Approximate analysis method based on nonlinear hydroelastic response of ultra-large floating structure
By combining homotopy analysis and the finite element method, the computational challenge of strongly nonlinear hydroelastic response is solved, providing an efficient and accurate analytical solution for hydroelastic response, supporting the design and construction of offshore floating structures.
Patent Information
- Application Number
- CN202610033579.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-01-12
- Publication Date
- 2026-05-12
AI Technical Summary
In the case of strongly nonlinear hydroelastic response problems, numerical methods such as perturbation methods fail, and the evolution process of nonlinear hydroelastic waves in the case of multi-module VLFS is complex, making it difficult to accurately measure the hydroelastic response using analytical methods.
Homotopy analysis is used to construct governing equations within the framework of potential flow theory. Through programming with Mathematics software, convergent control parameters are selected, and the problem is transformed into multiple linear subproblems. The influence of hinge connections is studied using the finite element method, providing convergent and accurate approximate analytical solutions.
It achieves a significant reduction in cost while ensuring computational accuracy, provides theoretical guidance for the design of offshore floating structures, and fills the gap in analytical analysis of strongly nonlinear hydroelastic responses.
Smart Images
Figure CN122021135A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of hydroelastic technology, and in particular to the analysis, calculation and simulation of the nonlinear hydroelastic response of offshore floating structures in complex marine environments. Background Technology
[0002] In order to make full use of marine resources, develop living space and protect my country's sea areas, the rational construction of very large floating structures (VLFS) such as offshore airports, offshore military bases and industrial sites has become an increasingly important topic in marine engineering and academia.
[0003] A significant geometric characteristic of VLFS (Volatile Water Frames) is that its horizontal scale is much larger than its vertical scale. Under wave action, the elastic deformation and rigid displacement of a VLFS are of the same order of magnitude. Moreover, in complex marine environments, the nonlinear effects of large-amplitude waves become very pronounced, making the strong nonlinear hydroelastic response of the structure extremely significant and important. Accurately measuring the hydroelastic response of VLFS in the ocean is one of the important technical issues for improving its design safety and economy.
[0004] For solving nonlinear hydroelastic responses, although numerical methods such as the boundary element method, finite element method, finite difference method, and mesh method have achieved great success, their computational approach involves discretizing the original equations and boundary or initial conditions. This discretization alters both the quantitative accuracy and qualitative properties of the equations, resulting in numerical results that cannot provide any functional formulas or provide reasonable theoretical analysis of the mathematical model. Therefore, analytical methods and analytical approximation methods should also be fully developed. Approximate analytical methods, primarily based on perturbation methods, are the main existing computational methods. The essence of any perturbation method is a Taylor series expansion of small physical parameters. However, in strongly nonlinear hydroelastic response problems, as wave amplitude gradually increases, wave steepness is no longer a small parameter. In this case, the perturbation solution cannot be expanded into a series, rendering the perturbation method ineffective.
[0005] To overcome the limitation of traditional perturbation methods failing under strongly nonlinear conditions, seeking other methods that do not rely on any small parameters and can ensure the convergence of analytical solutions is an effective approach for single-module VLFS. Furthermore, for multi-module VLFS, the evolution of nonlinear hydroelastic waves is very complex at the ends of the modules and at the connection points between the modules and hinges. The finite element method can be used to study the influence of hinge stiffness and hinge position on the elastic waves. Summary of the Invention
[0006] The purpose of this invention is to solve the problems of low efficiency and accuracy in the prediction of hydroelastic loads of ultra-large floating bodies, and to provide an approximate analysis method based on the nonlinear hydroelastic response of ultra-large floating structures.
[0007] This invention is achieved through the following technical solution: This invention relates to a nonlinear hydroelastic response analysis method for ultra-large floating structures, comprising the following steps: Step 1: Within the framework of potential flow theory, assuming that the fluid is inviscid, incompressible, and its motion is irrotational, construct the governing equations and nonlinear boundary conditions under the coupled action of hydrodynamic, elastic, and inertial forces. Step 2: For the case of a single-module elastic plate, the homotopy analysis method provides basic principles and many freedoms for selecting solution expressions, initial guesses, and linear operators. Based on the analysis of the actual problem background and equation type, it can fully link the solution of the equation with the essence of the problem, better reflect the inherent physical meaning of the equation expression, and transform the strongly nonlinear hydroelastic response model into multiple linear subproblems. At the same time, the velocity potential and plate deflection to be solved are expressed in series form. Using Mathematics software programming, the optimal convergence control parameter values are selected, and then the convergent approximate analytical solution is obtained. Step 3 shows the important physical quantities, including fluid parameters, incident wave amplitude, plate boundary conditions, plate viscoelastic parameters, and the Young modulus, thickness, and density of the elastic plate, on the dynamic characteristics of the ultra-large floating body. Step 4: For the case of a two-module combined floating body connected by a hinge, in addition to establishing the governing equations and surface kinematics and dynamic boundary conditions, the free boundary conditions of the plate should also be considered, that is, the bending moment and equivalent shear force at the end of the plate are zero; the boundary conditions at the junction of the plate and the hinge, that is, the bending moment of the plate is equal to the bending moment of the hinge; and the bending moment, shear force and deflection of the left and right plates are also equal.
