JP2002056036A - Buckling analysis method of structure - Google Patents

Abstract

PROBLEM TO BE SOLVED: To make the safety design and buckling analysis working for the buckling of a structure efficient by effectively utilizing an analysis method using a decrease stiffness method. SOLUTION: A linear buckling analysis is performed by a computer up to an order where the whole linear buckling load PL of the structure becomes 1.5 times as large as a primary PL at the largest, the lower limit PL* of the whole buckling load of the structure is next calculated with the decrease stiffness method by using the computer, all primary buckling modes are selected among all orders in which the calculation is performed, the existence/absence of an order buckling mode in which the PL* is smaller than the primary PL* is decided, when the smaller order buckling mode exists, adoption is selected, an order buckling mode that is subjected to shape similarity to deformation shape due to the whole linear stress analysis of the structure is also selected and set as initial imperfections corresponding only to the selected order buckling mode, and nonlinear buckling analysis is carried out.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a buckling analysis method for a structure having a spherical shell structure or a cylindrical shell structure made of a continuous body or a discontinuous body.

[0002]

2. Description of the Related Art Structures having a spherical shell structure or a cylindrical shell structure made of a continuum or discontinuous body have a non-buckling non-linearity caused by an initial shape irregularity or a load irregularity (hereinafter referred to as "initial irregularity"). Is expected to reduce the in-plane rigidity due to the influence of, which leads to a reduction in buckling load. Conventionally, the degree of the reduction of the buckling load due to the initial imperfection of such a structure cannot be predicted unless the initial imperfection is appropriately set and a nonlinear buckling analysis is performed. In the setting of the initial irregularities, the distribution shape and the size of the irregularities can be assumed to be innumerable, but a reasonable and appropriate method for evaluating the initial irregular shapes has not been established.

The procedure of a conventional buckling analysis method will be described with reference to FIG. Data relating to the structure is input by 31 data input means and stored in the design data storage means 32.
Structural design calculating means 34 based on the stored design data
Defines the basic structure. Further, based on the basic structure, an analysis model and analysis conditions of the structure are set by the analysis model creation means 33, and the linear static deformation shape, the linear buckling load and the linear buckling mode are set in the linear structure analysis means 35. It is calculated and stored in the analysis result storage means 36.
Next, based on the analysis result, the initial irregular shape is appropriately set by the initial irregular shape setting means 37, the nonlinear structural analysis means 38 is executed, the buckling evaluation is performed by the buckling evaluation means 39, and the result is output by the output means 40. Is output. Then, the non-linear structural analysis means 38 is executed again for a plurality of initial irregular shapes, and the procedure of the buckling evaluation means 39 and the output means 40 is sequentially repeated. If it is determined that buckling occurs in the buckling evaluation means 39, the member data or material data is changed, and a series of procedures are repeated from the data input means 31 to perform an analysis operation again. Will be

[0004]

In this conventional buckling analysis method, the initial irregular shape must be appropriately set from among a myriad of possible initial irregularities, but it most contributes to the reduction of the buckling load. Since an evaluation method of the initial irregular shape to be performed has not been established, the designer's empirical judgment largely depends on safety. In addition, since the safety was considered more than necessary, performing the non-linear structural analysis for all of the assumed buckling modes was an enormous amount of analysis work, and required time and effort.

Meanwhile, a technique for predicting the lower limit of the buckling load that decreases due to the influence of the initial irregularity, a reduced stiffness method (Redu
ced Stiffness method, hereinafter referred to as “RS method”, and the lower limit of the buckling load obtained by the same method is referred to as “RS value”. Effective use for buckling analysis has not been sufficient. In addition, the analysis by the RS method requires specialized knowledge about a program and the RS method, and is difficult for a general structural designer to handle.

SUMMARY OF THE INVENTION The present invention has been made in view of the above-mentioned problems of the prior art, and has a spherical shell structure or a cylindrical structure made of a continuous body or a discontinuous body by effectively utilizing an analysis method using the RS method. By selecting the order of the buckling mode in a structure having a buckling mode, setting an initial imperfection corresponding only to the selected buckling mode, and performing a non-linear buckling analysis, safety design against buckling and buckling analysis work The aim is to improve the efficiency of

[0007]

A buckling analysis method for a structure according to the present invention is a method for analyzing a structure such as a spherical shell structure or a cylindrical shell structure made of a continuous body or a discontinuous body by using a reduced rigidity method. calculated an analysis method for buckling analyzed by linear buckling load P _L of the entire structure is a computer linear buckling up to order to be 1.5 times at most to the primary of the P _L Then, the lower limit value P _L ^* of the buckling load of the entire structure is calculated by a computer using the reduced stiffness method, and the first-order overall buckling mode is selected from all the calculated orders. Then, the presence or absence of a buckling mode of an order in which P _L ^* is smaller than the first-order P _L ^* is determined, and if there is a buckling mode of a smaller order, the buckling mode is adopted and selected, and a linear stress analysis of the entire structure is performed. Buckling mode of similar order to the deformed shape due to Set as the corresponding initial imperfection only order buckling mode, and performs non-linear buckling analysis.

