CN113821945B - Random stability optimization method for latticed shell structure based on regional defect sensitivity difference - Google Patents
Random stability optimization method for latticed shell structure based on regional defect sensitivity difference Download PDFInfo
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Abstract
The invention discloses a random stability optimization method of a reticulated shell structure based on regional defect sensitivity difference, which quantitatively proves that the regional defect sensitivity difference exists and is obvious by setting Ji Min-degree test samples and establishing a regional sensitivity relative coefficient calculation formula. Dividing the defect sensitive areas of the reticulated shell structure by setting a sensitivity coefficient threshold value, and grouping the rod pieces based on the defect sensitive areas; and searching an optimal structure model taking the minimum coefficient of variation of stable bearing capacity as an objective function in the simulation defect sample set Sop by adopting a sequence two-stage algorithm, and optimizing the section model of rod member groups in different sensitive areas, thereby reducing the sensitivity of the stable bearing capacity of the structure to random defects and reducing the probability of unstable damage caused by insufficient stable bearing capacity of the structure on the premise of not increasing the construction difficulty and the steel consumption. The rod piece grouping mode based on the defect sensitive area enables the random optimization design to obtain good optimization effect under a small-scale sample set Sop, and time cost is saved.
Description
Technical Field
The invention relates to a random stability optimization method for a reticulated shell structure based on regional defect sensitivity difference.
Background
In a reticulated shell structure, which typically contains thousands of components, it is almost impossible to achieve complete and accurate fabrication. The defects of initial bending, initial internal stress, initial eccentricity of the rod piece to the node, spatial position deviation of the node and the like are always unavoidable. The effect of the defects of the bars themselves in the design of bars according to the specifications has been fully considered and limited to a certain extent, the effect of which on the stability of the reticulated shell structure is not a major factor. For the overall stability of the structure, a defect of installation deviation of the curved surface shape (mainly referred to as a defect of spatial position deviation of a node, hereinafter referred to as a defect) is a main cause of random fluctuation of the overall stable bearing capacity of the structure. Various conventional and abnormal single-layer reticulated shell structures belong to structures with more serious defect sensitivity, and are extremely easy to be unstable and damaged caused by defects.
Hutchinson J W.Impertection Sensitivity of Externally Pressurized Spherical Shells [ J ]. Journal of Applied Mechanics,1967,34 (1) (defect sensitivity of spherical shells under external pressure) and Koiter W.T.the stability of elastic equilibrium [ D ]. Delft, H.J.Paris publisher, amsterdam. English translation NASA ttf-10,1967 (stability of elastic equilibrium) concluded earlier that defects can have a significant impact on the stable load-bearing capacity of continuous shells.
In 1988, borri C., spinelli P.bucking and post-buckling behavior of single layer grid shells affected by random imperfections [ J ]. Computers & Structures,1988,30 (4): 937-943 (influence of random defects on buckling and post-buckling properties of single-layer latticed shells) employs a random defect method to conduct initial buckling and post-buckling analysis on a defective single-layer latticed shell structure, double nonlinearity of materials and geometry is considered, and the latticed shell structure and thin-shell structure are verified to belong to a defect sensitivity structure.
In the geometric and material dual nonlinear analysis, the value of the first extreme point of the elastoplastic stability analysis load-displacement curve can be used as the stable bearing capacity of the structure. Both the magnitude and the distribution of "defect samples" used in computer design can lead to significant fluctuations in the calculated model's stable bearing capacity values. Because of the random nature of the defect distribution in the actual structure, the defect samples used in the calculation model are necessarily different from the actual ones, and therefore, the stable bearing capacity value of the actual structure is most likely to be smaller than that of the calculation model. The higher the sensitivity of the stable bearing capacity value to the defective sample, the greater the potential safety hazard of the structure.
The most unfavorable defect method is to find a quasi- "most unfavorable defect distribution form" under a fixed defect amplitude, and apply the quasi- "most unfavorable stable bearing capacity" to a structure. The least disadvantageous defect method is a conventional method for solving the problem of structural defect sensitivity.
Liu et al analyzed the structure for its most unfavorable defects using random defect mode superposition (Liu H, zhang W., yuan H.Structure stability analysis of single-layer grid shells with stochastic imperfections [ J)]Stability analysis of single layer reticulated shells under random defects) Broggi and Schueler et al propose an effective defect model to analyze the minimum stable load-bearing capacity of a composite cylindrical shell. (Broggi, M.andEffective defect model for buckling analysis of composite cylindrical shells of g.i. (2011), efficient modeling of imperfections for buckling analysis of composite cylindrical shells, eng.struct.,33 (5), 1796-1806)
Random fluctuations in the structurally stable load bearing values will lead to structural reliability problems, and improving structural reliability by the least disadvantageous defect method has the following disadvantages:
(1) The true least disadvantageous defect cannot be obtained, and the structure is still more likely to be unstable and damaged.
(2) When the least disadvantageous defect method is used in conventional optimization design, the assumed least disadvantageous defect samples may cause the structure to be over designed and negatively affect.
For example, in the cross-section optimization design of the net shell structure taking the most steel consumption as the objective function, the structural model obtained by optimizing the most unfavorable defect method can ensure that the constraint condition is met under the assumed least unfavorable defect sample while the most steel consumption is saved, but at the same time, the optimized structural model does not meet the constraint condition under other random defect samples with high probability, and the reason is mainly that the structure is over-designed under the least unfavorable defect sample. The inventors of the present invention have demonstrated this conclusion by comparative analysis of the examples in the published article "optimizing design of cross section of reticulated shell structure based on the 'iso-stability' requirement". The calculation model of the "space position grouping method optimization" in fig. 9 is designed by adopting the most unfavorable defect method, and in the design process, first, the 28 random samples are subjected to trial calculation to obtain the most unfavorable defect sample with the number 16 sample being opposite; and (3) optimally designing the structure by using a number 16 sample to obtain an optimal structure which meets constraint conditions and has the lightest weight, wherein the bearing capacity of the optimal structure does not meet design requirements under other 27 defects. The stable bearing capacity performance of the equal stability optimization model is good, but in the equal stability optimization design, the grouping mode of the rod pieces is too random, and the essential dividing means of grouping based on the difference of regional defect sensitivity is not found.
