Method and device for analyzing water elastic response of large floating body under action of external load

Abstract

The invention relates to a water elastic response analysis method and device for a large floating body under the action of an external load, and the method comprises the steps: decomposing the velocity potential of a floating body coverage area into two sub-velocity potentials, and enabling the two sub-velocity potentials to meet homogeneous boundary conditions; a variable separation method is utilized to obtain two sub-velocity potential series expressions meeting a Laplace equation and homogeneous boundary conditions; in the process of solving the undetermined expansion coefficient, taking the elastic boundary condition as a matching condition for solving the undetermined expansion coefficient so as to obtain a solving result of the undetermined expansion coefficient; wherein the elastic boundary condition is obtained based on a kinematic boundary condition and a dynamic boundary condition of the surface of the floating body; performing hydroelastic response analysis based on the solution result of the undetermined expansion coefficient to obtain hydroelastic response parameters; wherein the water elasticity response parameter comprises at least one parameter of the deflection, the shearing force and the bending moment of the floating body, so that the water elasticity response analysis can be quickly and effectively carried out.

Description

Technical Field

[0001] The present invention relates to the technical field of hydrodynamic technology, and in particular, to a method and device for analyzing the hydroelastic response of a large floating body under external loads. Background Art

[0002] With the growth of the global population, the intensification of resource demands, and the enhancement of environmental protection awareness, the development of traditional land resources has become difficult to meet the comprehensive needs of social development, and the ocean has become a treasure trove for humans to seek new development space and resources. Large floating bodies are not only important supports for activities such as offshore oil exploitation and deep-sea scientific research exploration, but also gradually expand to multiple frontier fields such as the development of marine renewable energy, the construction of offshore cities, and marine environmental protection. Large floating bodies are usually flat and flexible structures, with the bottom surface of the structure in direct contact with the water surface, and their elastic deformation under external loads cannot be ignored. The interaction between the fluid and the large floating body is a very complex fluid-structure interaction problem. The presence of the floating body will change the flow field, and at the same time, the change in the flow field will also cause the floating body to deform. Therefore, the two must be analyzed by coupling. When the frequency of the external load is close to the natural frequency of the floating body, the floating body may produce a large-amplitude resonance response, leading to a series of safety problems such as mooring cable fracture, structural cracking, and damage to connecting components. Therefore, establishing an efficient computational analysis technology for the coupling between the fluid and the floating body under external loads to achieve the safe design and analysis of large floating bodies has very important theoretical significance and engineering value.

[0003] Based on the frequency-domain potential flow theory and the elastic thin plate theory, under the action of external loads (non-fluid loads), the elastic boundary condition of the interface between the large floating body and the water body is a non-homogeneous boundary condition, and it is impossible to directly use the method of separation of variables to derive the series expression of the velocity potential covering the water area of the floating body, thus making it difficult to establish a fast and effective analytical method for the hydroelastic response of a large floating body under external loads. In addition, in traditional frequency-domain potential flow analysis, there are obvious discontinuities in the calculation results of the deflection of the floating body and the height of the free water surface at the edge of the large floating body, resulting in the structural hydroelastic response in the area near the edge of the floating body not conforming to the actual situation, and the calculation results being difficult to effectively guide the actual engineering design. Summary of the Invention

[0004] (1) Technical Problems to be Solved

[0005] In view of the above-mentioned shortcomings and deficiencies of the prior art, the present invention provides a method and device for analyzing the hydroelastic response of a large floating body under external loads, which solves the technical problems in the prior art that it is difficult to establish a fast and effective analytical method for the hydroelastic response of a large floating body under external loads, and the problem that the calculation results in the traditional method are difficult to effectively guide the actual engineering design due to the discontinuity of the deflection of the floating body and the height of the free water surface at the edge of the floating body.

[0006] (2) Technical Solutions

[0007] To achieve the above object, the main technical solutions adopted by the present invention include:

[0008] In a first aspect, an embodiment of the present invention provides a method for analyzing the hydroelastic response of a large floating body under an external load, including: decomposing the velocity potential in the floating body coverage area into two sub-velocity potentials, and making both sub-velocity potentials satisfy the homogeneous boundary conditions; using the method of separation of variables to obtain the series expressions of the two sub-velocity potentials that satisfy the Laplace equation and the homogeneous boundary conditions; wherein, the series expressions of the two sub-velocity potentials include undetermined expansion coefficients; in the process of solving the undetermined expansion coefficients, taking the elastic boundary conditions as the matching conditions for solving the undetermined expansion coefficients to obtain the solution results of the undetermined expansion coefficients; wherein, the elastic boundary conditions are obtained based on the kinematic boundary conditions and the dynamic boundary conditions on the floating body surface; performing hydroelastic response analysis based on the solution results of the undetermined expansion coefficients to obtain hydroelastic response parameters; wherein, the hydroelastic response parameters include at least one of the deflection, shear force, and bending moment of the floating body.