[0008] Step 5: For the case of a two-module combined floating body connected by hinges, the boundary conditions are numerous and complex, making it difficult to study using approximate analytical methods. Based on previous research, this patent proposes to use a numerical method—the finite element method—to study how to select reasonable physical parameters to reduce the dynamic impact on nonlinear hydroelastic waves.
[0009] Preferably, in step 1, a rectangular coordinate system is first established in the model. ,in The axis is positive with vertically upward. The axis coincides with the water surface when at rest, with horizontal to the right being positive. An infinitely long elastic plate floats on the surface of water of finite depth and moves along... Extending infinitely in both axial directions, the plate thickness is The draft is zero.
[0010] Preferably, in step 1, the fluid is inviscid, incompressible, and its motion is irrotational, then the velocity potential... It exists and satisfies the Laplace governing equation. .
[0011] Preferably, in step 1, the The vertical deformation of the plate is the hydroelastic deformation.
[0012] Preferably, in step 1, in the model, at the interface between the elastic plate and the fluid... Obtain the nonlinear kinematic boundary conditions and nonlinear dynamic boundary conditions .
[0013] Preferably, in step 1, the It is the deflection of the elastic plate. It is the pressure on the underside of the plate. Given the fluid density, assuming the fluid and plate do not separate, the relationship between deflection and pressure on the lower surface of the plate is: flexural stiffness of the plate , The Young's modulus of the plate. It's the thickness of the plate. Compared to Poisson, It is gravitational acceleration. , It is the plate density.
[0014] In step 1, the model further includes: at the bottom of a fluid at a finite depth. Established solid-wall impermeable conditions .
[0015] Preferably, in step 1, in order to include more linear terms in the kinematic boundary conditions, the kinematic and dynamic boundary conditions are partially combined using independent variable transformation. With dimensionless transformation, the boundary conditions in the original model are transformed into: .
[0016] In step 2, the HAM algorithm, based on the idea of topology, constructs the zeroth-order deformation equation. , , .
[0017] Preferably, in step 2, the For linear operators, It is a nonlinear operator; For embedded variables. When As the number of consecutive increments from 0 to 1 increases, the two homotopies... Starting from the initial guesses respectively Obtain the exact solution to the system of equations and .
[0018] Preferably, in step 2, the two homotopic... To simplify complex calculations, a single convergence control parameter will still be used. Furthermore, subsequent verification using the squared residual method showed that: using only one This also ensures the validity and accuracy of the solution.
[0019] In step 2, the HAM will Expand on each of the following: Substituting the Maclaurin series into the zeroth-order deformation equation above, and setting the corresponding powers of both sides of the equation to be equal, we obtain the higher-order deformation equation.
[0020] In step 2, the HAM is used to establish the relationship between plate deflection and wave height in order to close the equation. Relationship .
[0021] Preferably, in step 2, the It is an even number. It is an odd number. It is the dimensionless first-order solution amplitude of the homotopy analytical solution of the plate deflection.
[0022] In step 2, to ensure the convergence of the approximate analytical series solution of the fluid's hydroelastic response to the elastic plate, the mathematical model introduces the total squared residual corresponding to the two boundary conditions. .
[0023] Preferably, in step 2, the Let represent the total number of discrete points, and assume . .
[0024] In step 2, the total squared residual of each order approximate solution With convergence control parameters It changes with the changes. Let ,exist Under the minimum condition, it can be obtained The optimal solution. For each order of solution, there is always... The minimum value exists, meaning an optimal solution exists. Furthermore, as the order increases... The increase, The value decreases rapidly. These conclusions guarantee that the approximate analytical solution is convergent and accurate.
