WO2014161364A1 - 一种轴压筒壳结构承载力折减因子确定方法 - Google Patents

一种轴压筒壳结构承载力折减因子确定方法 Download PDF

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WO2014161364A1
WO2014161364A1 PCT/CN2014/000152 CN2014000152W WO2014161364A1 WO 2014161364 A1 WO2014161364 A1 WO 2014161364A1 CN 2014000152 W CN2014000152 W CN 2014000152W WO 2014161364 A1 WO2014161364 A1 WO 2014161364A1
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defect
load
shell structure
point
axial
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PCT/CN2014/000152
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English (en)
French (fr)
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王博
郝鹏
李刚
田阔
孟增
杜凯繁
周演
张希
唐霄汉
王斌
骆洪志
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大连理工大学
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Priority to EP14779155.2A priority Critical patent/EP2983099B1/en
Priority to US14/781,941 priority patent/US9645054B2/en
Publication of WO2014161364A1 publication Critical patent/WO2014161364A1/zh

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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M99/00—Subject matter not provided for in other groups of this subclass
    • G01M99/007—Subject matter not provided for in other groups of this subclass by applying a load, e.g. for resistance or wear testing
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64C—AEROPLANES; HELICOPTERS
    • B64C1/00—Fuselages; Constructional features common to fuselages, wings, stabilising surfaces or the like
    • B64C1/06—Frames; Stringers; Longerons ; Fuselage sections
    • B64C1/068—Fuselage sections
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/10—Numerical modelling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2113/00—Details relating to the application field
    • G06F2113/28—Fuselage, exterior or interior
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Definitions

  • the invention relates to the technical field of stability checking of thin-walled members of aerospace and building structures, and particularly relates to a method for determining the bearing capacity reduction factor of a shaft cylinder shell structure.
  • the arch structure needs to withstand a large take-off thrust during the launch phase. For this reason, the axial load is the most important design condition of its bearing structure.
  • the all-metal mesh-reinforced propellant tank despite its secondary bearing structure, is also subject to a large axial pressure.
  • a new-generation large-diameter launch vehicle with a core structure of 5 meters in diameter which is being developed in China as an example, only the 3.35-meter-diameter all-metal mesh reinforced liquid oxygen tank in the boosting structure has a design axial pressure of more than 400. Ton.
  • Such a compressed thin-walled member is very sensitive to initial imperfections, especially to the initial geometrical imperfections of the structure, which results in a structural ultimate bearing capacity based on well-modeled theory or numerical predictions that is much smaller than it actually is.
  • the engineer often uses a "reduction factor” (or "correction factor”) that is much smaller than 1 to correct the predicted bearing capacity.
  • the axial compression shell structure The larger the ratio of diameter to thickness (the radius of the shell divided by the equivalent thickness of the shell), the higher the sensitivity of the defect and the smaller the reduction factor.
  • the allowable bearing capacity used in the structural design is more predictive than the bearing capacity predicted based on the perfect model. small.
  • the traditional shell structure defect sensitivity evaluation method represented by NASA SP-8007 is based on the semi-empirical formula.
  • the bearing capacity reduction factor (KDF) of the shell structure is given by a large number of experimental results.
  • KDF bearing capacity reduction factor
  • this method of determining the reduction factor is too conservative, the experiment cost is large, and brings about large design redundancy.
  • a large number of scholars have begun to use numerical analysis methods to study the defect sensitivity of the axial compression shell structure, that is, to introduce first-order modal defects, radial disturbance load defects and single-point quadrants in the perfect shell structure.
  • the initial defects such as defects are numerically calculated to give a reduction factor of the structural bearing capacity.
  • the object of the present invention is to propose a new based on the most unfavorable multi-point disturbance in view of the shortcomings of the existing method for determining the bearing capacity reduction factor of the shell structure, which is too conservative, the experiment cost is large, the lack of clear and sufficient physical meaning, and the like.
  • the method for determining the bearing capacity reduction factor of the load is: by introducing multi-point depression defects, based on the optimization techniques such as enumeration method, genetic algorithm or proxy model, the most unfavorable multi-point disturbance load combination under the finite number of depressions is obtained, and The bearing capacity reduction factor of the axial compression shell structure is thus determined.
  • this method is more convenient for experimental verification, and has more clear physical meaning and more realistic and reliable prediction results.
  • a method for determining the bearing capacity reduction factor of a shaft cylinder shell structure is provided, which specifically includes the following steps:
  • Step 1 In order to perfect the shell structure, the concave defect is introduced by applying the radial disturbance load.
  • the numerical analysis method such as finite element method is used to calculate the axial bearing capacity of the shell structure under different single point H trap defect amplitude, ie defect Sensitivity analysis obtains the relationship between the radial disturbance load and the sensitivity of the dent defect, and determines the reasonable load load amplitude range.
  • the maximum defect amplitude that is, the maximum radial disturbance load N Niax introduced can be determined by the manufacturing quality and detection. The tolerance is determined.
  • Step 2 Introducing a multi-point combined recess defect (the vertex of the regular polygon is the position of the radial disturbance load).
  • the defect sensitivity analysis is performed, and the multi-point combined recess defect introduction manner is consistent with the single-point recess defect in step 1.