[0009] In a possible embodiment, the two sub-velocity potentials include a first sub-velocity potential and a second sub-velocity potential The homogeneous boundary conditions are:

[0010]

[0011] In the formula, x represents the abscissa of the Oxz rectangular coordinate system; D represents a variable, and D = EI / (ρg), where EI represents the flexural rigidity of the floating body, ρ represents the fluid density, and g represents the acceleration due to gravity; ε represents a variable, and ε = (ρ s / ρ)c, where ρ s represents the density of the floating body, and c represents the thickness of the floating body; K represents the deep water wave number; z represents the ordinate of the Oxz rectangular coordinate system; h represents the water depth; b represents half of the width of the floating body.

[0012] In a possible embodiment, the series expressions of the two sub-velocity potentials are:

[0013]

[0014] In the formula, A n , B n , and C n are all undetermined expansion coefficients; λ n represents the first eigenvalue; Y n (z) represents the vertical eigenfunction; X n (x) represents the eigenfunction along the horizontal direction; α n represents the second eigenvalue.

[0015] In a possible embodiment, the elastic boundary conditions are:

[0016]

[0017] In the formula, D represents a variable, and D = EI / (ρg), where EI represents the flexural rigidity of the floating body, ρ represents the fluid density, and g represents the acceleration due to gravity; φ2 represents the velocity potential of the area covered by the floating body; ω represents the circular frequency; f(x) is the complex space external load, and it contains amplitude and phase information.

[0018] In a possible embodiment, the solution of the undetermined expansion coefficients is obtained by the partition matching solution method, and during the execution of the partition matching solution method, the following continuity conditions are introduced at the edge of the floating body:

[0019] η = ξ, x = ±b;

[0020] In the formula, η represents the free wave surface height; ξ represents the deflection of the floating body.

[0021] In a possible embodiment, the calculation expression of the deflection of the floating body is as follows:

[0022]

[0023] In the formula, ξ(x) represents the deflection of the floating body.

[0024] In a possible embodiment, the calculation expression of the shear force of the floating body is as follows:

[0025]

[0026] In the formula, S(x) represents the shear force of the floating body.

[0027] In a possible embodiment, the calculation expression of the bending moment of the floating body is as follows:

[0028]

[0029] In the formula, M(x) represents the bending moment of the floating body.

[0030] In a second aspect, an apparatus for analyzing the hydroelastic response of a large floating body under an external load according to an embodiment of the present invention includes:

[0031] A decomposition module, configured to decompose the velocity potential of the area covered by the floating body into two sub-velocity potentials, and make both of the two sub-velocity potentials satisfy homogeneous boundary conditions;

[0032] A separation of variables module, configured to obtain series expressions of the two sub-velocity potentials that satisfy the Laplace equation and the homogeneous boundary conditions; wherein, the series expressions of the two sub-velocity potentials include undetermined expansion coefficients;

[0033] A solution module, configured to use the elastic boundary condition as a matching condition for solving the undetermined expansion coefficients during the process of solving the undetermined expansion coefficients, so as to obtain a solution result of the undetermined expansion coefficients; wherein, the elastic boundary condition is obtained based on the kinematic boundary condition and the dynamic boundary condition of the floating body surface;

[0034] A hydroelastic response analysis module, configured to perform hydroelastic response analysis based on the solution result of the undetermined expansion coefficients to obtain hydroelastic response parameters; wherein, the hydroelastic response parameters include at least one of the deflection, shear force, and bending moment of the floating body.

[0035] In a third aspect, an embodiment of the present application provides a storage medium, on which a computer program is stored, and when the computer program is run by a processor, it executes the method described in the first aspect or any optional implementation manner of the first aspect.

[0036] In a fourth aspect, an embodiment of the present application provides an electronic device, including: a processor, a memory, and a bus, where the memory stores machine-readable instructions executable by the processor. When the electronic device runs, the processor communicates with the memory through the bus, and when the machine-readable instructions are executed by the processor, they execute the method described in the first aspect or any optional implementation manner of the first aspect.

[0037] In a fifth aspect, the present application provides a computer program product, which, when running on a computer, causes the computer to execute the method in the first aspect or any possible implementation manner of the first aspect.

