Buckling evaluation method and device for cylindrical tanks

Abstract

To provide a buckling evaluation method and a buckling evaluation device for a cylindrical tank, capable of ensuring sufficient safety compared to a conventional earthquake resistance evaluation method and buckling evaluation method, when executing fluid structure interaction analysis under assumption that a vertical cylindrical tank reaches buckling by an earthquake.SOLUTION: An evaluation based on fluid structure interaction analysis according to an implicit and weak coupled method, has: a procedure of executing an attenuation ratio confirmation / adjustment loop for adjusting an attenuation ratio of an interaction analysis model to a predetermined value or less, a procedure of executing a minimum reduction ratio derivation loop for deriving a minimum reduction ratio of an input acceleration upon buckling; and a procedure of performing buckling determination by applying a design earthquake waveform obtained by multiplying an acceleration amplitude of the design earthquake waveform by an inverse number of the minimum reduction ratio to expand the amplitude, to a model after the attenuation ratio confirmation / adjustment loop has finished.SELECTED DRAWING: Figure 6

Description

[Technical Field]

[0001] The present invention relates to a buckling evaluation method and a buckling evaluation device for a cylindrical tank. [Background technology]

[0002] Non-Patent Document 1 describes the reproduction of experimental results regarding the seismic resistance of tanks by applying an explicit method and a strongly coupled analysis solver. [Prior art documents] [Non-patent literature]

[0003] [Non-Patent Document 1] Akira Maekawa, Dynamic Buckling Analysis of Cylindrical Water Storage Tanks: A New Simulation Method Considering Coupled Vibration Between Fluid and Structure, ASME 2009 Pressure Vessels and Piping Conference -77083, pp. 77-86 Summary of the Invention [Problem to be solved by the invention]

[0004] It is empirically known that when large cylindrical water storage tanks are damaged by earthquakes, they will reach elephant foot buckling, which has a high buckling resistance. However, in design evaluations, a buckling evaluation formula with a high safety factor that assumes non-axisymmetric buckling, which has a low buckling resistance, is applied.

[0005] When applying the buckling evaluation formula assuming an earthquake, it is first necessary to evaluate the response of the cylindrical tank to an earthquake, but in order to evaluate this vibration, it is necessary to understand the effect that the internal fluid has on the vibration behavior.

[0006] A common method for evaluating the seismic resistance of cylindrical tanks is to consider the added mass of the fluid in the cylindrical tank, derive the maximum axial compressive stress in the cylindrical tank body based on the moment and shear force at the fixed point at the lower end of the cylindrical tank during vibration response, and then compare the obtained maximum axial compressive stress with the buckling stress obtained using an evaluation formula to perform a buckling evaluation.

[0007] Additionally, a paper has been published that introduces an example of reproducing experimental results using an explicit / strongly coupled analysis solver for the seismic resistance of a cylindrical tank (see, for example, Non-Patent Document 1). The strongly coupled analysis method introduced in Non-Patent Document 1 is effective when reproducing an experiment without considering the conservatism of the analysis results.

[0008] By applying analytical methods that can accurately simulate the behavior of actual equipment, it is possible to proceed with the design by determining whether or not a cylindrical tank will be damaged when hit by an earthquake. However, in design evaluation, it is necessary to estimate the buckling load by applying a safety factor to the results of experiments and analyses that provide solutions that are as close as possible to the experiments.

[0009] In vibration analysis, it is customary to perform an analysis assuming a damping ratio smaller than that of the actual structure to ensure a safety factor against the effects of factors such as waveform dependency of the response and structural uncertainty.In buckling analysis, it is thought that adding initial imperfections that are large enough to reduce the buckling strength can replace the process of applying a uniform large safety factor to the evaluation results.

[0010] Regarding the setting of the damping ratio, when applying the analysis results in seismic evaluation, the damping ratio of the analysis model must be set to a value below that specified in the standard, but in weakly coupled fluid-structure interaction analysis, the damping ratio cannot be set as an input value for a single solver.

[0011] For this reason, it is desirable to develop a method for setting damping ratios that comply with standards in fluid-structure interaction analysis.As with conventional analysis methods, even if Rayleigh damping is set for the structural analysis model, which is one of the weakly coupled models, the damping does not work on the water content, which accounts for most of the weight of the coupled analysis model, so the damping ratio does not become as set.

[0012] Regarding the setting of initial imperfections, because the diameter / wall thickness ratio of cylindrical tanks is large, the evaluation formula assumes diamond buckling mode and considers the effects of initial imperfections. However, it is known that the buckling mode that actually occurs in cylindrical tanks is elephant foot buckling, and the decrease in buckling strength is smaller than when diamond buckling mode is assumed. For this reason, when conducting seismic evaluations based on fluid-structure interaction analysis, it is desirable to be able to consider the effects of appropriate initial imperfections.

[0013] However, in order to take into account the effects of initial imperfections, it is necessary to carry out numerous analyses with different initial imperfection settings. For example, while the load in the internal pressure buckling analysis method is a gradually increasing internal pressure, the load in the seismic analysis is a time history acceleration waveform that simulates earthquake motion.

[0014] Therefore, when considering the effects of initial imperfections using the method applied in conventional internal pressure buckling evaluation methods, it is necessary to change the amplitude of the time history waveform and perform multiple analyses, which consumes a lot of analysis resources, so a new method is needed.