It can be seen that the design problem of optimizing the reticulated shell structure considering the defect sensitivity cannot directly use the least disadvantageous defect method, otherwise the structural safety is reduced.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a random stability optimization method for a latticed shell structure based on the difference of regional defect sensitivity.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
a method for optimizing random stability of a reticulated shell structure based on regional defect sensitivity difference comprises the following steps:
designing a sensitivity test sample and establishing a sensitivity relative coefficient xi i A calculation formula is used for determining the sensitivity difference of different areas to defects through quantitative calculation; dividing the latticed shell structure into defect sensitive areas with different levels according to sensitivity relative coefficients, and grouping rod pieces of the latticed shell structure according to the divided areas;
searching an optimal structure model taking the minimum stable bearing capacity variation coefficient as an objective function in a simulation defect sample set Sop by adopting a sequence two-stage algorithm; the aim of balancing the defect sensitivity of each region of the structure is achieved by optimizing the cross section size of the rod pieces of each different sensitive region, so that the fluctuation range of the stable bearing capacity value of the whole structure under random defects is narrower, and the robustness is better.
The sensitivity test sample is characterized in that a local area formed by related nodes is selected firstly, so that the defect value of the nodes in the local area is larger than that of the nodes in the non-local area, and the sensitivity test sample is formed. The sensitivity test sample is used to test the relative sensitivity of a "local area" in the sample to defects.
The simulated defect sample set Sop comprises a certain number of simulated defect samples with the same defect amplitude. Unlike the sensitivity test sample, the simulated defect sample is used to simulate defects that may occur in an actual structure. The simulated defect samples can be random defect samples conforming to a normal distribution rule, eigenvalue defect samples conforming to a lowest order modal distribution and possibly the least favorable defect samples.
The Li Yongmin degree relative coefficient formula can calculate the relative sensitivity degree of different areas of the reticulated shell structure, and quantitatively compare the defect sensitivity difference of the different areas. Sensitivity relative coefficient ζ i The calculation formula of (2) is as follows:
ξ i ＝(P 0 -SP i )/P 0 (1-1)
wherein i is the number of the simulated defect sample in the set Sop, P 0 Is the elastoplastic stable bearing capacity value of an ideal reticulated shell structure, SP i A structurally stable load bearing value at the occurrence of the ith sensitivity test specimen.
The mathematical optimization model with the minimum stable bearing capacity variation coefficient as an objective function is as follows:
wherein X= (X) 1 ,…,x i ,…,x m1 )，x i The section steel number used for the ith group of rod pieces is m1 is the rod piece grouping number, and the total number of the section steel is 63 kinds of optional steelAre arranged in ascending order according to the bending-resistant section coefficient and are arranged in a discrete set P of the profile steel; psi i Representing an ith simulated defect sample; l is the number of simulation defect samples; delta is the variation coefficient of the stable bearing capacity value of the structure under the L simulated defect samples; sop is a simulated defect sample set; s.t. is an abbreviation for constraint; z is Z j Representing a constraint function; z1 is the number of constraint conditions;
design variable X:
X＝(x 1 ,…,x i ,…,x m1 ) (1-3)
wherein x is i Numbering the section steel selected for the ith group of rod pieces;is x i The section property of the steel with the number A is the cross section area, and the unit m 2 ；I y ，I z Moment of inertia in the y and z axes, respectively, unit m 4 ；W y ，W z The bending-resistant section coefficients of the pair y and z axes are respectively shown as unit m 3 The method comprises the steps of carrying out a first treatment on the surface of the ρ is the linear density (kg/m)
Objective function δ:
δ＝σ/μ (1-5)
in the method, in the process of the invention,and->Respectively the standard deviation and the mean value of the structural stability bearing capacity under the L simulated defect samples; />The stable bearing capacity value of the structure under the ith defect sample in the Sop is obtained; l is the number of samples in the simulated defect sample set Sop.
Local constraint is the rod constraint condition:
λ-[λ]≤0 (1-7)
wherein N is the axial force of the rod piece; a is the cross-sectional area of the rod; e is the elastic modulus of the material; m is M y And M z Around the y-axis and around the y-axis respectively z Bending moment of shaft, for circular sectionWy and Wz are bending-resistant section coefficients about the y-axis and z-axis, respectively, for a circular section w=w y ＝W z ，γ y And gamma z Taking γ=γ as the section plasticity development coefficient y ＝γ z ＝1.15；f＝215MPa；/>l 0 For the length of the rod piece, I y ，I z Moment of inertia about the y-axis and z-axis, respectively, for a circular cross-section i=i y ＝I z ；[λ]The permissible slenderness ratio of the rod piece; n' E ＝π 2 EA/(1.1λ 2 ) For Euler critical force, ++>As the stability coefficient of the axial compression component; />The stability coefficient of the whole component; beta m ＝β t =1.0; η is the section influence coefficient taken to be 0.7.
Overall stability constraint, i.e., overall structural constraint:
2×Q-P crmin ≤0 (1-10)
in the method, in the process of the invention,the minimum value of the stable bearing capacity value of all the defect samples of the Sop is set; q is the uniform external load of the structure.
The random optimization of the structural stability bearing capacity adopts a combination of a sequence two-stage optimization algorithm and a simulation defect sample set Sop, and the random optimization program (CSY_FEM) is written by adopting large-scale general finite element analysis software ANSYS and compiling software Intel Visual Fortran (IVF). The elastoplastic stability analysis of the random defect structure is written by adopting APDL language in large-scale general finite element analysis software ANSYS, and the sequence two-stage optimization is written by adopting Intel Visual Fortran (IVF). The data transmission between the software is completed by adopting a mode of reading a notepad file, and an interface program is written in IVF to realize the call of ANSYS software.
Description: IVF (Intel Visual Fortran) is the Fortran compilation environment developed by intel corporation, ANSYS is large general purpose Finite Element Analysis (FEA) software developed by ANSYS corporation of america.
In the primary optimization, structural defects are not considered, and all the rods use the same section steel; selecting the section steel meeting the local constraint conditions (1-6, 1-7, 1-9) in the section steel set P by utilizing a one-dimensional search algorithm, meanwhile, marking the number as xm and marking the optimization result as X, wherein the steel consumption of the structure is the most saved 0 ；
Calculating a structural model X in a simulated defect sample set Sop 0 Minimum stable bearing capacity value under each defective sampleIf the constraint condition (formulas 1-10) of the whole structure is met, ending all optimization processes; if the optimization is not satisfied, the first-stage optimization is finished and enters a second-stage optimization, and the second-stage optimization adopts a relative difference quotient method for optimizing.