[0038] (III) Advantageous Effects

[0039] The advantageous effects of the present invention are:

[0040] The application embodiment provides a method and device for analyzing the hydroelastic response of a large floating body under external loads. First, the velocity potential of the water area covered by the floating body is decomposed, and the boundary conditions satisfied by the two sub-velocity potentials after decomposition are both homogeneous boundary conditions. Then, the separation of variables method is used to obtain the series expressions of the two sub-velocity potentials that satisfy the Laplace equation and the homogeneous boundary conditions. During the process of solving the undetermined expansion coefficients, the elastic boundary conditions are used as the matching conditions for solving the undetermined expansion coefficients to obtain the solution results of the undetermined expansion coefficients. Finally, based on the solution results of the undetermined expansion coefficients, the hydroelastic response analysis is carried out to obtain the hydroelastic response parameters, so that the hydroelastic response analysis can be carried out quickly and effectively. In addition, the present invention solves the problem that the deflection at the edge of the large floating body is discontinuous with the free water surface in the previous frequency-domain potential flow analysis results by introducing continuous conditions at the edge of the floating body. Compared with the previous potential flow methods, the method of the present application is simpler and more convenient to implement, and the calculation results are more in line with the actual situation, which can provide an efficient analysis means for the hydroelastic response of large floating bodies, and the analysis results can provide scientific guidance for engineering design.

[0041] In order to make the above-mentioned objects, features, and advantages to be achieved by the embodiments of the present application more obvious and understandable, the following specifically gives preferred embodiments and, in conjunction with the accompanying drawings, makes a detailed description as follows. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following will briefly introduce the drawings required to be used in the embodiments of the present application. It should be understood that the following drawings only show some embodiments of the present application, and therefore should not be regarded as limiting the scope. For those of ordinary skill in the art, other related drawings can be obtained based on these drawings without creative efforts.

[0043] Figure 1 Shows a flowchart of a method for analyzing the hydroelastic response of a large floating body under external loads provided by an embodiment of the present application;

[0044] Figure 2 Shows a schematic diagram of the hydroelastic response of a large floating body under external loads provided by an embodiment of the present application;

[0045] Figure 3 Shows a structural block diagram of a device for analyzing the hydroelastic response of a large floating body under external loads provided by an embodiment of the present application;

[0046] Figure 4 Shows a structural block diagram of an electronic device provided by an embodiment of the present application. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0047] In order to better explain the present invention for easy understanding, the following will make a detailed description of the present invention through specific embodiments in conjunction with the accompanying drawings.

[0048] At present, in addition to the problem that it is difficult to establish a fast and effective analytical method for the hydroelastic response of large floating bodies under external loads in the existing solutions, there are also the following problems: in the traditional frequency-domain potential flow analysis, there are obvious discontinuities in the calculation results of the floating body deflection and the free water surface height at the edge of the large floating body, resulting in the structural hydroelastic response in the area near the edge of the floating body not conforming to the actual situation, and the calculation results are difficult to effectively guide the actual engineering design.

[0049] To solve this problem, based on the potential flow theory and the elastic thin plate theory, the embodiments of the present application provide a method and device for analyzing the hydroelastic response of a large floating body under external loads. First, the velocity potential of the water area covered by the floating body is decomposed, and the boundary conditions satisfied by the two decomposed sub-velocity potentials are both homogeneous boundary conditions. Then, the series expressions of the two sub-velocity potentials that satisfy the Laplace equation and the homogeneous boundary conditions are obtained by using the method of separation of variables, and during the process of solving the undetermined expansion coefficients, the elastic boundary conditions are used as the matching conditions for solving the undetermined expansion coefficients to obtain the solution results of the undetermined expansion coefficients. Finally, based on the solution results of the undetermined expansion coefficients, the hydroelastic response analysis is carried out to obtain the hydroelastic response parameters, so as to be able to perform the hydroelastic response analysis quickly and effectively. In addition, the present invention solves the problem of the discontinuity between the deflection at the edge of the large floating body and the free wave surface in the previous frequency-domain potential flow analysis results by introducing a continuity condition at the edge of the floating body. Compared with the previous potential flow methods, the method of the present application is simpler and more convenient to implement, and the calculation results are more in line with the actual situation, which can provide an efficient analysis means for the hydroelastic response of large floating bodies, and the analysis results can provide scientific guidance for engineering design.

[0050] To better understand the above technical solutions, the exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although the exemplary embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided so that the present invention can be understood more clearly and thoroughly, and the scope of the present invention can be fully conveyed to those skilled in the art.