[0015] The present invention provides a buckling evaluation method and device for cylindrical tanks that can ensure sufficient safety compared to existing seismic evaluation methods and buckling evaluation methods when performing fluid-structure interaction analysis assuming that a vertical cylindrical tank will buckle due to an earthquake. [Means for solving the problem]

[0016] The present invention includes multiple means for solving the above-mentioned problems, and one example is a buckling evaluation method that assumes a case in which an earthquake load acts on a cylindrical tank, and includes the following steps in an evaluation based on implicit, weakly coupled fluid-structure coupled analysis: executing a damping ratio confirmation and adjustment loop to adjust the damping ratio of the coupled analysis model to a predetermined threshold value or less; executing a minimum reduction rate derivation loop to derive the minimum reduction rate of the input acceleration at buckling; and loading a design earthquake waveform, which has been amplified by multiplying the acceleration amplitude of the design earthquake waveform by the reciprocal of the minimum reduction rate, onto a model that has completed the damping ratio confirmation and adjustment loop, to perform a buckling judgment. [Effects of the Invention]

[0017] According to the present invention, it is possible to ensure sufficient safety compared to the existing seismic evaluation methods and buckling evaluation methods. Problems, configurations, and effects other than those described above will become clear from the following description of the embodiments. [Brief explanation of the drawings]

[0018] [Figure 1] FIG. 2 is a block diagram of a schematic configuration for explaining the generation of an analysis model in the buckling evaluation device in the first embodiment. [Figure 2] FIG. 2 is a block diagram of a schematic configuration for explaining buckling eigenmode analysis in the buckling evaluation device in the first embodiment. [Figure 3] FIG. 2 is a block diagram of a schematic configuration for explaining confirmation and adjustment of a damping ratio in the buckling evaluation device in the first embodiment. [Figure 4] FIG. 2 is a block diagram of a schematic configuration for explaining derivation of a minimum reduction rate γ in the buckling evaluation device in the first embodiment. [Figure 5] FIG. 2 is a block diagram of a schematic configuration for explaining seismic analysis using the buckling evaluation device in the first embodiment. [Figure 6] 4 is a flowchart illustrating a buckling analysis method in the first embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0019] Hereinafter, an embodiment of the cylindrical tank buckling evaluation method and buckling evaluation device of the present invention will be described with reference to the drawings.

[0020] The analytical methods, set values, and other specific configurations shown in the present invention are not limited to the embodiments and examples described here, and can be appropriately combined or improved within the scope that does not change the gist of the present invention. Furthermore, elements that are not directly related to the present invention are not shown in the drawings.

[0021] Furthermore, in the drawings used in this specification, identical or corresponding components are denoted by the same or similar reference numerals, and repeated description of these components may be omitted.

[0022] Example 1 A first embodiment of the cylindrical tank buckling evaluation method and buckling evaluation device of the present invention will be described with reference to FIGS. 1 to 6. FIG.

[0023] In design evaluations targeting events in which a vertical cylindrical tank is damaged by an earthquake and buckles, methods based on evaluation formulas first analyze the earthquake response, calculate the axial compressive stress based on the obtained bottom moment, and compare it with a predetermined buckling stress. Methods using fluid-structure coupled analysis involve analysis in which simulated seismic waves are applied as input acceleration to the coupled analysis model.

[0024] However, methods based on evaluation formulas have an excessive degree of safety against buckling that actually occurs, making it difficult to design cylindrical tanks that can withstand large earthquakes.On the other hand, methods using fluid-structure interaction analysis can obtain solutions that are close to reality, but because the evaluation results are under conditions that are more ideal than reality, it is necessary to multiply the evaluation results by a safety factor, and if a general value is used as the safety factor for buckling evaluation of thin-walled structures such as cylindrical tanks, the advantage of obtaining a solution that is close to reality is lost.

[0025] Furthermore, the damping ratio is important in vibration analysis, and the damping ratio must be set to a value smaller than the actual value specified by standards for each evaluation object before analysis.

[0026] However, in weakly coupled analyses, even if the damping ratio is defined in one solver, it will not be reflected as set in the coupled state, so confirmation and adjustment are required.

[0027] Furthermore, for buckling evaluation, it is necessary to perform a buckling judgment. However, in an analysis model that has been adjusted to obtain the minimum buckling load by defining a large amount of initial imperfections, it may be difficult to judge buckling. Therefore, in order to perform a clear buckling judgment, the amount of initial imperfections must be kept to a minimum.

[0028] In order to solve these problems, the buckling evaluation device and buckling evaluation method of this embodiment are equipped with a damping definition section that confirms that the damping ratio is sufficiently small and an initial imperfection effect consideration section that takes into maximum consideration the effect of initial imperfections, thereby improving the safety of the analysis results.

[0029] In other words, this is a buckling evaluation method that assumes a case where an earthquake load acts on a cylindrical tank, and in an evaluation based on an implicit, weakly coupled fluid-structure coupled analysis, it comprises the following steps: executing a damping ratio confirmation and adjustment loop to adjust the damping ratio of the coupled analysis model to a predetermined threshold value or less; executing a minimum reduction rate derivation loop to derive the minimum reduction rate of the input acceleration at buckling; and loading the design earthquake waveform, which has been expanded in amplitude by multiplying the acceleration amplitude of the design earthquake waveform by the reciprocal of the minimum reduction rate, onto the model that has completed the damping ratio confirmation and adjustment loop to make a buckling judgment.

[0030] In the present invention, the target damping ratio for adjustment is evaluated as being below a predetermined threshold of 10%, but this value can be changed as appropriate, for example, to 1% or 2.5%, depending on the reference value, etc.

[0031] The buckling evaluation method according to the present invention is suitable for evaluating, for example, nuclear equipment, but the use of the evaluation object is not particularly limited, and it can be applied to cylindrical tanks in various technical fields.