  • the distance between the circumscribed center and the apex of the triangle is defined as /, so that it changes from 0 value, the corresponding buckling load value is calculated, and the curve of the buckling load value and the distance/ is plotted, and The distance value corresponding to the minimum buckling load value is taken as the effective distance / e .
  • Such a combined mode of effective distances can approximate the reasonable distance between each defect and assume that it covers the adverse effects between adjacent load positions. .
  • the expressions of the axial and circumferential loading position intervals &, & and the corresponding number of loading positions n a , ⁇ can be determined as follows:
  • the / here is taken as / e .
  • assign a position number to each loading position (the position number starts from the 0 degree position at the bottom end of the cylinder, increases from the bottom end to the top end in the axial direction, and sequentially increases along the circumferential angle).
  • the minimum buckling load does not necessarily occur when a large radial disturbance load is applied, so the radial disturbance load N is set as an optimization variable, with N w « as the upper limit of the value, with zero Or the empirical small value is the lower limit of the value.
  • Step 3 The number of loading positions for the radial disturbance load N and the recessed defect. , " c as a variable for experimental design sampling.
  • Step 4 Based on the enumeration method, genetic algorithm or proxy model optimization technique, find the most unfavorable multi-point disturbance load combination of the shell structure.
  • the optimization goal is to minimize the buckling load value of the shell structure containing multi-point depression defects.
  • N is the position number of the “radial disturbance load”, which is the buckling load value of the axial compression shell structure, representing the first variable (including the number of loading positions of the radial disturbance load N and the concave defect, the upper limit of the « c , "represents the lower limit of the first variable (including the number of radial disturbance loads N and the number of loading positions of the concave defects, n c ).
  • the buckling load value of the axial compression shell structure under the combination of unfavorable multi-point disturbance load is to improve the buckling load value of the axial compression shell structure.
  • the beneficial effects of the present invention are as follows:
  • the present invention is distinguished from the conventional defect sensitivity evaluation method based on experimental experience represented by NASA SP-8007.
  • the concave defect is introduced by applying the radial disturbance load. Firstly, the influence law of the single-point depression defect amplitude on the axial bearing capacity of the axial compression cylinder shell is numerically analyzed to determine the reasonable loading load amplitude range. Secondly, the defect sensitivity of the multi-point depression defect is determined. Degree analysis; then the experimental design sampling (DOE) is carried out with the distribution of the load load and the distribution of the load position; finally, based on the optimization techniques such as enumeration method, genetic algorithm, and proxy model, the most unfavorable points for limiting the defect range are sought.
  • DOE experimental design sampling
  • Disturbing load combination determining the reduction factor of the bearing capacity of the axial cylinder shell structure, establishing a more realistic Reliable and more practical evaluation method for defect sensitivity and bearing capacity of shaft cylinder shell structure, it is expected to break through the existing domestic and foreign current traditional norms based on experimental experience, and become the grid-reinforced shell design in the field of heavy-duty launch vehicles in China.
  • Axial load bearing reduction factor prediction method DRAWINGS
  • FIG. 1 is a schematic view showing a layout manner of a three-point recessed defect loading point according to the present invention.
  • FIG. 2 is a schematic diagram of the numbering manner of the loading point position of the present invention.
  • Fig. 3 is a schematic view showing the defect sensitivity curve of the cylindrical shell structure of the present invention at different recessed positions.
  • Figure 4 is a schematic view showing the structure of a shaft-pressed metal cylinder and a T-ring according to the present invention.
  • Fig. 5 is a schematic view showing the distribution of five concave loading points along the axial direction (Z1-Z5) in the present invention.
  • Fig. 6 is a schematic view showing the influence of the distance/on the buckling load of the cylindrical shell in the present invention.
  • FIG. 7 is a schematic diagram of a combination search process of the most unfavorable multi-point disturbance load based on the enumeration method in the present invention.
  • FIG. 8 is a schematic diagram of a combination search process of the most unfavorable multi-point disturbance load based on the proxy model in the present invention.
  • FIG. 9 is a flow chart of a method for determining a bearing capacity reduction factor of a shaft cylinder shell structure according to the present invention.
  • Figure 10 is a schematic view showing the structure of a cylindrical composite material shell and a metal T-ring according to the present invention.
  • Fig. 11 is a schematic view showing the distribution of five concave loading points of the axial compression composite material casing in the axial direction (Z1-Z5) according to the present invention.
  • Fig. 12 is a schematic view showing the defect sensitivity curve of different axial positions of the axial compression composite material casing according to the present invention.
  • FIG. 13 is a schematic view showing the layout manner of the loading point of the four-point depression of the axial compression composite material casing according to the present invention.
  • Fig. 14 is a schematic view showing the combined search process of the most unfavorable multi-point disturbance load based on the enumeration method of the axial compression composite material casing of the present invention.
  • Fig. 15 is a schematic diagram showing the most unfavorable multi-point disturbance load combination search history of the axial compression composite material casing based on the proxy model.
  • Figure 16 is a schematic view showing the structure of a large-sized axially-pressed metal cylinder casing and a T-ring according to the present invention.
  • Figure ⁇ is a schematic view showing the distribution of five concave loading points along the axial direction (Z1-Z6) of the large-sized axially-pressed metal shell in the present invention.
  • Fig. 18 is a schematic view showing the defect sensitivity curve of the large-sized axially-pressed metal cylinder shell at different recessed positions in the present invention.