[0051] Please refer to Figure 1 , Figure 1The flowchart of a method for analyzing the hydroelastic response of a large floating body under external loads provided by an embodiment of the present application is shown. It should be understood that this hydroelastic response analysis method can be executed by an electronic device, and the specific device of this electronic device can be set according to actual needs, and the embodiments of the present application are not limited thereto. For example, this electronic device can be a terminal device or a server, etc. Among them, this terminal device can be an electronic device such as a desktop computer, a laptop computer, a tablet computer, a mobile phone, a personal digital assistant, a wearable device, etc.; this server can be an independent server or a server cluster. Specifically, this hydroelastic response analysis method includes:

[0052] Step S110, decompose the velocity potential in the area covered by the floating body into two sub-velocity potentials, and make both sub-velocity potentials satisfy the homogeneous boundary conditions;

[0053] Step S120, use the method of separation of variables to obtain the series expressions of the two sub-velocity potentials that satisfy the Laplace equation and the homogeneous boundary conditions; among them, the series expressions of the two sub-velocity potentials include undetermined expansion coefficients;

[0054] Step S130, in the process of solving the undetermined expansion coefficients, use the elastic boundary conditions as the matching conditions for solving the undetermined expansion coefficients to obtain the solution results of the undetermined expansion coefficients; among them, the elastic boundary conditions are obtained based on the kinematic boundary conditions and the dynamic boundary conditions on the surface of the floating body;

[0055] Step S140, perform hydroelastic response analysis based on the solution results of the undetermined expansion coefficients to obtain hydroelastic response parameters; among them, the hydroelastic response parameters include at least one of the deflection, shear force, and bending moment of the floating body.

[0056] Therefore, by means of the above technical solution, the present application first decomposes the velocity potential in the water area covered by the floating body and makes the boundary conditions satisfied by the two decomposed sub-velocity potentials be homogeneous boundary conditions, then uses the method of separation of variables to obtain the series expressions of the two sub-velocity potentials that satisfy the Laplace equation and the homogeneous boundary conditions, and in the process of solving the undetermined expansion coefficients, uses the elastic boundary conditions as the matching conditions for solving the undetermined expansion coefficients to obtain the solution results of the undetermined expansion coefficients, and finally performs hydroelastic response analysis based on the solution results of the undetermined expansion coefficients to obtain hydroelastic response parameters, so as to be able to provide an efficient analysis means for the hydroelastic response of a large floating body, and the analysis results can provide scientific guidance for engineering design.

[0057] To facilitate the understanding of the embodiments of the present application, the following will be described through specific embodiments.

[0058] Specifically, please refer to Figure 2 , Figure 2Shows a schematic diagram of the hydroelastic response of a large floating body under external loads. As Figure 2 shown, the water depth is h, the width of the floating body is B (B = 2b), the thickness of the floating body is c (much smaller than the width B), and the draft of the floating body is ignored. Under the action of external loads, the large floating body undergoes elastic deformation, thus causing water body movement. Establish a right-handed rectangular coordinate system Oxz, with the origin O located on the still water surface, the x-axis positive to the right, and the z-axis coinciding with the mid-perpendicular of the floating body and vertically upward. For the convenience of solution, the entire fluid domain is divided into three regions: Region 1 is the water area on the wave-facing side of the floating body (x ≤ -b); Region 2 is the water area covered by the floating body (-b ≤ x ≤ b); Region 3 is the water area on the wave-shadow side of the floating body (x ≥ b). Under the assumption of an ideal fluid, the entire fluid motion can be described by the velocity potential Φ(x, z, t). Considering the linear harmonic problem, the velocity potential can be expressed as:

[0059] Φ(x, z, t) = Re[φ(x, z)e -iωt (1);

[0060] where t represents time; Φ(x, z, t) represents the velocity potential at time t; Re represents taking the real part of the variable; φ(x, z) represents the spatial complex velocity potential; ω represents the circular frequency.

[0061] And, the velocity potential satisfies the Laplace equation, free surface condition, bottom condition, and far-field radiation condition, specifically:

[0062]

[0063] where the subscript j = 1, 2, 3 represents Region 1, Region 2, Region 3 respectively; φ j represents the velocity potential of the jth region; K represents the deep water wave number, K ≡ ω 2 / g, and g represents the acceleration due to gravity; k0 is the wave number, satisfying the dispersion equation K = k0tanh(k0h).

[0064] Assume that the floating body undergoes small-amplitude deformation under external loads, then the motion response of the floating body can be described using the elastic thin plate theory, satisfying the following differential equation:

[0065]

[0066] In the formula, EI represents the flexural rigidity of the floating body; W is the deflection of the floating body; m s is the mass per unit area of the floating body; t represents time; P represents the hydrodynamic pressure on the lower surface of the floating body; F(x, t) is the external load acting on the upper surface of the elastic plate.