In the second level of optimization, the sensitivity is first based onThe structural rod member is divided into m by the requirement of symmetry in the structural design of the area division and the net shell 1 Group, select first level optimization result X 0 As an initial structural model, denoted as X (k) ＝X 0 = (xm, xm, …, xm), k=1 for calculating structure X under each defect sample of Sop (1) Coefficient of variation delta of (2) (1) Steel amount W (1) Sum and difference quotientAs in formulas 1-11. The smaller the relative difference quotient (the code value) is, the smaller the steel consumption increment is, and the more the variation coefficient is reduced; the smaller the coefficient of variation is, the smaller the fluctuation of the structural stability bearing capacity value along with the defect is, and the higher the reliability of the structural stability bearing capacity is.
In the k-th iteration, the relative difference quotient corresponding to the ith group of rodsRepresented as
Wherein k is a natural number,for the coefficient of variation of the optimal model obtained in the kth iteration,/o>The stable bearing capacity variation coefficient of the corresponding model is obtained after the number of the ith group of rod pieces of the optimal model of the kth iteration is increased by 1; />Steel usage for optimal model in the kth iteration,/->The steel consumption of the corresponding model is increased by 1 for the number of the ith group of rod pieces;
k+1st round optimal structure model X (k+1) The calculation of (1) is shown in formulas 1-12,1-13 and 1-14
X (k+1) ＝X (k) +I (k) (1-12)
I (k) ＝(e 1 ，e 2 ，...，e m1 ) T (1-13)
Wherein X is (k) Iterating the optimal structure model for the kth round; x is X (k+1) Iterative optimal structural model for the (k+1) th round; i (k) Iterative optimal direction for the kth round; e, e i Equal to 1 or 0; m1 represents the grouping number of the rod pieces;the relative difference quotient corresponding to the ith group of bars in the kth iteration.
Calculating that each defect sample in the defect sample set Sop appears in the structural model X (k+1) At the time of loading, the minimum value of the structural stability bearing capacity valueJudging whether the constraint conditions (formulas 1-10) are satisfied, if so, ending the optimization, and if not, updating the design variable X (k) ＝X (k+1) The iteration is continued until the overall stability constraint is satisfied.
Due to the discretization of the latticed shell structure and the discretization of the model steel (the model steel must be in accordance with the modulus), the situation that the objective function is a local minimum value but the constraint condition is not satisfied may occur in the optimizing process.
The current local minimum point of the objective function can be jumped out by using the formulas 1-15, 1-16 and 1-17 to generate a new structural model X (*) And updating the structural model to obtain X (k) ＝X (*) 。
X (k) ＝X * (1-17)
And (3) jumping out of the current local minimum, and continuing the second-stage optimization iteration until all constraint conditions are met, namely searching an optimal solution of the objective function meeting all constraint conditions by the structural model under higher steel consumption.
In the invention, the different areas of the reticulated shell structure have different 'resistance' to defects and the defects with the same level can bring larger stable bearing capacity loss when the defects appear in the areas with weaker resistance; conversely, when it occurs in a region of greater resistance, the stable load bearing capacity of the structure is less lost. On the whole trend, the random fluctuation amplitude of the stable bearing capacity of the space reticulated shell structure increases along with the increase of the defect amplitude. The unified increase of the model of the structural rod member can reduce the fluctuation range of the random stable bearing capacity of the structure, and the reasonable increase of the model of the rod member in the defect sensitive area can more effectively reduce the variation coefficient of the random stable bearing capacity value and reduce the defect sensitivity of the whole structure.
The beneficial effects of the invention are as follows: on the premise of not increasing the difficulty of construction (reducing the amplitude of defects and increasing the difficulty of construction) and the steel consumption, the fluctuation range of the stable bearing capacity of the structure under random defects is narrowed, and the sensitivity of the stable bearing capacity to the defects is reduced. The comparative analysis of the calculation example shows that under the requirements of the same steel consumption and the same construction precision (defect amplitude), compared with an unoptimized structure, the failure rate of the stable bearing capacity of the optimized structure under 500 random defects is reduced by 14.6 percent. Meanwhile, a good optimizing effect can be obtained without adopting a large number of simulation defect samples in the random optimizing process, and the method is mainly attributed to a rod piece grouping method based on a defect sensitive area, so that double benefits in time and economy are brought.
Drawings
FIG. 1 is a schematic view of a partial region of a node number and sensitivity test sample;
FIG. 2 is a "center node" schematic of 42 sensitivity test samples;
FIG. 3 is a relative sensitivity coefficient ζ i Arranging the graphs in descending order;
FIG. 4 is a flow chart of a random stable bearing capacity optimization design based on a sequence two-stage algorithm;
FIGS. 5 (a), 5 (b), and 5 (c) are bar grouping diagrams based on a defect-sensitive area grouping method, respectively;
FIG. 6 shows the stable bearing capacity P of two models under 500 random defects cr /(kN/m 2 ) A figure;
FIG. 7 is a graph of the maximum and minimum values of the stable bearing capacity of two models in defect sets of different defect magnitudes;
FIG. 8 is a graph of the coefficient of variation corresponding to different defect magnitude samples.
Fig. 9 is a graph of the stable load bearing capacity for 28 defects in the background.
Detailed Description
The invention will be further described with reference to the drawings and examples.
The structures, proportions, sizes, etc. shown in the drawings attached hereto are for illustration purposes only and are not intended to limit the scope of the invention, which is defined by the claims, but rather by the claims. Also, the terms such as "upper," "lower," "left," "right," "middle," and "a" and the like recited in the present specification are merely for descriptive purposes and are not intended to limit the scope of the invention, but are intended to provide relative positional changes or modifications without materially altering the technical context in which the invention may be practiced.
As shown in fig. 1 to 8, the method for optimizing random stability of the reticulated shell structure based on the difference of regional defect sensitivity comprises the following steps:
1. the sensitivity test sample is designed, a sensitivity relative coefficient calculation formula is established, and the sensitivity difference of different areas to defects is defined through quantitative calculation.
The data dimension of one sensitivity test sample is Nd 3, nd is the number of spherical nodes of the net shell, and 3 represents the directions of three coordinate axes of each spherical node in the whole coordinate system;
and randomly generating two groups of data sets A0 and B0 by adopting a normal distribution model, and describing the defect displacement value of each node in the sensitivity test sample.
The mean value of the A0 group data is 0, standard deviation omega/2, (defect amplitude is omega), and dimension is Nd1 x 3. The mean value of the data in the B0 group is 0, the standard deviation alpha omega/2, (the defect amplitude is alpha omega (0 < alpha < 1)), and the dimension is Nd 3.
