A marine double-layer composite structure, an analytical calculation method and an optimization design method

Abstract

This invention discloses a marine double-layer composite structure, an analytical calculation method, and an optimization design method. The calculation method includes the following steps: S1, establishing an RVE model for multiple layers of the structure to obtain the functional relationship between the macroscopic mechanical performance parameters and microscopic components of the layers; S2, establishing a dynamic equivalent model of the structure to obtain the contact surface strain equation and the homogenized bending stiffness equation; S3, establishing a novel hydroelastic analytical model of the structure under wave action to obtain the contact surface strain equation of the layers; S4, obtaining the contact surface strain of the layers based on the structural parameters of the structure and the contact surface strain equation of the layers; S5, comparing the contact surface strain of the layers with the tensile yield strain to obtain the plastic damage region of the layers. The method of this application simultaneously considers multiple scale issues such as wave action, the layering and geometric characteristics of the composite structure, and the microscopic composition of the materials, resulting in more reliable analysis results.

Description

Technical Field

[0001] This invention relates to the field of marine structure design technology, specifically to a marine double-layer composite structure, analytical calculation method, and optimization design method. Background Technology

[0002] In recent years, photovoltaic (PV) power generation has become one of the important development directions of the new energy industry. However, PV power plants require a huge area, while coastal areas with high demand for new energy are often densely populated and land is scarce. To address these contradictions, many studies have proposed the concept of PV systems in marine environments. Due to the low ambient temperature, land use conflicts are avoided, and floating PV is more competitive than terrestrial PV in terms of production efficiency and cost. Unlike lakes or reservoirs, deploying PV facilities at sea requires the design of a stable and durable support platform to withstand continuous wave action. Considering the large-scale production of the PV industry, this support platform must be large enough. Ultra-large floating bodies are a new type of marine engineering structure that has been developed in recent decades. They play an important role in the utilization of marine space and provide new development ideas for the offshore PV industry.

[0003] Considering the continuous wave action and the low self-weight of photovoltaic modules, ultra-large floating photovoltaic support structures can be designed as lightweight, high-stiffness floating double-layer structures composed of ultra-high performance concrete (UHPC) panels and polystyrene foam (EPS) base plates. This structure is large-area and cost-controllable. EPS foam has a low market price and strong deformability, providing buoyancy while buffering the wave action on the concrete layer, which in turn suppresses excessive deformation of the foam structure, enhancing structural safety. However, most current analytical calculation methods for ultra-large floating structures are still limited to assuming a single-layer homogeneous structure, neglecting to control self-weight and improve structural performance (such as stiffness and strength). Furthermore, the calculation process generally does not involve the internal deformation response of the structure or the assessment of its elasto-plastic state. Taking traditional hydroelastic theory models as an example, the structural deflection, bending moment, and shear force calculated based on wave parameters and basic sea conditions cannot provide direct guidance for the design and analysis of structures in practical engineering. When designing the aforementioned ultra-large double-layer floating structure, it is essential to consider the sheer size of the overall structure, which can reach hundreds of meters in length. Compared to the overall structure, the microscopic components of the double-layer composite material are approximately millimeters or even micrometers in size. Modeling and analyzing the hydrodynamic, structural, and material properties at different geometric scales is a complex multi-scale problem. A key step is to achieve cascaded calculations of wave action, the layering and geometric characteristics of the floating structure, and the microscopic composition of the materials. To provide concrete guidance for engineering design, a novel multi-scale calculation method that couples hydrodynamics, structure, and materials, including elastoplastic state assessment, should be developed for the design of such marine structures. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the purpose of this invention is to provide an analytical calculation method for marine double-layer composite structures.

[0005] Furthermore, this application also provides an optimized design method for marine double-layer composite structures.

[0006] Furthermore, this application also provides a marine double-layer composite structure.

[0007] The technical solution adopted in this invention is:

[0008] An analytical calculation method for a marine double-layer composite structure, wherein the marine double-layer composite structure consists of a top layer and a bottom layer, the top layer consists of a UHPC matrix and steel fibers embedded in the UHPC matrix, and the bottom layer is EPS material;

[0009] The calculation method includes the following steps:

[0010] S1. Establish multiple surface layer RVE models, and obtain the functional relationship between the macroscopic mechanical property parameters and microscopic components of the surface layer based on the surface layer RVE models;

[0011] S2. Establish a dynamic equivalent model of the structure. Based on the dynamic equivalent model and the functional relationship between the macroscopic mechanical performance parameters and microscopic components of the surface layer, obtain the contact surface strain equation and the homogenized bending stiffness equation of the structure.

