JP4919875B2 - Structure stress analysis method and apparatus - Google Patents

Description

  The present invention relates to a stress analysis method and apparatus for a structure in a nuclear facility, for example.

  Structures in nuclear facilities are required to have a high level of safety due to their nature. However, this structure has a place where various stresses are generated, such as a place where various heat treatments such as welding are performed, a place where a large load is applied, and a place where heat is input from a fluid contacting outside or inside, In general, the shape is complicated. Therefore, when a crack occurs in this structure, it is indispensable for safety design to analyze how the crack progresses with changes in stress. (See, for example, Patent Document 1). In this case, the finite element method (see, for example, Patent Document 2) is usually used for the stress analysis.

  In the finite element method, when trying to analyze the deformation state or stress distribution state of a structure, the analysis target area is defined by a large number (but a finite number) of small areas defined by simple shapes such as triangles. This is a technique for performing analysis on the entire region by subdividing the region (element) and adding the analysis results in each small region.

While this finite element method has the advantage of being able to perform analysis with simple calculations even for structures with complex shapes, it requires a very long calculation time to repeat many operations. In addition, there is a disadvantage that the same calculation must be performed again from the beginning if the conditions change even a little.
JP 2006-71584 A Japanese Patent Laid-Open No. 2003-194637

  By the way, there is a probabilistic fracture mechanics method using a so-called “Monte Carlo method” as a method for obtaining a probability that a crack is generated in a structure and that the crack progresses and breaks. The Monte Carlo method is a calculation method in which a large number of input data whose values are randomly changed is given to a mathematical model, and an approximate solution is calculated from the distribution state of output data obtained thereby.

  In such a probabilistic fracture mechanics method using the Monte Carlo method, many operations are repeatedly performed based on the relational expression between the stress intensity count and the crack growth rate. Stress analysis is required. In this case, since the finite element method can be applied to a structure having a complicated shape, it would be advantageous if this finite element method could be used. However, there are two obstacles to using the finite element method for probabilistic fracture mechanics.

  The first obstacle is related to calculation time. That is, when obtaining the stress distribution in a region where cracks are likely to occur, such as a welded portion of a structure, by a finite element method, it usually takes several hours to several days of calculation time. On the other hand, in the Monte Carlo method, it is necessary to investigate changes in stress distribution in a very large number of states (tens of thousands to one million states).

  Therefore, for example, even if the calculation time per time of the finite element method is estimated to be 1 hour, and the change state to be examined by the Monte Carlo method is estimated to be a small number of 10,000, the calculation time for obtaining the failure probability is as follows: 1 hour × 10,000 times = 10,000 hours≈417 days, and the use of the finite element method is virtually impossible.

  The second obstacle relates to calculation accuracy. That is, various factors influence the crack growth of the structure. Therefore, even if the stress distribution at a certain point is found by the finite element method, if the stress is used as it is for the Monte Carlo method as input data, the result of the calculation is a faithful reflection of the actual crack growth state. It is difficult to say, and it is difficult to obtain calculation accuracy above a certain level.

  For example, assuming that the residual stress distribution in a section of a welded part of a structure is obtained by the finite element method, the value obtained by this finite element method is randomly changed as it is and applied to the Monte Carlo method. The calculation accuracy cannot be maintained. In order to maintain, the residual stress obtained by the finite element method is decomposed into a plurality of stresses such as a film stress, a bending stress, and a peak stress, and the values of these decomposed individual stresses are changed randomly. Can be considered.

  However, in reality, a certain balance is maintained between the film stress, bending stress, and peak stress, so the calculation results obtained by randomly changing the values of the individual decomposition stresses are significant. However, this has resulted in a decrease in calculation accuracy.

  Due to the two obstacles mentioned above, it is currently impossible to use the finite element method for probabilistic fracture mechanics.

