Condensation solving method and device of underwater structure fluid-solid coupling kinetic model and storage medium

Abstract

The invention discloses a polycondensation solving method and device for an underwater structure fluid-solid coupling dynamic model and a storage medium, and belongs to the field of computational mechanics. A structure and a surrounding flow field are divided into a left molecular structure and a right molecular structure, and modeling is conducted on the structure and the flow field through a finite element method; solving a fixed interface constraint mode of the substructure of the structure and a dynamic polycondensation conversion matrix of a flow field, combining the fixed interface constraint mode and the dynamic polycondensation conversion matrix into a first coordinate transformation matrix, and performing polycondensation on the finite element model of the substructure by utilizing the first coordinate transformation matrix; the finite element models of the two substructures are integrated, a second coordinate transformation matrix is obtained through the displacement coordination condition, the repeated interface freedom degree of the integrated finite element model is eliminated through the second coordinate transformation matrix, and the integral condensation finite element model of the underwater structure is obtained. The method is used for carrying out polycondensation on the traditional finite element model of the submerged structure, the precision of the calculation result is extremely high, and the efficiency of dynamic analysis and structure iterative design optimization of the underwater structure can be greatly improved.

Description

Technical Field

[0001] The present invention belongs to the field of computational mechanics, and particularly relates to a condensation solution method, device, and storage medium for the fluid-structure interaction dynamics model of an underwater structure. Background Art

[0002] Nowadays, the demand for marine equipment has been growing rapidly, and the corresponding dynamic analysis is widely carried out to determine the dynamic performance of the structural system. For example, for the vibration problem of a ship in water, since there are certain differences between the wet mode and the dry mode, it is often necessary to separately analyze the wet mode. In addition, in the research on the vibration problem of a submarine, the noise problem is very important, and a large amount of analysis and calculation is also required for the acoustic analysis of the hull in the sound field and the structural optimization design related to vibration reduction and noise reduction. Therefore, it is of great significance to optimize the relevant solution methods for the fluid-structure interaction dynamics model of underwater structures and improve the calculation speed and efficiency.

[0003] In engineering, the finite element method is generally used to analyze and design optimize the dynamics of underwater structures. When dealing with the wet mode of underwater complex structures, the traditional finite element method will create a large number of element meshes to ensure the calculation accuracy, which will greatly increase the degrees of freedom of the finite element model of the underwater structure, greatly limiting the wet mode analysis of the structure and the efficiency of other dynamic analysis and structural iterative optimization in water. This high calculation cost will lead to more engineering expenses and is very uneconomical.

[0004] The present invention proposes a method for analyzing the dynamics of an underwater structure based on substructure modal condensation and a framework for structural iterative optimization design. By this method, the degrees of freedom of the finite element model of the underwater structure can be greatly reduced, thereby achieving the purpose of improving the efficiency of underwater structure dynamics analysis and structural optimization design. At the same time, the calculation method proposed by the present invention is easy to understand and the framework structure is simple, which is conducive to programming and development. Summary of the Invention

[0005] The purpose of the present invention is to provide a condensation solution method, device, and storage medium for the fluid-structure interaction dynamics model of an underwater structure to solve the problem of too low efficiency in dynamic analysis and design optimization of underwater structures by the traditional finite element method.

[0006] The purpose of the present invention is achieved by the following technical solutions:

[0007] A condensation solution method for the fluid-structure interaction dynamics model of an underwater structure, the specific steps are as follows:

[0008] Step 1: Divide the underwater structure and the fluid domain into two substructures, and use the finite element method to model these two substructures;

[0009] Step 2: Solve the fixed-interface main modes of the structural substructure and distinguish the degrees of freedom of the fluid substructure into master, slave, and interface degrees of freedom. Truncate the fixed-interface main modes Φ of the structural substructure N and represent the slave degrees of freedom of the fluid substructure in terms of the master degrees of freedom, and combine the two to form the first coordinate transformation matrix Ψ1. Use the first coordinate transformation matrix Ψ1 to condense the finite element model of each substructure;

[0010] Step 3: Assemble the finite element models of the two condensed substructures, use the displacement compatibility condition on the contact surface between the substructures to obtain the second coordinate transformation matrix Ψ2, and use the second coordinate transformation matrix Ψ2 to eliminate the repeated interface degrees of freedom between the finite element models of multiple substructures to obtain the complete condensed finite element model of the underwater structure. Solve the wet modes of the underwater structure and the optimal dynamic response under specified working conditions.