[0025] In step 3, the Young's modulus of the plate When the plate deflection gradually increases from small to large, it is found that as... As the value increases, the change in plate deflection decreases.
[0026] In step 3, the thickness of the plated As the plate thickness gradually increases, the nonlinear hydroelastic response of the plate becomes flatter at the crest, and the change in the nonlinear hydroelastic response of the plate becomes smaller. Specifically, when... d= At time 0, the water wave becomes a pure gravity wave. This indicates that HAM not only does not depend on any small physical parameters, but also, compared to the perturbation method, the homotopy approximation solution has better convergence. In conclusion, using HAM to study the nonlinear hydroelastic response of floating elastic plates is feasible and effective.
[0027] In step 3, the plate density As the value increases, the peaks of the plate deflection become flatter, while the troughs become sharper. This is similar to the effect of the plate thickness parameter.
[0028] In step 4, for the two-module case, in addition to establishing the governing equations and surface kinematics and dynamic boundary conditions, the free boundary conditions of the plate should be considered, that is, the bending moment and equivalent shear force at the plate ends are zero; the boundary conditions at the junction of the plate and the hinge, that is, the bending moment of the plate is equal to the bending moment of the hinge; and the bending moment, shear force and deflection of the left and right plates are also equal.
[0029] In step 4, for the two-module case, the boundary conditions are numerous and complex, making it difficult to study using approximate analytical methods. Based on previous research, this patent proposes to use a numerical method—the finite element method—to study how to select reasonable physical parameters to reduce the dynamic impact on nonlinear hydroelastic waves.
[0030] The present invention has the following advantages: (1) The approximate analysis method involved in this invention can obtain the important physical parameters on the hydrodynamic characteristics of ultra-large floating structures at sea by calculating hydrodynamics, without the need for expensive test equipment and a large number of test personnel, which significantly reduces time and economic costs.
[0031] (2) The approximate analysis method for measuring the nonlinear hydroelastic response of the elastic plate proposed in this invention fills the gap in the approximate analysis technology of strongly nonlinear hydroelastic response.
[0032] (3) The approximate analysis method involved in this invention has obtained a convergent and accurate analytical solution of the hydroelastic response, which effectively reduces the computational resource requirements and improves the evaluation efficiency while ensuring computational accuracy.
[0033] (4) The evaluation method involved in this invention provides theoretical guidance for the design, construction and maintenance of offshore floating structures. Attached image description: Figure 1 This is a schematic diagram of the computational domain in an approximate analysis method based on the nonlinear hydroelastic response of ultra-large floating structures involved in this invention. Figure 2 A flowchart of an approximate analysis method based on the nonlinear hydroelastic response of ultra-large floating structures involved in this invention; Figure 3 The squared residual plot established in Example 1; Figure 4 shows the influence of important parameters obtained in Example 1, including the traveling wave amplitude, Young modulus, thickness, and density of the plate, on the hydroelastic response of the VLFS. Figure 5 This is the flowchart established in Example 2; Detailed Implementation
[0034] The present invention will now be described in detail with reference to specific embodiments. It should be noted that the following embodiments are merely further illustrations of the present invention, but the scope of protection of the present invention is not limited to the following embodiments.
[0035] Example 1 This embodiment relates to an approximate analysis method based on the nonlinear hydroelastic response of ultra-large floating structures, see [link to relevant documentation]. Figure 2 As shown, The specific steps are as follows: Step 1: Assume the VLFS is an infinitely long viscoelastic plate floating on a finite depth surface in a complex marine environment. Analyze the influence of the fluid on the nonlinear hydroelastic response of the infinitely long viscoelastic plate. Establish a Cartesian coordinate system. ,in The axis is positive with vertically upward. The axis coincides with the water surface when at rest, with the horizontal direction to the right being positive. An infinitely long viscoelastic plate floats at a depth of... On the sea and along Extending infinitely in both axial directions, the plate thickness is .
[0036] Step 1: Within the framework of potential flow theory, assuming the fluid is inviscid, incompressible, and its motion is irrotational, construct the governing equations and nonlinear boundary conditions under the coupled effects of hydrodynamic, elastic, and inertial forces. Specifically, the VLFS is set as a uniform thin viscoelastic material, and the fluid and plate are not separated; then the relationship between deflection and pressure on the lower surface of the plate is... .
[0037] Preferably, in step 1, the The pressure on the underside of the plate. To delay time, The mass per unit length of the plate, It is the plate density. It's the thickness of the plate. It is the deflection of a viscoelastic plate. The bending stiffness of the plate.