  The present invention has been made in view of the above circumstances, and can reduce the calculation time and prevent a decrease in calculation accuracy, and can use the finite element method for the stochastic fracture mechanics method. An object of the present invention is to provide a stress analysis method and apparatus for a structure.

As means for solving the above problems,
The invention described in claim 1
A first step of setting a plurality of stress influencing factors as factors affecting the stress generated in a predetermined region of the structure, and setting the number of levels and the level value in the experimental design for each of the plurality of stress influencing factors, A second step of setting a predetermined number of combinations of level values of each stress influencing factor, and a stress distribution in the predetermined region in each state of the predetermined number of combinations relating to the level values are calculated by a finite element method In the third stage, an evaluation point is set at a predetermined position in the predetermined region, and an approximate function established between the stress influencing factor and the generated stress is calculated by the finite element method for the evaluation point. In a method for analyzing the stress of a structure having a fourth stage obtained using
The stress influencing factor values are used as input data of the Monte Carlo method in the stochastic fracture mechanics method, and the values of the generated stresses at the evaluation points when changed randomly are calculated using the approximate function. And a fifth step of obtaining a failure probability that a crack generated in a predetermined region of the structure progresses and the structure is in a damaged state based on each generated stress value .

The invention according to claim 2
The invention according to claim 1 is characterized in that the generated stress calculated using the approximate function is further decomposed into a plurality of decomposition stresses, and the failure probability is obtained using the values of the respective decomposition stresses .

The invention described in claim 3
Stress influence factor setting means for setting a plurality of stress influence factors as factors affecting the stress generated in a predetermined region of the structure, and setting the number of levels and the level value in the experimental design for each of the plurality of stress influence factors. , A level value combination setting means for setting a predetermined number of combinations of level values of each stress influencing factor, and a stress distribution in the predetermined region in each state of the predetermined number of combinations related to the level value by a finite element method A finite element method calculating means for calculating, an evaluation point is set at a predetermined position in the predetermined region, and an approximation function established between the stress influencing factor and the generated stress with respect to the evaluation point is expressed by the finite element method. A stress analysis apparatus for a structure, comprising:
The stress influencing factor values are used as input data of the Monte Carlo method in the stochastic fracture mechanics method, and the values of the generated stresses at the evaluation points when changed randomly are calculated using the approximate function. And a failure probability calculating means for calculating a failure probability that a crack generated in a predetermined region of the structure progresses and the structure reaches a damaged state based on the generated stress values .

  The invention according to claim 4 is the invention according to any one of claims 1 to 3, wherein the predetermined region of the structure is one of a one-dimensional region to a three-dimensional region. .

  The invention according to claim 5 is the invention according to any one of claims 1 to 4, wherein the stress generated in the structure is a residual stress generated due to welding.

  The invention according to claim 6 is the invention according to any one of claims 1 to 4, wherein the generated stress of the structure is a thermal stress generated due to variation in temperature distribution of the structure. Features.

  The invention according to claim 7 is the invention according to any one of claims 1 to 4, wherein the generated stress of the structure is caused by a force applied to the structure from the outside or a displacement based on the force. It is generated.

  The invention according to claim 8 is the invention according to claim 2, wherein the generated stress calculated using the approximate function is further decomposed into a plurality of decomposition stresses, and the failure probability is calculated using the values of the respective decomposition stresses. It is characterized by seeking.

  According to a ninth aspect of the present invention, there is provided a stress influencing factor setting means for setting a plurality of stress influencing factors as factors influencing the stress generated in a predetermined region of a structure, and an experiment design method for each of the plurality of stress influencing factors. A level value combination setting means for setting a number of levels and a level value, and setting a predetermined number of combinations of level values of each stress affecting factor, and a predetermined number of combinations related to the level value in the predetermined region in each state A finite element method computing means for computing the stress distribution by the finite element method, and an evaluation point is set at a predetermined position in the predetermined region, and the evaluation point is established between the stress influencing factor and the generated stress. And an approximate function calculating means for obtaining an approximate function using a calculation result by the finite element method.