A "local area" of Nd1 related nodes is created. For example, the dashed line in FIG. 1 shows a hexagonal partial region of seven associated nodes.
Firstly, designating the data in B0 as defect displacement of each node of the whole reticulated shell structure in three coordinate directions, and then replacing the defect displacement values of Nd1 nodes in a 'local area' with the data in A0, wherein the defect displacement values of the nodes in the 'local area' are larger than those of the nodes in other areas. To this end, a sensitivity test sample L i (or Z) i ) The establishment is completed, wherein i is the number of the central node of the local area, and if the i node is on the main rib, the sensitivity test sample is marked as L i Otherwise marked as Z i 。
For example, the sensitivity test sample shown in FIG. 1 is designated L2, and the local area center point is numbered 2, which is on the main rib. The defect displacement values of the local area related nodes (2, 1, 3, 9, 8, 19 and 7) are taken from the data in A0, and the defect displacement values of other nodes are taken from the data in B0.
By using the data A0 and B0, a plurality of sensitivity test samples can be established by changing the position of the local area, and each sensitivity test sample corresponds to a sensitivity relative coefficient xi related to the defect sensitivity of the local area i ”。
The elastic-plastic stable bearing capacity value of the ideal reticulated shell structure is recorded as P 0 When a certain sensitivity test sample L i (or Z) i ) Is structurally characterized in that the limit value of the stable bearing capacity is changed to SP i 。
The sensitivity test sample corresponds to the sensitivity relative coefficient xi of the' local area i The calculation formula of (c) is as follows,
ξ i ＝(P 0 -SP i )/P 0 (1-1)。
2. structural defect sensitive area division based on sensitivity relative coefficient
Taking a hemispherical latticed shell structure as an example, the defect sensitive area of the structure is divided according to the sensitivity coefficient. The rod piece takes 34 th section steel in the discrete set P. Taking ω=s/300, α=1/3. According to the symmetry of the latticed shell structure, the analysis can be performed in only one 1/6 sector. The "local area" location of each sensitivity test sample may be determined by the location of the central node, see FIG. 2. A total of 42 sensitivity test samples are generated, constituting a sensitivity test sample set C0. By traversing the sensitivity test sample set C0, the sensitivity relative coefficient ζ of each "local area" can be calculated by the formula (1-1) i See table 1.
TABLE 1 Integrated stability bearing force value SP for defective structure i (kN/m 2 ) Sensitivity relative coefficient ζ of each local area i
As can be seen from the data in table 1,
(1) The overall stable bearing capacity of the ideal structure is 6.39kN/m 2 When the sensitivity test specimen Z21 appears on an ideal structure, the stable load bearing value of the structure is significantly reduced (SP i ＝5.09kN/m 2 ) About 21% lower than the ideal structure; when the defect sample L219 appears on the ideal structure, the stable bearing capacity value of the structure is reduced by only 2%. The defect values for sample Z21 and sample L219 are the same, both from set A0 and set B0, but the larger defects from A0 occur at different points"local area". It can be seen that the different areas of the reticulated shell structure have different resistances to defects, and that larger defects occur in areas with weaker resistances, which necessarily result in larger loss of bearing capacity, whereas the loss of bearing capacity is smaller.
(2) Looking at samples numbered 1 through 12, the center points (1, 8, 20, …,332, see fig. 5) of the 12 sensitivity test samples sequentially varied from top to bottom along the main rib direction. Wherein, the relative sensitivity coefficient of the samples numbered 1 to 6 is larger and is larger than 0.06; the samples numbered 7 through 12 have a small relative sensitivity coefficient, each less than 0.03. The samples numbered 13 to 42 were observed with their center points distributed between the two main ribs, arranged in a high to low order. Wherein, the relative sensitivity coefficients of samples No. 13 to No. 17 are larger and are all larger than 0.1; the relative sensitivity coefficients of samples No. 18 to No. 42 are small, which are all less than 0.03. The sensitivity to structural defects is a rule that decreases from top to bottom.
(3) When the central node is on the same ring, the sensitivity relative coefficient difference is smaller, and the defect sensitivity difference in the ring direction can be ignored.
The sensitivity coefficient ζ in Table 1 i The arrangement is in descending order, see fig. 3.
As can be seen from the figure 3 of the drawings,
the sample Z21 is arranged at the first position of the abscissa and has a relative sensitivity coefficient xi 21 At maximum, this represents the "local area" bounded by nodes 21, 8, 9, 22, 40, 39, 20 as the critical area of the overall structure where defect sensitivity is highest. The last bit of sample Z218, on the abscissa, has its relative sensitivity coefficient ζ 218 At a minimum, this means that the local area enclosed by the nodes 218, 170, 219, 273, 272, 331, 271 is the area of least defect sensitivity in the overall structure.
(1) Maximum sensitivity coefficient ζ 21 =0.203, minimum sensitivity coefficient ζ 218 =0.022, the drop amplitude is about 90%. The large difference in the relative sensitivity coefficients of the different areas on the surface of the shell indicates that the difference in the resistance capability of the different areas to the defects is significant.
(2) The structural model may be divided into a plurality of regions according to the distribution characteristics of the sensitive regions. In this example, a boundary value of 0.05 is taken as a sensitivity coefficient, and local areas corresponding to sensitivity test samples L2, Z21, L8, Z63, L38, Z40 and the like are divided into high-sensitivity areas (corresponding to areas in a ring with the top down 1-5 rings), and other areas are defined as low-sensitivity areas (corresponding to areas in a ring with the top down 6-12 rings).
3. Random optimization design based on regional defect sensitivity difference:
the simulated defect sample set Sop is a set of a plurality of 'simulated defect samples' established under the determined defect amplitude, each simulated defect sample is used for simulating defects possibly occurring in an actual structure, and samples in the set Sop can comprise random defect samples conforming to a normal distribution rule, lowest-order characteristic value modal defect samples and quasi 'least advantageous defect samples' obtained through various methods.
The design method commonly used in engineering is as follows: traversing the simulation defect sample set Sop to find the opposite 'least favorable defect sample' and take the same as a 'design defect', and increasing the model of all components to ensure that the strength, the rigidity and the overall stability conditions based on the 'design defect' of the structure are all satisfied, and the design is finished. However, when the defect amplitude is large, the stable bearing capacity fluctuates significantly with the defect, and the true least adverse defect cannot be included in the aggregate Sop, so that the structure still has the risks of instability and damage.