[0032] Next, the configuration and operation of the buckling evaluation device will be described with reference to the block diagrams of Figures 1 to 5. Figure 1 is a block diagram of a schematic configuration for explaining the generation of an analytical model in the buckling evaluation device in Example 1, Figure 2 is a block diagram of a schematic configuration for explaining buckling eigenmode analysis, Figure 3 is a block diagram of a schematic configuration for explaining damping ratio confirmation and adjustment, Figure 4 is a block diagram of a schematic configuration for explaining the derivation of the minimum reduction rate γ, and Figure 5 is a block diagram of a schematic configuration for explaining seismic analysis.

[0033] The buckling evaluation device 50 shown in Figure 1 is composed of an input unit 1 for inputting analysis settings, a calculation unit 2 for performing fluid-structure interaction analysis, and a display unit 3 for displaying the results.Data is input into the input unit 1, and the calculation unit 2 performs analysis based on the data, and the results obtained from the analysis are displayed on the display unit 3.

[0034] This buckling evaluation device 50 is composed of a general PC (Personal Computer) including input devices such as a keyboard and mouse, a CPU (Central Processing Unit), storage devices such as an HDD, SSD, and memory, an LCD display, etc., and can be operated by a computer program, but a dedicated device may also be used.

[0035] First, the block diagram in Figure 1 shows the state in which data is input and the model shape is displayed.

[0036] The input section 1 is a section for inputting dimensional information and material information of the object to be evaluated, input acceleration waveform, and damping ratio specified in the standard, and is provided with input sections for content liquid characteristics 11, dimensions 12, and material characteristics 13 as the characteristics of the object to be evaluated.

[0037] The calculation unit 2 performs an analysis based on the data inputted by the input unit 1 and displays the obtained results on the display unit 3 .

[0038] This calculation unit 2 may include, for example, a CPU (Central Processing Unit), a memory (storage device), etc., and may be configured to operate with a computer program, and is equipped with a damping setting unit that creates a damping-adjusted structural analysis model, an initial imperfection setting unit, an initial imperfection effect consideration unit that creates an input waveform to be applied to seismic analysis, and a buckling evaluation unit that performs buckling judgment.

[0039] In FIG. 1, the calculation unit 2 has an implicit fluid analysis solver 21 and an implicit structural analysis solver 22, and can output evaluation results with improved safety from two aspects, vibration analysis and buckling analysis, for the buckling analysis results obtained by fluid-structure coupled analysis.

[0040] The damping setting unit executes a process of repeatedly setting Rayleigh damping in the structural analysis model and performing free vibration analysis, and a process of adjusting the damping ratio of the fluid-structure interaction analysis model so that it is equal to or less than a predetermined damping ratio.

[0041] By setting the damping ratio, safety in vibration analysis can be improved, and by using the minimum reduction rate due to initial imperfections, safety in buckling analysis can be improved.

[0042] Furthermore, compared to simple evaluation formulas, etc., it is possible to obtain a large buckling strength that is closer to reality, but in contrast to buckling analysis using fluid-structure interaction analysis, which may produce results that are less safe because it is more ideal than reality, it is possible to obtain evaluation results that improve safety while maintaining the characteristic of obtaining a large buckling strength that is closer to reality.

[0043] When performing free vibration analysis in a coupled analysis, it is preferable to use a method in which horizontal gravitational acceleration is applied to the structural analysis model, and then the gravitational acceleration is instantaneously removed to initiate free vibration. The response displacement history of the upper lid is then checked, the natural frequency is calculated from the reciprocal of the average vibration period, and the damping ratio is calculated from the reduction rate of the amplitude of the response waveform. Then, a gravitational acceleration can be set so that the maximum stress generated in the analysis model under horizontal gravitational acceleration is within the elastic range. Based on the obtained natural frequency and damping ratio, the Rayleigh damping setting of the structural analysis model can be updated, and the free vibration analysis can be performed again to adjust the damping ratio until it is equal to or less than the damping ratio specified by the standard.

[0044] Here, the structural analysis model consists of a fixed bottom disk, a cylindrical tank body plate, and a cylindrical tank lid, and can accommodate large deformations of the structure and nonlinear behavior of materials, and can be applied to an implicit structural analysis solver.

[0045] In addition, the fluid analysis model takes into account the liquid surface and has the ability to follow the deformation of the wall surface, and can apply an implicit fluid analysis solver.

[0046] Furthermore, in coupled analysis, the pressure acting on the wall surface in the fluid analysis model is input to the structural analysis model, and the displacement occurring on the wall surface of the structural analysis model is input to the fluid analysis model. At each time step, repeated calculations are performed until the displacement and pressure converge, allowing for convergence calculations even in a weakly coupled environment.

[0047] When creating a structural analysis model, it is preferable that the bottom and lid surfaces of the analysis model be elastic bodies, and the copper plate of the cylindrical tank be an elasto-plastic body.

[0048] The initial imperfection setting unit executes a step of performing a buckling eigenvalue analysis under an axial compressive load, and a step of setting a buckling mode symmetric with respect to a rotation axis as an initial imperfection shape.

[0049] The initial imperfection effect consideration unit executes a step of performing a buckling analysis using an input waveform of a gradually increasing simple harmonic motion, and a step of determining a minimum reduction rate as the initial imperfection effect on the input acceleration at buckling.

[0050] Among these, when performing a buckling analysis using gradually increasing simple harmonic motion in the coupled analysis, it is preferable to load the acceleration waveform of the gradually increasing simple harmonic motion onto the lower end of the structural analysis model, and determine the input acceleration at buckling relative to the initial imperfection by taking the absolute value of the extreme value of the input acceleration immediately before buckling occurs as the input acceleration at buckling.