[0012] S3. Establish a novel hydroelastic analytical model for structures under waves. Based on the novel hydroelastic analytical model, the contact surface strain equation and the homogenized bending stiffness equation of the structure, obtain the contact surface strain equation of the surface layer.

[0013] S4. Obtain the contact surface strain of the surface layer based on the structural parameters of the structure and the contact surface strain equation of the surface layer;

[0014] S5. Compare the contact surface strain of the surface layer with the tensile yield strain of the material. If the contact surface strain of the surface layer is greater than the tensile yield strain of the material, it indicates that the surface layer has a plastic damage area.

[0015] Furthermore, in step S1, multiple surface layer RVE models are established, specifically including the following steps:

[0016] S11. Establish a UHPC matrix model based on the performance parameters of the UHPC matrix material;

[0017] S12. Based on the volume fraction of steel fibers, establish multiple randomly distributed steel fiber units;

[0018] S13. Embed the steel fiber unit into the UHPC matrix model to complete the surface assembly;

[0019] S14. Mesh the UHPC matrix and steel fiber separately to form surface layer RVE models with different microstructures.

[0020] Furthermore, in step S1, obtaining the functional relationship between the macroscopic mechanical property parameters and microscopic components of the surface layer based on the surface layer RVE model specifically includes the following steps:

[0021] S15. Perform displacement loading analysis on each surface layer RVE model under periodic boundary conditions to obtain the macroscopic mechanical performance parameters of each surface layer RVE model.

[0022] S16. Based on the macroscopic mechanical property parameters and microscopic composition of each surface layer RVE model, obtain the functional relationship between the macroscopic mechanical property parameters and microscopic composition of the surface layer.

[0023] Furthermore, step S2 specifically includes the following steps:

[0024] S21. Construct the bending moment-curvature equation of the structure during the elastic deformation stage;

[0025] S22. Assuming the structure is a perfectly fitted homogeneous double-layer composite structure, construct the deflection differential equation of the structure during the elastic deformation stage.

[0026] S23. Construct the continuity equation of the non-uniform interface of the structure during the elastic deformation stage;

[0027] S24. Construct the equation for the total bending moment of the structure during the elastic deformation stage;

[0028] S25. Based on the moment-curvature relationship equation, the deflection differential equation, the non-uniform interface continuity equation, and the total moment equation, the strain equation of the overall structure at the contact surface and the homogenized bending stiffness equation of the double-layer structure are obtained.

[0029] Furthermore, the strain equation for the contact surface of the structure in step S2 is:

[0030]

[0031] Where, ε int E1 is the strain at the contact surface, E2 is the elastic modulus of the first layer material, E2 is the elastic modulus of the second layer material, t1 is the thickness of the first layer, t2 is the thickness of the second layer, R is the radius of curvature of the structure under external bending moment, and W is the deflection generated when the structure bends.

[0032] Furthermore, the homogenized bending stiffness equation of the structure in step S2 is:

[0033]

[0034] Among them, K b E represents the uniform bending stiffness of a double-layer floating structure. b It refers to the homogenized equivalent elastic modulus of the double-layer structure, I b It refers to the homogenized equivalent cross-sectional moment of inertia of a double-layer structure, where v1 is the Poisson's ratio of the first layer material and v2 is the Poisson's ratio of the second layer material.

[0035] Furthermore, step S3 specifically includes the following steps:

[0036] S31. Establish a novel hydroelastic analytical model for structures under waves;

[0037] S32. Divide the fluid domain in which the structure is located into three regions, and establish the boundary condition equations that the spatial velocity potential of each region needs to satisfy, as well as the end condition equations of the structure.

[0038] S33. Based on the homogenized bending stiffness equation of the structure, the new hydroelastic model, the boundary condition equation of the region, and the end condition equation of the structure, the spatial deflection equation of the double-layer floating structure is obtained.

[0039] S34. Based on the contact surface strain equation and spatial deflection equation of the structure, obtain the contact surface strain equation of the surface layer;

[0040] S35. Based on the new hydroelastic model, the contact surface strain equation of the surface layer obtained in step S34 is transformed into a linear equation.

[0041] Furthermore, in step S3, the strain function of the contact surface of the surface layer is:

[0042]

[0043] Where, ε int (x,t) is the strain function of the contact surface of the surface layer, W′(x,t)=Re[w′(x)e -iωt ],W″(x,t)=Re[w″(x)e -iωt ].

