KR20190073984A - Method for increasing effective modal mass in dynamic analysis for fixed platform - Google Patents

Abstract

The present invention relates to a method for performing a dynamic analysis of a structure installed in the ocean, which comprises the steps of: (A) performing beam or finite element (FE) modeling; (B) performing a dynamic analysis using a modal effective mass on structural analysis software; and (C) deriving stress or strain through seismic spectrum analysis of the structure. As a result, complex dynamic analysis can be simply and quickly performed in the offshore plant design, saving time in the range of 60% to 70% while maintaining accuracy and reliability of structural analysis.

Description

[0001] The present invention relates to a method for increasing a mode effective mass for dynamic analysis of a fixed platform,

The present invention relates to the design of an offshore plant, and more particularly to a method for increasing the mode effective mass for dynamic analysis of a fixed platform for performing structural analysis based on predetermined software.

In the dynamic analysis of a fixed platform, which is a kind of offshore plant, the effective mass is defined to have the usefulness of analysis when the structure is 90% in the X and Y directions and 80% in the Z direction.

In the conventional method, since the mass participation is calculated in the process of performing the dynamic analysis on the predetermined structural analysis program, the effective mass (effective modal mass) per mode can be known, It is necessary to spend time and effort. That is, since the mode effective mass can be known once the result of the program is derived, it is time consuming and it is difficult to obtain the target mode effective mass as a result of once derived.

With respect to interpretation of offshore structures, reference can be made to Korean Patent Laid-Open Publication No. 2017-0011562 and Korean Patent Registration No. 1711606, which are incorporated herein by reference.

(B) selecting a load case; (c) generating input data for load analysis; (d) calculating load data; (e) (F) evaluating the strength of the DSF, and (e) reinforcing the quay wall according to the load analysis value. Therefore, it is expected that the interaction between the topside model and the DSF will be reflected and the result close to the actual result will be obtained.

(A) the rate of change of the natural frequency according to the stiffness change of the target structure is calculated; (D) Estimating whether the damage of the target structure and the time of occurrence of the damage are estimated by analyzing the variation of the estimated natural frequency and determining the danger signal; And the like. Therefore, it is expected to accurately estimate the time when damage occurs to the structure, and to eliminate the work such as additional analysis or model improvement.

However, according to the above-mentioned prior art documents, since it does not reflect the design factor for increasing the mode effective mass during the operation of the structural analysis software, it can be used as a simple reference material.

Korean Patent Laid-Open Publication No. 2017-0011562 "Method and Apparatus for Analyzing Load of Offshore Structures" (Publication Date: Feb. 2, 2017). Korean Patent Registration No. 1711606, "Estimation Method of Damage to Offshore Structures Based on Similarity" (Publication Date: Mar. 23, 2013).

It is an object of the present invention to solve the above-mentioned problems of the prior art. It is an object of the present invention to predict a mode effective mass without an additional modeling operation before performing a kinetics analysis of an offshore plant, And to provide a method for increasing mode effective mass for dynamic analysis of a fixed platform that eliminates error processes.

In order to accomplish the above object, the present invention provides a method for performing a dynamic analysis on a structure installed on the ocean, comprising the steps of: (A) performing beam or finite element (FE) modeling; (B) performing kinetic analysis on the structural analysis software using the mode effective mass; And (C) deriving stress or strain through analysis of the seismic spectrum of the structure.

In the detailed configuration of the present invention, the step (A) includes dividing the stationary platform into a jacket and a top side, and the jacket mass M _J , the topside mass M _T , the jacket stiffness K _J , The mass correlation α, the stiffness correlation β, the eigenvalues λ1 and λ2, and the mode-specific mass participation vector Γ are calculated through the modeling of the model _KT .

In the detailed construction of the present invention, the step (B) calculates the cumulative effective mass M _eff based on the modeling of the step (A) (S50), and calculates the mass correlation degree? The change in the stiffness correlation? Is displayed in a correlation graph (S60), and the final effective mass M _eff is calculated on the correlation graph (S70).

As a detailed configuration of the present invention, the step S50 is calculated by the following equation (24).

수식 (24)

Equation (24)

As a detailed configuration of the present invention, the step S60 is to calculate the change amount? 'Of the mass correlation degree? And the change amount?' Of the rigidity correlation degree? To the following equations (28) and .

수식 (28)

Equation (28)

수식 (30)

Equation (30)

As a detailed configuration of the present invention, the step S70 is characterized by calculating the total stiffness change amount (DELTA K _S ) by integrating the jacket and the top side with the following equation (36).

수식 (36)

Equation (36)

As a detailed configuration of the present invention, the step S70 is a process for determining the jacket mass (M _J ), the dry condition and the top side mass (M _T ) for the NTE condition, the jacket stiffness K _J ) and top side rigidity (K _T ) are calculated, and a provisional stiffness correlation (?) Is derived using the calculated top side stiffness (K _T ).