  The invention according to a tenth aspect is the invention according to the ninth aspect, wherein each of the evaluation points when the stress influence factor value is randomly changed as input data of the Monte Carlo method in the stochastic fracture mechanics method. The value of the generated stress is calculated using the approximate function, and based on the calculated value of each generated stress, the failure probability that a crack generated in a predetermined region of the structure progresses and the structure is in a damaged state is calculated. It is characterized by comprising damage probability calculating means for calculating.

  According to the present invention, the calculation of the finite element method is performed a minimum necessary number of times only for a predetermined number of combinations of the level values of the stress influencing factors, and the evaluation result set at a desired position is determined from the calculation result. Since the approximate function between the stress influencing factor and the generated stress is obtained, the use of this approximate function can shorten the calculation time and prevent the calculation accuracy from being lowered.

  FIG. 1 is a flowchart of a stress analysis method for a structure according to an embodiment of the present invention. As shown in this figure, this analysis method has a first stage to a fifth stage.

  The first stage is to set a plurality of stress influencing factors x1 to x8 as factors affecting the stress generated in the predetermined region R of the structure.

As shown in FIG. 2, in the present embodiment, the region R is set in a virtual cross section Ms of the structure M, and is a two-dimensional region including a welding point. Therefore, the generated stress in the region R is a residual stress generated due to welding, and the following are used as specific examples of the stress influencing factors x1 to x8.

x1: Young's modulus (molten metal part)
x2: Yield stress x3: Work hardening coefficient x4: Inner inner layer heat input x5: Outer inner layer heat input x6: Inner surface layer heat input x7: Outer surface layer heat input x8: Heat input time (welding speed)

  In the second stage, the number of levels and level values in the experimental design method are set for each of the stress influencing factors x1 to x8, and a predetermined number of combinations of the level values of the stress influencing factors x1 to x8 (this embodiment). In this case, only 18 cases) are set.

  FIG. 3 is a chart showing specific examples of the number of levels and the level values set for each of the stress influencing factors x1 to x8. In the present embodiment, the number of levels is set to 2 only for x1, and two types of level values “low” and “high” are set. For x2 to x8, the number of levels is set to 3, and the level values of "level 3" and "level 1" are varied up and down with the level value of "level 2" as a reference. The reason why the number of levels is set to 2 only for x1 is to keep the number of combinations of each level value in 18 cases.

  FIG. 4 is a chart showing a specific example of the case where the number of combinations of the level values is determined based on an orthogonal table called L18 for the stress influence factors x1 to x8 for which the level values are set as shown in FIG. is there. An orthogonal table is a table that has been conceived so that the same results can be obtained as when all combinations of experiments were performed with a small number of experiments.

In other words, considering all combinations of the level values of each of the stress influencing factors x1 to x8 in FIG. 3, 2 × 3 ⁷ = 4,374 cases, and a great number of operations must be performed. By using it, the number of combinations can be reduced to 18 cases. Therefore, in the present invention, in most cases, the number of combinations is determined using an orthogonal table in most cases. However, when all the combinations are not so many, it is not always necessary to use an orthogonal table (in the case of so-called “multiple arrangement”).

  The third step is to calculate the stress distribution in the region R in the above 18 cases by the finite element method, and the fourth step has evaluation points P1 to Pm at predetermined positions in the region R. (M: 1,000, for example) is set, and approximate functions Y1 to Ym that are established between the stress influencing factors and the generated stress are calculated by the finite element method in the third stage for each of the evaluation points P1 to Pm. The content is to be obtained using the result.

  FIG. 5 is an explanatory diagram for the contents of the third stage and the fourth stage. As shown in this figure, the finite element method is sequentially executed for each of the cases 1 to 18 so as to obtain the stress distribution in the region R in each case.

