KR101122562B1 - Method for predicting buckling strength considering curvature - Google Patents

Abstract

Disclosed is a method for evaluating buckling strength considering curvature. Method for buckling strength evaluation according to an embodiment of the present invention comprises the steps of obtaining the curvature of the bending angle and the design factors of the curved plate, calculating the elastic buckling stress and fine equipment of the curved plate using the design factor, Calculating the buckling strength increase according to the curvature effect by using the curvature and the thin equipment; calculating the bending buckling stress by using the elastic buckling stress and the buckling strength increase; And predicting the safety of the curved sheet.

Description

Buckling Strength Evaluation Method Considering Curvature {METHOD FOR PREDICTING BUCKLING STRENGTH CONSIDERING CURVATURE}

The present invention relates to a method for evaluating buckling strength in consideration of curvature, and more particularly, to a method for evaluating buckling strength in consideration of curvature applicable to a material or member that can be subjected to a load.

In general, a solid material or member has a mechanical behavior corresponding to the load, such as causing a deformation or bending under load.

For example, a cylindrical cylinder may be in a buckling state that is axially bent or struck when subjected to excessive compressive load rather than being directly destroyed by the compressive load.

The conventional method of calculating the buckling strength of a cylindrical cylinder subjected to compressive load can be made by using a known formula of compressive buckling strength.

In addition, the calculation of the buckling strength of the curved panel can use the formulas defined in the design codes of each country (standards).

In particular, in the case of hulls, the buckling strength is determined by the use of formulas for buckling strength provided by the respective classifications (ABS), Norwegian (DnV), British (Lloyd) and Japanese (NK). It is being calculated.

However, these equations may differ significantly from the experimental values as theoretical values.

For example, although the researchers studying the buckling strength of the prior art have modified the equations by performing various experiments and simulations related to the compression buckling of a cylindrical cylinder, for various reasons such as a defect function, the difference between the theoretical value and the experimental value is significant. Could not be narrowed.

That is, the buckling strength calculation of the class according to the prior art, that is, the buckling stress for the cylindrical cylinder fixed to the end shown in Figure 1a can be calculated by the following equation (1).

Where t is the panel thickness, E is the elastic modulus, R is the radius, υ is the Poisson's ratio, and υ is 0.3 when the material of the curved panel is steel.

However, the conventional method of calculating the buckling strength does not consider the panel width but only the radius (R). Therefore, it is difficult to calculate the exact value of the compressive buckling stress when the compressive load is applied in the plate with finite width. have.

That is, as shown in Figure 1b, the result value (1) using the classification criteria for the curved panel is much lower than the comparative example (2) by the finite element method, and shows a significant difference between the two, the calculation accuracy is Can be rated very poor. Here, the graph vertical axis of FIG. 1B corresponds to the final strength obtained by dividing the compressive buckling stress by the yield stress and dimensionless, and the graph horizontal axis corresponds to the thin equipment.

The conventional buckling strength calculation method uses a cylindrical cylinder structure, and since the structure has the same length as the circumference, the change in the buckling strength due to the change in the radius or curvature is insignificant, but the influence of the calculation is small. In other words, when evaluating buckling strength by using a radius in a curved panel having a panel width, the buckling strength change according to the panel width change is very large, and thus buckling strength cannot be accurately predicted.

According to the embodiment of the present invention, the bending buckling stress is defined using the curvature which is the bending angle value of the curved plate, so that the buckling strength design can be accurately predicted according to the panel width change while easily performing the buckling strength design in terms of the buckling strength design. It is possible to provide a method for evaluating buckling strength considering the curvature of the buckling.

According to an aspect of the present invention, the step of obtaining a curvature and the design factors of the curved plate and the bending angle value of the curved plate to be described in detail below, using the design factor to calculate the elastic buckling stress and fine equipment of the curved plate and Calculating the buckling strength increase according to the curvature effect using the curvature and the thin equipment; calculating the curved buckling stress using the elastic buckling stress and the buckling strength increase; It provides a buckling strength evaluation method comprising the step of predicting the safety of the curved plate.

According to another aspect of the present invention, there is implemented a program of instructions that can be executed by the buckling strength evaluation apparatus to perform the buckling strength evaluation method, the recording medium recording a program that can be read by the buckling strength evaluation apparatus Comprising: Obtaining the curvature of the bending angle of the curved plate and the design factor of the curved plate, Computing the elastic buckling stress and fine equipment of the curved plate using the design factor, Curvature influence using the curvature and the thin equipment Calculating a buckling strength increase according to the step; calculating a curved buckling stress using the elastic buckling stress and the buckling strength increase; and estimating the stability of the curved plate from the calculated curved buckling stress. A recording medium for recording the program is provided.