As a detailed configuration of the present invention, the step S70 is characterized in that an effective mass (M _eff ) of 90% or more is derived using the provisional stiffness correlation coefficient (?) And the total stiffness variation amount (? K _S ).

As described above, according to the present invention, it is possible to perform complex dynamics analysis in an offshore plant design simply and quickly, and it is possible to maintain the accuracy and reliability of the structural analysis while reducing the number of hours in the range of 60% to 70%.

Figure 1 is a diagram of the overall flow chart to which the method according to the invention is applied.
FIGS. 2 and 3 are diagrams for explaining the conventional method in FIG. 1
4 is a flow chart showing the main steps of the method according to the invention
Figures 5 to 7 are schematic diagrams of the formula data applied to the method according to the invention
Figures 8-11 illustrate the result graphs < RTI ID = 0.0 >

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings.

The present invention proposes a method for performing kinetic analysis on structures installed in the ocean. Structural analysis of marine civil structures is intended, but not necessarily limited to. The main steps in Figure 1 utilize DNV software Genie or Bentley software SACS (Structural Analysis Computer System).

Conventionally, dynamical analysis software and modeling module are utilized to increase the effective mass. Generally, increasing the mode increases the effective mass. However, the time required for solving results in Figure 1 also increases do. Alternatively, as shown in FIG. 2 (a), a weak member inducing a local mode in the dynamic analysis module, that is, a member having small stiffness and processed into a dummy, can be removed. However, as shown in FIG. 2 (b), it is expected that the effective mass can reach 90% in the X, Y, and Z directions by setting the mode to more than 200. Alternatively, as shown in FIG. 3 (a), the contribution of the global mode can be increased by constructing a super element at the intersection of the primary member in the dynamic analysis module. However, as shown in FIG. 3 (b), it is expected that the effective mass can reach 90% in the X and Y directions and reach 80% in the Z direction by setting the mode to 160 or more.

Thus, the conventional method applies software but reflects the model to predict the effective mass increase width. As a result, it takes a long time to perform at least two or three times within the dynamics analysis software or module in order to obtain the increase amount of effective mass.

Step (A) according to the present invention proceeds with beam or finite element (FE) modeling. Using known software such as TRIBON, beam modeling and finite element modeling are performed for specific offshore structures. Certain offshore structures illustrate a fixed platform, but are not limited thereto.

In the detailed configuration of the present invention, the step (A) includes dividing the stationary platform into a jacket and a top side, and the jacket mass M _J , the topside mass M _T , the jacket stiffness K _J , The mass correlation α, the stiffness correlation β, the eigenvalues λ1 and λ2, and the mode-specific mass participation vector Γ are calculated through the modeling of the model _KT . Step (A) derives the modeling result for the fixed platform, and then uses the known formulas as shown in FIGS. 5 to 7 to define the physical quantity related to the jacket and the top side.

5, the modeling of the jacket mass M _J , the topside mass M _T , the jacket stiffness K _J , and the topside stiffness K _{T are} shown, and a known Discrete Dynamical System ) Can be defined as a simple model.

)의 식에 대입하고 이를 이용하여 질량참여벡터(Γ)를 구할 수 있다.6 and 7, a homogeneous equation of motion in a free vibration state in which no external force is applied is expressed by a 2 < 2 > matrix such as Equation (1), and eigenvalues are expressed by Equation ) Of the determinant. This corresponds to step S10 in Fig. 4 and ignores the damping effect, the rotation condition, the orthogonal condition, and the like. The mass correlation degree alpha and the stiffness correlation coefficient beta are defined in the equations (3) and (4) as in step S20 in Fig. Subsequently, the eigenvalues (? 1,? 2) are calculated through the calculations of the equations (5) to (7) as in the equations (8) and (9). This is derived by substituting the mass correlation degree alpha and the rigidity correlation degree beta into the equation (2) as a part corresponding to step S30 in Fig. In other words, the equation (2) can be solved to rearrange the general harmonic equation, and the eigenvalues and eigenvectors for the first and second governing can be obtained. Subsequently, the equation (1) is rearranged as in the equation (10), and the eigenvector matrix of the equation (11) is calculated using the eigenvalues (? 1,? 2) And the mass participation vector (Γ) is derived. This corresponds to step S40 of FIG. 4 and is a unit ground displacement term applied to the static stiffness as a coefficient vector (

) And can be used to obtain the mass participation vector (Γ).

Step (B) according to the present invention performs kinetic analysis using the mode effective mass on the structural analysis software. This includes the steps of performing steps S10 to S40 and steps S50 to S70 described above in advance of dynamics analysis, by removing the conventional method described in Figs. 2 and 3 from performing simultaneous with dynamics analysis.