  • FIG. 19 is a schematic view showing the layout manner of a four-point recessed defect loading point of a large-sized axially-pressed metal cylinder according to the present invention.
  • Fig. 20 is a schematic diagram showing the most unfavorable multi-point disturbance load combination search history of the large-size axial pressure metal cylinder casing based on the enumeration method.
  • Figure 21 is the most unfavorable multi-point disturbance load combination search history of the large-size axial pressure metal cylinder shell based on the proxy model in the present invention. Schematic diagram.
  • a method for determining a bearing capacity reduction factor of a shaft cylinder shell structure comprises the following steps: Step 1: For improving the shell structure, introducing a recessed defect by applying a radial disturbance load, firstly using limited Yuan and other numerical analysis methods calculate the axial bearing capacity of the axial compression shell structure under different single point depression defect amplitudes, that is, the defect sensitivity analysis, and obtain the relationship between the radial disturbance load and the depression defect sensitivity, and determine the reasonable loading the load amplitude range, wherein the maximum amplitude of the defect i.e. a maximum radial perturbations introduced by N max load mass manufacturing tolerances and detection determination.
  • Step 2 Introducing a multi-point combined recessed defect to perform defect sensitivity analysis, and the multi-point combined recessed defect introducing manner is consistent with the single-point recessed defect introducing manner in the step 1.
  • the distance between the circumscribed center and the apex of the triangle is defined as /, so that it changes from 0 value, and the corresponding buckling load value is calculated, and the buckling load value and the distance/change are plotted.
  • the graph, and the distance value corresponding to the minimum buckling load value as the effective distance, such a combined mode of effective distance can approximate the reasonable distance between each defect, and assume that it covers the position between adjacent loads Negative Effects.
  • the expressions of the axial and circumferential loading position intervals &, & and the corresponding number of loading positions " a can be derived as follows:
  • each loading position is assigned a position number, which starts from the 0 degree position at the bottom end of the casing, increases from the bottom end to the top end in the axial direction, and also increases along the circumferential direction ( That is, sorted in the axial direction and the circumferential direction); the radial disturbance load N Set to an optimization variable, ⁇ is the upper limit of the value, and zero or the empirical small value is the lower limit.
  • the recommended number of defects is set to 3.
  • the minimum buckling load does not necessarily occur when a large radial disturbance load is applied, so the radial disturbance load N is set as an optimization variable, and the upper limit is taken, and the value of zero or the empirical small value is the lower limit. .
  • the radial disturbance load N is set as an optimization variable, and the upper limit is taken, and the value of zero or the empirical small value is the lower limit. .
  • Step 3 The number of loading positions for the radial disturbance load N and the recessed defect. , " c as a variable for experimental design sampling.
  • Step 4 Based on the enumeration method, genetic algorithm or proxy model optimization technique, find the most unfavorable multi-point disturbance load of the shell structure.
  • the optimization is shown below. Referring to Figure 2, the optimization objective is to minimize the buckling load value of the shell structure containing the multi-point depression.
  • N represents the position number of the wth radial disturbance load, which is the buckling load value of the axial compression shell structure
  • X! represents the first variable (including the number of loading positions of the radial disturbance load N and the concave defect
  • n c The upper limit of XI 1 represents the first variable (including the number of loading positions of the radial disturbance load N and the concave defect, the lower limit of ".
  • KDF structure reduction factor
  • a T-ring is placed at the bottom and top of the cylindrical shell, the material is the same as the cylindrical shell. The bottom end of the T-ring is fixed, and the top end is all constrained except for the axial translational displacement.
  • an initial disturbance is introduced by applying a radial disturbance load along the axial halving, and a graph of the radial disturbance load and the structural buckling load value is plotted.
  • the dynamic load c is 30N.
  • the most unfavorable multi-point disturbance load combination search is performed by enumeration method and proxy model optimization technique respectively.
  • Agent model technology In the design domain, 100 sample combinations were selected to carry out the experimental design, the proxy model was established, and the multi-island genetic algorithm was used for optimization calculation. After 13 iterations, the optimized solution is obtained. If it is shown in Figure 8, and finally the reduction factor is 0.42, it is better than the existing NASA SP-8007 reduction factor recommendation value of 0.32, which effectively reduces the design redundancy, and this part is improved. The reduction factor can be converted into a weight loss benefit.
  • the bottom end of the T-ring is fixed, and the top end is all constrained except for the axial translational displacement.
  • a radial disturbance load is applied along the axial five equal divisions to introduce an initial defect, and a graph 12 of the radial disturbance load and the structural buckling load value is plotted.
  • the corresponding radial disturbance load is calculated using the finite element numerical analysis method.
  • four-point defects ( ⁇ , ⁇ 2 , N 3 and N 4 ) are introduced. After calculation, the value of the minimum buckling load value is found to be / e , and then the axis can be derived from this.
  • the number of loadings in the direction of the ring and the " a and c values that is, the position where all the dents on the casing may occur.
  • the lower side uses the enumeration method and the proxy model optimization technique to perform the most unfavorable multi-point disturbance load combination search.
  • (1) Enumeration method Ten combinations are randomly generated from the above-mentioned set of position points where the depression may occur, and the structural bearing capacity analysis is performed. As shown in FIG. 14, the fifth iteration has the lowest buckling load, and thus is considered to be the most unfavorable multi-point disturbance load combination. . Of course, the more enumeration times, the more advantageous it is to objectively determine the most unfavorable recess combination.