[0051] Furthermore, when estimating the minimum reduction rate of the input acceleration at buckling, it is preferable to carry out several cases where the initial imperfection is small and several cases where the initial imperfection is too large for the relationship between the input acceleration at buckling and the initial imperfection, formulate an approximate formula for each range, and estimate the initial imperfection and minimum reduction rate that will give the minimum input acceleration at buckling by extrapolating the two approximate formulas.

[0052] The buckling evaluation unit performs the steps of: generating an evaluation waveform to be applied to seismic analysis for buckling evaluation by multiplying the input acceleration waveform by the inverse of the minimum reduction rate; and performing a time history analysis using the evaluation waveform with enlarged amplitude to make a buckling judgment.

[0053] The display unit 3 is the above-mentioned liquid crystal display or the like, and displays a fluid analysis model 31 and a structural analysis model 32 that display information such as the shape of the analysis model to be generated.

[0054] Next, the process of deriving the buckling eigenmode will be explained using the block diagram in FIG.

[0055] As shown in Figure 2, in the process of deriving the buckling eigenmode, a structural analysis model 32 and analysis conditions 16 are input to input unit 1, and calculation unit 2 performs buckling eigenvalue analysis based on the analysis model and loading conditions using buckling eigenvalue analysis unit 24 in structural analysis solver 22. Display unit 3 displays buckling eigenmode 33 as the result of buckling eigenvalue analysis unit 24.

[0056] Here, a rotation-axis symmetric buckling eigenmode can be searched for from among the modes and used as the initial imperfect shape.

[0057] Furthermore, when performing a buckling eigenvalue analysis on a structural analysis model to create an initial imperfect shape, the analysis can be preferably performed by applying a vertical gravitational acceleration as a unit load to the structural analysis model. The obtained buckling eigenmode shapes can be displayed on the display unit 3, allowing for the search for axisymmetric buckling eigenmodes.

[0058] Next, the process of deriving the free vibration waveform and vibration characteristics will be explained using the block diagram in FIG.

[0059] The process of deriving this free vibration waveform and vibration characteristics corresponds to the procedure for executing a damping ratio confirmation and adjustment loop, in which the damping ratio is calculated based on the reduction rate of the vibration amplitude of the response amplitude waveform obtained as a result of free vibration analysis by coupled analysis, the magnitude of the Rayleigh damping coefficient of the structural analysis model is adjusted so that the damping ratio becomes the maximum value that is smaller than the set target value, and the damping ratio can be adjusted to below a predetermined threshold by performing free vibration analysis by coupled analysis one or more times.

[0060] As shown in FIG. 3, a damping ratio target value 14, a fluid analysis model 31, a structural analysis model 32, and analysis conditions 16 are input to the input unit 1.

[0061] The calculation unit 2 includes a non-stationary transient analysis unit 26 of the fluid analysis solver 21, a time history dynamic analysis unit 25 of the structural analysis solver 22, and a free vibration analysis unit 27 that performs analysis of free vibration behavior of the coupled analysis solver 23. The coupled analysis solver 23 operates the non-stationary transient analysis unit 26 and the time history dynamic analysis unit 25 in a mutually coupled manner.

[0062] As a result, the display unit 3 displays an upper end displacement waveform 34, and displays vibration characteristics 35 consisting of the natural frequency calculated from the period between the maximum values ​​and the damping ratio ζ2 calculated from the rate of decrease in amplitude between the maximum values.

[0063] Next, the process of deriving the input acceleration-initial imperfection relationship at buckling and the minimum reduction rate γ will be explained using the block diagram in FIG.

[0064] The process of deriving this input acceleration-initial imperfection relationship at buckling and the minimum reduction rate γ corresponds to the procedure of executing a minimum reduction rate derivation loop. By applying different initial imperfections and applying gradually increasing simple harmonic input acceleration that excites the natural frequency of the model, the effect of the initial imperfection can be grasped by performing a single fluid-structure interaction analysis for one case of initial imperfection.

[0065] Furthermore, in the procedure for executing the minimum reduction rate derivation loop, three or more cases of fluid-structure interaction analysis are performed to understand the tendency for the buckling strength to decrease or increase due to the influence of the initial imperfection, and an approximate formula is estimated for the initial imperfection and the input acceleration at buckling, and the minimum reduction rate can be derived based on the approximate formula using a model with no initial imperfection set as the standard.

[0066] Furthermore, in the procedure for executing the minimum reduction rate derivation loop, the minimum reduction rate can be derived based on an analytical model in which the reduction rate of the input acceleration at buckling due to initial imperfections is 95% or more.

[0067] Furthermore, in the procedure for executing the minimum reduction rate derivation loop, it is possible to confirm that the initial imperfection shape is functioning to improve maintainability by finding that the reduction rate of the input acceleration at buckling is less than 99% among multiple buckling analyses performed to understand the influence of the initial imperfection, and that the influence of the initial imperfection is reflected in the evaluation results by finding that the minimum reduction rate is less than 95%.

[0068] The input unit 1 receives the fluid analysis model 31, the structural analysis model 32, the acceleration waveform 17 of the incremental simple harmonic motion, and the results displayed in the vibration characteristics 35, and inputs the damping definition 18 of the Rayleigh damping of the structural analysis model, and receives the results displayed in the buckling eigenmode 33, and inputs the initial imperfection condition 19 consisting of the initial imperfection shape and the initial imperfection amount.

[0069] The coupled analysis solver 23 of the calculation unit 2 includes a buckling analysis unit 28 that analyzes buckling using incremental simple harmonic motion, and performs buckling analysis.