[0044] Furthermore, this application also provides an optimized design method for a marine double-layer composite structure, comprising the following steps:

[0045] S100. Construct an initial design structure with initial structural parameters and initial microstructure based on the design conditions;

[0046] S200. Based on the above calculation method, determine whether the structure has a plastic damage area under the design working conditions; if so, proceed to step S300.

[0047] S300: Optimize the structural parameters and / or microstructure of the initial design structure to obtain the optimized structure; and repeat step S200 until there is no plastic damage area.

[0048] Furthermore, this application also provides a marine double-layer composite structure designed using the above-mentioned optimization design method, wherein the volume fraction of the steel fiber is 1% to 4%.

[0049] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application. Attached Figure Description

[0050] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn to scale.

[0051] Figure 1 To establish the microscopic composition RVE model of ultra-high performance concrete material as described in this invention;

[0052] Figure 2 This is a schematic diagram of the equivalent dynamic model of the small flexural deformation of the floating double-layer structure described in this invention;

[0053] Figure 3 This is a strain distribution diagram of the equivalent overall structure of the floating double-layer structure described in this invention in the separated state for each individual layer and in the laminated state;

[0054] Figure 4 This is a schematic diagram illustrating the hydroelasticity problem of the floating double-layer structure described in this invention under wave action;

[0055] Figure 5 This is a schematic diagram of the engineering design dimensions of the floating double-layer structure in an embodiment of the present invention;

[0056] Figure 6 The curves showing the variation of reflection coefficient and transmission coefficient with wavenumber obtained from the original design calculations in this embodiment of the invention are shown.

[0057] Figure 7 The results are the dimensionless deflection, dimensionless bending moment, dimensionless shear force, and contact surface strain amplitude obtained from the original design calculations in the embodiments of the present invention.

[0058] Figure 8 The results of dimensionless deflection, dimensionless bending moment, and dimensionless shear force calculated by each model in the embodiments of the present invention are as follows:

[0059] Figure 9 These are the frequency domain solutions of the contact surface strain amplitudes calculated by each model in the embodiments of the present invention, and the time domain solutions of the strain with the corresponding maximum amplitude.

[0060] Figure 10 The curves showing the variation of the maximum contact surface strain calculated by each model in the embodiments of the present invention with the change of the volume fraction of steel fibers in UHPC material are shown. Detailed Implementation

[0061] The embodiments of the technical solution of the present invention will be described in detail below with reference to specific examples. These embodiments are only used to more clearly illustrate the technical solution of the present invention, and are therefore merely examples and should not be used to limit the scope of protection of the present invention.

[0062] It should be noted that, unless otherwise stated, the technical or scientific terms used in this application should have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0063] Example 1

[0064] This embodiment provides an analytical calculation method for a marine double-layer composite structure, which consists of a surface layer and a bottom layer. The surface layer is composed of a UHPC matrix and steel fibers embedded in the UHPC (ultra-high performance concrete) matrix. The volume of the steel fibers accounts for 1%-4% of the total volume of the surface layer. The bottom layer is EPS (polystyrene foam) material.

[0065] The double-layered composite structure at sea is subjected to continuous waves, and the self-weight of the solar power generation components on it is relatively low, so its weight can be ignored in the calculation.

[0066] The analytical calculation method for marine double-layer composite structures includes the following steps:

[0067] S1. Establish multiple surface layer RVE (representative volume element) models, and obtain the functional relationship between the macroscopic mechanical property parameters and microscopic components of the surface layer based on the surface layer RVE models.

[0068] Specifically, in step S1, multiple surface layer RVE models are established in the simulation software, which includes the following steps:

[0069] S11. Establish a UHPC matrix model based on the performance parameters of the UHPC matrix material.

[0070] The performance parameters of the UHPC matrix material can be obtained through matrix material performance tests, mainly including the elastic modulus, Poisson's ratio and yield strength of the UHPC matrix. Based on the UHPC matrix material performance parameters obtained from the tests, a UHPC matrix model is established.

[0071] S12. Based on the volume fraction of steel fibers, establish multiple randomly distributed steel fiber units.

[0072] The volume fraction of steel fibers is defined as the percentage of the steel fiber volume relative to the total volume of the surface layer. In this embodiment, the volume of steel fibers accounts for 1% to 4% of the total volume of the surface layer (the total volume of the surface layer is the sum of the UHPC matrix volume and the steel fiber volume).

[0073] Specifically, the volume fraction of steel fibers can be 1%, 2%, 3%, and 4%, respectively.

[0074] Both the UHPC matrix and the steel fiber elements are modeled using solid elements, and then materials are assigned to them after modeling.