  • Agent model technology In the design domain, 100 sample combinations were selected to carry out experimental design, a proxy model was established, and multi-island genetic algorithm was used for optimization calculation. After 12 iterations, an optimized solution is obtained, if 15 is shown and finally Set the reduction factor.
  • a T-ring is placed at the bottom end and the top end of the cylindrical shell, and the material is identical to the cylindrical shell. The bottom end of the T-ring is fixed, and the top end is all constrained except for the axial translational displacement.
  • a radial disturbance load is applied to each of the six bisectors in the axial direction to introduce an initial defect, and a graph 18 of the radial disturbance load and the structural buckling load value is plotted.
  • the corresponding radial disturbance load ⁇ is calculated using a finite element numerical analysis method.
  • four-point defects ( ⁇ , ⁇ 2 , ⁇ 3 and ⁇ ) are introduced. After calculation, the value of the minimum buckling load value is found to be 4, and then the axial sum can be derived from this.
  • the number of loadings in the hoop ⁇ ⁇ and ⁇ values that is, the positions where all the recesses on the housing may occur.
  • the most unfavorable multi-point disturbance load combination search is performed by enumeration method and proxy model optimization technique respectively.
  • Agent model technology In the design domain, 100 sample combinations were selected to carry out the experimental design, the proxy model was established, and the multi-island genetic algorithm was used for optimization calculation. After 14 iterations, an optimized solution is obtained, if 21 is shown, and the reduction factor is finally determined.

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Abstract

一种轴压筒壳结构承载力折减因子确定方法，涉及航空航天、建筑结构主承力薄壁构件的稳定性校核。区别于以NASA SP-8007为代表的基于实验经验的传统缺陷敏感度评价方法，以施加径向扰动载荷的方式引入凹陷缺陷。首先，使用数值分析单点凹陷缺陷幅度对轴压承载力的影响规律，确定加载载荷的幅度范围；再进行多点凹陷缺陷的缺陷敏感度分析；然后以加载载荷的幅值和加载位置的分布为设计变量进行实验设计抽样；最后基于枚举法、遗传算法、代理模型等优化技术，寻找限定缺陷幅度的最不利多点扰动载荷，确定轴压筒壳结构承载力的折减因子。建立一种更具有物理意义的轴压筒壳结构缺陷敏感度和承载性能的评价方法。

Description

一种轴压筒壳结构承载力折减因子确定方法
技术领域
本发明涉及航空航天、 建筑结构主承力薄壁构件的稳定性校核技术领域， 特别涉及一 种轴压筒壳结构承载力折减因子的确定方法。
