A method for determining the buckling load reduction factor of axially compressed thin-walled cylindrical shell structures

Abstract

The present invention relates to the technical field of design of main load-bearing thin-walled components in aerospace, petrochemical and nuclear engineering, and discloses a method for determining the buckling load reduction factor of an axially compressed thin-walled cylindrical shell structure. By introducing a detection displacement load, the relationship curve between the detection support reaction force and the radial detection displacement of the cylindrical shell under different design input-structural response parameter combinations is obtained, and then the trough value on the detection support reaction force-displacement curve is extracted, and the corresponding lower limit predicted value of the axial compression buckling load of the cylindrical shell when the trough value is zero can be determined based on a machine learning model of an artificial neural network, and finally the buckling load reduction factor of the axially compressed thin-walled cylindrical shell can be determined through calculation. Compared with the existing methods, the present invention is more efficient and convenient, has a clearer physical meaning, and the determined buckling load reduction factor is robust and effective; while ensuring the safety of the design, it is closer to the test results, and has important application value for the lightweight design of large-scale axially compressed thin-walled cylindrical shell structures in engineering.

Description

Technical Field

[0001] The invention relates to the fields of aerospace, petrochemical engineering and nuclear engineering, and in particular to a method for determining a buckling load reduction factor of an axially compressed thin-walled cylindrical shell structure. Background Art

[0002] As one of the most basic structural units in engineering, thin-walled cylindrical shells are widely used in aerospace, petrochemical, civil engineering, and nuclear engineering due to their efficient load-bearing performance and excellent functional structural design. Typical thin-walled cylindrical shell structures, such as interstages of launch vehicles, nuclear containment, and large oil storage tanks, not only have a large diameter-to-thickness ratio (usually the ratio of the radius of the cylindrical shell to its thickness), but also are very susceptible to huge pressure loads along the axial direction of the shell under conditions such as rocket launches, equipment hoisting, and earthquakes, which puts them at risk of buckling failure. Buckling is also the main failure mode of such structures in actual engineering. It is well known that there is a significant difference between the actual value of the buckling critical load of thin-walled cylindrical shell structures under axial pressure and the theoretical calculated value of ideal elastic cylindrical shells. The former is usually only 20% to 50% of the latter, and the dispersion is very large. Research has shown that the high sensitivity of axially compressed thin-walled cylindrical shells to initial defects is the fundamental reason for this phenomenon. Accurately considering the sensitivity of shell initial defects is a prerequisite for accurately predicting the critical load of axial compression buckling of real thin-walled cylindrical shell structures, and is also the key to establishing a reasonable, safe and economical axial compression thin-walled cylindrical shell buckling design method.

[0003] In order to characterize the initial defect sensitivity of axially compressed cylindrical shells, it is often necessary to introduce a load reduction factor ρ in actual engineering design. KDF The concept of axial compression is defined as the ratio of the critical load of buckling of a real cylindrical shell structure under axial compression to the critical load of buckling calculated theoretically for an ideal cylindrical shell. It is a coefficient greater than 0 and less than 1. When designing a cylindrical shell structure, the product of the load reduction factor and the ideal cylindrical shell buckling load is usually taken as the design load for axial compression buckling of the cylindrical shell. The core problem of axial compression buckling design of thin-walled cylindrical shell structures is to determine a reasonable load reduction factor for cylindrical shell buckling. The more accurately the load reduction factor can reflect the weakening effect of the real initial defects on the axial compression bearing capacity of the cylindrical shell, the more it can minimize the axial compression buckling design cycle of the cylindrical shell structure and the material and manufacturing costs, thereby promoting the thin-walled cylindrical shell structure in actual engineering to further develop in the direction of large-scale, lightweight and high reliability. The high-precision determination of the critical load reduction factor for axial compression buckling of cylindrical shells is also regarded by the National Aeronautics and Space Administration (NASA) as a new generation of weight reduction technology for large-diameter cylindrical shell structures.