Further, the above-mentioned buckling analysis method for a structure is based on data input means for inputting data on the structure, design condition data storage means for storing the data and constructing a design condition database, and based on the data. A basic structure design database for constructing a basic structural condition database and storing it in a structural design calculation result file; and an analytical model creating unit for creating an analysis condition for the structure and constructing an analytical condition database. A buckling experiment / measurement database and RS buckling lower limit database that can be applied to the basic structure are constructed, search means for searching the above database is provided, and linear stress analysis and linear buckling analysis are performed based on the above data. Perform buckling analysis using the linear stress analysis means and linear buckling analysis means stored in the structural analysis result file and the reduced stiffness method. R to be stored in RS analysis results file
S analysis means, RS value determination means for determining the lower limit of the buckling load, initial irregular shape setting means for setting the initial irregularity from the selected buckling mode, and non-linear structural analysis on the set initial irregular shape A non-linear structural analysis means stored in a non-linear structural analysis file, an RS buckling evaluation means for performing buckling evaluation based on the non-linear structural analysis result and storing the result in the database and the file, and an output means for outputting the result. And a computer processing system having the same.

[0009]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of a buckling analysis method for a structure according to the present invention will be described with reference to FIGS. 1 to 5 and Tables 1 to 3. FIG.

FIG. 1 shows a reduced stiffness method.
FIG. 3 is a functional block diagram showing a procedure of an analysis method using the method “RS method”), which includes a data input unit 11, a design condition data storage unit 12, an analysis model creation unit 13, a structural design calculation unit 14, a search unit 15, Database D, File F,
Linear stress analysis means 16, linear buckling analysis means 17, RS analysis means 18, RS value determination means 19, initial irregular shape setting means 20, nonlinear structure analysis means 21, RS buckling evaluation means 2
2. It comprises output means 23 and the like.

FIG. 2 is an analysis flow of the RS method, showing the contents of the RS analysis means 18 shown in FIG. In order to perform RS analysis, first, a general-purpose structural analysis code (for example, C
OSMOS / M: using trademark), previously obtained the entire structure of the linear buckling load P _L of at the linear buckling analysis means 17 to the n-th order. Then, the linear stiffness matrix [K _L obtained a plane axes rigidity reduced by pre imperfections as zero
^*] And strain energy U ^* with, an energy U was calculated strain using conventional linear stiffness matrix [K _L], "RS value 'from the energy quotient, i.e. the entire structure by RS Analysis buckling Calculate the lower limit value P _L ^* of the load.

The order n for calculating the linear buckling load is:
Compared to the primary of the P _L values, by performing up to order n which is 1.5 times the P _L value at most, typically, be a material strength safety factor of the steel is 1.5 times, and short-term permissible stress Judging from the fact that the degree is 1.5 times the long-term allowable stress level, etc., this is a rational and optimal selection criterion for examining buckling strength and performing safety design of a structure. Then, an order in which the calculated P _L ^* is smaller than the first-order P _L ^* , for example, a value of about 90% or less, that is, an order in which the RS value becomes extremely small is determined. Then, the the calculated total order buckling mode, first-order and overall buckling mode, the P _L ^* is primary P _L ^* Small and order buckling mode than, and the structure of the entire linear stress A buckling mode of an order similar to the shape of the deformed shape by analysis is selected. The primary buckling mode selected above is a mode in which the buckling load in the linear buckling analysis is minimized, and is one of the shapes most likely to occur when a load is applied to the structure. This is an important mode for stable stability evaluation. The selected buckling mode in which P _L ^* is significantly reduced is a mode in which the in-plane strain energy component is large, and the buckling load may be significantly reduced due to the initial irregularity. Furthermore, the buckling mode of the order similar to the deformed shape by the linear stress analysis of the entire selected structure is most likely to occur when a load is applied to the structure, similarly to the first buckling mode. Although it is one of the shapes, the shape is not necessarily similar to the first-order buckling mode. Only the buckling mode of the order selected as described above is set as the corresponding initial imperfection, and by performing nonlinear buckling analysis, analysis time can be reduced and buckling evaluation of structures can be performed efficiently. Becomes The above P _L
^{If *} does not have a buckling mode of a smaller order than the first order P _L ^* , there is no need to select.