[0038] In step 1, the model further includes: at the bottom of a fluid at a finite depth. Established solid-wall impermeable conditions .
[0039] Preferably, in step 1, This represents the actual wave frequency of the water wave. This represents the linearized water wave frequency. Because the problem under consideration is nonlinear, the actual wave frequency... With linearized wave frequency There is a certain error between them, so let In step 1, the It is a constant slightly greater than 1. Independent variable transformation is established based on the traveling wave method. By merging the kinematic and dynamic boundary conditions and making them dimensionless, new kinematic and dynamic boundary conditions are obtained. , .
[0040] In step 1, the dimensionless dispersion relation expression
[0041] In step 2, based on homotopy analysis, the obtained mathematical model is transformed into another form of differential equation system. Let... and They represent and If two homotopies satisfy the following governing equations and boundary conditions, namely the zeroth-order deformation equations... , , ,
[0042] In step 1, the step 1, the and These are velocity potentials With plate deflection The initial guess solution. These are non-zero control convergence parameters. These are embedding coefficients. When the coefficients When the number of consecutive increases from 0 to 1, homotopy From the initial guess solution From continuous change to exact solution Homosexuality From the initial guess solution From continuous change to exact solution .
[0043] Step 2: Nonlinear Differential Operator and , , In step 2, the .
[0044] Step 2: Following the usual procedure, you should select... and The linear part , , As an auxiliary linear operator. However, repeated experiments showed that simply using the linear term did not yield satisfactory results. Fortunately, homotopy analysis provides us with sufficient freedom to choose a suitable auxiliary linear operator. Therefore, based on experiments, we selected the following auxiliary linear operator. ,
[0045] Step 2 attempted to change the formula above. Deleting the item directly made the calculation process much smoother, but because The term is directly related to the viscoelastic relaxation time; removing it would prevent us from calculating the relationship between the viscoelastic relaxation time and the plate deflection. After several adjustments, we finally chose to superimpose multiple linear solutions without violating the physical context, thus resolving the fifth derivative term. The resulting problems.
[0046] Step 2 Unknown variables and Expand on each of the following: The Maclaurin series is substituted into the zeroth-order deformation equation above, and both sides of the equation are let about The coefficients of the same power are equal, thus transforming the strongly nonlinear hydroelastic response model into multiple linear subproblems, i.e., higher-order deformation equations: , , In step 2, the , .
[0047] Step 2: Based on the physical background, we can obtain a linear solution expression for the hydroelastic waveform change and velocity potential. By superimposing these linear solution expressions, we can obtain a suitable solution expression for this nonlinear problem.
[0048] , , Step 2: The , , and The coefficients to be determined are denoted as .
[0049] Step 2: Based on the above solution expression, and to simplify the calculation, we choose the following initial conjecture solution. ,
[0050] Step 2: The The solution was still not found, and the equation remained unclosed. Therefore, a relationship between plate deflection and wave height was established. Relationship:
[0051] Preferably, in step 2, the It is an even number. It is an odd number. It is the dimensionless first-order solution of the homotopy approximate analytical solution of the wave height, which is the wave amplitude.
[0052] In step 2, to ensure the convergence of the approximate analytical series solution of the fluid's hydroelastic response to the elastic plate, the mathematical model introduces squared residuals corresponding to the two boundary conditions.
[0053] Preferably, in step 2, the Let represent the total number of discrete points, and assume . .
[0054] In step 2, the total squared residual of each order approximate solution With convergence control parameters It changes with the changes. Let Using Mathematics software programming, in Under the minimum condition, it can be obtained The optimal solution. For each order of solution, there is always... The existence of a minimum value indicates the existence of an optimal solution. Furthermore, as the order increases... The increase in total squared residuals The value decreases rapidly. These conclusions guarantee that the approximate analytical solution is convergent and accurate.
[0055] Step 2: The calculation includes dimensional parameters as follows: , , , , , , , , , . Figure 3 show exist There exists a minimum value. When the order of the approximate analytical solution... hour, The optimal solution is At this point, the total squared residual The minimum value of . These results guarantee that the homotopy approximation analytical solution is convergent and accurate.