[0070] The display unit 3 displays the results of the buckling analysis unit 28 due to gradually increasing simple harmonic motion as a post-buckling deformation shape 36, which shows a deformation diagram in which the equivalent plastic strain of the neutral plane of the cylindrical tank shell plate is contoured, and the input acceleration at buckling - initial imperfection relationship 37, which shows the influence of initial imperfection.

[0071] Furthermore, when carrying out buckling assessment, the calculation unit 2 defines buckling as the point at which plasticity of elements is recognized in the neutral plane of bending of the cylindrical tank body panel for a portion that deforms by bulging outward due to elephant foot buckling, for example, and by carrying out quantitative buckling assessment, it is possible to assess buckling even for analytical models with defined initial imperfections.

[0072] Furthermore, the minimum reduction rate γ derived as the effect of initial imperfection is displayed on the display unit 3. Here, the minimum reduction rate γ is expressed as γ=Bcr / Bcr0, which is the ratio of the buckling input acceleration Bcr under the condition of no initial imperfection to the minimum buckling input acceleration Bcr.

[0073] Next, the process of deriving the results of seismic analysis will be explained using the block diagram in Figure 5.

[0074] The process of deriving the results of this seismic analysis corresponds to the procedure for determining buckling, and allows the design seismic waveform to be loaded onto a model with no initial imperfections set.

[0075] In addition, the procedure for determining buckling involves monitoring the equivalent plastic strain at the neutral plane of the bottom shell of a cylindrical tank, where wrinkles form as the shell bulges outward due to elephant foot buckling. Buckling can be determined to have occurred when the equivalent plastic strain reaches zero or greater.

[0076] Furthermore, in the procedure for buckling assessment, an amplified design seismic waveform can be loaded onto an analytical model in which the reduction rate of the input acceleration at buckling due to initial imperfections is 95% or more.

[0077] In the input section 1, in addition to the fluid analysis model 31, the structural analysis model 32, and the acceleration waveform 17 of the gradually increasing simple harmonic motion, an evaluation waveform 20 is input, which is the input acceleration waveform 15 multiplied by the reciprocal of the minimum reduction rate γ to increase the amplitude.

[0078] When performing a buckling analysis using an input acceleration waveform, the amplitude of the input acceleration waveform is expanded by multiplying the amplitude of the input acceleration waveform by the inverse of the minimum reduction rate, and the resulting evaluation input waveform is loaded onto an analysis model in which the influence of initial imperfections is small, thereby enabling a buckling evaluation that takes the influence of initial imperfections into maximum consideration.

[0079] The calculation unit 2 includes a seismic analysis unit 29, which performs a buckling analysis.

[0080] The display unit 3 displays a deformation diagram in which the equivalent plastic strain of the neutral plane of the cylindrical tank body plate is contoured as the post-buckling deformation shape 36, and also displays the judgment result 39 as to whether the evaluation object will buckle or not as a result of the series of analyses.

[0081] Next, a buckling evaluation method according to the first embodiment of the present invention will be described with reference to the flowchart shown in Fig. 6. Fig. 6 is a flowchart illustrating a buckling analysis method according to the first embodiment.

[0082] In the following description, a buckling evaluation technique will be described when the method of the first embodiment shown in the flowchart of FIG. 6 is applied to the buckling evaluation device shown in FIGS.

[0083] 6, FIG. 1 is up to steps S31 and S32, FIG. 2 is up to steps S24 and S33, FIG. 3 is up to step S35, FIG. 4 is up to step S38, and FIG. 5 is up to step S39.

[0084] First, in step S11, data on the liquid characteristics of the cylindrical tank to be evaluated is input, in step S12, the dimensions of the cylindrical tank are input, in step S13, the material properties of each part of the cylindrical tank are input, in step S14, the reference damping ratio ζ1 that needs to be set in the vibration evaluation is input, and in step S15, an input acceleration waveform that simulates the seismic waveform to be applied in the buckling evaluation is input.

[0085] A fluid analysis model is created in step S31 based on the content liquid characteristics and dimensions, and a structural analysis model is created in step S32 based on the dimensions and material characteristics.

[0086] In step S270, a free vibration analysis is performed by fluid-structure interaction analysis using the fluid analysis model and the structural analysis model, and the natural frequency is determined in step S350.

[0087] In step S24, a buckling eigenvalue analysis is performed using a structural analysis model, applying an axial compressive load as a unit load, and the resulting buckling eigenmode shape is displayed on the display unit 3 to search for a buckling eigenmode symmetric with respect to the rotation axis, and an initial imperfect shape is created in step S33.

[0088] Next, a description will be given of the loop (damping ratio setting section) that sets the damping ratio of the analytical model and checks whether the damping ratio ζ2≦ζ1.

[0089] In step S18, the Rayleigh damping of the structural analysis model is set based on the natural frequency of the overturning mode of the coupled analysis model obtained in step S350. Since a free vibration analysis was performed in step S270, in step S27, the damping ratio ζ2 is obtained from the waveform of the upper-end response displacement, and in step S34, it is compared with the input reference damping ratio ζ1. If ζ2 > ζ1, the process returns to step S18, adjusts the Rayleigh damping setting again, and steps S18, S27, and S34 are repeated. Note that if ζ2 << ζ1, adjustments can be made to increase the damping to bring it closer to the reference value. Once ζ2 ≦ ζ1 and the damping ratio setting section is completed, in step S35, a damping ratio-adjusted structural analysis model is obtained.

[0090] Next, we will explain the loop (initial imperfection effect consideration part) that derives the minimum reduction rate γ, which is the initial imperfection effect to maximize the effect of reducing the buckling strength due to the influence of initial imperfections in buckling analysis.

