on both sides and then take the residual Can be expressed as:

Then, n points on the S-N curve can be selected to obtain the corresponding damage parameters with the minimum residual error. The specific process is shown in Figure 2;

(5) Use the finite element secondary development to write the damage mechanics finite element method program. When the damage degree of the unit with the largest relative damage degree accumulates to 1, the structural fatigue damage is judged, and the structural fatigue life N and mass M are extracted;

(6) Combining the non-probabilistic uncertain vertex propagation analysis method with the finite element of damage mechanics, and substituting the interval uncertain variable into the structural fatigue finite element analysis, the upper and lower bounds of fatigue life are obtained, which are expressed as N and The vertex propagation analysis method can be expressed as:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\underset{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; ,</span>\underset{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; ,</span>\underset{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\underset{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; ,</span>\underset{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ <span\; class="notranslate">\; \&CenterDot;</span>\\ {\mathrm{<span\; class="notranslate">\; u</span>}}_{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}<span\; class="notranslate">\; )</span>\end{array}\right.$

in, Respectively represent the combined values of vertices of uncertain variables, f _i and represent the lower and upper bounds of uncertain variables, respectively;

(7) The fatigue reliability analysis index is established according to the structural non-probabilistic reliability model based on interval variables, and the interference interval can be expressed as:

${\mathrm{<span\; class="notranslate">\; N</span>}}^{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; \&lsqb;</span>\underset{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; \&rsqb;</span>$

${\mathrm{<span\; class="notranslate">\; S</span>}}^{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; \&lsqb;</span>\underset{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; \&rsqb;</span>$

Among them, f _i ^I represents the interval range of the i-th uncertain variable, N ^I represents the life interval calculated by finite element calculation with uncertain damage mechanics, and S ^I represents the design fatigue life range of the structure, which can generally be obtained through the service life of the structure Ability to perform interval planning to obtain values. Taking M(R,S)=NS=0 for the limit state plane, the non-probabilistic collective failure degree defined by the interference model can be expressed as:

Among them, F _reliability represents fatigue reliability, δ _N and δ _S represent the normalized space of calculated life and design life respectively δ _N ＝(NN ^c )/N ^r and δ _S ＝(SS ^c )/S ^r , and S _{safety domain} represents The area of the safety zone, S _total represents the total area, Figure 3 shows the entire non-probability interval interference model, and Figure 4 shows the calculation method of the area ratio of the reliability;

(8) Taking the reliability as the constraint condition and the weight as the optimization objective, the fatigue life optimization design model of the engineering structure is constructed according to the design variables. The complete optimization iterative process is realized with the global optimization algorithm until the algorithm termination criterion is satisfied, that is, convergence is achieved during the global optimization, and the optimal design variable results searched by the algorithm are output as the final structural optimization design scheme.

Example:

In order to more fully illustrate the characteristics of the invention, the present invention conducts non-probability interval reliability analysis and optimization design based on damage mechanics for the standard metal fatigue structural member model shown in FIG. 5 . The material of the rectangular plate is LY12CZ aluminum alloy, and the chemical composition of the material is shown in Table 1 below. The initial design dimensions of the plate are 210mm, 100mm, and 10mm in length, width, and central hole diameter, respectively. The load is 150MPa uniform tensile stress at both ends, and the stress ratio is 0.2. The finite element mesh division is shown in Fig. 7. According to the content described in the above invention, the thickness of the plate is used as the design variable, the reliability is greater than 0.95 as the constraint condition, and the minimum mass of the plate is used as the objective function, and the optimization process in Figure 6 is used for iterative analysis using the ASA global optimization algorithm.

Table 1

Search the standard experiment manual to get the SN curve of the corresponding material, the expression of the curve is N=6.997421×10 ⁷ (S-124) ^-1.274268 , and the stress value corresponding to the infinite life is 127MPa. According to the method shown in Figure 2, the parameters of the damage evolution equation are fitted, and the uncertainty information of the model and damage parameters is shown in Table 2 below.

Table 2

In this embodiment, the reliability analysis and optimal design of the plate structure containing 4 parameter uncertainty information are carried out. Figure 8 shows the convergence curve of the optimization iterative process, and the optimal solution finally obtained is: thickness 1.74 mm, reliability 0.9505, with a mass of 27.467 grams. In summary, the present invention utilizes the uncertain information of interval process characterization parameters, introduces interval vertex uncertainty propagation analysis to obtain the life interval range, and introduces a non-probabilistic reliability analysis method to obtain the plate The optimal design thickness.