[0004] However, with the continuous improvement of the processing technology of large-scale thin-walled cylindrical shell structures in engineering, the continuous updating of shell material systems, and the gradual enrichment of quality control experience. The recommended value of the critical load reduction factor for axial compression buckling of cylindrical shells given by the classic NASA SP-8007 design guide has been proven to be too conservative. The load-bearing efficiency of the thin-walled cylindrical shell structure designed based on this guide cannot be effectively exerted, and the structural strength and stiffness design are too redundant. In recent years, domestic and foreign researchers have proposed various methods for predicting the buckling load reduction factor of axial compression cylindrical shells that consider the influence of initial defects, but all of them have limitations to varying degrees. For example, the measured initial geometric defect method cannot be used in practice, the single-point perturbation load method is too aggressive, the linear eigenvalue buckling modal defect method is too conservative, and the calculation cost of the most unfavorable multi-point perturbation load method and the probability statistics method is too high. So far, a relatively complete method for determining the buckling load reduction factor of axial compression cylindrical shells has not been established, which can be both safe and reliable, simple and fast, and has clear physical meaning.

[0005] With the continuous exploration of the new generation of launch vehicles and future heavy launch vehicles, super-large oil storage tanks and large nuclear containment, the buckling problem of thin-walled cylindrical shell structures under axial compression loads has become more prominent. Therefore, it is urgent to establish a more reasonable and complete method for determining the buckling load reduction factor of axially compressed thin-walled cylindrical shell structures. Summary of the invention

[0006] The present invention aims at the problems that the load reduction factor determination method in the buckling design of axially compressed thin-walled cylindrical shell structure is too conservative and the physical meaning is unclear, and proposes a new method for determining the buckling load reduction factor of axially compressed thin-walled cylindrical shell structure based on machine learning. By introducing the detection displacement load, the relationship curve between the detection support reaction force and the detection displacement of the thin-walled cylindrical shell structure under different design input-structural response parameter combinations is obtained, and then the trough value (local minimum) on the detection support reaction force-displacement curve is extracted, and the corresponding lower limit prediction value of the axial compression buckling load of the cylindrical shell can be determined based on the machine learning model of the artificial neural network when the trough value is zero. Finally, the buckling load reduction factor of the axially compressed thin-walled cylindrical shell can be determined by calculation. Compared with the existing methods, the present invention has a clearer physical meaning and is more convenient to use. The buckling load reduction factor predicted by the present invention is robust and effective, and is closer to the test results while ensuring safety.

[0007] The technical solution adopted by the present invention is: a method for determining the buckling load reduction factor of an axially compressed thin-walled cylindrical shell structure is proposed, which specifically comprises the following steps:

[0008] Step 1: Conduct experimental design within the design range, and perform initial sampling of the structural characteristic parameters and material performance parameters of the thin-walled cylindrical shell based on the optimized Latin cube method; the structural characteristic parameters include radius R, length L and thickness t, and the material performance parameters include elastic modulus E, Poisson's ratio v and yield strength R eL ;

[0009] Step 2: Select a sample data for each physical quantity to form a set of design parameter combinations f(R, L, t, E, v, R eL );

[0010] Step 3: Calculate the critical load N of the ideal elastic cylindrical shell under axial compression according to the following formula: cr per :

[0011]

[0012] Step 4: Based on the design input parameter combination determined in step 2, the buckling critical load N of the axially compressed cylindrical shell is calculated using the nonlinear finite element analysis method. cr ;

[0013] Step 5: Apply an axial compressive load N on the top of the cylindrical shell. The axial compressive load N should satisfy: 0.4N cr ≤N <N cr ;

[0014] Step 6: Add the axial compressive load N determined in step 5 to the design input parameter combination in step 2 to form the design input-structural response parameter combination g(R, L, t, E, v, R eL ,N);

[0015] Step 7: Keep the axial pressure load N unchanged and apply a radial displacement load u to the outer surface of the cylindrical shell at half the height. p Conduct disturbance detection;

[0016] Step 8: Detect displacement load u as dimensionless radial disturbance p / t is the horizontal coordinate, and the support reaction force F of the cylindrical shell at the detection point p As the ordinate, draw the cylindrical shell F under this N value p -u p / t relationship curve;

[0017] Step 9: Extract the F p -u p / tThe trough value F on the relationship curve p min ;

[0018] Step 10: Change the structural characteristic parameters and material performance parameters of the cylindrical shell, and calculate the corresponding critical buckling load N of the cylindrical shellcr Repeat steps 2 to 9 to obtain the F of the cylindrical shell under different design input-structural response parameter combinations. p min value;