背景技术
箭体结构在发射阶段需要承受巨大的起飞推力， 为此轴压载荷是其承力结构最重要的 设计工况。 全金属网格加筋的推进剂贮箱尽管作为箭体结构的次承力结构， 其承受的轴压 也十分巨大。 以我国正在研制的芯级结构直径 5米的新一代大直径运载火箭 CZ-5为例， 仅其助推结构中直径 3.35米的全金属网格加筋液氧箱， 设计轴压也超过 400吨。这样的受 压薄壁构件对初始缺陷， 尤其对结构初始几何缺陷十分敏感， 这导致基于完善模型理论或 数值预测的结构极限承载力要比实际情况小得多。 工程师在实际设计中， 往往会采用一个 规范建议的远小于 1的 "折减因子"（或称之为 "修正系数"） 对预测的承载力给予修正， 一般来说， 轴压筒壳结构的径厚比（筒壳半径除以壳的等效厚度）越大， 缺陷敏感度越高、 折减因子越小， 结构设计中所采用的许用承载力相对基于完善模型预测的承载力也就越 小。 伴随我国新一代运载火箭和未来重型运载火箭跨越式提高的发射载荷， 火箭的直径将 大幅度提高， 其中作为承力结构的筒壳结构的缺陷敏感性问题亦将凸显， 因此迫切需要一 种新的轴压筒壳结构承载力折减因子的确定方法。
以 NASA SP-8007为代表的传统筒壳结构缺陷敏感度评价方法多基于半经验公式， 通 过大量的实验结果给出筒壳结构承载力折减因子 （KDF)。 随着制造技术和材料系统的发 展， 这种确定折减因子的方法显得过于保守、 实验成本较大， 且带来了较大的设计冗余。 基于这种现状， 大量学者开始采用数值分析的方法来研究轴压筒壳结构的缺陷敏感性问 题， 即在完善筒壳结构中引入一阶模态缺陷、 径向扰动载荷缺陷和单点四陷缺陷等初始缺 陷， 经过数值计算后给出结构承载力的折减因子。 虽然已开展了大量工作， 但仍未有给出 一种物理意义明确、 考虑最不利缺陷的折减因子确定方法。
综上所述， 目前有必要提出一种物理意义明确且便于实验验证的轴压筒壳结构承载力 折减因子的确定方法。 发明内容
本发明的目的是： 针对现有的确定筒壳结构承载力折减因子方法中过于保守、 实验成 本较大、 缺乏明确而充分物理意义等缺点， 提出了一种新的基于最不利多点扰动载荷的筒 壳承载力折减因子确定方法： 通过引入多点凹陷缺陷， 基于枚举法、 遗传算法或代理模型 等优化技术得到了有限个数凹陷作用下的最不利多点扰动载荷组合， 并由此确定了轴压筒 壳结构的承载力折减因子。 相比 NASA SP-8007为代表的基于实验经验的传统缺陷敏感度 评价方法， 本方法更便于实验验证， 且具有更明确的物理意义和更真实可靠的预测结果。
为达到上述目的， 本发明采用的技术方案是： 提供了一种轴压筒壳结构承载力折减因 子确定方法， 具体包括以下步骤：
步骤 1 : 针对完善筒壳结构， 以施加径向扰动载荷的方式引入凹陷缺陷， 首先运用有 限元等数值分析方法计算出不同单点 H陷缺陷幅度下的筒壳结构轴压承载力， 即缺陷敏感 度分析，得到径向扰动载荷与凹陷缺陷敏感度之间的关系，确定合理的加载载荷幅度范围， 其中， 最大的缺陷幅度亦即所引入的最大径向扰动载荷 Nniax可由制造质量和检测公差确 定。
步骤 2: 引入多点组合凹陷缺陷 （正多边形的顶点为径向扰动载荷作用位置） 进行缺 陷敏感度分析， 所述多点组合凹陷缺陷引入方式与步骤 1中单点凹陷缺陷一致。
以三点凹陷缺陷为例， 定义外接圆心与三角形顶点的距离为 /, 使其从 0值开始变化， 计算得出相应的屈曲载荷值， 绘制出屈曲载荷值与距离 /的变化曲线图， 并以最小屈曲载 荷值所对应的距离值作为有效距离 /e, 这样一种有效距离的组合模式可以近似地预测每个 缺陷之间合理距离， 并假设其涵盖了相邻载荷位置之间的不利影响。 假设载荷位置均匀地 分布在筒壳上，可由此确定轴向和环向的加载位置间隔&、 &及相应的加载位置的数目 na、 ^的表达式如下：
So = / + 0.5/ = 1.5/
Figure imgf000004_0001
L 7L .
"。 = 1 = 1
Sa 3/ _ 2nR _ ΑπΚ 其中， z为筒壳轴向高度， a为筒壳半径， "点凹陷缺陷情况下距离 /的定义方式与三 点凹陷缺陷情况一致， 即以外接圆心与正 "边形顶点间的距离来定义 I。
考虑到计算规模和效率， 这里的 /取为 /e。 确定了 " a、 后， 为每个加载位置分配一 个位置编号 （位置编号从筒壳底端的 0度位置开始， 沿轴向由底端至顶端依次增大， 并沿 着环向角度依次增大）。 据大量前期分析经验可知， 最小屈曲载荷不一定发生在施加较大 径向扰动载荷的情况下， 所以将径向扰动载荷 N设为优化变量， 以 Nw«为取值上限， 以零 或者经验小值为取值下限。 同时， 也需要确定凹陷缺陷的数目， 考虑到较多的凹陷缺陷数 目会带来后续实验设计过程中取样数目的增加、 进而会极大地提高计算成本， 并且含有过 多缺陷数目的航空航天筒壳结构会在生产实际中认定为不合格产品， 所以建议基于三点凹 陷缺陷开展后续优化工作。
步骤 3: 以径向扰动载荷 N和凹陷缺陷的加载位置的数目《。、《c作为变量进行实验设 计抽样。