  Here, as described above, the calculation time per time in the finite element method is long, and if this is performed 18 times, the calculation time becomes considerable. However, in the present invention, it is assumed that such a calculation time is unavoidable and must be accepted.

  As described above, if the finite element method is executed for 18 cases, next, the evaluation points P1 to Pm are set at 1,000 predetermined positions in the region R. In the present embodiment, the number of evaluation points is 1,000, but this may be increased or decreased as necessary, and a predetermined position can be freely set.

Next, for each of the 1,000 evaluation points P1 to Pm, approximate functions Y1 to Ym of stress using the stress influence factors x1 to x8 as variables are obtained as follows. In this case, the 18 stress data when the combinations of the values of the stress influencing factors x1 to x8 are changed in 18 ways at the respective evaluation points P1 to Pm are already given by the calculation of the finite element method. Using these data, approximate functions Y1 to Ym of stress can be obtained. Although it is not possible to obtain an exact solution from these data, it is known that an approximate solution can always be obtained by a statistical mathematics method.

Y1 = f1 (x1, x2,..., X8)
Y2 = f2 (x1, x2,..., X8)
…………
Ym = fm (x1, x2,..., X8)

  As described above, in the stress analysis method according to the present embodiment, the stress approximation functions Y1 to Ym using the stress influencing factors x1 to x8 as variables are obtained for the evaluation points P1 to Pm set in the region R. Therefore, x1 Even if the combination of the values of .about.x8 is changed in various ways other than the above 18 ways, the stress generated at that time can be immediately obtained based on a simple arithmetic expression without using the finite element method. Therefore, various effects such as efficient design calculation can be obtained in addition to obtaining the breakage probability.

  Next, in the fifth stage, the generated stress at the evaluation points P1 to Pm when the Monte Carlo method is applied and the values of the stress influencing factors x1 to x8 are randomly changed a great number of times is calculated as described above. The calculation is performed using the approximate functions Y1 to Ym, and the crack probability of the structure is analyzed based on each generated stress to determine the failure probability.

  FIG. 6 is an explanatory diagram of the fifth stage. That is, in the expression of the approximate functions Y1 to Ym obtained in the fourth stage, for example, the values of x1 to x8 are randomly changed in 10,000 ways, and the values of the generated stresses Y1 to Ym at that time are calculated. . At this time, the calculation time per time is considered to be about 1 second at most even if the evaluation points P1 to Pm are 1,000 points, so the calculation time for 10,000 times is 10,000 seconds≈ 2.8 hours. This is a short calculation time that can be well tolerated in practice compared to the aforementioned 417 days.

  When the values of x1 to x8 are randomly changed, for example, for Young's modulus (x1), which is one of material property values, the data obtained in the material test has a normal distribution centered on the average value. If it is known, it is preferable to randomly generate along this distribution. In the present embodiment, the stress influencing factors x4 to x7 are the products IVη of the welding current I, the welding voltage V, and the welding efficiency η. However, it is also possible to use I, V, and η individually as stress influencing factors. It is done.

  Next, a known relational expression between 10,000 values of each of the generated stresses Y1 to Ym when the values of x1 to x8 are randomly changed in 10,000 ways, the stress expansion count and the crack growth rate. Are sequentially substituted to calculate the crack propagation in each state. If the crack calculated at this time is larger than the thickness of the structure, for example, it is determined that the structure is in a damaged state when the combination of the values of x1 to x8 is used. If 10,000 cases of such a broken state appear 10 times, the breakage probability is 10 ÷ 10,000 = 0.1%.

  As described above, according to the stress analysis method according to the present embodiment, the influence of a plurality of stresses at an evaluation point set at a desired position in a predetermined region is obtained by performing the finite element method as many times as necessary. An approximate function between the factor and the generated stress can be obtained. Therefore, by using this approximate function, it is possible to calculate each generated stress at the evaluation point when the value of each stress influencing factor is changed in a very short time.