[0056] Step 3: Figure 4-1 The display shows the viscoelastic relaxation time. As the time increases from 0.5 s to 1 s, the deformation of the viscoelastic plate... along with As the wave increases, the peaks become flatter and the troughs become steeper. Figure 4-2 In the middle, plate deflection With amplitude The increase is significant; Figure 4-3 Display board deflection , and As it gradually increases, It decreases as the Young's modulus of the plate increases; from Figure 4-4 Discover, With plate thickness Decrease due to increase; according to Figure 4-5 It can be known that With dimensionless coefficient The increase is significant with the increase of the nonlinear wave amplitude, which suggests that if a linear dispersion relation is used, we may underestimate the change in the nonlinear wave amplitude. Figure 4-6 This demonstrates the plate deflection in , and When it increases, The magnitude of the change decreases as the water depth increases; Figure 4-7 In the middle, frequency With amplitude The increase with the increase of amplitude indicates that the nonlinearity of the hydroelastic response of the floating viscoelastic plate changes with the amplitude. The increase in amplitude enhances the effect. Comparative results show that when the amplitude... viscoelastic relaxation time Young's modulus of the plate and plate thickness When the deformation is changed, the viscoelastic plate shows a clearly visible change.
[0057] Example 2 This embodiment relates to an approximate analysis method based on the nonlinear hydroelastic response of ultra-large floating structures, see [link to relevant documentation]. Figure 2 Show, The specific steps are as follows: Step 1: From the perspective of ease of design, manufacturing, transportation, and installation, VLFS is usually designed as a multi-module form connected by hinges in actual engineering. This patent assumes that VLFS is a two-module floating body connected by hinges.
[0058] Step 1: Within the framework of potential flow theory, assuming the fluid is inviscid, incompressible, and its motion is irrotational, construct the governing equations and nonlinear boundary conditions under the coupled effects of hydrodynamics, elasticity, and inertia. Furthermore, construct the free boundary conditions for the plate, i.e., the bending moment and equivalent shear force at the plate ends are zero. Boundary conditions of the plate and hinge ( That is, the bending moment of the plate is equal to the bending moment of the hinge. , Preferably, in step 1, the Let the rotational stiffness be at the hinge. The elastic stiffness of the plate. This is the junction between the left and right panels.
[0059] Step 1: Also includes in At that point, the bending moment, shear force, and deflection are also equal: Step 2: For the two-module case, the boundary conditions are numerous and complex, making it difficult to study using approximate analytical methods. Based on previous research, this patent proposes to use a numerical method—the finite element method—to investigate how to select reasonable physical parameters to reduce the dynamic impact on nonlinear hydroelastic waves in the presence of rotary shear flow. See the flowchart. Figure 5 . Step 2: For the two-module case, the boundary conditions are numerous and complex, making it difficult to study using approximate analytical methods. Based on previous research, this patent proposes to use a numerical method—the finite element method—to investigate how to select reasonable physical parameters to reduce the dynamic impact on nonlinear hydroelastic waves in the presence of rotary shear flow. See the flowchart. Figure 5 . This invention establishes a computational domain using Mathematics software to analyze the hydrodynamic effects of fluids on different floating structures. By selecting appropriate boundary conditions and solvers, it performs hydrodynamic characteristic analysis of the floating body within a steady-state flow field, enabling reliable prediction of key parameters for the nonlinear hydroelastic effects on ultra-large marine floating structures. The approximate analytical analysis method for measuring the nonlinear hydroelastic response of elastic plates proposed in this invention fills a gap in analytical analysis techniques for nonlinear hydroelastic responses. It achieves high computational efficiency while maintaining high accuracy, significantly reducing the time and economic costs of analyzing hydroelastic responses, and providing crucial theoretical support for the design, construction, and maintenance of offshore floating structures. Notably, this invention focuses on proposing an approximate analytical method for the nonlinear hydroelastic response of ultra-large floating structures, and is not limited by complex sea conditions or the inherent physical properties of the structure itself.
[0060] The specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various modifications or variations within the scope of the claims, which do not affect the essence of the present invention.
Claims
1. An approximate analytical method for the nonlinear hydroelastic response of very large floating structures (VLFS), characterized in that, Includes the following steps: Step 1: Within the framework of potential flow theory, construct the governing equations and nonlinear boundary conditions under the coupled effects of hydrodynamics, elasticity, and inertia. Step 2: For the single-module case, the Homotopy Analysis Method (HAM) is used to transform it into multiple linear subproblems. At the same time, the velocity potential and plate deflection to be determined are expressed in series form. The optimal convergence control parameter values are selected using Mathematics software to obtain its convergent approximate analytical solution. Step 3: Analyze the influence of important physical quantities such as the Young's modulus, thickness, density, and traveling wave amplitude of the plate on the dynamic characteristics of the buoy; Step 4: For the case of a two-module combined floating body connected by hinges, the finite element method is used to analyze how to select reasonable modules, connection stiffness and form to reduce the impact of the dynamic characteristics of the floating body.