[0011] Further, the fluid interface degrees of freedom in Step 2 include the degrees of freedom on the fluid-structure coupling interface and the degrees of freedom on the connection interface of the fluid substructure.

[0012] Further, the fixed-interface main modes Φ of the structural substructure in Step 2 are obtained by the following method N :

[0013]

[0014] Let F I = 0;

[0015] Therefore, the finite element fixed-interface motion equation of the structural substructure is:

[0016]

[0017] The first coordinate transformation matrix Ψ1 has the following formula:

[0018]

[0019] where is the fixed-interface main mode of the truncated structural substructure, and the superscript L represents the truncated low-order components; I is the identity matrix; the subscripts I and B represent the internal and interface degrees of freedom of the structure, and I,s and I,m represent the slave and master degrees of freedom of the fluid substructure respectively.

[0020] Further, use the first coordinate transformation matrix Ψ1 to condense the finite element model of each substructure, and the formula is as follows:

[0021]

[0022] where

[0023]

[0024] Among them:

[0025]

[0026] Among them, M FSI and K FSI are respectively the mass and stiffness matrices of the substructure finite element model, F FSI is the force vector of the substructure finite element model. The subscripts "I" and "B" respectively represent the internal and interface degrees of freedom of the structure, and I,s and I,m respectively represent the slave degrees of freedom and master degrees of freedom of the fluid substructure.

[0027] Furthermore, in step 3, the finite element models of the two substructures are assembled, and the assembled finite element motion equation is:

[0028]

[0029] Among them, the subscripts "1" and "2" respectively represent substructure 1 and 2;

[0030]

[0031] Using the interface coordination conditions between the substructures, the following relationship is obtained:

[0032]

[0033] Among them, Ψ2 is the second coordinate transformation matrix.

[0034] Furthermore, the second coordinate transformation matrix Ψ2 is used to eliminate all the repeated interface degrees of freedom of the substructure finite element models, and thus the condensed assembled dynamic finite element equation is:

[0035]

[0036] Among them:

[0037]

[0038] The connection loads generated by the two substructures are:

[0039] R c,1 + R c,2 = 0 and F c,1 + F c,2 = 0,

[0040]

[0041] An electronic device includes a processor and a memory, the processor being interconnected with the memory. Among them, the memory is used to store a computer program, the computer program includes computer-readable instructions, and the processor is configured to call the computer-readable instructions to execute a condensation solution method for an underwater structure fluid-structure interaction dynamics model.

[0042] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, it implements a condensation solution method for an underwater structure fluid-structure interaction dynamics model.

[0043] The beneficial effects of the present invention are as follows:

[0044] 1. The present invention uses the Guyan method and the Craig-Bampton method to condense the finite element model of an underwater structure. For example, the ship model fixed in water selected in the embodiment, its structural parameters are given in Table 1 and the material parameters are elastic modulus E = 194 GPa, density ρ s = 7850 kg / m 3 , Poisson's ratio μ = 0.3, and the density of water is ρ f = 1000 kg / m 3 . The present invention can be used for any structure in water.

[0045] Table 1 Ship model structural parameters

[0046]

[0047] 2. The accuracy of the condensation calculation results of the method of the present invention is extremely high.

[0048] 3. The method of the present invention can greatly improve the efficiency of dynamic analysis and structural iterative design optimization of underwater structures.

[0049] 4. The theoretical framework of the method of the present invention is simple and easy to be implemented by programming.. Description of the drawings

[0050] Figure 1 It is a schematic diagram of the structural size of a submerged ship model;

[0051] Figure 2 It is a schematic diagram of the substructure division of the structure of a submerged ship model;

[0052] Figure 3 It is a comparison diagram of the first-order modes of the complete finite element model and the condensed finite element model;

[0053] Figure 4 It is a comparison diagram of the second-order modes of the complete finite element model and the condensed finite element model;

[0054] Figure 5The third-order mode comparison diagram of the complete finite element model and the condensed finite element model;

[0055] Figure 6 The fourth-order mode comparison diagram of the complete finite element model and the condensed finite element model;

[0056] Figure 7 The modal accuracy comparison diagram of the complete finite element model and the condensed finite element model;

[0057] Figure 8 The schematic diagram of the substructure of the immersed ship model used for iterative optimization;

[0058] Figure 9 The comparison diagram of the iterative optimization calculation time of the complete finite element model and the condensed finite element model;

[0059] Figure 10 The optimized first-order mode diagram of the complete finite element model and the condensed finite element model;

[0060] Figure 11 The optimized second-order mode diagram of the complete finite element model and the condensed finite element model;

[0061] Figure 12 The flow schematic diagram of the method of the present invention. Specific embodiments

[0062] The present invention will be further described below with reference to the accompanying drawings.