  And if stress influence factor is used as input data of Monte Carlo method in probabilistic fracture mechanics method, the above approximate function is used for each stress when the value of this stress influence factor is randomly changed many times. It is possible to calculate easily, and the calculation time can be shortened.

  In addition, in the conventional concept, various stresses such as film stress, bending stress, and peak stress are used as input data of the Monte Carlo method, and these stresses are randomly selected without considering the balance between each other. As a result, the calculation accuracy was lowered. However, since the stress analysis method according to the present embodiment uses not the stress itself but the stress influencing factor as input data of the Monte Carlo method, such a balanced relationship between various stresses is automatically considered. As a result, the calculation accuracy is not lowered.

  As described above, the stress analysis method according to the present invention does not directly combine the finite element method, which takes a long time, and the Monte Carlo method, which requires a large number of repetitions. It can be said that this is an indirect combination of the finite element method and the Monte Carlo method, with an approximate function between the stress influencing factor and the generated stress obtained as a result of performing as many times as necessary. With this configuration, it is possible to obtain a calculation result almost equivalent to a configuration in which the finite element method and the Monte Carlo method are directly combined in a short time without reducing the calculation accuracy.

  Since the stress analysis method of the present invention widely includes the following forms in addition to the above-described embodiment, this will be described next.

  (1) In the above embodiment, the case where the predetermined region R of the structure M is a two-dimensional region set in the virtual cross section Ms has been described, but this region R is a one-dimensional region (line-shaped region), or It may be a three-dimensional area. Among these regions, one-dimensional and two-dimensional regions may be obtained from two-dimensional analysis such as axisymmetric analysis, or may be obtained from three-dimensional analysis. A three-dimensional region is a three-dimensional finite element method. Obtained from analysis only. When obtained from a three-dimensional finite element method analysis, the approximate function of the generated stress using the stress influencing factor as a variable has six components (three components in the x, y, and z directions for principal stress, and xy, yz, and zx planes for shear stress). 3 components).

  (2) In the fifth stage in the above embodiment, 10,000 values of each of the generated stresses Y1 to Ym when the values of x1 to x8 are randomly changed, for example, in 10,000 ways, are used as the stress expansion count. In some cases, a known relational expression between the crack growth rate and the crack is sequentially substituted. If the 10,000 generated stresses Y1 to Ym are further decomposed into a plurality of decomposition stresses, and the values of the respective decomposition stresses are substituted into the above relational expressions, a more accurate failure probability can be obtained. Obtainable.

  For example, assuming that the stress distribution of the structure M as shown in FIG. 7A is obtained, the value of this stress distribution is not substituted into the above relational expression as it is, but FIGS. 7B and 7C. , (D) can be decomposed into respective decomposition stresses of film stress, bending stress, and peak stress, and the values of the respective decomposition stresses can be substituted into the above relational expressions. According to the conventional idea, the values of the film stress, bending stress, and peak stress are varied independently and used as input data for the Monte Carlo method, but the calculation accuracy is reduced. Since the stresses shown in b), (c), and (d) are stresses in a balanced state, the calculation accuracy is not lowered.

  (3) Although the generated stress of the structure in the above embodiment has been described with respect to the case of residual stress generated due to welding, the present invention generates this generated stress due to variations in the temperature distribution of the structure. It can also be applied to the case of thermal stress.

  For example, consider the case of a stepped cylindrical structure M as shown in FIG. FIG. 8B is an enlarged cross-sectional view of a portion B in FIG.

  An annular stepped portion M2 is formed substantially at the center on the inner surface side of the side wall portion M1, and fluids 1 and 2 flowing in the direction of the arrow are in contact with the upper and lower surfaces of the stepped portion M2. The fluid 3 flowing in the direction of the arrow is in contact with the outer surface side of the side wall M1. Assuming that the temperature of the fluids 1 to 3 has changed from a high temperature to a low temperature, the region related to the formation position of the stepped portion M2 in the side wall portion M1 is delayed in following the temperature decrease compared to other regions. Therefore, as shown in the drawing, a high temperature portion and a low temperature portion are generated, and a thermal stress is generated due to this temperature difference.