[0019] Step 11: Take the different structural characteristic parameters, material performance parameters and axial pressure load of the cylindrical shell in step 10 as input variables and transform the cylindrical shell F p -u p / tThe trough value F on the relationship curve p min As output variables, a machine learning model based on artificial neural network is constructed;

[0020] Step 12: Repeatedly train the machine learning model constructed in step 11 to obtain different shell structure characteristic parameters, material performance parameters, and axial pressure loads, and then output different F p min Value ability;

[0021] Step 13: Fix a set of cylindrical shell structural characteristics and material properties, use the dichotomy method, continuously adjust the axial pressure load N input value, and use the machine learning model trained in step 12 to predict different F p min Value, until F p min is equal to or approximately equal to 0, the corresponding axial compressive load N value at this time can be used as the reduced buckling load value N of the cylindrical shell KDF ;

[0022] Step 14: Determine the buckling load reduction factor ρ of the axially compressed thin-walled cylindrical shell structure according to the following formula KDF :

[0023]

[0024] Furthermore, the radial displacement load u described in step 7 p Should meet: p =5t.

[0025] Furthermore, the number of different design input-structural response parameter combinations described in step 10 should be greater than 100.

[0026] Furthermore, in step 13, F p min Approximately equal to 0, the convergence condition F should be met p min / N<1e-6.

[0027] Furthermore, the material of the thin-walled cylindrical shell structure is a metal material or a composite material.

[0028] Furthermore, the metal material of the thin-walled cylindrical shell structure is carbon steel, low alloy steel or high alloy steel.

[0029] Compared with the existing method, the beneficial effects of the present invention are:

[0030] 1. Determining the trough value on the cylindrical shell detection support reaction-displacement curve under different structural characteristic parameters and material performance parameters based on machine learning models is essentially a design method based on data-driven calculation. Whether in terms of computational efficiency or computational scale, it can accurately and effectively predict the buckling load reduction factor of axially compressed cylindrical shells and guide related designs. It is an advanced design method for typical engineering foundation parts under the background of big data.

[0031] 2. The physical meaning is clearer. Based on the idea of ​​disturbance detection, the inherent properties of the cylindrical shell are characterized on its detection support reaction force-detection displacement curve, and then the degree of buckling load reduction when the cylindrical shell is affected by initial defects is determined. This is a new method that essentially reveals the sensitivity of the cylindrical shell to initial defects.

[0032] 3. The application is more efficient and convenient, and more suitable for actual engineering design. Through numerical simulation calculation, the cylindrical shell detection support reaction force-detection displacement curve can be easily obtained. The calculation cost is low but the calculation result is accurate and effective. Compared with the most unfavorable multi-point disturbance load method and probability statistics method, the calculation efficiency is significantly improved.

[0033] 4. The determined load reduction factor is more robust and effective, and is closer to the test results while ensuring safety. Compared with the NASA SP-8007 design guide, the present invention can effectively reduce the conservatism of the design, significantly improve the economic benefits in practical application, and greatly improve the load-bearing efficiency of the designed cylindrical shell structure; compared with the single-point perturbation method, the present invention is safer and ensures the safety of the design.

[0034] In summary, the method for determining the buckling load reduction factor of an axially compressed thin-walled cylindrical shell structure proposed in the present invention will play an important role in the lightweight design of large thin-walled cylindrical shell structures in my country's aerospace, petrochemical, nuclear engineering and other fields, and has great engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a schematic diagram of applying axial compressive load on the thin-walled cylindrical shell structure of the present invention.

[0036] Figure 2 It is a schematic diagram of applying a radial detection displacement load at half the height of the thin-walled cylindrical shell structure of the present invention.

[0037] Figure 3 The detection support reaction force F on the thin-walled cylindrical shell structure under the specific axial pressure load of the present invention pand radial disturbance detection displacement load u p / t relationship curve.

[0038] Figure 4 Schematic diagram of the machine learning model based on artificial neural network constructed for the present invention. DETAILED DESCRIPTION

[0039] The present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, rather than to limit the present invention, and the accompanying drawings only illustrate the contents related to the specific embodiments, rather than the entire contents of the present invention.