步骤 4: 基于枚举法、 遗传算法或代理模型优化技术寻找筒壳结构的最不利多点扰动 载荷组合。 优化目标为最小化含有多点凹陷缺陷的筒壳结构的屈曲载荷值，
设计变量： X - lNH ^N
目标函数:
约束条件： ≤A≤ ; = 1，2，...，" + 1
其中， N„为第 "个径向扰动载荷的位置编号， 为轴压筒壳结构屈曲载荷值， 代 表第 个变量 （包括径向扰动载荷 N和凹陷缺陷的加载位置的数目 、 «c 的上限， "代 表第 个变量 （包括径向扰动载荷 N和凹陷缺陷的加载位置的数目 、 nc) 的下限。 优化结束后， 通过公式 = ^得到结构折减因子 （KDF); 其中 Ρ 为考虑最不利多点扰动载荷组合条件下的轴压筒壳结构屈曲载荷值， 为完 善轴压筒壳结构屈曲载荷值。
本发明的有益效果是： 本发明区别于以 NASA SP-8007为代表的基于实验经验的传统 缺陷敏感度评价方法。 以施加径向扰动载荷的方式引入凹陷缺陷， 首先数值分析单点凹陷 缺陷幅度对轴压筒壳轴压承载力的影响规律， 确定合理的加载载荷幅度范围； 其次进行多 点凹陷缺陷的缺陷敏感度分析； 然后以加载载荷的幅值和加载位置的分布为设计变量进行 实验设计抽样 （DOE); 最后基于枚举法、 遗传算法、 代理模型等优化技术， 寻找限定缺 陷幅度的最不利多点扰动载荷组合， 确定轴压筒壳结构承载力的折减因子， 建立了更真实 可靠、 更具有物理意义的轴压筒壳结构缺陷敏感度和承载性能的评价方法， 预期突破现有 国内外目前基于实验经验的传统规范， 成为我国重型运载火箭等领域网格加筋壳设计中轴 压承载折减因子预测方法。 附图说明
图 1为本发明三点凹陷缺陷加载点布局方式示意图。
图 2为本发明加载点位置的编号方式示意图。
图 3为本发明圆筒壳结构不同凹陷位置下的缺陷敏感性曲线示意图。
图 4为本发明中轴压金属筒壳和 T型环结构示意图。
图 5为本发明中沿轴向 （Z1-Z5) 五个凹陷加载点分布示意图。
图 6为本发明中距离 /对圆柱壳屈曲载荷的影响示意图。
图 7为本发明中基于枚举法的最不利多点扰动载荷组合搜索历程示意图。
图 8为本发明中基于代理模型的最不利多点扰动载荷组合搜索历程示意图。
图 9为本发明一种轴压筒壳结构承载力折减因子确定方法的流程图。
图 10为本发明中轴压复合材料筒壳和金属 T型环结构示意图。
图 11为本发明中轴压复合材料筒壳沿轴向 （Z1-Z5) 五个凹陷加载点分布示意图。 图 12为本发明中轴压复合材料筒壳不同凹陷位置下的缺陷敏感性曲线示意图。
图 13为本发明中轴压复合材料筒壳四点凹陷缺陷加载点布局方式示意图。
图 14 为本发明中轴压复合材料筒壳基于枚举法的最不利多点扰动载荷组合搜索历程 示意图。
图 15 为本发明中轴压复合材料筒壳基于代理模型的最不利多点扰动载荷组合搜索历 程示意图。
图 16为本发明中大尺寸轴压金属筒壳和 T型环结构示意图。
图 Π为本发明中大尺寸轴压金属筒壳沿轴向 （Z1-Z6) 五个凹陷加载点分布示意图。 图 18为本发明中大尺寸轴压金属筒壳不同凹陷位置下的缺陷敏感性曲线示意图。 图 19为本发明中大尺寸轴压金属筒壳四点凹陷缺陷加载点布局方式示意图。
图 20 为本发明中大尺寸轴压金属筒壳基于枚举法的最不利多点扰动载荷组合搜索历 程示意图。
图 21 为本发明中大尺寸轴压金属筒壳基于代理模型最不利多点扰动载荷组合搜索历 程示意图。
具体实施方式
下面结合附图和实施例对本发明进行详细说明。
参照图 9， 本发明一种轴压筒壳结构承载力折减因子确定方法， 具体包括以下步骤- 步骤 1 : 针对完善筒壳结构， 以施加径向扰动载荷的方式引入凹陷缺陷， 首先运用有 限元等数值分析方法计算出不同单点凹陷缺陷幅度下的轴压筒壳结构的轴压承载力， 即缺 陷敏感度分析， 得到径向扰动载荷与凹陷缺陷敏感度之间的关系， 确定合理的加载载荷幅 度范围， 其中， 最大的缺陷幅度亦即所引入的最大径向扰动载荷 Nmax可由制造质量和检测 公差确定。
步骤 2: 引入多点组合凹陷缺陷进行缺陷敏感度分析， 所述多点组合凹陷缺陷引入方 式与步骤 1中单点凹陷缺陷引入方式一致。
参照图 1， 以三点凹陷缺陷为例， 定义外接圆心与三角形顶点的距离为 /， 使其从 0值 开始变化， 计算得出相应的屈曲载荷值， 绘制出屈曲载荷值与距离 /的变化曲线图， 并以 最小屈曲载荷值所对应的距离值作为有效距离 ， 这样一种有效距离的组合模式可以近似 地预测每个缺陷之间合理距离， 并假设其涵盖了相邻载荷位置之间的不利影响。 假设载荷 位置均匀地分布在筒壳上， 可推出轴向和环向的加载位置间隔&、 &和相应的加载位置的 数目 "a、 的表达式如下：
Sa = / + 0.5/ = 1.5/
Figure imgf000007_0001
ηα = 1 = 1
Sa 3/
_ 2πΚ _ AnR 其中， 代表筒壳轴向高度， 代表筒壳半径， 《点凹陷缺陷情况下距离 /的定义方式 与三点凹陷缺陷情况一致， 即以外接圆心与正 n边形顶点间的距离来定义 /。