In order to further improve the stability bearing capacity safety of the structure, firstly, analyzing the defect sensitive areas of the structure and grouping the rod pieces, and then searching an optimal design which minimizes the stability bearing capacity variation coefficient in a simulated defect sample set Sop, namely, optimizing the cross section size of the rod piece to enable the resistance capacity of each area of the structure to the defect to be more balanced. Compared with an un-optimized structure under the same steel consumption, the numerical calculation result shows that the stability bearing capacity of the optimized structure is better in robustness, and the stability bearing capacity reliability is higher under the random defect beyond the aggregate Sop.
3.1 optimizing mathematical model
Wherein X= (X) 1 ,…,x i ,…,x m1 )，x i The section steel used for the ith group of rod pieces is numbered, m1 is the grouping number of the rod pieces, and 63 kinds of optional steel are arranged in an ascending order according to the bending section coefficients and are arranged in a section steel discrete set P; psi i Representing an ith simulated defect sample; l is the number of simulation defect samples; delta is the variation coefficient of the stable bearing capacity value of the structure under the L simulated defect samples; sop is a simulated defect sample set; s.t. is an abbreviation for constraint; z is Z j Representing a constraint function; z1 is the number of constraint conditions;
design variable X:
X＝(x 1 ,…,x i ,…,x m1 ) (1-3)
in the method, in the process of the invention,is x i The section property of the steel with the number A is the cross section area, and the unit m 2 ；I y ，I z Moment of inertia in the y and z axes, respectively, unit m 4 ；W y ，W z The bending-resistant section coefficients of the pair y and z axes are respectively shown as unit m 3 The method comprises the steps of carrying out a first treatment on the surface of the ρ is the linear density (kg/m)
Objective function δ:
δ＝σ/μ (1-5)
in the method, in the process of the invention,and->Respectively the standard deviation and the mean value of the structural stability bearing capacity under the L simulated defect samples; />Is the Sop of the firstStable bearing capacity values of the structure under i defect samples; l is the number of samples in the simulated defect sample set Sop.
Local constraint is the rod constraint condition:
λ-[λ]≤0 (1-7)
wherein N is the axial force of the rod piece; a is the cross-sectional area of the rod; e is the elastic modulus of the material; m is M y And M z Around the y-axis and around the y-axis respectively z Bending moment of shaft, for circular section Wy and Wz are bending-resistant section coefficients about the y-axis and z-axis, respectively, for a circular section w=w y ＝W z ，γ y And gamma z Taking γ=γ as the section plasticity development coefficient y ＝γ z ＝1.15；f＝215MPa；/>l 0 For the length of the rod piece, I y ，I z Moment of inertia about the y-axis and z-axis, respectively, for a circular cross-section i=i y ＝I z ；[λ]The permissible slenderness ratio of the rod piece; n' E ＝π 2 EA/(1.1λ 2 ) For Euler critical force, ++>As the stability coefficient of the axial compression component; />The stability coefficient of the whole component; beta m ＝β t =1.0; η is the section influence coefficient taken to be 0.7.
Overall stability constraint, i.e., overall structural constraint:
2×Q-P crmin ≤0 (1-10)
in the method, in the process of the invention,the minimum value of the stable bearing capacity value of each defect sample of the Sop is set; q is the uniform external load of the structure.
The random optimization of the structural stability bearing capacity adopts a combination of a sequence two-stage optimization algorithm and a simulation defect set Sop, and the random optimization program (CSY_FEM) is written by adopting large-scale general finite element analysis software ANSYS and compiling software Intel Visual Fortran (IVF). The elastoplastic stability analysis of the random defect structure is written by APDL language in large-scale general finite element analysis software ANSYS, and the sequence two-stage optimization program is written by Intel Visual Fortran (IVF) software. The data transmission between ANSYS and IVF is completed by adopting a notepad file reading mode, and the IVF is realized by adopting an interface program to call ANSYS.
Description: IVF (Intel Visual Fortran) is the Fortran compilation environment developed by intel corporation, ANSYS is large general purpose Finite Element Analysis (FEA) software developed by ANSYS corporation of america.
3.2 optimization steps and flow chart
In the first-stage optimization, structural defects are not considered, and all rod pieces use the same section steel; selecting the smallest section steel number xm. first-stage optimization result meeting the locality constraint condition (1-6, 1-7,1-8, 1-9) from the discrete set P by utilizing a one-dimensional search algorithm, and marking the result as X 0 ；
Calculation of the structural model X in the simulated defect set Sop 0 Minimum value of corresponding stable bearing capacity valueIf the constraint condition (formulas 1-10) of the whole structure is met, ending all optimization processes; if it isNot satisfied, a second level of optimization is entered. The second level of optimization is optimized by adopting a relative difference quotient method.
In the second-level optimization, firstly, the structural rod piece is divided into m according to the sensitive area division and the symmetry principle of the structure 1 A group of first-level optimization results X 0 As an initial variable, denoted as X (k) ＝(x 1 ,x 2 ,...,x m1 ) = (xm, xm,) xm, k=1. Calculation of the current Structure X in Sop (1) Coefficient of variation delta of (2) (1) And structural steel amount W (1) Relative difference quotient corresponding to each set of barsAs shown in the formulas 1-10, the smaller the value of the relative difference quotient (not the absolute value) is, the least increment of the steel consumption is represented, and the more the variation coefficient is reduced. The smaller the variation coefficient is, the smaller the fluctuation of the structural stability bearing capacity value along with the defect is, and the higher the reliability of the structural stability bearing capacity is; in the kth iteration, the corresponding relative difference quotient of the ith group of bars +. >Represented as
Wherein k is a natural number,for the coefficient of variation of the optimal model obtained in the kth iteration,/o>The number of the ith group of rods of the optimal model of the kth iteration is increased by 1, and then the coefficient of variation of the corresponding model is increased; />Steel usage for optimal model in the kth iteration,/->The steel consumption of the corresponding model is increased by 1 for the number of the ith group of rod pieces;
optimal structural model X of the (k+1) th round (k+1) The calculation is shown in 1-11,1-12 and 1-13
X (k+1) ＝X (k) +I (k) (1-11)
I (k) ＝(e 1 ，e 2 ，...，e m1 ) T (1-12)
Wherein X is (k) Is the current design variable; x is X (k+1) Is the updated design variable; i (k) The current optimal direction; e, e i Equal to 1 or 0, m1 represents the number of groups of bars;is the relative difference quotient corresponding to the ith group of rods.