The above are only the specific steps of the present invention, and do not constitute any limitation to the protection scope of the present invention; it can be extended and applied to the field of predicting structural life of uncertain damage mechanics, and all technical solutions formed by equivalent transformation or equivalent replacement fall into the Within the protection scope of the present invention.

Parts not described in detail in the present invention belong to the known techniques of those skilled in the art.

Claims (7)

1. A metal structure fatigue reliability analysis and optimization design method based on damage mechanics is characterized by comprising the following implementation steps:

the first step is as follows: according to the geometrical characteristics of the engineering structure, the length l of the rod piece, the thickness B of the plate and the size of the diameter D of the hole or the connecting shaft are optimally designed for the critical position where fatigue easily occurs, and the variable is recorded as x ═ x₁,x₂,…x_n) Wherein x is_iRepresenting any geometrical characteristic information, the structure size being allowed to fluctuate within a certain range, i.e. x_i∈[x_{i min},x_{i max}]1,2, …, n, wherein each set of design variables has values corresponding to a design scheme, and each size information is given an initial design value;

the second step is that: using the interval vector f ═ f₁,f₂,…f_m) Reasonably characterizing the uncertainty information of the structural parameters, where the uncertainty parameter f_iWhere i is 1,2, …, the upper and lower bound values of m can be expressed as:

$f^U=(f_1^c+f_1^r,f_2^c+f_2^r,\mathrm{...},f_m^c+f_m^r)$

$f^L=(f_1^c-f_1^r,f_2^c-f_2^r,\mathrm{...},f_m^c-f_m^r)$

the superscript U represents a parameter value upper bound, the superscript L represents a parameter value lower bound, the superscript c represents a parameter central value, and the superscript r represents a parameter radius;

the third step: establishing a geometric model of a structure, realizing automatic generation of the model when design variables are changed within a feasible range during geometric modeling, finishing geometric parameterized modeling based on the design variables by using CAD software macro recording, further associating the CAD model with CAE analysis software, realizing parameterized grid division, unit attribute assignment, material attribute assignment and boundary condition setting based on finite element software, and finishing updating of the whole parameterized model according to the selected design variables;

the fourth step: selecting a damage evolution model, and fitting damage evolution equation parameters according to the fatigue test value of the optimized structure material query standard test piece, wherein the general damage evolution equation can be expressed in the following form:

$\frac{dD}{dN}=\frac{\mathrm{\&beta;}}{E^m}\frac{{({\mathrm{\&sigma;}}_{max}-{\mathrm{\&sigma;}}_{th})}^m}{{(1-D)}^{\frac{3}{2}m}}$

where D is the scalar damage degree varying between 0 and 1, E is the modulus of elasticity, N is the fatigue life, σ_maxIs the cell equivalent stress, σ_thFor the stress threshold, β and m are the damage parameters that need to be fitted, let σ_maxAnd N is regarded as a point on the S-N curve, σ_thTaking fatigue limit stress intensity, and integrating the damage degree D from 0 to 1, the damage evolution equation can be expressed as:

${({\mathrm{\&sigma;}}_{max}-{\mathrm{\&sigma;}}_{th})}^{m}N=\frac{E^m}{\mathrm{\&beta;}(\frac{3}{2}m+1)}$

in the above formula, only the damage parameters β and m are unknown, and α ═ E^mPer β ((3/2) m +1) two-side logarithm residual errorCan be expressed as:

then N points on the S-N curve can be taken to obtain the corresponding damage parameters by minimum residual error;

the fifth step: utilizing finite element secondary development to compile a damage mechanics finite element method program, judging structural fatigue damage after the damage degree of the unit with the maximum relative damage degree is accumulated to 1, and extracting the structural fatigue life N and the structural fatigue quality M;

and a sixth step: combining a non-probability uncertain vertex propagation analysis method with a damage mechanics finite element, substituting interval uncertain variables into structural fatigue finite element analysis to obtain upper and lower bounds of fatigue life, which are respectively expressed asNAndthe vertex propagation analysis may be expressed as:

$\left\{\begin{array}{c}{U}_1=(\underset{\&OverBar;}{f_1},\underset{\&OverBar;}{f_2},\mathrm{...},\underset{\&OverBar;}{f_m})\\ U_2=(\underset{\&OverBar;}{f_1},\underset{\&OverBar;}{f_2},\mathrm{...},\stackrel{\&OverBar;}{f_m})\\ .\\ .\\ .\\ U_{2^m}=(\stackrel{\&OverBar;}{f_1},\stackrel{\&OverBar;}{f_2},\mathrm{...},,\stackrel{\&OverBar;}{f_m})\end{array}\right.$

wherein,respectively represent the peak combination values of the uncertain variables,f _i and(i ═ 1,2, …, m) represent the lower and upper bounds, respectively, of the uncertain variable;

the seventh step: establishing a fatigue reliability analysis index according to a structural non-probability reliability model based on interval variables, wherein an interference interval can be expressed as:

$N^I=N(f_1^I,f_2^I,\mathrm{...},f_m^I)=\&lsqb;\underset{\&OverBar;}{N},\stackrel{\&OverBar;}{N}\&rsqb;$

$S^I=S(f_1^I,f_2^I,\mathrm{...},f_m^I)=\&lsqb;\underset{\&OverBar;}{S},\stackrel{\&OverBar;}{S}\&rsqb;$

wherein f is_i ^IRange of intervals representing the ith uncertain variable, N^IRepresenting the life span range obtained by finite element calculation of the mechanics with uncertain damage, S^IThe design fatigue life range of the structure is represented, interval planning value is carried out through the service capacity of the structure, M (N, S) ═ N-S ═ 0 is taken for a limit state plane, and the non-probability set failure degree defined by the interference model can be expressed as follows:

wherein, F_reliabilityThe degree of reliability of the fatigue is indicated,_Nand_Snormalized space for representing calculated lifetime and design lifetime, respectively_N＝(N-N^c)/N^rAnd_S＝(S-S^c)/S^r，S_{security domain}Representing the area of the Security Domain, S_{General assembly}Represents the total area;

eighth step: and (3) taking the reliability as a constraint condition, taking the weight as an optimization target, constructing an engineering structure fatigue life optimization design model aiming at design variables, realizing a complete optimization iterative process by using a global optimization algorithm until an algorithm termination criterion is met, namely convergence is achieved during global optimization, and outputting an optimal design variable result searched by the algorithm as a final structure optimization design scheme.

2. The metal structure fatigue reliability analysis and optimization design method based on damage mechanics according to claim 1, characterized in that: the dimensions of the structure in said first step are allowed to fluctuate within a range which is generally determined by engineering experience and by engineering costs, and which dimensions do not allow to modify the geometrical characteristics of the structure.

3. The metal structure fatigue reliability analysis and optimization design method based on damage mechanics according to claim 1, characterized in that: the uncertainty of the structural parameter characterized by the interval vector in the second step can also be represented as:

f＝[f^L,f^U]＝[f^c-f^r,f^c+f^r]

＝f^c+f^r[-1,1]

＝f^c+f^r×e

wherein the uncertain parameter f_iI 1,2, …, m may represent structural dimensions, material modulus of elasticity, density, damage parameters of the load and damage evolution equations, etc. e ∈ xi^m，Ξ^mIs defined as all elements contained in [ -1,1 [ ]]The m-dimensional vector set in (i) and the symbol "×" is defined as the operator by which the corresponding elements of two vectors are multiplied, the product still being a vector of dimension m.

4. The metal structure fatigue reliability analysis and optimization design method based on damage mechanics according to claim 1, characterized in that: the least square method of damage parameter fitting in the fourth step can be applied to any metal damage evolution equation, and the selection of the damage evolution equation is generally based on the connection form of the structure and the load condition.

5. The metal structure fatigue reliability analysis and optimization design method based on damage mechanics according to claim 1, characterized in that: when carrying out finite element analysis of damage mechanics in the fifth step, setting the initial damage degrees of all the units to be zero, and taking the calculated Vonmises stress of the units as the maximum equivalent stress of the units under external load; and continuously accumulating the damage degrees of the superposed units in the calculation process, and judging that the fatigue damage of the structure occurs when the damage degree of any unit reaches 1.

6. The metal structure fatigue reliability analysis and optimization design method based on damage mechanics according to claim 1, characterized in that: and introducing a vertex method of interval propagation analysis in the sixth step, selecting upper and lower limits of vertexes of uncertain parameters to perform non-probability uncertainty propagation analysis, ensuring that the researched problem is monotonous when introducing the vertex method to perform propagation analysis, and aiming at that the damage degree and the service life of the fatigue life of the damage mechanics finite element analysis are monotonously increased along with the increase of iteration times.

7. The metal structure fatigue reliability analysis and optimization design method based on damage mechanics according to claim 1, characterized in that: and defining a fatigue non-probability reliability index in the seventh step, and using the ratio of the volume of the structural security domain to the total volume of the basic interval variable domain as structural reliability measurement to realize non-probability reliability analysis and optimization design of constraint conditions.