  The analysis of the thermal stress generated in the discontinuous part of such a structure is complicated because the temperature difference of fluids 1-3 and the difference in rigidity of each member must be taken into account. Will be used. Therefore, the stress analysis method according to the present invention is effective for analyzing such thermal stress. As main stress influencing factors in this case, the temperature of the fluids 1 to 3 or the rate of temperature change, the flow rate, the heat transfer coefficient between the fluids 1 to 3 and the side wall portion M1 and the stepped portion M2 can be considered.

  (4) The present invention is also applicable to a case where the generated stress is generated due to a force applied to the structure from the outside or a displacement based on this force.

  For example, consider a structure called “Y-piece” as shown in FIG. The Y-piece-like structure M has a cylindrical part M1 and a skirt part M2 whose upper end is fixed to the building fixing wall and is suspended. Is formed.

  Assuming that the cylindrical portion M1 is subjected to an axial displacement due to an external load, thermal expansion, thermal contraction, or the like as indicated by an arrow, and an internal pressure is applied to the inner surface, the axial displacement is Y The internal pressure acts in the direction of opening the piece, while the internal pressure acts in the direction of closing the Y piece. In such a case, stress concentration occurs depending on the value of the curvature R at the root of the Y piece, and the stress distribution is very complicated. Therefore, the finite element method is used for the stress analysis. Therefore, also in this case, the stress analysis method of the present invention is effective. As main stress influencing factors in this case, the rigidity difference between the cylindrical portion M1 and the skirt portion M2, the curvature R, the internal pressure received by the cylindrical portion M1, the axial displacement (or axial force), the ambient temperature, and the like can be considered.

  FIG. 10 is a block diagram showing a configuration of a stress analysis apparatus for carrying out the stress analysis method according to the embodiment of the present invention. As shown in this figure, the present stress analysis apparatus includes a stress influence factor setting means 1, a level value combination setting means 2, a finite element method calculating means 3, an approximate function calculating means 4, a failure probability calculating means 5, The failure probability calculation means 5 includes a crack growth calculation unit 6, a damage state determination unit 7, and a determination result storage unit 8.

  The stress influence factor setting means 1 is a means for executing the first stage of the stress analysis method described above, and sets the stress influence factors x1 to x8 having the contents as shown in FIG.

  The level value combination setting means 2 is a means for inputting the stress influence factors x1 to x8 and performing the second stage. Then, after setting the number of levels and the level values as shown in FIG. 3, a predetermined number of combinations of the level values of each stress influencing factor as shown in FIG. Set.

  The finite element method computing means 3 is means for performing the third stage based on the predetermined number of combinations. That is, the stress distribution in a predetermined region in each state of the above combination is calculated by the finite element method.

  The approximate function calculation means 4 is a means for performing the fourth stage from the calculated stress distribution and the evaluation point setting data given in advance. That is, an approximate function between the stress influencing factor and the generated stress, which is established at each evaluation point, is calculated from the stress distribution relating to the predetermined number of combinations.

  The failure probability calculating means 5 is means for performing the fifth stage using the stress influencing factors. That is, initial conditions such as material property values, initial crack size, crack growth rate, and the like are given to the crack propagation calculation unit 6 in advance. When random data of the stress influencing factors x1 to x8 is input, Each generated stress at each evaluation point is calculated using an approximate function. Then, the values of these generated stresses are sequentially substituted into a known relational expression between the stress expansion count and the crack growth rate to calculate the crack growth in each state.

  The damage state determination unit 7 determines whether or not the progress of the crack calculated at this time leads to damage of the structure, and stores the determination result in the determination result storage unit 8. The damage probability calculating means 5 calculates the damage probability of the structure from the accumulation determination result obtained in this way.