Calculation of Sop lower Structure model X (k+1) Minimum value of corresponding stable bearing capacity valueJudging whether the constraint conditions (formulas 1-10) are satisfied, ending if the constraint conditions are satisfied, and updating the design variables to enable X if the constraint conditions are not satisfied (k) ＝X (k+1) And continuing the second-stage optimization iteration until the overall stability constraint condition is met.
Due to the discretization of the latticed shell structure and the discretization of the model steel (the model steel must be in accordance with the modulus), the situation that the objective function is a local minimum value but the global constraint condition is not satisfied may occur in the optimizing process.
The new structural model X can be generated by using the formulas (1-14), the formulas (1-15) and the formulas (1-16) to jump out the local minimum point of the current objective function (*) And take X (k) ＝X (*) 。
X (k) ＝X * (1-16)
And (3) jumping out of the current local minimum, and continuing the second-stage optimization iteration until all constraint conditions are met, namely searching an optimal solution of the objective function meeting all constraint conditions by the structural model under higher steel consumption.
The flow chart of the stable bearing capacity optimization design based on the random sequence two-stage algorithm is shown in fig. 4.
4. Optimizing calculation analysis:
the fluctuation of the stable bearing capacity of the structure can be weakened by reducing the defect amplitude or increasing the model of the bar section steel, but the construction difficulty is increased and the cost is increased. Taking a hemispherical net shell commonly used in engineering as an example, a random optimization method based on regional defect sensitivity difference is adopted to optimally design the random stable bearing capacity of the structure, and on the premise of not increasing the steel consumption of the structure and not increasing the construction difficulty, the fluctuation range of the random stable bearing capacity value of the structure is reduced, and the stability and safety of the structure are improved.
According to the dividing structure of the sensitive area of the reticulated shell structure, all the rods are divided into 3 groups according to the requirement of symmetry of the structure and continuity of stress of the rods, see (a) - (c) of fig. 5, namely, all radial rods are 1 st group, annular rods with 1-5 rings at the top are 2 nd group, and annular rods with 6-12 rings are 3 rd group. The hemispherical latticed shell structure uniformly distributes external load Q to obtain 2.35kN/m 2 And the full span is uniformly distributed.
1/300 of the span of defect amplitude omega is used for establishing 51 simulated defect samples and generating a set Sop. Fifty simulated defect samples are generated according to standard normal distribution rules (mean is 0 and variance is omega/2), and one sample is generated according to a mode method of the lowest-order eigenvalue.
The random optimization iterative process of the hemispherical net shell structure based on the regional defect sensitivity difference analysis and the sequence two-stage random optimization algorithm is shown in table 2.
TABLE 2 random stability optimization iterative Process for half ball net Shell Structure
/>
Note 1: the thick part in the table is the final optimal result.
The iterative process of the optimization method herein can be clearly seen from table 2.
In the first-stage optimization (iteration 0), 33-numbered steel in the discrete set P is selected, and the local constraint conditions (formulas 1-6 to 1-9) are all satisfied at the moment, and the first-stage optimization is finished. Current structure X in simulated defect sample set Sop 0 The minimum stable load limit is 4.002kN/m 2 From (equations 1-10), it is known that the global constraint is not satisfied, and therefore the second level of optimization is entered.
In the second-stage optimization, the result X is optimized by the first stage (0) = (33# ) is the initial calculation model. Its corresponding structural stability bearing capacity variation coefficient delta 0 Equal to 0.053, steel consumption W 0 Equal to 96t.
In table 2, the judging process of the "optimal searching direction" of the 1 st iteration is shown in table 3, and the "optimal searching direction" of the current iteration is determined according to the difference quotient. The relative difference quotient values corresponding to the three models are respectively β1= -0.49, β2= -5.18 and β3=6.30, see table 2, wherein Δδ is 1 ＝△δ/δ 0 、△w 1 ＝△w/W 0 ，βi＝△δ 1 /△w 1 Taking the minimum difference quotient value beta 2 as the optimal searching direction according to the optimizing rule of the relative difference quotient method, and taking the model '33#34#33#' as the optimal structure of the current iteration and simultaneously taking the model as the initial structure of the next iteration.
TABLE 3 determination of optimal search direction in iteration 1
After 6 iterations in table 2, an optimal model "34#38#33#" is obtained, which meets the overall stability constraint and the rod constraint, and the optimization is completed.
Compared with an unoptimized model (34#34#34#) under the same steel consumption, the stable bearing capacity variation coefficient of the optimized model (34#38#33#) is reduced by about 44%, the variation coefficient is a representation of the data discrete degree, and the reduction of the variation coefficient indicates that the stable bearing capacity value of the optimized structure is smaller along with the fluctuation range of the defect, and the sensitivity of the structure to the defect is lower.
It can also be seen from the results of the optimization that the section steel numbers of the second set of bars are relatively maximum because the second set of bars are all in the high defect sensitivity region of the structure, with the bars in the higher defect sensitivity region being reinforced during the optimization process. It can be seen that increasing the bar cross-sectional size of the high defect sensitivity region can enhance the resistance of the region to defects, thereby reducing the overall structural defect sensitivity.
The whole optimizing process is carried out in a simulation defect sample set Sop, and the optimizing direction always advances towards the direction with the most reduction of the variation coefficient of the stable bearing capacity and the least difference of the regional sensitivity of the structure, so that the optimized structure meets the requirements of' the relatively minimum dispersion degree of the stable bearing capacity value and the relatively minimum defect sensitivity
Because the rod pieces are subjected to grouping optimization based on the defect sensitive area in the optimizing process, the rod pieces in the defect sensitive area are reinforced, namely the resistance of the whole structure to defects is more balanced. Therefore, when defects beyond the simulated defect set Sop occur, the structure will also have good stable bearing capacity, and the subsequent numerical experiment results also verify the conclusion.
5. Optimization result verification
And respectively carrying out elastoplastic stability analysis on the optimized model (34#38#33#) and the non-optimized model (34#34#34#) with the same steel consumption for 500 times under 500 new random defect samples, and checking the sensitivity of the stable bearing capacity of the optimized model to random defects.
The stable load bearing extremum distribution of the two models at 500 randomly generated defects is shown in figure 6.
(1) The stable load bearing average of the optimized structure (34#3833#) was 5.314kN/m at 500 random defect samples 2 A stable load bearing average value of 5.045kN/m greater than that of the non-optimized structure (34#34#34#) 2 . It is also evident from the distribution of 500 data points in fig. 6 that the stability limit of the optimized model is generally greater than that of the non-optimized model.