The buckling strength evaluation method considering the curvature according to the embodiment of the present invention can easily perform the buckling strength design work by reasonably reflecting the effect of curvature in the design and evaluation of the buckling strength of the curved plate, There is an advantage that can accurately predict the buckling strength change.

In addition, the buckling strength evaluation method considering the curvature according to the embodiment of the present invention has an advantage of accurately calculating the value of the curved plate buckling stress in consideration of the change in the width of the curved plate.

In addition, the buckling strength evaluation method considering the curvature according to an embodiment of the present invention is further obtained by applying a plastic modification formula to the plastic correction buckling stress, and then using either one of the bending buckling stress and the plastic modification buckling stress more accurately buckling There is an advantage that can determine the safety of the strength.

1A is a perspective view illustrating a curved panel for buckling strength calculation according to the prior art.
Figure 1b is a graph showing a comparative example by the finite element method and the result value using the classification criteria according to the prior art.
2 is a flowchart illustrating a buckling strength evaluation method in consideration of curvature according to an embodiment of the present invention.
3 is a perspective view for explaining a curved sheet used in the evaluation method shown in FIG.
4 is a graph comparing the final strength of the evaluation method shown in FIG. 2 with the final strength of the finite element method.

Hereinafter, the buckling strength evaluation method considering the curvature according to the embodiment of the present invention will be described in detail with reference to FIGS. 2 to 4.

The following specific examples are merely illustrative for the buckling strength evaluation method considering the curvature according to the embodiment of the present invention, it is not intended to limit the scope of the present invention.

As shown in Figure 2, the buckling strength evaluation method considering the curvature according to the embodiment of the present invention can calculate and check whether the buckling strength acts on the structure in consideration of the curvature of the structure of the hull or in any mechanical structure.

The method of evaluating buckling strength according to an embodiment of the present invention includes obtaining a curvature which is a bending angle value of a curved sheet and a design factor of the curved sheet (S110), and an elastic buckling stress and slenderness ratio of the curved sheet using a design factor. Calculating (S120), calculating a buckling strength increase according to curvature influence using curvature and fine equipment (S130), and calculating a curved buckling stress using the elastic buckling stress and the buckling strength increase. (S140) and using the curved sheet buckling stress may include a step of predicting the buckling strength for the curved sheet (S150).

2 and 3, the first step (S110) of the present invention, the bending angle value of curvature (θ), the design factor width (b), thickness (t), the elastic modulus, according to the material The feeding ratio and the like can be obtained from the shape and mechanical property data table of the curved sheet 10.

In this embodiment, the curvature θ is traditionally defined as an angle rather than a radius.

)을 하기의 [수학식 2]를 이용하여 연산할 수 있다.In the second step (S120), the traditional or ideal elastic buckling stress for the curved plate 10 using the aforementioned design factors (

) Can be calculated using Equation 2 below.

In Equation 2, π is pi, E is elastic modulus, υ is Poisson's ratio, k is coefficient for boundary condition (condition that simply supports four sides of the curved plate), b is width, t is thickness It can be defined as.

)은 수 많은 실험과 시뮬레이션을 통하여 검증이 완료된 평판의 좌굴강도 계산시에 사용될 수 있는 오일러 좌굴 공식(Euler Buckling Formula)을 적용하여 정의할 수 있다.Elastic buckling stress

) Can be defined by applying the Euler Buckling Formula, which can be used to calculate the buckling strength of verified plates through numerous experiments and simulations.

In addition, in the second step S120, the slenderness ratio may be calculated using Equation 3 below.

In Equation 3, β may be defined as thin equipment, b is width, t is thickness, is yield stress, and E is an elastic modulus.

)은 실험을 통해 얻거나, 해당 곡판(10)에 대해 미리 준비되어 있는 재료의 기계적 성질 색인표를 통해서 얻을 수 있다.Yield stress (

) Can be obtained through an experiment or through a mechanical property index of the material prepared in advance for the curved sheet 10.

The thin equipment β of the present embodiment may be understood as a design variable for coupling the material properties such as the width and the thickness t of the curved plate 10 to the buckling strength.

)은 곡판(10)의 하중 변형율 성분과 곡률(θ)과 세장비(β)와 곡률 감쇄계수(

)를 고려한 하기의 [수학식 4]를 통해 산출될 수 있다.In the third step (S130), the increase in the buckling strength due to the curvature effect (

) Is the load strain component of curvature 10, curvature (θ), fine equipment (β) and curvature attenuation coefficient (

) Can be calculated through Equation 4 below.