[0091] In the initial imperfection setting in step S19, a structural analysis model in which the initial imperfection is adjusted is created by multiplying the initial imperfection shape in step S33 by a coefficient with respect to the structural analysis model whose damping ratio has been adjusted in step S35.

[0092] In the buckling analysis using gradually increasing simple harmonic motion in step S28, the coupled analysis model consisting of the structural analysis model and fluid analysis model for which initial imperfections were set in step S19 is subjected to an input load of an acceleration waveform of simple harmonic motion with gradually increasing amplitude at the natural frequency of the overturning mode.

[0093] In the evaluation of the input acceleration at buckling in step S36, the maximum value of the input acceleration amplitude immediately before buckling occurs is grasped as the input acceleration at buckling.

[0094] In the calculation of the reduction rate in step S37, the reduction rate is calculated by comparing the buckling input acceleration obtained in the evaluation of the buckling input acceleration in step S36 with the buckling input acceleration obtained in an analysis without the influence of initial imperfections. Here, the calculation of the reduction rate in steps S19, S28, S36, and S37 is repeated until the minimum reduction rate is obtained.

[0095] Based on the results of multiple analyses in which the initial imperfections are changed, the relationship between the input acceleration at buckling and the initial imperfections is determined, and the minimum reduction rate is derived in step S38. In step S20, the evaluation waveform generation is performed by multiplying the amplitude of the input acceleration waveform in step S15 by the reciprocal of the minimum reduction rate in step S38 to generate an evaluation waveform with an expanded amplitude.

[0096] In step S20, the generated evaluation waveform (input acceleration waveform 15 / γ) is input, and in the seismic analysis in step S29, a coupled analysis model for fluid structure is constructed from the damping-adjusted structural analysis model in step S35 and the fluid analysis model in step S31.

[0097] In the buckling assessment in step S39, if the result of the buckling assessment in step S29 is that buckling does not occur, the cylindrical tank being assessed will not buckle in response to the input acceleration waveform in step S15. This assessment has high safety in both vibration analysis and buckling analysis.

[0098] On the other hand, if it is judged that buckling will occur, a review is necessary (step S40), so the process returns to the start and buckling evaluation is performed again.

[0099] Next, the effects of this embodiment will be described.

[0100] The first embodiment of the present invention described above includes an implicit fluid analysis solver, an implicit structural analysis solver, and a coupled analysis solver capable of coupling the two solvers. The damping ratio is adjusted by performing multiple free vibration analyses to set the damping ratio as a vibration analysis model. To account for the effects of initial imperfections, the buckling analysis model is performed multiple times using an acceleration waveform of a simple harmonic motion with gradually increasing amplitude as the input acceleration, thereby deriving the minimum reduction rate of the input acceleration at buckling. Therefore, by multiplying the input acceleration waveform used in seismic evaluation by the reciprocal of the minimum reduction rate, buckling evaluation with high safety is possible. Since the buckling analysis using fluid-structure coupled analysis can obtain a solution close to the actual capacity, it is assumed that a safe response can be achieved by setting a damping ratio lower than the actual value and that a safe buckling strength can be simulated by accounting for the effects of initial imperfections. This makes it possible to design a flat-bottom, vertical cylindrical tank for storing water, the bottom of which is fixed to the ground by bolts or the like, so as to prevent damage during an earthquake.

[0101] Furthermore, with regard to the maintainability of vibration analysis, the damping setting section can set a vibration model with a damping ratio that is empirically considered to be sufficiently small as defined by standards, etc., thereby improving maintainability. As a result, with regard to the maintainability of buckling analysis, the initial imperfection influence consideration section obtains the minimum reduction rate when the input acceleration at buckling is reduced the most due to the influence of initial imperfections, and multiplies the input acceleration waveform by the reciprocal of this minimum reduction rate to create an evaluation waveform, thereby improving the maintainability of seismic analysis.

[0102] Furthermore, by performing a buckling assessment on the results of the seismic analysis described above, conservative buckling analysis results can be obtained for the case in which the original input acceleration waveform (design seismic wave) acts on the cylindrical tank being evaluated.

[0103] Furthermore, the above-mentioned buckling evaluation results are close to the actual results obtained by applying fluid-structure interaction analysis, and can improve maintainability from the standpoint of both vibration evaluation and buckling evaluation.

[0104] <Example 2> Second Embodiment A buckling evaluation method and a buckling evaluation device for a cylindrical tank according to a second embodiment of the present invention will be described.

[0105] In the first embodiment, when checking and adjusting the damping ratio, the calculated damping ratio ζ2 must be equal to or less than the reference damping ratio ζ1. However, when considering the stability of the fluid-structure interaction analysis, it is conceivable that there may be models that cannot satisfy this requirement.

[0106] In this case, the following changes are made to the method described in Example 1. Specifically, in the procedure for executing the damping ratio confirmation / adjustment loop, if the damping ratio does not fall below the set value, the adjustment loop is not continued and the amplitude of the evaluation input wave is increased by the difference in the response magnification.

[0107] Since the flow is only partially changed, the diagram is omitted.

[0108] First, the conditions leading to step S35 for obtaining a damping ratio adjusted structural analysis model are eliminated, and only the current ζ2 is grasped.

[0109] Next, the amplitude of the evaluation waveform 20 is expanded by the ratio between the response magnification of the single-degree-of-freedom system at the reference damping ratio ζ1 and the response magnification of the single-degree-of-freedom system at the damping ratio ζ2.

[0110] This offsets the effect of a high damping ratio that reduces the response magnification, allowing for highly safe evaluation.

[0111] The other configurations and operations are substantially the same as those of the buckling evaluation method and buckling evaluation device of the first embodiment, and details thereof will be omitted.