(2) Under 500 random defect samples, the standard deviation of the stable bearing capacity of the optimized model (34#38# 33#) is 0.189 (the coefficient of variation is 0.035), and the standard deviation of the stable bearing capacity of the non-optimized model (34#3834#) is 0.368 (the coefficient of variation is 0.073). Compared with an unoptimized model with the same steel consumption, the variation coefficient of the optimized model is obviously reduced, namely the fluctuation of the stable bearing capacity of the optimized model is weakened, and the sensitivity of the structural defect is improved. It is also evident from the distribution of 500 data points in fig. 6 that the stability limit of the non-optimized model fluctuates more severely.
(3) Of 500 random defect samples, the optimization model does not meet the global constraint condition only under four defect samples (sample numbers: 70, 301, 349, 350), wherein the stable bearing capacity corresponding to the defect sample number 301 is the minimum, which is 4.409kN/m 2 The probability of destabilization failure of the structure was 4/500=0.8%. The unoptimized structure (34#34#34#) under the same steel consumption does not meet the design requirement under the condition of seven seventeen defect samples, wherein the stable bearing capacity value corresponding to the defect sample number 70 is minimum and is 3.676kN/m 2 The probability of destabilization failure of the structure was 77/500=15.4%. Comparison shows that the destabilization destruction probability of the optimized model is reduced by 14.6%. Obviously, from the perspective of probability analysis, the failure probability of the optimization model is lower, and the reliability is higher;
(4) The optimized simulation defect sample set Sop only has 51 defect samples, but the obtained optimal model is excellent under 500 new random defect samples, which is mainly attributed to a rod piece grouping method based on a defect sensitive area. The method effectively avoids the problems of calculation and economy caused by a large amount of samples.
The span of the latticed shell structure is S, and the defect amplitude is S/300, S/400, S/500, S/600, S/700, S/800, S/900, S/1000and S/1500 respectively, wherein each simulated defect sample set A, B, C, D, E, F, G, H and I comprises 100 defect samples. In addition, the set J represents that no defect appears on the structural model, which is an ideal structural model. Within the sample set of ten different defect magnitudes, the optimized structural model (34#38#33#) and the non-optimized model (34#34#34#) stabilize the maximum and minimum values of load bearing capacity, see FIG. 7.
(1) The maximum value curve of the stable bearing capacity of the two models is gentler, but the slope of the minimum value curve is larger, which shows that the change of the defect amplitude has obvious influence on the minimum value of the stable bearing capacity of the structure, but has no obvious influence on the maximum value. The slope of the minimum trend line of the optimized model (34#38#33#) is significantly smaller than that of the un-optimized structure (34#34#34#), which indicates that after optimization, the stable bearing capacity minimum of the structure model is weakened due to the influence of the defect amplitude.
(2) As can be seen from fig. 7, the difference between the maximum and minimum values of the optimized structure (34#38#33#) is always smaller than that of the non-optimized model (34#34#34#). Fig. 8 shows the stable load-bearing coefficient variation curves of the two models in the ten simulated defect sample sets, and the coefficient of variation of the optimized model (34#38# 33#) is always lower than that of the non-optimized structure. The conclusion shows that the structure (34#38# 33#) optimized in the set Sop (defect amplitude is S/300) has the characteristics of smaller fluctuation of stable bearing capacity value and lower defect sensitivity of the whole structure under the smaller defect amplitude (set B-J).
(3) When the defect amplitude is smaller than S/1000 (the corresponding defect set is H, I and J), the variation coefficient curves of the two structural models are close to be coincident (see figure 8), the optimization model loses advantages, but at the moment, the minimum value of the stable bearing capacity value of the structure is far larger than the design value of the stable bearing capacity, and the structure is safe enough.
While the foregoing description of the embodiments of the present invention has been presented in conjunction with the drawings, it should be understood that it is not intended to limit the scope of the invention, but rather, it is intended to cover all modifications or variations within the scope of the invention as defined by the claims of the present invention.
Claims (4)
1. A method for optimizing random stability of a reticulated shell structure based on regional defect sensitivity difference is characterized by comprising the following steps:
designing a sensitivity test sample, establishing a sensitivity relative coefficient formula, determining the sensitivity difference of each region to defects through quantitative calculation, dividing the reticulated shell structure into a plurality of defect sensitive regions according to the sensitivity relative coefficient, and grouping the rods of the reticulated shell structure based on the defect sensitive region division;
searching an optimal structure model taking the minimum coefficient of variation of stable bearing capacity as an objective function in a simulation defect sample set Sop by adopting a sequence two-stage algorithm, and optimizing the cross section sizes of rod pieces in different sensitive areas to ensure that the fluctuation range of the stable bearing capacity value of the space reticulated shell structure is narrower under random defects, thereby reducing the probability of unstable damage of the structure;
the minimum variation coefficient of the stable bearing capacity is taken as an objective function, and the mathematical optimization model is as follows:
wherein X= (X) 1 ,…,x i ,…,x m1 )，x i The section steel used for the ith group of rod pieces is numbered, m1 is the grouping number of the rod pieces, and 63 kinds of optional steel are arranged in an ascending order according to the bending section coefficients and are arranged in a section steel discrete set P; psi i Representing an ith simulated defect sample; l is the number of simulation defect samples; delta is the variation coefficient of the stable bearing capacity value of the structure under the L simulated defect samples; sop is a simulated defect sample set; s.t. is an abbreviation for constraint; z is Z j Representing a constraint function; z1 is the number of constraint conditions;
design variable X:
X＝(x 1 ,…,x i ,…,x m1 ) (1-3)
in the method, in the process of the invention,is x i The section property of the steel with the number A is the cross section area, and the unit m 2 ；I y ，I z Moment of inertia in the y and z axes, respectively, unit m 4 ；W y ，W z The bending-resistant section coefficients of the pair y and z axes are respectively shown as unit m 3 The method comprises the steps of carrying out a first treatment on the surface of the ρ is the linear density in units of: kg/m;
objective function δ:
δ＝σ/μ (1-5)
in the method, in the process of the invention,and->Respectively the standard deviation and the mean value of the structural stability bearing capacity under the L simulated defect samples; />The stable bearing capacity value of the structure under the ith defect sample in the Sop is obtained; l is the number of samples in the simulation defect sample set Sop;