는 좌굴강도 증가분, υ는 푸아송비, θ는 곡률, β는 세장비,

는 항복응력, E는 탄성계수,

은 곡률 감쇄계수로서 정의될 수 있다.In [Equation 4],

Is buckling strength increase, υ is Poisson's ratio, θ is curvature, β is thin equipment,

Is yield stress, E is elastic modulus,

Can be defined as the curvature attenuation coefficient.

The load strain component corresponds to the first item of [Equation 4] using the Poisson's ratio (υ), and can be understood as the first design variable for coupling the shrinkage of the material to the buckling strength of the curved sheet 10. have.

)은 상기 [수학식 4]의 두 번째, 세 번째 항목에 해당하는 것으로서, 세장비(β)와 곡률(θ)의 영향을 곡판(10)의 좌굴강도, 즉 하기의 곡판좌굴응력(

)에 결부시키기 위한 두 번째와 세 번째 설계변수로 이해될 수 있다.Buckling Strength Increment (

) Corresponds to the second and third items of Equation 4, and the influence of the thin equipment β and the curvature θ is applied to the buckling strength of the curved sheet 10, that is, the curved buckling stress (

Can be understood as the second and third design variables for

)는 상기 [수학식 4]의 네 번째 항목에 해당하는 것으로서, 실험을 통해 색인 데이터 표로서 정리될 수 있는 경험치로서, 역시 곡판(10)의 좌굴강도에 결부되는 네 번째 설계변수로 이해될 수 있다.Also, the curvature attenuation coefficient (

) Corresponds to the fourth item of Equation 4, and can be understood as the fourth design variable that is also connected to the buckling strength of the curved plate 10 as an empirical value that can be arranged as an index data table through experiments. have.

)는 곡률(θ)에 대응하도록 0.1 ~ 1.0 사이에서 선택될 수 있다. 곡률 감쇄계수(

)가 0.1 ~ 1.0의 범위 내에서 선택되는 경우에 곡판좌굴응력(

)의 비선형 성분이 보정될 수 있고, 상기 범위를 벗어나는 경우 정확도가 떨어질 수 있다. This curvature reduction factor (

) May be selected from 0.1 to 1.0 to correspond to the curvature θ. Curvature reduction factor (

) Is selected in the range of 0.1 to 1.0

The nonlinear component of) may be corrected, and the accuracy may fall if it is out of the above range.

)는 미리 실험 및 수치해석을 통해 정리 해놓은 색인 데이터 표에서 선택되는 0.4일 수 있다.For example, when the curvature θ is an angle of 45 °, the attenuation coefficient (

) May be 0.4 selected from an index data table prepared through experiments and numerical analysis.

)이 상기 탄성좌굴응력(

)과 상기 좌굴강도 증가분(

)을 이용하는 아래의 [수학식 5]를 통해 산출될 수 있다.In the fourth step S140 of the present embodiment, the curved buckling stress (

Is the elastic buckling stress (

) And the buckling strength increase (

) Can be calculated through Equation 5 below.

는 곡판좌굴응력,

은 탄성좌굴응력으로서 앞서 [수학식 2]를 통해 산출될 수 있고,

는 좌굴강도 증가분으로서 [수학식 4]를 통해 산출될 수 있다.here,

Curve buckling stress,

Is the elastic buckling stress can be calculated through Equation 2 above,

Is an increase in buckling strength can be calculated through [Equation 4].

)은 곡판(10)에서 유한한 폭(b)과 두께(t)를 고려하여 좌굴강도를 정의할 때, 좌굴강도 증가분(

)에 의한 곡률 효과를 상기 좌굴강도에 결부시켜 반영함에 따라, 결국 폭(b) 변화에 따른 좌굴강도를 정확하게 산출할 수 있다.Curved buckling stress of this embodiment

) Is defined as the buckling strength increase in consideration of the finite width (b) and thickness (t) in the curved plate 10,

By reflecting the curvature effect by) in conjunction with the buckling strength, it is possible to accurately calculate the buckling strength according to the width (b) change.

)으로부터 상기 곡판(10)의 안전성이 예측될 수 있다.In the fifth step (S150) of the present embodiment the calculated buckling stress (

The safety of the curved plate 10 can be predicted from.

)은 수치적으로 산출된 좌굴강도로서, 곡판(10)에 대해 미리 정한 좌굴 안전 기준치와 비교 판단될 수 있다.Curved buckling stress calculated previously

) Is a numerically calculated buckling strength, which may be compared with a predetermined buckling safety reference value for the curved plate 10.