[0063] Refer to Figure 1 and Figure 12 The specific implementation manners will be specifically described. The method for condensing and solving the fluid-structure interaction dynamics model of the underwater structure by using the Guyan method and the Craig-Bampton method according to the present embodiment includes:

[0064] Step 1. Model the structure in water according to the actual situation, and thereby determine the basic dimensions of the structure and the flow domain and the material properties they adopt. Then divide the structure and the flow domain into two substructures together, and use the finite element method to model the structure and the flow domain, as Figure 2 shown. The basic dimensions such as Figure 1 include: the length L3 of the structural substructure 1, the upper width W1, the lower width W2, the distances W3 and W4 from the lower bottom plate of the structure to the front and rear wall surfaces of the flow domain, the exposed water surface H1, the immersion depth H2, the distance H3 from the bottom surface of the flow domain, the distance L1 from the left wall surface of the flow domain, the included angle θ between the side plate and the bottom plate, the thickness t, the length L4 of the structural substructure 2, and the thickness t; the material properties include the elastic modulus E, the density ρ s , the Poisson's ratio μ; the density of water is ρ f ;

[0065] Step 2: Simplification in mathematical form, truncating the fixed interface main modes of the structural substructure, transforming the fluid from the degrees of freedom to the main degrees of freedom, and combining the two to form the first coordinate transformation matrix:

[0066] The finite element motion equation of the substructure can be written as:

[0067]

[0068] Integrate it into the following form:

[0069]

[0070] Where

[0071]

[0072] Where, M FSI and K FSI are the mass and stiffness matrices of the substructure finite element model respectively, F FSI is the force vector of the substructure finite element model, and the subscripts "I" and "B" represent the internal and interface degrees of freedom of the structure respectively, and I,s and I,m represent the slave and main degrees of freedom of the flow domain respectively.

[0073] The first coordinate transformation matrix Ψ1 can be written as:

[0074]

[0075] Where, is the fixed interface main mode of the structural substructure, the superscript L represents the truncated low-order component, and I is the identity matrix.

[0076] Φ N can be obtained in the following way,

[0077]

[0078] Let

[0079] F I = 0

[0080] Therefore, the finite element fixed interface motion equation of the substructure can be written as:

[0081]

[0082] Solving the above equation can obtain the fixed interface main mode Φ N , and then select the low-order components among them.

[0083] Therefore, the first coordinate transformation matrix Ψ1 is obtained. Use the first coordinate transformation matrix to condense the substructure finite element model, and the formula is as follows:

[0084]

[0085] Wherein:

[0086]

[0087] In this way, the degree - of - freedom condensation of the sub - structure finite - element model is completed.

[0088] Step 3: Assemble the finite - element models of the two sub - structures. The assembled finite - element motion equation can be written as:

[0089]

[0090] Where the subscripts "1" and "2" represent Sub - structure 1 and Sub - structure 2 respectively. And:

[0091]

[0092] Using the interface coordination conditions between the sub - structures, the following relationships can be obtained:

[0093]

[0094] Where Ψ2 is the second - order coordinate transformation matrix. Using the second - order coordinate transformation matrix to eliminate all the repeated interface degrees of freedom of the sub - structure finite - element models, the assembled dynamic finite - element equation after condensation is obtained as:

[0095]

[0096] Wherein:

[0097]

[0098] Also, because the connection loads generated by the two sub - structures are:

[0099] R c,1 +R c,2 = 0 and F c,1 +F c,2 = 0,

[0100]

[0101] All the processes of the condensation solution method for the underwater structure fluid-structure interaction dynamics model disclosed in the above embodiments can be embedded in an electronic device for operation. The electronic device includes a processor, a memory, a communication interface, and a communication bus. The processor, the memory, and the communication interface complete communication with each other through the communication bus. The memory is used to store at least one executable instruction, and the executable instruction causes the processor to execute all the process steps of the condensation solution method for the underwater structure fluid-structure interaction dynamics model disclosed in the above embodiments, which will not be elaborated here.