local constraint is the rod constraint condition:
λ-[λ]≤0 (1-7)
wherein N is the axial force of the rod piece; a is the cross-sectional area of the rod; e is the elastic modulus of the material; m is M y And M z Around the y-axis and around the y-axis respectively z Bending moment of shaft, for circular sectionWy and Wz are bending-resistant section coefficients about the y-axis and z-axis, respectively, for a circular section w=w y ＝W z ，γ y And gamma z Taking γ=γ as the section plasticity development coefficient y ＝γ z ＝1.15；f＝215MPa；/>l 0 For the length of the rod piece, I y ，I z Moment of inertia about the y-axis and z-axis, respectively, for a circular cross-section i=i y ＝I z ；[λ]The permissible slenderness ratio of the rod piece; n' E ＝π 2 EA/(1.1λ 2 ) For Euler critical force, ++>As the stability coefficient of the axial compression component; />The stability coefficient of the whole component; beta m ＝β t =1.0; η is the section influence coefficient taken to be 0.7;
Overall stability constraint, i.e., overall structural constraint:
2×Q-P crmin ≤0 (1-10)
in the method, in the process of the invention,the minimum value of the stable bearing capacity value of each defect sample of the Sop is set; q is uniform external load of the structure;
the random optimization of the structure stable bearing capacity is realized by combining a sequence two-stage optimization algorithm with a simulation defect sample set Sop, the compiling of a random optimization program is realized by adopting large-scale general finite element analysis software ANSYS and compiling software Intel Visual Fortran, the elastoplastic stability analysis of the random defect structure is realized by adopting APDL language in the large-scale general finite element analysis software ANSYS, the sequence two-stage optimization is realized by adopting Intel Visual Fortran, the data transmission between the software is realized by adopting a notepad file reading mode, and the calling between the software is realized by adopting an interface program;
in the primary optimization, structural defects are not considered, and all the rods use the same section steel; selecting a section steel set P to meet a locality constraint condition by utilizing a one-dimensional search algorithm; meanwhile, the steel with the most saved steel amount is used for the structure, the number is marked as xm, the first-stage optimization is finished, and the optimization result is marked as X 0 ；
Calculating a structural model X in a simulated defect sample set Sop 0 Minimum stable bearing capacity value under each defective sampleIf the constraint condition of the whole structure is met, ending all optimization processes; if the optimization is not satisfied, the first-stage optimization is finished and enters a second-stage optimization, and the second-stage optimization adopts a relative difference quotient method for optimizing;
In the second-stage optimization, firstly, the structural rod pieces are divided into m according to the division of sensitive areas and the symmetry requirement in the design of the net shell structure 1 Group, select first level optimization result X 0 As an initial structural model, denoted as X (k) ＝X 0 = (xm, fxm,..xm), k=1, structure X under each defect sample of Sop was calculated (1) Coefficient of variation delta of (2) (1) Steel amount W (1) Sum and difference quotientThe smaller the relative difference quotient, the smaller the steel consumption increment, and the more the variation coefficient is reduced; the smaller the variation coefficient is, the smaller the fluctuation of the structural stability bearing capacity value along with the defect is, and the higher the reliability of the structural stability bearing capacity is;
in the k-th iteration, the relative difference quotient corresponding to the ith group of rodsRepresented as
Wherein k is a natural number,for the coefficient of variation of the optimal model obtained in the kth iteration,/o>The stable bearing capacity variation coefficient of the corresponding model is obtained after the number of the ith group of rod pieces of the optimal model of the kth iteration is increased by 1; />Steel usage for optimal model in the kth iteration,/->The steel consumption of the corresponding model is increased by 1 for the number of the ith group of rod pieces;
k+1st round optimal structure model X (k+1) The calculation of (1) is shown in formulas 1-12, formulas 1-13 and formulas 1-14
X (k+1) ＝X (k) +I (k) (1-12)
I (k) ＝(e 1 ，e 2 ，...，e m1 ) T (1-13)
Wherein X is (k) Iterating the optimal structure model for the kth round; x is X (k+1) Iterative optimal structural model for the (k+1) th round; i (k) Iterative optimal direction for the kth round; e, e i Equal to 1 or 0; m1 represents the grouping number of the rod pieces;iterating the relative difference quotient corresponding to the ith group of rod pieces for the kth round;
calculating that each defect sample in the defect sample set Sop appears in the structural model X (k+1) At the time of loading, the minimum value of the structural stability bearing capacity valueJudging whether the overall constraint condition is satisfied, if so, finishing optimization, and if not, updating the design variable X (k) ＝X (k+1) Continuing iteration until the integral stability constraint condition is met;
due to the discreteness of the latticed shell structure and the discreteness of the model steel, the situation that the objective function is a local minimum value but the constraint condition is not satisfied possibly occurs in the optimizing process;
the current local minimum point of the objective function is jumped out by using the formulas 1-15, 1-16 and 1-17 to generate a new structural model X (*) And updating the structural model to obtain X (k) ＝X (*) ；
X (k) ＝X * (1-17)
And (3) jumping out of the current local minimum, and continuing the second-stage optimization iteration until all constraint conditions are met, namely searching an optimal solution of the objective function meeting all constraint conditions by the structural model under higher steel consumption.
2. The method for optimizing random stability of a reticulated shell structure based on regional defect sensitivity difference according to claim 1, wherein the sensitivity test sample is a "local region" formed by the relevant nodes according to the connection form of the structural nodes, so that the defect value of the nodes in the "local region" is larger than that of the nodes in the non-local region ", thereby forming the sensitivity test sample.
3. The method for optimizing random stability of a reticulated shell structure based on regional defect sensitivity differences as recited in claim 1, wherein the sensitivity relative coefficient ζ i The calculation formula of (2) is as follows:
ξ i ＝(P 0 -SP i )/P 0 (1-1)
wherein P is 0 Is the elastoplastic stable bearing capacity value of an ideal reticulated shell structure, and SP is the sample L for testing a certain sensitivity i Or Z is i A stable load bearing limit when present on the structure.
4. The method for optimizing random stability of a reticulated shell structure based on regional defect sensitivity difference according to claim 1, wherein a plurality of simulated defect samples are established under the determined defect amplitude to form a sample set Sop, each simulated defect sample can be used for simulating possible defects of an actual structure, and samples in the simulated defect sample set Sop comprise random defect samples conforming to a normal distribution rule, defect samples conforming to a lowest-order eigenvalue modal distribution and quasi-least-favorable defect samples obtained through various algorithms.
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