The buckling safety reference value of the curved plate 10 may mean a design reference value or a recommendation value of a structural safety association or class so that buckling does not occur in the curved plate 10 due to a load (for example, a compressive load).

)에 대한 산출값이 곡판(10)의 좌굴 안전 기준치와 비교 판단될 수 있다.When predicting buckling strength, curved buckling stress (

The calculated value for) may be compared with the buckling safety reference value of the curved plate 10.

)에 대한 산출값이 좌굴 안전 기준치에 비해 크면 좌굴강도 측면에서 안전하다고 예측할 수 있고, 좌굴 안전 기준치에 비해 작으면 불안전하다고 예측할 수 있다.Curved Buckling Stress (

If the calculated value for) is larger than the buckling safety threshold, it can be predicted to be safe in terms of buckling strength, and if it is smaller than the buckling safety threshold, it can be predicted to be unsafe.

)이 항복응력(

)의 50% 이상인 경우에도 정확한 좌굴강도를 평가할 수 있도록, 하기의 [수학식 6]과 같은 소성 수정식을 적용하여 소성수정좌굴응력(

)을 구하는 단계가 더 포함될 수 있다.On the other hand, in the present embodiment curved plate buckling stress (

This yield stress is

In order to evaluate the exact buckling strength even when 50% or more of the), the plastic correction buckling stress (

) May be further included.

In this case, the 50% corresponds to an experimental threshold, and may be a criterion that becomes a scattering state in which convergence drops sharply from 50%.

는 소성수정좌굴응력, λ는 치환인자,

는 항복응력,

는 곡판좌굴응력으로서 정의될 수 있다.In Equation 6,

Is the plastic correction buckling stress, λ is the substitution factor,

Yield stress,

Can be defined as curved buckling stress.

Here, the plastic modification formula may be a buckling strength plastic modification formula of Johnson-Ostenfeld.

)이 항복응력(

)의 50% 미만일 경우, 곡판좌굴응력(

)은 곡판(10)의 좌굴강도 안전성 비교 판단용 수치로서 채택될 수 있고, 좌굴 안전 기준치와의 비교 판단에 사용될 수 있다.When estimating the buckling strength, the curved buckling stress (

This yield stress is

Less than 50% of the

) May be adopted as a numerical value for determining the buckling strength safety of the curved plate 10, and may be used for comparison with the buckling safety reference value.

)이 항복응력(

)의 50% 이상일 경우, 소성수정좌굴응력(

)은 곡판(10)의 좌굴강도 안전성 비교 판단용 수치로서 채택되어 좌굴 안전 기준치와의 비교 판단에 사용될 수 있다.On the other hand, curved buckling stress (

This yield stress is

When more than 50% of), the plastic correction buckling stress (

) Is adopted as a numerical value for determining the buckling strength safety of the curved plate 10 and can be used for comparison with the buckling safety reference value.

The graph of FIG. 4 shows the results of predicting buckling strength by applying the evaluation method of the present invention. The numerical values of the horizontal axis and the vertical axis mean buckling strength obtained by dividing the curved buckling stress or plastically modified buckling stress by yield stress.

Referring to FIG. 4, the buckling strength according to the evaluation method of the present invention reflects the curvature effect, based on the graph horizontal axis of FIG. 4, by a first mark 20 such as a triangle point corresponding to each specimen. Can be displayed.

Here, each specimen may have a length (a) 3000 mm and a width (b) 1000 mm according to the shape of the curved plate 10 shown in Figure 3, the thickness (t) increased by 5mm from 10 to 35mm There are a total of six can be prepared to have.

Each specimen may have an elastic modulus of 205.8 GPa, a yield stress of 352.8 MPa, a Poisson's ratio of 0.3, a curvature (θ) of 45 °, and a damping coefficient of 0.4.

As a comparative example, the buckling strength by the finite element method is analyzed using the same physical property data as the specimen, and may be displayed by a second mark 30 such as a dotted line based on the graph vertical axis of FIG. 4.

The buckling strength according to the evaluation method of the present embodiment shows a result that is almost completely consistent with the buckling strength by the finite element method, through which the accuracy of the evaluation method of the present invention can be proved.

So far, the buckling strength evaluation method considering the curvature according to the embodiment of the present invention has been described with reference to FIGS. 2 to 4. Here, it will be apparent to those skilled in the art in view of the technical spirit of the present invention that the buckling strength evaluation apparatus for performing the buckling strength evaluation method according to the present embodiment may be variously implemented.