[0102] The electronic device can also communicate with one or more external devices (such as a keyboard, a pointing device, a Bluetooth device, etc.), and can also communicate with one or more devices that enable a user to interact with the electronic device, and / or communicate with any device that enables the electronic device to communicate with one or more other computing devices (such as a router, a modem, etc.). Such communication can be carried out through an input / output (I / O) interface. Moreover, the electronic device can also communicate with one or more networks (such as a local area network LAN), a wide area network WAN, and / or a public network, such as the Internet, through a network adapter. The network adapter communicates with other modules of the electronic device through the bus. It should be understood that although not shown in the figure, other hardware and / or software modules can be used in combination with the electronic device, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems, etc.

[0103] In addition, all the processes of the condensation solution method for the underwater structure fluid-structure interaction dynamics model disclosed in the above embodiments can be implemented in whole or in part by software, hardware, firmware, or any other combination. When implemented using software, the above embodiments can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions or computer programs. When the computer instructions or computer programs are loaded or executed on a computer, the processes or functions described in the embodiments of the present application are generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center by wire (such as infrared, wireless, microwave, etc.). The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device such as a server or data center that contains a collection of one or more available media. The available medium can be a magnetic medium (such as a floppy disk, hard disk, magnetic tape), an optical medium (such as a DVD), or a semiconductor medium. The semiconductor medium can be a solid-state drive.

[0104] Embodiment 1:

[0105] 1. Considering a section of the ship's cabin according to the actual situation of the ship, a floating cabin model is designed. According to its specific dimensions and selected structural materials, this structure is divided into two sub-structures, as Figure 2 shown. In this embodiment, the material parameters include: elastic modulus E = 194 GPa, density ρ s = 7850 kg / m 3 , Poisson's ratio μ = 0.3, and the density of water is ρ f = 7850 kg / m 3 . The structural parameters of Sub-structures 1 and 2 are given in Table 1.

[0106] II. After determining the structural parameters and material parameters of the flooded cabin section, first use the finite element method to model the left and right substructures respectively to obtain their finite element dynamic models. Secondly, by solving the fixed interface modes of the structural substructures and the distinction and dynamic condensation of the master-slave degrees of freedom of the fluid domain substructures and combining the two to form the first coordinate transformation matrix, the first condensation of the substructure finite element model is completed. Then, integrate the finite element models of the two substructures. Finally, use the consistency of the degree-of-freedom motion between the substructures to obtain the second coordinate transformation matrix, and use the second coordinate transformation matrix to assemble all the substructure models to eliminate the repeated interface degrees of freedom between the substructure models, and then a complete finite element condensed model of the flooded structure can be obtained.

[0107] III. After completing the second step, in order to verify the calculation accuracy of the method of the present invention, calculate the natural frequencies and modes of the finite element model of the flooded cabin section by the condensation method and the non-condensation method respectively and make a comparison. The comparison results of the natural frequencies are given in the following table

[0108] Table 2 Natural frequencies of the wet modes of the ship model with both ends fixed

[0109]

[0110] It can be seen from the table that the calculation accuracy of the natural frequencies of the condensed finite element model is very high. The comparison diagrams of the first-order modes of the non-condensed finite element model and the condensed finite element model are as Figure 3 shown, the comparison diagram of the second-order mode is as Figure 4 shown, the comparison diagram of the third-order mode is as Figure 5 shown, and the comparison diagram of the fourth-order mode is as Figure 6 shown. Since the number of degrees of freedom of the condensed finite element model of the method of the present invention is only 9.6% of that of the traditional finite element model, the calculation time consumed is also greatly reduced. Figure 7 The calculation accuracy of the condensed finite element model compared with the traditional finite element model is shown.

[0111] IV. Next, verify the efficiency of the dynamic analysis and design optimization of the finite element model of the method of the present invention. Divide the structure of the flooded ship model into three sections: left, middle, and right, as Figure 8 shown, assign different materials to these sections for iterative calculation. It can be seen from Figure 9 that the difference in the calculation time consumed is very obvious. The repeated iterative calculation time of the finite element model of the method of the present invention is reduced by about 99% compared with the traditional finite element model. This proves that the efficiency of the dynamic analysis of the finite element model of the method of the present invention is extremely high. The calculation results when the material of the left end is aluminum are as Figure 10 and Figure 11 shown. It can be seen from the figures that the calculation results of the new and old methods are very close, and the accuracy of the design optimization of the finite element model of the method of the present invention is also extremely high.