[0040] The embodiment of the present invention provides a method for determining a buckling load reduction factor of an axially compressed thin-walled cylindrical shell structure, which specifically includes the following steps:

[0041] Step 1: Conduct experimental design within the design range, and optimize the structural characteristic parameters (radius R, length L, thickness t) of the thin-walled cylindrical shell, material performance parameters (elastic modulus E, Poisson's ratio v, yield strength R eL ) to perform initial sampling;

[0042] Step 2: Select a sample data for each physical quantity to form a set of design input parameter combinations f(R = 500mm, L = 560mm, t = 1.2mm, E = 210GPa, v = 0.3, R eL =280MPa);

[0043] Step 3: Calculate the critical load N of the ideal elastic cylindrical shell under axial compression according to the following formula: cr per :

[0044]

[0045] Step 4: Based on the design input parameter combination determined in step 2, the buckling critical load N of the axially compressed cylindrical shell is calculated using the nonlinear finite element analysis method. cr =914.3kN;

[0046] Step 5: Reference Figure 1 Apply an axial compressive load N=365.72kN to the top of the cylindrical shell model;

[0047] Step 6: Add the axial compressive load N determined in step 5 to the design input parameter combination in step 2 to form the design input-structural response parameter combination g (R = 500 mm, L = 560 mm, t = 1.2 mm, E = 210 GPa, v = 0.3, R eL =280MPa, N = 365.72kN);

[0048] Step 7: Reference Figure 2 Keeping the axial pressure load N constant, a radial displacement load u is applied to the outer surface of the cylindrical shell at half its height. p =5t=6mm for disturbance detection;

[0049] Step 8: Reference Figure 3 , using dimensionless radial disturbance to detect displacement load u p / t is the horizontal coordinate, and the support reaction force F of the cylindrical shell at the detection point p As the ordinate, draw the cylindrical shell F under this N value p -u p / t relationship curve;

[0050] Step 9: Extract the F p -u p / tThe trough value F on the relationship curve p min ;

[0051] Step 10: Change the structural characteristic parameters (R, L, t) and material performance parameters (E, v, R eL ), and calculate the corresponding cylindrical shell buckling critical load N cr Repeat steps 2 to 9 to obtain the F of the cylindrical shell under different design input-structural response parameter combinations. p min value;

[0052] Step 11: Reference Figure 4 , taking the different structural characteristic parameters, material performance parameters and axial pressure load of the cylindrical shell in step 10 as input variables, the cylindrical shell F p -u p / tThe trough value F on the relationship curve p min As output variables, a machine learning model based on artificial neural network (ANN) is constructed;

[0053] Step 12: Repeatedly train the machine learning model established in step 11 to obtain different shell structure characteristic parameters, material performance parameters, and axial pressure loads, and then output different F p min Value ability;

[0054] Step 13: Fix a set of cylindrical shell structural characteristics and material properties, use the dichotomy method, continuously adjust the axial pressure load N input value, and use the ANN-based machine learning model trained in step 12 to predict different F p min Value, until F p minis equal to (or approximately equal to) 0, the corresponding axial compressive load N value at this time can be used as the reduced buckling load value N of the cylindrical shell KDF =573.6kN;

[0055] Step 14: Determine the buckling load reduction factor ρ of the axially compressed thin-walled cylindrical shell structure according to the following formula KDF :

[0056]

[0057] The comparison between the buckling load reduction factor of the axially compressed thin-walled cylindrical shell structure given in this embodiment and the value determined by other existing methods is shown in Table 1.

[0058] Table 1 Comparison of the buckling load reduction factor of the axially compressed thin-walled cylindrical shell structure given in this embodiment with other existing methods

[0059] method Test value The present invention NASA SP-8007 Single point disturbance load method Load reduction factor 0.591 0.499 0.350 0.624

[0060] It can be seen from Table 1 that the buckling load reduction factor of the axially compressed thin-walled cylindrical shell determined by the present invention is closer to the test value under the premise of ensuring design safety (the predicted result is less than the test value), which effectively reduces the conservative degree of design. In particular, compared with the traditional NASA SP-8007 design guide, the load reduction factor is increased by 42.6%, which has obvious lightweight design benefits.