[0112] The buckling evaluation method and buckling evaluation device of Example 2 of the present invention also achieve substantially the same effects as those of the buckling evaluation method and buckling evaluation device of Example 1 described above, and can be configured to be able to offset the effects of an increased damping ratio even if the damping ratio of the coupled analysis model exceeds a reference value.

[0113] Example 3 Third Embodiment A buckling evaluation method and a buckling evaluation device for a cylindrical tank according to a third embodiment of the present invention will be described.

[0114] In the first and second embodiments, it is necessary to understand the relationship between the input acceleration at buckling and the initial imperfection for all cylindrical tanks and derive the minimum reduction rate γ.

[0115] However, cylindrical tanks generally have similar shapes, and by repeating buckling evaluations on various cylindrical tanks, it is thought that it will be possible to roughly estimate the minimum reduction rate γ from the dimensional characteristics.

[0116] Therefore, in this embodiment, the procedure for executing the minimum reduction rate derivation loop involves determining the minimum reduction rate in advance for cylindrical tanks of different dimensions, deriving an approximate formula for calculating the minimum reduction rate based on the dimensions of the cylindrical tank, and then deriving the minimum reduction rate using the approximate formula.

[0117] That is, instead of deriving the minimum reduction rate γ each time, a plurality of minimum reduction rates are derived in advance for cylindrical tanks of similar structure, and an approximate formula for deriving the minimum reduction rate from dimensional information is provided, whereby γ for the cylindrical tank being evaluated is estimated from the relationship between the minimum reduction rate γ for a cylindrical tank that has already undergone buckling evaluation and the cylindrical tank dimensions.

[0118] In this case, the method shown in the first embodiment is modified as follows.

[0119] Since the flow is only partially changed, the diagram is omitted.

[0120] First, the initial imperfection influence consideration part consisting of step S24, step S33 and step S28 is deleted.

[0121] At this position, a step of deriving the minimum reduction rate based on the relational expression between the cylindrical tank dimensions and the minimum reduction rate γ is added.

[0122] The other configurations and operations are substantially the same as those of the buckling evaluation method and buckling evaluation device of the first embodiment, and details thereof will be omitted.

[0123] The buckling evaluation method and buckling evaluation device according to the third embodiment of the present invention also provide substantially the same effects as those of the buckling evaluation method and buckling evaluation device according to the first embodiment described above.

[0124] <Other> It should be noted that the present invention is not limited to the above-described embodiment, and includes various modifications. The above-described embodiment has been described in detail to clearly explain the present invention, and the present invention is not necessarily limited to an embodiment having all of the described configurations.

[0125] It is also possible to replace part of the configuration of one embodiment with the configuration of another embodiment, or to add the configuration of another embodiment to the configuration of one embodiment, or to add, delete, or replace part of the configuration of each embodiment with the configuration of another embodiment.

[0126] For example, in the examples described so far, the evaluation of the influence of initial imperfections is based on the analysis results without adding initial imperfections.

[0127] In cylindrical tanks, initial imperfections of less than 1 / 10 of the wall thickness have an almost negligible effect, so instead of comparing with the analysis results without adding initial imperfections, Cases where the initial irregularities are almost negligible can be used.

[0128] In addition, in the procedure for buckling assessment, instead of performing a time history analysis using fluid-structure coupled analysis when performing buckling assessment, for example, an analysis is performed in which an evaluation input wave whose amplitude is multiplied by the inverse of the minimum reduction rate is applied to a single-degree-of-freedom system having a natural frequency of a cylindrical tank overturning mode, and the maximum response displacement is obtained.The response displacement at the time of buckling of the fluid-structure coupled analysis model obtained when obtaining the input acceleration at buckling - initial imperfection relationship is then compared with the maximum response displacement, and if the response displacement of the single-degree-of-freedom system is smaller than the response displacement at the time of buckling, it is determined that buckling will not occur, and if the maximum response displacement exceeds the response displacement at the time of buckling, it can be determined that buckling has occurred. [Explanation of symbols]

[0129] 1: Input section 2: Arithmetic section 3: Display section 11: Content liquid characteristics 12: Dimensions 13: Material properties 14: Damping ratio target value 15: Input acceleration waveform 16:Analysis conditions 17: Acceleration waveform of gradually increasing simple harmonic motion 18: Attenuation definition 19: Initial irregularity conditions 20: Evaluation waveform 21:Fluid analysis solver 22: Structural analysis solver 23: Coupled analysis solver 24: Buckling eigenvalue analysis section 25: Time history dynamic analysis section 26: Unsteady transient analysis section 27: Free vibration analysis department 28: Buckling analysis by incremental simple harmonic motion 29: Seismic analysis department 31: Fluid analysis model 32: Structural analysis model 33: Buckling eigenmode 34: Upper end displacement waveform 35: Vibration characteristics 36: Post-buckling deformation shape 37: Buckling input acceleration-initial imperfection relationship 39: Judgment result 50: Buckling evaluation device Bcr: Input acceleration at buckling Bcr0: Input acceleration at buckling ζ1: Reference damping ratio ζ2: Calculated damping ratio γ: Minimum reduction rate

Claims

1. A buckling assessment method assuming a case where an earthquake load acts on a cylindrical tank, In an evaluation based on an implicit, weakly coupled fluid-structure interaction analysis, a step of executing a damping ratio confirmation and adjustment loop for adjusting the damping ratio of the coupled analysis model to a predetermined threshold value or less; a step of executing a minimum reduction rate derivation loop for deriving a minimum reduction rate of the input acceleration at buckling; and a procedure of applying a design earthquake waveform obtained by multiplying the acceleration amplitude of the design earthquake waveform by the reciprocal of the minimum reduction rate to increase the amplitude to the model that has completed the damping ratio confirmation and adjustment loop, thereby performing a buckling judgment. Buckling assessment method for cylindrical tanks.