In the detailed construction of the present invention, the step (B) calculates the cumulative effective mass M _eff based on the modeling of the step (A) (S50), and calculates the mass correlation degree? The change in the stiffness correlation? Is displayed in a correlation graph (S60), and the final effective mass M _eff is calculated on the correlation graph (S70). As a detailed configuration of the present invention, the equation (24) to be described later in the step S50 of FIG. 4 is calculated, the equations (28) and (30) to be described later are calculated in the step S60, and the equation do. This will be described sequentially.

The effective mass M _eff for the mode ii is given by the following equation (18).

수식 (18)

Equation (18)

Modes 1 and 2 are summarized in equations (19) and (20).

수식 (19)

Equation (19)

수식 (20)

Equation (20)

When the equation (7) is substituted into the equations (19) and (20), the sum of the effective masses (M _eff ) is as follows.

수식 (21)

Equation (21)

The maximum total effective mass based on the top side mass (M _T ) is the minimum value based on the jacket mass (M _J ), and the equation (22) is calculated through the derivative of the equation (21).

Equation (22)

The maximum total effective mass based on jacket stiffness ( _KJ ) is the minimum based on topside stiffness (K _T ) as follows.

수식 (23)

Equation (23)

The equation (21) is rearranged to increase the cumulative mass participation and obtain the effective mass coefficient (γ).

수식 (24)

Equation (24)

To summarize step S50, the effective mass for the obtained primary mode and secondary mode is calculated and added to calculate the final cumulative effective mass. At this time, the mass correlation (α) and the stiffness correlation (β) for the topside and the jacket are substituted into the final cumulative effective mass expression. It is advantageous to compute the relation for the low-volatility jacket rather than the high-side topside as in Equation (24).

Next, the relation of the effective mass coefficient (γ) for increasing cumulative mass participation is as follows.

수식 (25)

Equation (25)

Where φ is the pre-increment coefficient of the cumulative mass participation (the equation of α and β), and φ 'is the post-increment coefficient of the cumulative mass participation (the equation of α' and β ').

Assuming no change in the stiffness of the jacket and topside,

수식 (26)

Equation (26)

For convenience of calculation, substituting 1 / α for t is summarized as equation (27).

수식 (27)

Equation (27)

Substituting 1 / α and 1 / α 'for t and t' and solving the equation (27), the relational expression is calculated as shown in equation (28).

수식 (28)

Equation (28)

The minimum value (α ' _min ) for increasing the cumulative mass participation by substituting the equation (22) into the equation (28) is as follows.

수식 (29)

Equation (29)

In Equation (27), if t and t 'are replaced by 1 / α and the solution is obtained for β', the relation for increasing the cumulative mass participation is calculated as shown in Equation (30).

수식 (30)

Equation (30)

When the equation (22) is substituted into the equation (30), the maximum value (α ' _max ) for increasing the cumulative mass participation is as follows.

수식 (31)

Equation (31)

To summarize step S60, the minimum mass correlation (?) Is obtained from the quadratic differential equation and the maximum stiffness correlation (?) Is obtained by using the minimum mass correlation (?). However, it is assumed that there is almost no difference between the initial stiffness correlation (?) And the later stiffness correlation (? ') Before substitution. Finally, the correlation between the initial mass correlation (α) and the stiffness correlation (β) is expressed in a graph.

The total stiffness (K _S ) before increasing the effective mass and the total stiffness (K _S ') after the increase are as follows.

수식 (32)

Equation (32)

K_J′, K_T

K_T′로 가정하면 유효질량 증가 후 전체 강성(K_S′)은 다음과 같다.K _J

K _J ', K _T

K _T ', the total stiffness (K _S ') after effective mass increase is as follows.

수식 (33)

Equation (33)

수식 (34)

Equation (34)

Finally, the total stiffness variation (ΔK _S = K _S - K _S ') is derived as follows.

수식 (35)

Equation (35)

수식 (36)

Equation (36)

Using equation (36), the overall stiffness variation can be adjusted for dry conditions with no fluid in the topside and NTE conditions with fluids in the topside.

In order to summarize Step S70, the total rigidity difference before and after the rearrangement is calculated according to the equation related to the stiffness correlation (?). This is summarized as topside stiffness (K _T ) and jacket stiffness (K _J ), and the difference between the initial mass and the latter mass is set and the amount of change in stiffness is obtained. This change amount is substituted by the change amount of the stiffness with respect to the jacket and the soil, and the effective mass as a final target is obtained.

Meanwhile, in the past, the present invention is performed only in software, but the present invention can be performed in offline by outputting to Excel. FIG. 9 shows the change in mass correlation (α) as the cumulative mass participation increases with graph and Excel data, and FIG. 10 shows the change in stiffness correlation (β) with increase in cumulative mass participation as graph and Excel data.