[0067] Moreover, for a simple harmonic varying external load, the deflection of the floating body, hydrodynamic pressure and external load can be further expressed as:

[0068] W(x,t) = Re[ξ(x)e -iωt (8);

[0069] P = Re[pe -iωt (9);

[0070] F(x,t) = Re[f(x)e -iωt (10);

[0071] In the formulas, ξ(x) represents the complex spatial deflection of the floating body; p represents the complex spatial hydrodynamic pressure; f(x) is the complex spatial external load, including amplitude and phase information.

[0072] Furthermore, formulas (8) to (10) can be substituted into formula (7) to eliminate the time factor e -iωt , and the following can be obtained:

[0073]

[0074] Moreover, the kinematic boundary condition and dynamic boundary condition on the surface of the floating body are respectively:

[0075]

[0076] p = iωρφ2 - ρgξ, z = 0 (13);

[0077] In the formula, ρ represents the fluid density.

[0078] Furthermore, by using formulas (12) and (13) to eliminate p and ξ in formula (11), the elastic boundary condition expressed only by the velocity potential can be obtained:

[0079]

[0080] In the formula, the variable D is expressed as D = EI / (ρg); the variable ε is expressed as ε = (ρ s / ρ)c, ρ s is the density of the floating body.

[0081] Moreover, by using the method of separation of variables, the velocity potential expressions in region 1 and region 3 can be obtained, specifically as follows:

[0082]

[0083] In the formula, R n (n ≥ 0) and T n (n ≥ 0) are both undetermined expansion coefficients; Z n(z)(n≥0) represents the vertical eigenfunction; k n (n≥1) is the eigenvalue, and k n satisfies K = -k n tan(k n h).

[0084] And, Z n (z) is calculated as follows:

[0085]

[0086] It should be noted here that since formula (14) is a non - homogeneous elastic boundary condition, the velocity potential expression of the water body movement under the floating body cannot be directly derived by the method of separation of variables. Here, the velocity potential decomposition method is used to solve this problem. Therefore, first, the velocity potential in the floating body - covered area 2 needs to be decomposed into two sub - velocity potentials:

[0087]

[0088] where φ2 represents the velocity potential in the floating body - covered area 2; represents the first sub - velocity potential; represents the second sub - velocity potential.

[0089] At the same time, let the two decomposed sub - velocity potentials satisfy the following homogeneous boundary conditions:

[0090]

[0091] Subsequently, using the method of separation of variables, the series expressions of the two sub - velocity potentials that satisfy the Laplace equation and the above homogeneous boundary conditions (i.e., the homogeneous boundary conditions corresponding to formulas (19) to (23)) are as follows:

[0092]

[0093] where A n , B n and C n are undetermined expansion coefficients; λ n represents the first eigenvalue; Y n (z) represents the vertical eigenfunction; X n (x) represents the eigenfunction along the horizontal direction; α n represents the second eigenvalue.

[0094] Furthermore, the calculation formula of this Y n (z) is as follows:

[0095]

[0096] Furthermore, this X n(x) is calculated as follows:

[0097] X n (x) = sin[α n (x - b)] (27).

[0098] Furthermore, this λ n satisfies the following formula:

[0099]

[0100] Furthermore, this α n is calculated as follows:

[0101]

[0102] And the undetermined coefficients in the velocity potential expression need to be solved by matching the following boundary conditions:

[0103]

[0104] Furthermore, substituting formula (25) into formula (31), multiplying both sides of the equation by the eigenfunction system X m (x), and then integrating x from -b to b, using the orthogonality of the eigenfunction system X m (x), the following formula can be obtained:

[0105]

[0106] Furthermore, substituting formula (15) and formula (24) into formula (30), multiplying both sides of the equation by Z m (z), and then integrating z from -h to 0, the following formula can be obtained:

[0107]

[0108] In the formula, κ0 = -ik0; κ m = k m (m ≥ 1);

[0109]

[0110] Furthermore, substituting formula (15), formula (24) and formula (25) into formula (31), multiplying both sides of the equation by Y m (z), and then integrating z from -h to 0, the following formula can be obtained:

[0111]

[0112] In the formula,

[0113] Similarly, using the same method as above, the following formulas can be obtained:

[0114]

[0115] In the formulas,

[0116] In addition, considering that the ends of the floating body are in a free state, the shear force and bending moment at the ends are both zero, and the mathematical expressions for the end conditions are:

[0117]

[0118] Furthermore, substituting formulas (24) and (25) into formulas (40) and (41), the following formulas can be obtained:

[0119]

[0120] Although all the expansion coefficients in the velocity potential expression are obtained by appropriate truncation using formulas (35) - (39) and formulas (42) - (45), for this truncation solution method, there are obvious discontinuity problems in the floating body deflection and the free wave surface height at the ends of the floating body (x = ±b). To solve this problem, the following conditions are introduced:

[0121] η = ξ, x = ±b (46);

[0122] In the formulas, η represents the free wave surface height; ξ represents the deflection of the floating body.