考虑到计算规模和效率， 这里的！取为 !e， 这样一种组合模式可近似地表示每个加载 位置间的合理距离， 进而寻找三点凹陷缺陷的最不利缺陷。 参照图 2, 确定了 、 后， 每个加载位置都会被分配一个位置编号， 位置编号从筒壳底端的 0度位置开始， 沿轴向由 底端至顶端增加， 并且也沿着环向增加 （即沿轴向和环向依次排序)； 将径向扰动载荷 N 设定为一个优化变量， 以 Λ^αχ为取值上限， 以零或者经验小值为取值下限； 考虑到计算效 率， 建议缺陷数目设为 3。
参照图 3, 可知最小屈曲载荷不一定发生在施加较大径向扰动载荷的情况下， 所以将 径向扰动载荷 N设为优化变量，以 为取值上限，以零或者经验小值为取值下限。同时， 也需要确定凹陷缺陷的数目， 考虑到较多的凹陷缺陷数目会带来后续实验设计过程中取样 数目的增加、 进而会极大地提高计算成本， 并且含有过多缺陷数目的航空航天筒壳结构会 在生产实际中认定为不合格产品， 所以建议基于三点凹陷缺陷开展后续优化工作。
步骤 3: 以径向扰动载荷 N和凹陷缺陷的加载位置的数目《。、《c作为变量进行实验设 计抽样。
步骤 4: 基于枚举法、 遗传算法或代理模型优化技术寻找筒壳结构的最不利多点扰动 载荷。 优化列示如下所示， 参照图 2， 优化目标为最小化含有多点凹陷缺陷的筒壳结构的 屈曲载荷值，
设计变量： X
Figure imgf000008_0001
目标函数
约束条件：
Figure imgf000008_0002
其中， N„代表第 w个径向扰动载荷的位置编号， 为轴压筒壳结构屈曲载荷值， X！ 代表第 个变量 （包括径向扰动载荷 N和凹陷缺陷的加载位置的数目 、 nc) 的上限， XI1 代表第 个变量 （包括径向扰动载荷 N和凹陷缺陷的加载位置的数目 、 " 的下限。 优化结束后， 通过公式 £>F = ^ 导到结构折减因子 （KDF); 其中 P 为考虑最不利多点扰动载荷组合条件下的轴压筒壳结构屈曲载荷值， Pr e为完 善轴压筒壳结构屈曲载荷值。
实施例 1 :
参照图 4， 金属圆柱壳半径 ? = 250 mm， 长度 £ = 510 mm， 厚度 t = 0.5 mm。 材料采 用 2024铝合金： 弹性模量 E = 72 GPa, 泊松比 t> = 0.31, 屈服应力 σ5 = 363 MPa, 极限应力 ab = 463 MPa, 密度 p = 2.8E-6 kg/mm3。 为了便于夹持和加载， 在圆柱壳底端和顶端设置 T 型环， 材料和圆柱壳一致。 T型环底端固支， 顶端除轴向平动位移外全部约束。
参照图 5, 沿轴向五等分处分别施加径向扰动载荷引入初始缺陷， 绘制出径向扰动载 荷与结构屈曲载荷值的曲线图。假设有壳体厚度 3倍的初始缺陷（1.5mm)， 对应的径向扰 动载荷 c为 30N。 如图 1所示， 引入三点缺陷 （M， N2和 N3)， 由图 6可知最小屈曲载 荷值发生在 / = 45mm时， 令其为 ， 继而可据此推算出《。 = 7和《c = 40， 即壳体上共布置 有 280个凹陷可能发生的位置。 下边分别以枚举法和代理模型优化技术进行最不利多点扰 动载荷组合搜索。
( 1 ) 枚举法。 从上述 280个可能发生凹陷的位置点中随机生成 10个组合， 进行结构 承载力分析， 结果如图 7所示， 第 8次迭代的结构屈曲载荷最低， 因此被认为是最不利多 点扰动载荷组合。 当然， 更多的枚举次数越有利于客观地确定最不利凹陷组合。
( 2 ) 代理模型技术。 在设计域内选取 100个样点组合来进行实验设计， 建立代理模 型， 并采用多岛遗传算法进行优化计算。 迭代 13步后得到优化解， 如果 8所示， 并最终 确定折减因子为 0.42， 其优于既有的 NASA SP-8007折减因子建议值 0.32， 有效减少了设 计冗余， 而这部分提高的折减因子可以转化为减重效益。
实施例 2:
参照图 10, 复合材料圆柱壳半径 R = 250 mm， 长度 = 510 mm。 圆柱壳铺层为 [45/-45/45/-45/45] , 单层厚度为 0.1mm, 材料常数为： E = 84.56 GPa， E22 = 6.86 GPa, G12 = Gis = 4.9 GPa, G = 1.96 GPa， v12 = .3 , = 1.7E-6 kg/mm3 o 为了便于夹持和加载， 在 圆柱壳底端和顶端设置 T型环， 采用 2024铝合金： 弹性模量 E = 72 GPa, 泊松比 ϋ = 0.31， 屈服应力 σ5 = 363 MPa, 极限应力 ob = 463 MPa，密度 p = 2.8E-6 kg/mm3。 T型环底端固支， 顶端除轴向平动位移外全部约束。
参照图 11， 沿轴向五等分处分别施加径向扰动载荷引入初始缺陷， 绘制出径向扰动载 荷与结构屈曲载荷值的曲线图 12。 假设有壳体厚度 3倍的初始缺陷 （1.5mm) , 运用有限 元数值分析方法计算出对应的径向扰动载荷 \ 。 如图 13所示， 引入四点缺陷 （Μ， Ν2, N3和 N4)， 计算后找出最小屈曲载荷值发生时的 /值， 令其为 /e, 继而可据此推算出轴向 和环向的加载数目 "a和 c值， 即壳体上所有布置的凹陷可能发生的位置。 下边分别以枚 举法和代理模型优化技术进行最不利多点扰动载荷组合搜索。