2. The approximate analysis method for the nonlinear hydroelastic response of ultra-large floating structures according to claim 5, characterized in that, The aforementioned ultra-large floating structure is assumed to be an elastic plate. It is the deflection of the elastic plate. It is the pressure on the underside of the plate. Given the fluid density and the fact that the fluid and the plate are not separated, the relationship between the deflection and the pressure on the lower surface of the plate is: flexural stiffness of the plate , The Young's modulus of the plate. It's the thickness of the plate. Compared to Poisson, It is gravitational acceleration. , It is the plate density.
3. The approximate analysis method for the nonlinear hydroelastic response of ultra-large floating structures according to claim 1, characterized in that, In step 2, homotopy analysis (HAM) is used, based on topological principles, to transform the mathematical model in claim 8 into a zero-order deformation equation. .
4. The approximate analysis method for the nonlinear hydroelastic response of ultra-large floating structures according to claim 9, characterized in that, The For linear operators, It is a nonlinear operator; For embedded variables. When As the number of consecutive increments from 0 to 1 increases, the two homotopies... Starting from the initial guesses respectively Obtain the exact solution to the system of equations and .
5. The approximate analysis method for the nonlinear hydroelastic response of ultra-large floating structures according to claim 1, characterized in that, In step 2, based on the HAM algorithm, Expand on each of the following: Substituting the Maclaurin series into the above zeroth-order deformation equation, let both sides of the equation with respect to... Equal powers of the same order are equal, thus yielding higher-order deformation equations.
6. The approximate analysis method for the nonlinear hydroelastic response of ultra-large floating structures according to claim 1, characterized in that, In step 3, to ensure the convergence of the homotopy analytical series solution to the hydroelastic response problem of an infinitely long plate in a single-layer fluid, a total squared residual corresponding to the two boundary conditions is introduced. .
7. The approximate analysis method for the nonlinear hydroelastic response of a large-scale floating structure according to claim 14, characterized in that, The Let represent the total number of discrete points, and set . .
8. The approximate analysis method for the nonlinear hydroelastic response of ultra-large floating structures according to claim 14, characterized in that, The total squared residual of each order approximate solution With convergence control parameters It changes with the changes. For each order of solution, there is always... The existence of a minimum value indicates the existence of an optimal solution. Furthermore, as the order increases... The increase, The value decreases rapidly. Therefore, the final result is... The optimal solution is found. These results guarantee that the homotopy approximation analytical solution is convergent and accurate.
9. The approximate analysis method for the nonlinear hydroelastic response of ultra-large floating structures according to claim 1, characterized in that, In step 3, important physical quantities such as the Young's modulus, thickness, density, and traveling wave amplitude of the plate have a significant impact on the dynamic characteristics of the buoy. When the Young's modulus of the plate... E As the values gradually increase from small to large, the change in plate deflection becomes smaller; as the plate thickness increases, the nonlinear hydroelastic response of the plate becomes flatter at the crest, and the change in the nonlinear hydroelastic response of the plate becomes smaller. This variation continues with increasing plate density. As the plate thickness increases, the peaks of the plate deflection become flatter, while the troughs become sharper. This is similar to the effect of plate thickness; the incident wave amplitude... As the wave size increases, the plate deflection changes significantly, becoming sharper at the crests and steeper at the troughs. The results demonstrate the feasibility and effectiveness of using HAM to study the nonlinear hydroelastic response of floating VLFS.
10. The approximate analysis method for the nonlinear hydroelastic response of ultra-large floating structures according to claim 1, characterized in that, In step 4, in addition to establishing the governing equations and surface kinematics and dynamic boundary conditions, the free boundary conditions of the plate should be considered, namely, the bending moment and equivalent shear force at the plate ends are zero; the boundary conditions at the junction of the plate and the hinge are, namely, the bending moment of the plate is equal to the bending moment of the hinge; and the bending moment, shear force and deflection of the left and right plates are also equal. The boundary conditions are numerous and complex, making it difficult to study using approximate analytical methods. Based on previous research, this patent proposes to use a numerical method—the finite element method—to study how to select reasonable physical parameters to reduce the dynamic impact on nonlinear hydroelastic waves.