[0123] It should be noted here that the truncation solution method (Truncation Methods) refers to a method in mathematics, physics, and engineering calculations to approximately solve complex equations or systems by finitely considering certain terms or steps in order to simplify the problem or accelerate the calculation process.

[0124] Furthermore, formula (46) can be expressed as:

[0125]

[0126] Subsequently, substituting formulas (15), (16), (24), and (25) into formulas (47) and (48), the following can be obtained:

[0127]

[0128] Further, truncate both m and n in formulas (35), (36), and (38) to N terms (N is an integer), truncate n in formulas (37) and (39) to N terms and m to N - 1 terms, and truncate n in formulas (42) - (45), (49), and (50) to N terms, then a linear equation system with 5N + 9 unknowns can be obtained, and by solving the equation system, the solution results of all expansion coefficients in the velocity potential expression can be obtained.

[0129] After obtaining all the expansion coefficients in the velocity potential expression, perform a hydroelastic response analysis based on the solution results of the undetermined expansion coefficients to obtain hydroelastic response parameters. Among them, the hydroelastic response parameters include at least one of the deflection ξ(x), shear force S(x), and bending moment M(x) of the floating body.

[0130] Further, the calculation expression of the deflection ξ(x) is as follows:

[0131]

[0132] And, the calculation expression of the shear force S(x) is as follows:

[0133]

[0134] And, the calculation expression of the bending moment M(x) is as follows:

[0135]

[0136] It should be noted here that A in the above formulas (51) to (53) n 、B n and C n all represent the solution results of the expansion coefficients, and for the sake of distinction, A in formulas (51) to (53) n 、B n and C n can also be replaced by A' n 、B' n and C' n .

[0137] Therefore, with the help of the above technical solutions, compared with the previous potential flow methods, the method of the present application is more simple and convenient to implement, the calculation results are more in line with the actual situation, it can provide an efficient analysis means for the hydroelastic response of large floating bodies, and the analysis results can provide scientific guidance for engineering design.

[0138] It should be understood that the above method for analyzing the hydroelastic response of a large floating body under external loads is only exemplary, and those skilled in the art can make various deformations according to the above method, and the deformed solutions also fall within the protection scope of the present application.

[0139] See also Figure 3 , Figure 3 The structural block diagram of a hydroelastic response analysis device 300 for a large floating body under an external load provided in an embodiment of the present application is shown. It should be understood that the hydroelastic response analysis device 300 is capable of executing each step in the above method embodiment. The specific functions of the hydroelastic response analysis device 300 can be found in the description above. To avoid repetition, the detailed description is appropriately omitted here. The hydroelastic response analysis device 300 includes at least one software function module that can be stored in a memory in the form of software or firmware or solidified in the operating system (OS) of the hydroelastic response analysis device 300. Specifically, the hydroelastic response analysis device 300 includes:

[0140] A decomposition module 310 is used to decompose the velocity potential of the floating body coverage area into two sub-velocity potentials, and make the two sub-velocity potentials satisfy homogeneous boundary conditions;

[0141] The separation variable module 320 is used to obtain the series expressions of the two sub-velocity potentials satisfying the Laplace equation and the homogeneous boundary conditions by using the separation variable method; wherein the series expressions of the two sub-velocity potentials include the expansion coefficients to be determined;

[0142] A solution module 330 is used for using elastic boundary conditions as matching conditions for solving the undetermined expansion coefficients in the process of solving the undetermined expansion coefficients, so as to obtain a solution result of the undetermined expansion coefficients; wherein the elastic boundary conditions are obtained based on the kinematic boundary conditions and dynamic boundary conditions of the floating body surface;

[0143] The hydroelastic response analysis module 340 is used to perform hydroelastic response analysis based on the solution result of the undetermined expansion coefficient to obtain hydroelastic response parameters; wherein the hydroelastic response parameters include at least one parameter of the deflection, shear force and bending moment of the floating body.

[0144] Since the device described in the above embodiment of the present invention is a device used to implement the method of the above embodiment of the present invention, based on the method described in the above embodiment of the present invention, a person skilled in the art can understand the specific structure and deformation of the device, so it is not described here. All devices used in the method of the above embodiment of the present invention belong to the scope of protection of the present invention.