[0075] S13. Embed the steel fiber unit into the UHPC matrix model to complete the surface assembly.

[0076] Specifically, steel fiber units with different volume fractions are embedded into the corresponding UHPC matrix model to complete the assembly of multiple surface layers.

[0077] During assembly, an embedded constraint method with built-in regions is used to enable interaction between the steel fiber unit interface and the UHPC matrix model, so that both the UHPC matrix and the steel fiber can be separately meshed with structured meshes.

[0078] S14. Mesh the UHPC matrix and steel fiber separately to form surface layer RVE models with different microstructures.

[0079] Micro-components refer to the volume fraction of steel fibers in the surface layer RVE model.

[0080] like Figure 1 As shown in this embodiment, four surface layer RVE models are established with steel fiber volume fractions of 1%, 2%, 3%, and 4%, respectively.

[0081] In step S1, the functional relationship between the macroscopic mechanical property parameters and microscopic components of the surface layer is obtained based on the surface layer RVE model. This specifically includes the following steps:

[0082] S15. Perform displacement loading analysis on each surface layer RVE model under periodic boundary conditions to obtain the macroscopic mechanical performance parameters of each surface layer RVE model.

[0083] By applying periodic boundary conditions to the surface layer RVE model using the micromechanics plugin in the simulation software, displacement loading analysis was performed on the surface layer RVE model to verify the stress and strain continuity of the surface layer. The analysis results were then processed to obtain the macroscopic mechanical performance parameters of each surface layer RVE model.

[0084] The macroscopic mechanical performance parameters of the surface layer RVE model include: homogenized elastic modulus, Poisson's ratio, and tensile yield strength.

[0085] S16. Based on the macroscopic mechanical property parameters and microscopic composition of each surface layer RVE model, obtain the functional relationship between the macroscopic mechanical property parameters and microscopic composition of the surface layer.

[0086] That is, by fitting the macroscopic mechanical property parameters and microscopic components of multiple surface layer RVE models, the functions of elastic modulus and steel fiber volume fraction, Poisson's ratio and steel fiber volume fraction, and tensile yield strength and steel fiber volume fraction of the surface layer are obtained, which are used as parameters for establishing the overall dynamic equivalent model of the double-layer composite structure.

[0087] After obtaining the functional relationship between the macroscopic mechanical properties of the surface layer and its microscopic components, the goodness of fit of the above functional relationship can be verified through physical experiments.

[0088] S2. Establish a dynamic equivalent model of the structure. Based on the dynamic equivalent model and the functional relationship between the macroscopic mechanical performance parameters and microscopic components of the surface layer, obtain the contact surface strain equation and the homogenized bending stiffness equation of the structure.

[0089] Specifically, when the method of this application is used for analytical calculation of existing ultra-large double-layer floating structures, a dynamic equivalent model is established based on the macroscopic structural parameters and microscopic components of the double-layer floating structure to determine whether the structure has any safety risks under the corresponding working conditions.

[0090] When the method of this application is applied to the design of ultra-large floating structures, a dynamic equivalent model of the double-layer floating structure can be established based on the macroscopic structural parameters and microscopic composition of the initially designed ultra-large double-layer floating structure, according to engineering requirements. The plastic damage region of the double-layer floating structure can be obtained, and the parameters and microscopic composition of the structure can be optimized based on the plastic damage region. Iterative calculations are performed until the structure has no potential damage risk under the design conditions.

[0091] Structural parameters refer to the length (l), width (d), and thickness (t) of the double-layer floating structure, the thickness of the top layer (t2), and the thickness of the bottom layer (t1).

[0092] Step S2 specifically includes the following steps:

[0093] S21. Construct the bending moment and curvature equations for the structure during the elastic deformation stage.

[0094] like Figure 2 As shown, a rectangular coordinate system is established with the length of the double-layer floating structure as the x-axis, the thickness as the z-axis, and the center of the bottom surface of the bottom layer as the origin.

[0095] During the elastic deformation stage, the double-layer floating structure is subjected to an external bending moment M, which causes it to deform from a straight shape into a curved shape with a radius of curvature R. Assuming that the two layers are separate and do not affect each other, the relationship between the bending moment M and the resulting R on each layer and the material properties and geometric dimensions of each layer can be listed.

[0096]

[0097] Among them, M i R is the bending moment experienced by the i-th layer of the structure. i Let be the radius of curvature of the i-th layer. Let E be the moment of inertia of the cross section of the i-th layer structure. i Let v be the elastic modulus of the i-th layer material. i Let be the Poisson's ratio of the i-th layer material, d be the width of the double-layer floating structure (the length and width of the top and bottom layers are the same), and t be the length of the top layer material. i Let be the thickness of the i-th layer.