[0112] It can be seen from this embodiment that the calculation accuracy of the finite element model of the method of the present invention is extremely high, and the efficiency of dynamic analysis and design optimization is also greatly improved compared with before.

[0113] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A condensation solution method for the fluid-structure interaction dynamics model of an underwater structure, characterized in that: The specific steps are as follows: Step 1: Divide the underwater structure and the fluid domain into two substructures, and use the finite element method to model these two substructures; Step 2: Solve the fixed-interface main modes of the structural substructures and distinguish the degrees of freedom of the fluid substructures into master, slave, and interface degrees of freedom. Truncate the fixed-interface main modes Φ of the structural substructures and express the slave degrees of freedom of the fluid substructures in terms of the master degrees of freedom, and combine the two to form the first coordinate transformation matrix Ψ1. Use the first coordinate transformation matrix Ψ1 to condense the finite element model of each substructure; N Perform truncation and express the slave degrees of freedom of the fluid substructures in terms of the master degrees of freedom, and combine the two to form the first coordinate transformation matrix Ψ1. Use the first coordinate transformation matrix Ψ1 to condense the finite element model of each substructure; Step 3: Assemble the finite element models after condensing the two substructures. Use the displacement coordination conditions on the contact surface between the substructures to obtain the second coordinate transformation matrix Ψ2. Use the second coordinate transformation matrix Ψ2 to eliminate the repeated interface degrees of freedom between the finite element models of multiple substructures, obtain the complete condensed finite element model of the underwater structure, and solve the wet modes of the underwater structure and the optimal dynamic response under specified working conditions.

2. The condensation solution method for the fluid-structure interaction dynamics model of the underwater structure according to claim 1, characterized in that: In step 2, the fluid interface degrees of freedom include the degrees of freedom on the fluid-structure coupling interface and the degrees of freedom on the connection interface of the fluid substructure.

3. The condensation solution method for the underwater structure fluid-structure interaction dynamics model according to claim 1, characterized in that: In step 2, the main mode Φ of the substructure fixed interface of the structure is obtained by the following method N :[[]]END]] Let F I = 0; Therefore, the finite element fixed interface motion equation of the structural substructure is: The first coordinate transformation matrix Ψ1 has the following formula: Among them, is the fixed interface main mode of the structural substructure after truncation, where the superscript L represents the truncated low-order component; I is the identity matrix; the subscripts I and B represent the internal and interface degrees of freedom of the structure, and I,s and I,m represent the slave and master degrees of freedom of the fluid substructure, respectively.

4. The condensation solution method for the fluid-structure interaction dynamics model of the underwater structure according to claim 3, wherein: In step 2, use the first coordinate transformation matrix Ψ1 to condense the finite element model of each substructure, and the formula is as follows: Among them, Where: where M FSI and K FSI are the mass and stiffness matrices of the substructure finite element model, respectively, and F FSI is the force vector of the substructure finite element model. The subscripts "I" and "B" represent the internal and interface degrees of freedom of the structure, respectively, and I,s and I,m represent the slave and master degrees of freedom of the fluid substructure.

5. The condensation solution method for the underwater structure fluid-structure interaction dynamics model according to claim 1, characterized in that: In step 3, assemble the finite element models of the two substructures. The finite element motion equation after assembly is: Among them, the subscripts "1” and "2” respectively represent substructure 1 and substructure 2; Using the interface coordination conditions between the substructures, the following relationship is obtained: Where Ψ2 is the second coordinate transformation matrix.

6. The condensation solution method for the fluid-structure interaction dynamics model of the underwater structure according to claim 5, characterized in that: In step 3, use the second coordinate transformation matrix Ψ2 to eliminate the repeated interface degrees of freedom of all substructure finite element models. Thus, the condensed and assembled dynamic finite element equation is: Where: The connection loads generated by the two substructures are: R c,1 +R c,2 = 0 and F c,1 +F c,2 = 0, 7. An electronic device, characterized in that: It includes a processor and a memory. The processor is connected to the memory. Among them, the memory is used to store a computer program. The computer program includes computer-readable instructions. The processor is configured to call the computer-readable instructions and execute the method according to any one of claims 1-6.

8. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by the processor, it implements the method according to any one of claims 1-6.

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