FIG. 3 shows an example of a hardware configuration of a computer processing system for executing the buckling analysis method. The main control unit 1, the input / output control unit 2, the input device 4, the storage device 3, and the display device 5 and an output device 6. The storage device 3 stores the design condition database D
1. Basic structure database D2, analysis condition database D3, experiment / measurement database D4, database D such as RS buckling lower limit database D5, structural design calculation result file F1, linear structure analysis result file F2,
Files F such as a nonlinear structural analysis result file F3, an RS analysis result file F4, and an RS buckling evaluation result file F5, as well as a structural design program P1, a linear stress analysis program P2, a linear buckling analysis program P3, a nonlinear structural analysis program P4, A program P such as an RS analysis program P5 is stored.

The procedure of the computer processing system for executing the structure buckling analysis method according to the present invention will be described in further detail with reference to the functional block diagram of FIG. Design condition data such as the shape, dimensions, constituent members, and design loads of the structure for which buckling analysis is to be performed are input by the data input means 11, and these data are stored in the design condition data storage means 12, and the design condition database It is stored in D1. Based on the stored design condition data, the basic structure is determined by the structural design calculation means 14 (P1) and stored in the basic structure database D2 and the structural design calculation result file F1, respectively.

Here, the search means 15 searches the design condition data D1 and the basic structure database D2 for design condition data and basic structure data equivalent to or similar to the design condition data and the basic structure data, respectively. If the data exists, the experimental / measurement data and the RS buckling lower limit data on the buckling applicable to the basic structure are respectively stored in the experiment / measurement database D4.
And from the RS buckling lower limit value database D5, and immediately proceeds to the buckling evaluation means 22 based on the extracted data to perform buckling evaluation on the design conditions of the basic structure. When it is determined that buckling of the entire structure does not occur, the buckling evaluation result is output by the output unit 23 and the process is terminated. Therefore, buckling is immediately performed from the accumulated data without performing buckling analysis. Crouching evaluation becomes possible. Where R
When it is determined that buckling occurs in the S buckling evaluation means 22, the process returns to the beginning, changes the design condition data and the like, and repeats a series of procedures from the data input means 11.

If the search means 15 finds no corresponding design condition data and basic structure data, the analysis model and the analysis condition of the structure are analyzed based on the design condition data and the basic structure data. 1
3 and stored in the analysis condition database D3. Based on the analysis condition data, the linear static deformation shape, the linear buckling load, and the linear buckling mode are respectively determined by the linear stress analysis means 16 (P2) and the linear buckling mode. It is calculated by the buckling analysis means 17 (P3) and stored in the linear structure analysis result file F2. Next, RS analysis is performed by the RS analysis means 18 (P5) using the linear buckling analysis result stored in the file F2, and the result is stored in the RS analysis result file F4. At this time,
Regarding the determination of the target order for executing the RS analysis, the linear buckling analysis load is 1.5 times at most the primary linear buckling load.
Up to the order that is doubled.

Next, from the RS analysis result, the first order R
If an S value is selected, and a buckling mode similar in shape to the static deformation shape calculated by the linear stress analysis means 16 (P2) exists, an RS value of that order is selected.
When the value judging means 19 (P5) detects an RS value smaller than the primary RS value, the RS value of this order is selected and stored in the RS buckling lower limit database D5. And the linear buckling mode of the order giving the RS value is extracted as an initial irregular shape.

The extracted initial irregular shape is normalized by the maximum initial irregular amplitude value by the initial irregular shape setting means 20, and is set as the initial irregular shape. Here, for example, in the case of a single-layer lattice shell structure, it is sufficient to consider the maximum initial irregular amplitude value up to about three times the secondary radius of the cross section of the component. For each of the set initial irregular shapes, the nonlinear structure analysis is performed by the nonlinear structure analysis means 21 (P4), and stored in the nonlinear structure analysis result file F3.

The buckling evaluation is performed by the RS buckling evaluation means 22 (P5) from the result of the nonlinear structural analysis, and the result is stored in the RS buckling evaluation result file F5. It is only necessary to set an initial irregular shape corresponding to only the buckling mode of a very limited order selected in this way, and it is predicted that the set initial irregular shape will greatly contribute to a reduction in the buckling load of the entire structure. Therefore, if a non-linear buckling analysis is performed on this initial irregular shape, a reasonable buckling evaluation can be obtained.
In this buckling evaluation, if it is confirmed that the buckling load does not fall below the RS buckling lower limit value and the design load by the nonlinear structural analysis, it is determined that buckling does not occur. The buckling evaluation result is output.
However, if the buckling load obtained by the nonlinear structural analysis is lower than the design load, it is determined that buckling will occur, and the procedure returns to the beginning, changes the design condition data, and returns to the data input means 11 again. repeat.