( 1 ) 枚举法。 从上述可能发生凹陷的位置点集合中随机生成 10个组合， 进行结构承 载力分析， 结果如图 14所示， 第 5次迭代的结构屈曲载荷最低， 因此被认为是最不利多 点扰动载荷组合。 当然， 更多的枚举次数越有利于客观地确定最不利凹陷组合。
( 2 ) 代理模型技术。 在设计域内选取 100个样点组合来进行实验设计， 建立代理模 型， 并采用多岛遗传算法进行优化计算。 迭代 12步后得到优化解， 如果 15所示并最终确 定折减因子。
实施例 3 :
参照图 16, 金属圆柱壳半径 ? = 300 mm， 长度 = 600 mm, 厚度 / = 0.5 mm。 材料 采用 2024铝合金： 弹性模量 E = 72 GPa, 泊松比 ϋ = 0.31, 屈服应力 σ5 = 363 MPa, 极限应 力^ = 463 1^«½, 密度 J - 2.8E-6 kg/mm3。为了便于夹持和加载，在圆柱壳底端和顶端设置 T型环， 材料和圆柱壳一致。 T型环底端固支， 顶端除轴向平动位移外全部约束。
参照图 17， 沿轴向六等分处分别施加径向扰动载荷引入初始缺陷， 绘制出径向扰动载 荷与结构屈曲载荷值的曲线图 18。 假设有壳体厚度 3倍的初始缺陷 （1.5mm)， 运用有限 元数值分析方法计算出对应的径向扰动载荷^。 如图 19所示， 引入四点缺陷 （Μ， Ν2, ^3和^)， 计算后找出最小屈曲载荷值发生时的 /值， 令其为 4， 继而可据此推算出轴向 和环向的加载数目 ηα和^值， 即壳体上所有布置的凹陷可能发生的位置。 下边分别以枚 举法和代理模型优化技术进行最不利多点扰动载荷组合搜索。
( 1 ) 枚举法。 从上述可能发生凹陷的位置点集合中随机生成 10个组合， 进行结构承 载力分析， 结果如图 20所示， 第 6次迭代的结构屈曲载荷最低， 因此被认为是最不利多 点扰动载荷组合。 当然， 更多的枚举次数越有利于客观地确定最不利凹陷组合。
(2) 代理模型技术。 在设计域内选取 100个样点组合来进行实验设计， 建立代理模 型， 并采用多岛遗传算法进行优化计算。 迭代 14步后得到优化解， 如果 21所示， 并最终 确定折减因子。
以上内容是结合优选技术方案对本发明所做的进一步详细说明， 不能认定发明的具体 实施仅限于这些说明。 对本发明所属技术领域的普通技术人员来说， 在不脱离本发明的构 思的前提下， 还可以做出简单的推演及替换， 都应当视为本发明的保护范围。

Claims

权 利 要 求 书
1、 一种轴压筒壳结构承载力折减因子确定方法， 具体包括以下步骤- 步骤 1 : 针对完善筒壳结构以施加径向扰动载荷的方式引入凹陷缺陷， 首先运用有限 元等数值分析方法计算出不同单点凹陷缺陷幅度下的筒壳结构轴压承载力， 即缺陷敏感度 分析， 得到径向扰动载荷与凹陷缺陷敏感度之间的关系， 确定合理的加载载荷幅度范围， 其中， 最大的缺陷幅度亦即所引入的最大径向扰动载荷 Nmax可由制造质量和检测公差确 定；
步骤 2: 引入多点组合凹陷缺陷进行缺陷敏感度分析， 其中正多边形的顶点为径向扰 动载荷作用位置， 所述多点组合凹陷缺陷的引入方式与步骤 1中单点凹陷缺陷一致； 以三点凹陷缺陷为例， 定义外接圆心与等边三角形顶点的距离为 /， 使其从 0值开始 变化， 计算得出相应的屈曲载荷值， 并绘制出屈曲载荷值与距离 /的变化曲线图。 定义最 小屈曲载荷值所对应的距离值为有效距离 /e， 轴向和环向的加载位置间隔&、 &及相应的 加载位置的数目《。、 ^的表达式如下-
5'0 = / + 0.5/ = 1.5/
Figure imgf000011_0001
L . 2L .
n„ = 1 = 1
Sa 31
其中， Z为筒壳轴向高度， 为筒壳半径， 《点凹陷缺陷情况下距离 /的定义方式与三 点凹陷缺陷情况一致， 即以外接圆心与正 "边形顶点间的距离来定义 I；
考虑到计算规模和效率， 这里的 /取为 /e。 确定了《α、 后， 为每个加载位置分配一 个位置编号， 其中位置编号从筒壳底端的 0度位置开始， 沿轴向由底端至顶端依次增大， 并沿着环向角度依次增大； 然后将径向扰动载荷 N设为优化变量， 以 N 为取值上限， 以 零或者经验小值为取值下限； 考虑到计算效率， 建议缺陷数目设为 3 ;
步骤 3 : 以径向扰动载荷 N和凹陷缺陷的加载位置的数目 、《c作为变量进行实验设 计抽样；
步骤 4: 基于枚举法、 遗传算法或代理模型优化技术寻找筒壳结构的最不利多点扰动 载荷； 优化目标为最小化含多点凹陷缺陷的筒壳结构屈曲载荷值， 优化列式如下
设计变量： Χ^Ν,Νγ,υ ]
目标函数:
约束条件： ≤ ,.≤ ; = 1，2， ，" + 1
其中， N„为第《个径向扰动载荷的位置编号， Ρ„为轴压筒壳结构屈曲载荷值， 代 表第 /个变量的上限， "代表第 ί个变量的下限； 优化结束后， 通过公式： DF- 得到结构折减因子；
cr
其中 P:为考虑最不利多点扰动载荷条件下的轴压筒壳结构屈曲载荷值， 为完善轴 压筒壳结构屈曲载荷值。
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