The flowchart about the stress analysis method of the structure which concerns on embodiment of this invention. Explanatory drawing which shows the specific example of the area | region R and the stress influence factor x1-x8 in the 1st step of FIG. FIG. 3 is a table showing specific examples of the number of levels and the level values set for each of the stress influencing factors x1 to x8 in the second stage of FIG. 1; FIG. 4 is a chart showing a specific example when the number of combinations of level values of stress influencing factors x1 to x8 is determined from the chart shown in FIG. 3 in the second stage of FIG. Explanatory drawing about the content of the 3rd step of FIG. 1, and a 4th step. Explanatory drawing about the content of the 5th step of FIG. Explanatory drawing about embodiment included by the stress analysis method of this invention. Explanatory drawing about embodiment included by the stress analysis method of this invention. Explanatory drawing about embodiment included by the stress analysis method of this invention. The block diagram which shows the structure of the stress analyzer for enforcing the stress analysis method which concerns on embodiment of this invention.

Explanation of symbols

M: Structure R: Predetermined areas x1 to x8: Stress influencing factors P1 to Pm: Evaluation points Y1 to Ym set in the area R: Approximate function 1 at the evaluation points P1 to Pm 1: Stress influencing factor setting means 2: Level value combination setting means 3: Finite element method calculating means 4: Approximate function calculating means 5: Failure probability calculating means 6: Crack growth calculating part 7: Damage state determining part 8: Determination result accumulating part

Claims (3)

A first stage of setting a plurality of stress influencing factors as factors influencing the generated stress in a predetermined region of the structure;
A second stage of setting the number of levels and level values in the experimental design for each of the plurality of stress influencing factors, and setting a predetermined number of combinations of the level values of each stress influencing factor;
A third step of calculating a stress distribution in the predetermined region in each state of a predetermined number of combinations related to the level value by a finite element method;
A fourth point is obtained by setting an evaluation point at a predetermined position in the predetermined region and obtaining an approximate function established between the stress influencing factor and the generated stress with respect to the evaluation point by using a calculation result by the finite element method. And the stage
In a stress analysis method for a structure having
The stress influencing factor values are used as input data of the Monte Carlo method in the stochastic fracture mechanics method, and the values of the generated stresses at the evaluation points when changed randomly are calculated using the approximate function. Based on the value of each generated stress, it has a fifth step of obtaining a failure probability that a crack generated in a predetermined region of the structure progresses and the structure reaches a damaged state.
A stress analysis method for a structure characterized by the above. The generated stress calculated using the approximate function is further decomposed into a plurality of decomposition stresses, and the failure probability is obtained using the value of each decomposition stress,
The stress analysis method for a structure according to claim 1. A stress influence factor setting means for setting a plurality of stress influence factors as factors affecting the generated stress in a predetermined region of the structure;
  Level value combination setting means for setting the number of levels and level values in the experimental design for each of the plurality of stress influence factors, and setting a predetermined number of combinations of the level values of each stress influence factor;
  A finite element method computing means for computing a stress distribution in the predetermined region in each state of a predetermined number of combinations relating to the level value by a finite element method;
  An approximation function that sets an evaluation point at a predetermined position in the predetermined region and obtains an approximation function that is established between the stress influencing factor and the generated stress with respect to the evaluation point by using the calculation result of the finite element method Computing means;
  In the structure stress analysis apparatus characterized by comprising:
  The stress influencing factor values are used as input data of the Monte Carlo method in the stochastic fracture mechanics method, and the values of the generated stresses at the evaluation points when changed randomly are calculated using the approximate function. Based on the value of each generated stress, comprising a failure probability calculating means for calculating the failure probability that a crack generated in a predetermined region of the structure progresses and the structure reaches a damaged state,
  A structure stress analysis apparatus characterized by the above.

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