[0145] See also Figure 4 , Figure 4 FIG. 4 shows a structural block diagram of an electronic device 400 provided in an embodiment of the present application. Figure 3As shown, the electronic device 400 may include a processor 410, a communication interface 420, a memory 430, and at least one communication bus 440. Among them, the communication bus 440 is used to enable direct connection communication between these components. Among them, in the embodiments of the present application, the communication interface 420 of the device is used to communicate signaling or data with other node devices. The processor 410 may be an integrated circuit chip with signal processing capabilities. The above-mentioned processor 410 may be a general-purpose processor, including a central processing unit (CPU for short), a network processor (NP for short), etc.; it may also be a digital signal processor (DSP for short), an application-specific integrated circuit (ASIC for short), a field programmable gate array (FPGA for short), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components. It can implement or execute the various methods, steps, and logic block diagrams disclosed in the embodiments of the present application. The general-purpose processor may be a microprocessor or the processor 410 may also be any conventional processor, etc.

[0146] The memory 430 may be, but is not limited to, a random access memory (RAM for short), a read-only memory (ROM for short), a programmable read-only memory (PROM for short), an erasable programmable read-only memory (EPROM for short), an electrically erasable programmable read-only memory (EEPROM for short), etc. The memory 430 stores computer-readable instructions. When the computer-readable instructions are executed by the processor 410, the electronic device 400 can execute each step in the above method embodiments.

[0147] The electronic device 400 may further include a storage controller, an input / output unit, an audio unit, and a display unit.

[0148] The components of the memory 430, the storage controller, the processor 410, the peripheral interface, the input / output unit, the audio unit, and the display unit are electrically connected to each other directly or indirectly to achieve data transmission or interaction. For example, these components can be electrically connected to each other through one or more communication buses 440. The processor 410 is configured to execute the executable modules stored in the memory 430, such as software function modules or computer programs included in the electronic device 400.

[0149] The input / output unit is used to provide a user with an input interface to implement the interaction between the user and the server (or local terminal). The input / output unit can be, but is not limited to, a mouse, a keyboard, etc.

[0150] The audio unit provides an audio interface to the user, which may include one or more microphones, one or more speakers, and an audio circuit.

[0151] The display unit provides an interaction interface (such as a user operation interface) between the electronic device and the user or is used to display image data for the user to reference. In this embodiment, the display unit can be a liquid crystal display or a touch display. If it is a touch display, it can be a capacitive touch screen or a resistive touch screen that supports single-point and multi-point touch operations, etc. Supporting single-point and multi-point touch operations means that the touch display can sense touch operations generated simultaneously at one or more positions on the touch display and hand over the sensed touch operations to the processor for calculation and processing.

[0152] It can be understood that Figure 4 the structure shown is only illustrative, and the electronic device 400 may further include more or fewer components than those shown Figure 4 or have a different configuration from that shown Figure 4 . Figure 4 The components shown can be implemented using hardware, software, or a combination thereof.

[0153] This application provides a storage medium, on which a computer program is stored. When the computer program is run by a processor, it executes the method described in the embodiment.

[0154] This application also provides a computer program product. When the computer program product runs on a computer, it causes the computer to execute the method described in the method embodiment.

[0155] Those skilled in the art should understand that the embodiments of the present invention can be provided as a method, a system, or a computer program product. Therefore, the present invention can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0156] The present invention is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to embodiments of the present invention. It should be understood that each flow and / or block in the flowchart and / or block diagram, as well as the combination of flows and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions.

[0157] It should be noted that in the claims, any reference signs placed between parentheses shall not be construed as limiting the claim. The word "comprising" does not exclude the presence of elements or steps not listed in the claim. The word "a" or "an" preceding an element does not exclude the presence of a plurality of such elements. The present invention can be implemented by means of hardware including several different elements and by means of a suitably programmed computer. In a claim listing several means, several of these means can be embodied by the same piece of hardware. The use of the words first, second, third, etc. is only for convenience of expression and does not denote any order. These words can be understood as part of the name of the element.

[0158] In addition, it should be noted that in the description of this specification, the description of terms such as "an embodiment", "some embodiments", "embodiments", "examples", "specific examples", or "some examples" means that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, without conflict, those skilled in the art can combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples.

[0159] Although the preferred embodiments of the present invention have been described, those skilled in the art can make additional changes and modifications after learning the basic creative concept. Therefore, the claims should be construed to include the preferred embodiments as well as all changes and modifications falling within the scope of the present invention.