An analysis model shown in Table 1 and FIG. 4 (case 1)
Table 2 shows the results of the above buckling analysis performed on The analysis model of Case 1 is a case of a shell or a single-layer lattice structure “lattice shell structure” of a spherical shell structure composed of a continuous body or a discontinuous body. A spherical dome with joined units. In this case 1, the order n for performing the RS analysis is the first order P
Up to a maximum degree which is 1.5 times the _{P L} with respect to _L, i.e. primary _{P L} value 3.097 1.5 times greater than 4.922 with respect to the order, by calculating up to seventh order I just need.
Note that, in this case 1, the values are calculated and displayed up to the 10th order for reference.

The buckling mode selected from the calculated buckling modes of all orders is the first-order overall buckling mode, and the analysis value “RS value” P _L ^* by the RS method is the first-order P _L ^*. And a buckling mode of an order similar to the deformed shape obtained by linear stress analysis of the entire structure. In case 1 above, as shown in Table 2,
P _L ^* is selected because it is smaller at one place of the sixth order.
Since the secondary value is close to the primary value, the secondary value is selected in consideration of safety, and a total of three orders are selected in combination with the primary value.

FIG. 5 shows a linear buckling mode selected from ten first-order to tenth-order buckling analysis of the analysis model of Case 1 described above. As shown in FIG. 5, the shape of the initial irregularities that can greatly contribute to the reduction of the buckling load is relatively linear and linear with a large wavelength (peaks and valleys or gaps between valleys and valleys). It can be predicted that the shape corresponds to the buckling mode, that is, the selected first-order, second-order, and sixth-order linear buckling modes. In the case of the analysis model of Case 1, there was no buckling mode having a shape similar to the deformed shape obtained by the linear stress analysis of the entire structure. Then, the total of the selected primary, secondary and sixth order is 3
Non-linear buckling analysis may be performed only for a small number of buckling modes, that is, three.

Although not shown, for example, in the case of an analytical model of a roof-type single-layer cylindrical lattice shell in which steel pipe members are rigidly connected to an isosceles triangle, the second-order linear buckling mode is linear static deformation. It became the shape similar to. As described above, when a buckling mode of an order similar to the shape is generated in the deformed shape by the linear stress analysis of the entire structure, the nonlinear buckling analysis is performed on the initial irregular shape corresponding to the buckling mode of this order. In the case of the analysis model of this case, a nonlinear buckling analysis is performed by setting initial imperfections corresponding to a total of two buckling modes of the first order and the second order, and the buckling evaluation is rationally performed. I was able to.

Next, for comparison, for example, a conventional example in which nonlinear buckling analysis is performed on all calculated orders, and a buckling analysis method according to the present invention using the RS method, the order is selected and the nonlinear buckling analysis is performed. Table 3 shows the results of a trial calculation of the required analysis time when buckling analysis was performed. Case 1 is shown in Table 1 above.
In addition, a trial calculation was made for the case of the analysis model shown in FIG. 4, and in case 2, a trial calculation was performed for a structure similar to that of case 1, that is, a large-scale dome (dome having a span of about 200 m) having a rigid-shell single-layer lattice shell structure. is there.

As shown in Table 3, according to the buckling analysis method according to the present invention using the RS method, in case 1, three cases out of ten orders, and in case two, five cases out of 80 orders,
A nonlinear buckling analysis may be performed, and the time required for analysis is reduced by about 70% in case 1 and about 94% in case 2.

[0026]

As is clear from the description, the present invention
The buckling analysis method according to
_LIs the first P_LOrder at most 1.5 times
Perform linear buckling analysis by computer until then, then reduce
Lower limit of buckling load P by rigidity method_L ^* On a computer
Calculated and, of all orders for which the calculation has been performed, the entire first order
Selection of buckling mode and P_L ^*Is the primary P_L ^*than
The presence or absence of a buckling mode of a small order is determined,
If there are a number of buckling modes, select and adopt
Locus of order similar to deformed shape by linear stress analysis of body
Selects the bending mode, which can lead to countless possible initial imperfections
Most likely to occur when a load is applied to the structure for the shape
It can be set reasonably and easily as an easy-to-use shape.
The appropriate buckling mode from the viewpoint of the safety design of the structure.
It becomes possible to select. And the selected less
Initial imperfections corresponding only to buckling modes of number order
Buckling analysis can be performed by setting
Analytical work time is greatly reduced, efficient and economical buckling solution
Analysis can be performed.