An example of the design will be described assuming a model of a fixed platform as shown in FIG.

Topside Mass (M _T ): Dry Condition 38507.8 tonne, NTE Condition 54283.4 tonne

Jacket mass (M _J ): 34168.3 tonne

? = 1.485 (dry condition) and 1.054 (NTE condition)

K _J , K _T are computed with separate software for deflection of four support points (see FIG. 8) of the jacket, and deflection for eight support points of the topside (see FIG. 8).

K _J : 3.98E + 14, K _T : 1.114E + 15

beta = 0.357 (dry and NTE)

This can be confirmed through the graphs shown in FIGS. 9 and 10 and the Excel data. As a result, the total amount of stiffness change under the dry condition and the NTE condition is as follows.

Dry condition: ΔK _S (%) = 4.2 (%) reduction of K _J

NTE Condition: ΔK _S (%) = 4.8 (%) reduction of K _J

As a detailed configuration of the present invention, the step S70 is characterized in that an effective mass (M _eff ) of 90% or more is derived using the provisional stiffness correlation coefficient (?) And the total stiffness variation amount (? K _S ).

Referring to FIG. 11, in the conventional upper graph, the effective mass is less than 90% in the X, Y, and Z directions in the mode 30, and the effective mass in the Z direction is less than 70% Is low. On the other hand, even if the mode 30 is set in the lower graph of the present invention, the efficiency reaches the level that satisfies the efficiency in the X, Y, and Z directions and the effective mass approaches the 80% from the mode 200 to the Z direction. It can be implemented with only equation (36), graph, and Excel data without running software that takes a lot of time.

Step (C) according to the present invention derives stress or strain through seismic spectrum analysis of the structure. This can be processed to minimize repetitive tasks using the above-described software based on the results derived from steps S50 to S70 of the present invention. Accordingly, as shown by No. 4 on the right side in Fig. 8 (b), the work time (Man Hour) is significantly shortened as compared with the left side.

It will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the spirit and scope of the invention. It is therefore intended that such variations and modifications fall within the scope of the appended claims.

M _J : jacket mass M _T : topside mass
K _J : Jacket stiffness K _T : Top side stiffness
M _eff : effective mass lambda 1, lambda 2: eigenvalue
L: coefficient vector Γ: mass participation vector
α: jacket vs topside mass ratio (mass correlation)
β: jacket vs topside stiffness ratio (stiffness correlation)

Claims (8)

CLAIMS What is claimed is: 1. A method for performing a dynamic analysis on a structure installed in the ocean, comprising:
(A) performing beam or finite element (FE) modeling;
(B) performing kinetic analysis on the structural analysis software using the mode effective mass; And
(C) deriving a stress or strain through an analysis of the seismic spectrum of the structure. The method of increasing the mode effective mass for dynamic analysis of a fixed platform. The method according to claim 1,
In the step (A), the stationary platform is divided into a jacket and a top side,
Through the modeling of jacket mass (M _J ), topside mass (M _T ), jacket stiffness (K _J ) and topside stiffness (K _T ), mass correlation (α), stiffness correlation (β) lambda 1, lambda 2), and a mass-dependent mass participation vector (&ggr;) are calculated. The method for increasing the mode effective mass for dynamics analysis of a fixed platform. The method according to claim 1,
The step (B) calculates the cumulative effective mass M _eff based on the modeling of the step (A) (S50), and compares the mass correlation α and the stiffness correlation β with the increase in the cumulative mass participation (S60), and calculating a final effective mass (M _eff ) on the correlation graph (S70). The method of increasing the mode effective mass for dynamic analysis of a fixed platform. The method of claim 3,
Wherein the step S50 is calculated by the following equation (24).

Equation (24) The method of claim 3,
Wherein the step S60 calculates the amount of change? 'Of the mass correlation degree? And the amount of change?' Of the stiffness degree of correlation with the following equations (28) and (30) Increasing mode effective mass for dynamic analysis of platform.

Equation (28)

Equation (30) The method of claim 3,
Wherein the step S70 calculates the total stiffness change amount? K _S by integrating the jacket and the top side with the following equation (36).

Equation (36) The method of claim 3,
The step S70 is a jacket mass in a separate software to target specific of the fixed platform top side mass for (M _J), dry (Dry) condition and NTE condition (M _T), the jacket stiffness (K _J), top side stiffness (K _T ) and deriving a provisional stiffness correlation coefficient (β) by using the calculated effective stiffness coefficient (K _T ). The method of claim 3,
The step S70 derives an effective mass M _{eff of} 90% or more by using the provisional stiffness correlation coefficient? And the total stiffness change amount? K _S. Increase method.

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