[0160] Obviously, those skilled in the art can make various modifications and variations to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention should also cover these modifications and variations.

Claims

1. A method for analyzing the hydroelastic response of a large floating body under external loads, characterized in that Including: Decompose the velocity potential in the region covered by the floating body into two sub-velocity potentials, and make both of the two sub-velocity potentials satisfy the homogeneous boundary conditions; Using the method of separation of variables, obtain the series expressions of the two sub-velocity potentials that satisfy the Laplace equation and the homogeneous boundary conditions; wherein, the series expressions of the two sub-velocity potentials include undetermined expansion coefficients; In the process of solving the undetermined expansion coefficients, use the elastic boundary conditions as the matching conditions for solving the undetermined expansion coefficients to obtain the solution results of the undetermined expansion coefficients; wherein, the elastic boundary conditions are obtained based on the kinematic boundary conditions and the dynamic boundary conditions on the surface of the floating body; Based on the solution results of the undetermined expansion coefficients, conduct a hydroelastic response analysis to obtain hydroelastic response parameters; wherein, the hydroelastic response parameters include at least one of the deflection, shear force, and bending moment of the floating body.

2. The hydroelastic response analysis method according to claim 1, wherein The two sub-velocity potentials include a first sub-velocity potential and a second sub-velocity potential The homogeneous boundary condition is as follows: In the formula, x represents the abscissa of the Oxz rectangular coordinate system; D represents a variable, and D = EI / (ρg), EI represents the flexural rigidity of the floating body, ρ represents the fluid density, and g represents the acceleration due to gravity; ε represents a variable, and ε = (ρ s / ρ)c, where ρ s represents the density of the floating body, c represents the thickness of the floating body; K represents the deep water wave number; z represents the ordinate of the Oxz rectangular coordinate system; h represents the water depth; b represents half of the width of the floating body.

3. The hydroelastic response analysis method according to claim 2, wherein The series expressions of the two sub-velocity potentials are: where A n , B n and C n are all the expansion coefficients to be determined; λ n represents the first eigenvalue; Y n (z) represents the vertical eigenfunction; X n (x) represents the eigenfunction along the horizontal direction; α n represents the second eigenvalue.

4. The water elastic response analysis method according to claim 3, characterized in that The elastic boundary conditions are: where φ2 represents the velocity potential of the floating body covering area; ω represents the circular frequency; f(x) is the complex space external load, and it contains amplitude and phase information.

5. The water elastic response analysis method according to claim 4, characterized in that The undetermined expansion coefficients are obtained through a partition matching solution method, and in the process of performing the partition matching solution method, the following continuity conditions are introduced at the edge of the floating body: η = ξ, x = ±b; In the formula, η represents the free wave surface height; ξ represents the deflection of the floating body.

6. The hydroelastic response analysis method according to claim 4, characterized in that The calculation expression of the deflection of the floating body is as follows: In the formula, ξ(x) represents the deflection of the floating body.

7. The water elastic response analysis method according to claim 4, characterized in that, The calculation expression of the shear force of the floating body is as follows: In the formula, S(x) represents the shear force of the floating body.

8. The water elastic response analysis method according to claim 4, characterized in that The calculation expression of the bending moment of the floating body is as follows: In the formula, M(x) represents the bending moment of the floating body.

9. An apparatus for analyzing the hydroelastic response of a large floating body under external loads, characterized in that Including: A decomposition module, configured to decompose the velocity potential in the region covered by the floating body into two sub-velocity potentials, and make both of the two sub-velocity potentials satisfy the homogeneous boundary conditions; A separation of variables module, configured to obtain the series expressions of the two sub-velocity potentials that satisfy the Laplace equation and the homogeneous boundary conditions; wherein, the series expressions of the two sub-velocity potentials include undetermined expansion coefficients; A solution module, configured to use the elastic boundary conditions as the matching conditions for solving the undetermined expansion coefficients in the process of solving the undetermined expansion coefficients to obtain the solution results of the undetermined expansion coefficients; wherein, the elastic boundary conditions are obtained based on the kinematic boundary conditions and the dynamic boundary conditions on the surface of the floating body; A hydroelastic response analysis module, configured to conduct a hydroelastic response analysis based on the solution results of the undetermined expansion coefficients, and calculate hydroelastic response parameters; wherein, the hydroelastic response parameters include at least one of the deflection, shear force, and bending moment of the floating body.

10. An electronic device, comprising a processor, a memory, and a computer program stored on the memory, characterized in that, The processor executes the computer program to implement the hydroelastic response analysis method of a large floating body under external loads as described in any one of claims 1-8.

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