2. The method for evaluating the buckling of a cylindrical tank according to claim 1, In the procedure for determining buckling, the design seismic waveform is applied to a model with no initial imperfections set. Buckling assessment method for cylindrical tanks.

3. The method for evaluating the buckling of a cylindrical tank according to claim 1, In the step of executing the damping ratio confirmation and adjustment loop, calculating the damping ratio based on a reduction rate of the vibration amplitude of the response amplitude waveform obtained as a result of the free vibration analysis by the coupled analysis; The magnitude of the Rayleigh damping coefficient of the structural analysis model is adjusted so that the damping ratio becomes a maximum value that is smaller than the set target value, The damping ratio is adjusted to be equal to or less than the predetermined threshold value by performing free vibration analysis by the coupled analysis at least once. Buckling assessment method for cylindrical tanks.

4. The method for evaluating the buckling of a cylindrical tank according to claim 1, In the procedure for executing the minimum reduction rate deriving loop, By adding different initial imperfections to excite the natural frequency of the model and applying gradually increasing simple harmonic input acceleration, the influence of the initial imperfections can be understood by performing one fluid-structure interaction analysis for each case of initial imperfection. Buckling assessment method for cylindrical tanks.

5. The method for evaluating the buckling of a cylindrical tank according to claim 4, In the procedure for executing the minimum reduction rate deriving loop, Furthermore, the fluid-structure interaction analysis is performed for three or more cases to understand the tendency of the buckling strength to decrease or increase due to the influence of the initial imperfection, and an approximate formula is estimated for the initial imperfection and the input acceleration at the time of buckling, and the minimum reduction rate is derived based on the approximate formula using a model in which the initial imperfection is not set as a reference. Buckling assessment method for cylindrical tanks.

6. The method for evaluating the buckling of a cylindrical tank according to claim 1, In the procedure for executing the minimum reduction rate derivation loop, the minimum reduction rate is derived based on an analysis model in which the reduction rate of the input acceleration at buckling due to initial imperfection is 95% or more. Buckling assessment method for cylindrical tanks.

7. The method for evaluating the buckling of a cylindrical tank according to claim 1, In the procedure for determining buckling, the equivalent plastic strain of the neutral plane of the bottom shell of the cylindrical tank, where wrinkles bulge outward due to elephant foot buckling, is monitored, and buckling is determined to have occurred when the equivalent plastic strain is equal to or greater than zero. Buckling assessment method for cylindrical tanks.

8. The method for evaluating the buckling of a cylindrical tank according to claim 1, In the procedure for determining buckling, the amplified design seismic waveform is loaded onto an analysis model that has an initial imperfection effect in which the reduction rate of input acceleration at the time of buckling due to initial imperfection is 95% or more. Buckling assessment method for cylindrical tanks.

9. The method for evaluating the buckling of a cylindrical tank according to claim 1, In the procedure for executing the minimum reduction rate deriving loop, It was confirmed that the initial imperfection shape was functioning to improve maintainability by finding cases in which the reduction rate of the input acceleration at buckling was less than 99% in multiple buckling analyses conducted to understand the influence of the initial imperfections. It is confirmed that the impact of initial imperfections is reflected in the evaluation results by checking that the minimum reduction rate is less than 95%. Buckling assessment method for cylindrical tanks.

10. The method for evaluating the buckling of a cylindrical tank according to claim 1, In the procedure for executing the minimum reduction rate derivation loop, the minimum reduction rate is determined in advance for cylindrical tanks of different dimensions, an approximate formula for calculating the minimum reduction rate is derived based on the dimensions of the cylindrical tank, and the minimum reduction rate is derived using the approximate formula. Buckling assessment method for cylindrical tanks.

11. The method for evaluating the buckling of a cylindrical tank according to claim 1, In the step of executing the damping ratio confirmation / adjustment loop, if the damping ratio does not fall below a set value, the adjustment loop is not continued and the amplitude of the evaluation input wave is increased by the difference in the response magnification. Buckling assessment method for cylindrical tanks.

12. The method for evaluating the buckling of a cylindrical tank according to claim 1, In the procedure for determining buckling, an analysis is performed in which an evaluation input wave whose amplitude is multiplied by the reciprocal of the minimum reduction rate is applied to a single-degree-of-freedom system having a natural frequency of the cylindrical tank overturning mode, and the maximum response displacement is obtained.The response displacement at the time of buckling of the fluid-engine coupled analysis model obtained when obtaining the input acceleration at buckling - initial imperfection relationship is then compared with the maximum response displacement.If the response displacement of the single-degree-of-freedom system is smaller than the response displacement at the time of buckling, it is determined that buckling will not occur, and if the maximum response displacement exceeds the response displacement at the time of buckling, it is determined that buckling has occurred. Buckling assessment method for cylindrical tanks.

13. A buckling evaluation device that assumes a case where an earthquake load acts on a cylindrical tank, In an evaluation based on an implicit, weakly coupled fluid-structure interaction analysis, A damping ratio check and adjustment loop is executed to adjust the damping ratio of the coupled analysis model to a predetermined threshold or less. Execute a minimum reduction rate derivation loop to derive a minimum reduction rate of the input acceleration at buckling; The design earthquake waveform is multiplied by the reciprocal of the minimum reduction rate to increase the acceleration amplitude of the design earthquake waveform, and the resulting waveform is loaded onto the model that has completed the damping ratio confirmation and adjustment loop to determine buckling. Cylindrical tank buckling evaluation device.

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