[0061] The above is a further detailed description of the present invention in combination with the preferred embodiments, and is not a limitation of the present invention. It should be pointed out that for ordinary technicians in the technical field to which the present invention belongs, any simple deduction and optimization of the present invention based on the core idea of ​​the present invention should be regarded as within the scope of protection of the present invention.

Claims

1. A method for determining the buckling load reduction factor of an axially compressed thin-walled cylindrical shell structure, characterized in that: The following steps are involved: Step 1: Conduct experimental design within the design range, and perform initial sampling of the structural characteristic parameters and material performance parameters of the thin-walled cylindrical shell based on the optimized Latin cube method; the structural characteristic parameters include radius R, length L and thickness t, and the material performance parameters include elastic modulus E, Poisson's ratio v and yield strength R eL ; Step 2: Select a sample data for each physical quantity to form a set of design input parameter combinations f(R, L, t, E, v, R eL ); Step 3: Calculate the critical load N of the ideal elastic cylindrical shell under axial compression according to the following formula: cr per : Step 4: Based on the design input parameter combination determined in step 2, the structural response of the axially compressed cylindrical shell is calculated using the nonlinear finite element analysis method; the structural response is the critical buckling load N of the cylindrical shell. cr ; Step 5: Apply an axial compressive load N on the top of the cylindrical shell. The axial compressive load N should satisfy: 0.4N cr ≤N <N cr ; Step 6: Add the axial compressive load N determined in step 5 to the design input parameter combination in step 2 to form the design input-structural response parameter combination g(R, L, t, E, v, R eL ,N); Step 7: Keep the axial pressure load N unchanged and apply a radial displacement load u to the outer surface of the cylindrical shell at half the height. p Conduct disturbance detection; Step 8: Detect displacement load u as dimensionless radial disturbance p / t is the horizontal coordinate, and the support reaction force F of the cylindrical shell at the detection point p As the ordinate, draw the cylindrical shell F under this N value p -u p / t relationship curve; Step 9: Extract the F p -u p / tThe trough value F on the relationship curve p min ; Step 10: Change the structural characteristic parameters and material performance parameters of the cylindrical shell, and calculate the corresponding critical buckling load N of the cylindrical shell cr Repeat steps 2 to 9 to obtain the F of the cylindrical shell under different design input-structural response parameter combinations. p min value; Step 11: Take the different structural characteristic parameters, material performance parameters and axial pressure load of the cylindrical shell in step 10 as input variables and transform the cylindrical shell F p -u p / tThe trough value F on the relationship curve p min As output variables, a machine learning model based on artificial neural network is constructed; Step 12: Repeatedly train the machine learning model constructed in step 11 to obtain different shell structure characteristic parameters, material performance parameters, and axial pressure loads, and then output different F p min Value ability; Step 13: Fix a set of cylindrical shell structural characteristics and material properties, use the dichotomy method, continuously adjust the axial pressure load N input value, and use the machine learning model trained in step 12 to predict different F p min Value, until F p min is equal to or approximately equal to 0, the corresponding axial compressive load N value at this time can be used as the reduced buckling load value N of the cylindrical shell KDF ; Step 14: Determine the buckling load reduction factor ρ of the axially compressed thin-walled cylindrical shell structure according to the following formula KDF :

2. The method for determining the buckling load reduction factor of an axially compressed thin-walled cylindrical shell structure according to claim 1, characterized in that: The radial displacement load u described in step 7 p Should meet: p =5t.

3. The method for determining the buckling load reduction factor of an axially compressed thin-walled cylindrical shell structure according to claim 1, characterized in that: The number of different design input-structural response parameter combinations described in step 10 should be greater than 100.

4. The method for determining the buckling load reduction factor of an axially compressed thin-walled cylindrical shell structure according to claim 1, characterized in that: Step 13 F p min Approximately equal to 0, the convergence condition F should be satisfied p min / N<1e-6.

5. The method for determining the buckling load reduction factor of an axially compressed thin-walled cylindrical shell structure according to any one of claims 1 to 4, characterized in that: The material of the thin-walled cylindrical shell structure is a metal material or a composite material.

6. The method for determining the buckling load reduction factor of an axially compressed thin-walled cylindrical shell structure according to claim 5, characterized in that: The metal material of the thin-walled cylindrical shell structure is carbon steel, low alloy steel or high alloy steel.

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