For example, each step (eg, each step in FIG. 2) of the buckling strength evaluation method according to the present embodiment, or a device / module / configuration that performs one or more of the steps may be provided, and the device The device including the / module / configuration may be the buckling strength evaluation device for performing the buckling strength evaluation method according to the present embodiment. That is, it is clear that the buckling strength evaluation device according to the embodiment of the present invention is performed when the function of the configuration included therein is performed regardless of the name of the hardware or the device when performing the above-described buckling strength evaluation method.

In addition, the buckling strength evaluation method according to an embodiment of the present invention is implemented in the form of program instructions that can be executed by various computer means may be recorded on a computer readable medium. Computer-readable media may include, alone or in combination with the program instructions, data files, data structures, and the like.

The program instructions recorded on the computer readable medium may be those specially designed and constructed for the present invention, or may be known and available to those skilled in the computer software arts. Magnetic media, optical media such as CD-ROMs, DVDs, magneto-optical media such as floptical disks, and ROMs, RAMs Hardware devices specifically configured to store and execute program instructions, such as flash memory). In addition, the above-described medium may be a transmission medium such as an optical or metal wire, a waveguide, or the like including a carrier wave for transmitting a signal specifying a program command, a data structure, and the like. Examples of program instructions include not only machine code generated by a compiler, but also high-level language code that can be executed by a computer using an interpreter or the like.

The hardware device described above may be configured to operate as one or more software modules to perform the operations of the present invention and vice versa.

Such a technical configuration of the present invention will be understood by those skilled in the art that the present invention can be implemented in other specific forms without changing the technical spirit or essential features of the present invention. Therefore, the scope of the present invention is represented by the following claims rather than the foregoing description, and all changes or modifications derived from the meaning and scope of the claims and equivalent concepts are included in the scope of the present invention. Should be interpreted.

10: curved sheet 20: first mark
30: second marker

Claims (8)

Acquiring curvature which is a bending angle value of the curved sheet and a design factor of the curved sheet;
Calculating elastic buckling stress and fine equipment of the curved plate by using the design factor;
Calculating an increase in buckling strength according to the curvature effect by using the curvature and the thin equipment;
Calculating a curved plate buckling stress using the elastic buckling stress and the buckling strength increase;
Estimating the stability of the curved sheet from the calculated curved sheet buckling stress.
Buckling Strength Evaluation Method Considering Curvature.
The method of claim 1,
The three pieces of the equation

Buckling strength evaluation method in consideration of the curvature, characterized in that calculated by.
Where β is the equipment, b is the width, t is the thickness, is the yield stress, and E is the elastic modulus.
The method of claim 1,
The buckling strength increase is expressed by equation

It is calculated by the buckling strength evaluation method.
here,

Is buckling strength increase, υ is Poisson's ratio, θ is curvature, β is thin equipment,

Is yield stress, E is elastic modulus,

Is the curvature attenuation factor.
The method of claim 1,
The curved buckling stress is

The buckling strength evaluation method characterized by the above-mentioned.
here,

Curve buckling stress,

Elastic buckling stress,

Is the buckling strength increase, k is the coefficient for boundary condition, π is pi, E is elastic modulus, υ is Poisson's ratio, b is width and t is thickness.
The method of claim 1,
When the curved buckling stress is more than 50% of the yield stress, applying a plastic correction formula to obtain a plastic correction buckling stress, the buckling strength evaluation method considering the curvature.
The method of claim 5,
In the step of predicting the buckling strength for the curved plate, when the curved buckling stress is 50% or more of the yield stress, the plastically modified buckling stress is adopted as a numerical value for the comparison of the buckling strength safety of the curved plate and compared with the buckling safety standard value. Buckling strength evaluation method considering the curvature used in the
The method of claim 1,
In the step of predicting the buckling strength for the curved plate, when the curved buckling stress is less than 50% of the yield stress, the curved buckling stress is adopted as a numerical value for the comparison of the buckling strength safety of the curved plate to be compared with the buckling safety reference value. Buckling strength evaluation method considering the curvature used.
In the recording medium recording a program that can be read by the buckling strength evaluation apparatus is implemented to perform the buckling strength evaluation method,
Acquiring curvature which is a bending angle value of the curved sheet and a design factor of the curved sheet;
Calculating elastic buckling stress and fine equipment of the curved plate by using the design factor;
Calculating an increase in buckling strength according to the curvature effect by using the curvature and the thin equipment;
Calculating a curved plate buckling stress using the elastic buckling stress and the buckling strength increase;
A recording medium having recorded thereon a program for executing the step of predicting the safety of the curved plate from the calculated curved buckling stress.

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