In the buckling analysis method, design condition data such as a structure to be analyzed and past analysis examples, analysis condition data, experiment / measurement data, and RS buckling lower limit data are constructed as a database. Search for data related to the structure to be analyzed from the database, and link the files such as linear structure analysis and linear buckling analysis with the RS analysis method and their calculation results and analysis results by computer processing. By systemizing the process up to evaluation, a more rational structural design can be realized. In addition, even a general structural designer can easily perform calculation by the reduced stiffness method, and can efficiently perform structural analysis in a short time.

[0028]

[Brief description of the drawings]

FIG. 1 is a system diagram showing a procedure of a buckling analysis method according to the present invention.

FIG. 2 is an explanatory diagram showing an analysis flow of the RS method.

FIG. 3 is an explanatory diagram illustrating an example of a hardware configuration of a computer processing system that executes a buckling analysis method.

FIG. 4 is an explanatory plan view showing an example of an analysis model.

FIG. 5 is an explanatory plan view showing a linear buckling mode of the analysis model of FIG. 4;

FIG. 6 is an explanatory view showing a procedure of a conventional buckling analysis method.

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 1 Main control part 2 Input / output control part 3 Storage device 4 Input device 5 Display device 6 Output device 11 Data input means 12 Design condition data storage means 13 Analysis model creation means 14 Structural design calculation means 15 Search means 16 Linear stress analysis means 17 Linear buckling analysis means 18 RS analysis means 19 RS value determination means 20 Initial irregular shape setting means 21 Nonlinear structure analysis means 22 RS buckling evaluation means 23 Output means 31 Data input means 32 Design condition data storage means 33 Analysis model creation means 34 Structural design calculation means 35 Linear structure analysis means 36 Analysis result storage means 37 Initial irregular shape setting means 38 Nonlinear structure analysis means 39 Buckling evaluation means 40 Output means

 ────────────────────────────────────────────────── ─── Continuing from the front page (72) Inventor Akiko Utsumi 6-5-1 Higashi-Kojiya, Ota-ku, Tokyo F-term in Ishii Iron Works Co., Ltd. 5B046 JA08 KA05

Claims (2)

[Claims] 1. A spherical shell structure comprising a continuous body or a discontinuous body.
Uses the reduced stiffness method to control structures such as cylindrical shells.
This is an analysis method for calculating and buckling analysis using a computer.
Linear buckling load P of the whole object_LIs the first P_LUp to
But the linear buckling analysis is calculated up to the order of 1.5 times.
Buckling of the entire structure using the reduced stiffness method
Lower limit P of weight_L ^*Is calculated by a computer, and the calculation is
Selection of the first-order overall buckling mode from all the orders performed
And the above P_L ^*Is the primary P_L ^* Buckling of orders less than
Mode is determined, and the buckling mode of the small order is
In some cases, adoption selection and linear stress analysis of the entire structure
Buckling mode of similar order to the deformed shape
And only for the buckling mode of the selected order
Specially, it is set as an initial imperfection and a nonlinear buckling analysis is performed.
A buckling analysis method for a structure. 2. The buckling analysis method for a structure includes data input means for inputting data relating to the structure, design condition data storage means for storing the data and constructing a design condition database, and based on the data. Design the basic structure
A structural design calculation means for building a basic structure condition database and storing it in a structural design calculation result file, and an analysis model creation means for creating an analysis condition of a structure and constructing an analysis condition database are provided, and are applicable to the basic structure. A buckling experiment / measurement database and RS buckling lower limit database are constructed, search means for searching these databases is provided, and linear stress analysis and linear buckling analysis are performed based on the above data, and a linear structure analysis result file is generated. Linear stress analysis means and linear buckling analysis means to be stored, RS analysis means to perform buckling analysis by the reduced stiffness method and to be stored in an RS analysis result file, and RS value determination means to determine the lower limit of the buckling load; Initial imperfect shape setting means for setting the initial imperfection from the selected buckling mode, and a nonlinear structure for the set initial imperfection shape Non-linear structure analysis means for performing analysis and storing the results in a nonlinear structure analysis file, RS buckling evaluation means for performing buckling evaluation based on the results of the non-linear structure analysis and storing the results in the database and file, and outputting the results 2. A buckling analysis method for a structure according to claim 1, wherein the computer processing system comprises means.