[0098] In this embodiment, the first layer is the bottom layer, and the second layer is the top layer.

[0099] S22. Assuming the structure is a perfectly fitted, homogeneous double-layer composite structure, construct the flexural differential equation of the structure during the elastic deformation stage.

[0100] Assuming that the deformation state of each individual layer is the same as the final state of the combined layer, i.e., the two layers are completely bonded to form a homogenized double-layer composite structure, and considering the small deflection deformation condition of a large-area thin plate, the deflection and curvature of the double-layer structure can be considered to satisfy R1≈R2≈R and W1≈W2≈W. Then, the deflection differential equation of each layer can be listed as follows:

[0101]

[0102] Among them, W i Let represent the deflection of the i-th layer of the structure when it bends, W represent the overall structural deflection, and R represent the radius of curvature of the overall structure.

[0103] S23. Construct the continuity equation of the non-uniform interface of the structure during the elastic deformation stage.

[0104] In a multilayer double-layer composite structure, the strain (internal deformation) of each layer at the contact surface between different material layers is equal, and the corresponding expression can be written as:

[0105]

[0106] Where, ε int The strain at the contact surface of the overall structure. Let ε be the strain at the contact surface of the i-th layer.bi For the i-th layer structure at bending moment M i The strain ε produced under action ei Let be the strain of the i-th layer under the action of force P to maintain its laminated state. Since the layers do not separate, the strain is such that under bending moment M... i Under the influence of force, in order to maintain the laminated state, the i-th layer will be subjected to a compressive or tensile force P, and will generate a corresponding strain ε. ei In this deformed state, the two layers of material at z = t1 (e.g., Figure 2 The strain at time ) can be expressed as follows:

[0107]

[0108]

[0109] When a double-layered structure undergoes small flexural deformation, the strain generated in each layer under the action of force P to maintain the laminated state can be expressed as follows:

[0110]

[0111]

[0112] S24. Construct the equation for the total bending moment of the structure during the elastic deformation stage.

[0113] In addition, the force P acting on each layer forms a pair of bending moments M. 12 And M 12 =P×(t1+t2) / 2, then the total bending moment of the overall double-layer structure can be listed as:

[0114] M = M1 + M2 + M 12 (6)

[0115] Where M is the total bending moment of the double-layer floating structure, M1 is the bending moment of the first layer structure, M2 is the bending moment of the second layer structure, and M... 12 The bending moment is the force P acting on each layer.

[0116] S25. Based on the moment-curvature relationship equation, the deflection differential equation, the non-uniform interface continuity equation, and the total moment equation, the strain equation of the overall structure at the contact surface and the homogenized bending stiffness equation of the double-layer structure are obtained.

[0117] Specifically, based on formulas (2), (3), (4a), (4b), (5a), and (5b), the applied force P and the strain ε at the contact surface are calculated. int :

[0118]

[0119]

[0120] Based on formulas (2), (3), (4a), (4b), (5a), (5b) and (6), calculate the total bending moment M on the double-layer floating structure:

[0121]

[0122] Considering the basic assumptions of the subsequent hydroelastic analysis model, during the bending process of the double-layer structure, the dimensions of the length l and width d of the floating element are l = d = 1. The double-layer structure can be equivalent to a homogeneous structure. According to formulas (9) and (1), the homogenized bending stiffness K of the double-layer structure is calculated. b :

[0123]

[0124] Among them, E b It is the homogenized equivalent elastic modulus of the double-layer structure, I b It refers to the homogenized equivalent cross-sectional moment of inertia of a double-layer structure.

[0125] like Figure 3 As shown, it should be noted that because the elastic modulus of the surface layer material is much greater than that of the bottom layer material, the neutral plane of the double-layer floating structure is roughly at the same position as the neutral plane of the surface layer, and the maximum strain of the surface layer is located at the contact surface. Furthermore, EPS foam has strong deformation capacity, while UHPC material is prone to cracking after deformation; therefore, the design primarily considers the plastic cracking of the surface layer.

[0126] S3. Establish a novel hydroelastic analytical model for structures under waves. Based on the novel hydroelastic analytical model, the contact surface strain equation and the homogenized bending stiffness equation of the structure, obtain the contact surface strain equation of the surface layer.

[0127] S31. Establish a novel hydroelastic analytical model for structures under wave action.

[0128] A rectangular coordinate system is established with the length of the double-layer floating structure as the x-axis, the thickness as the z-axis, and the midpoint as the origin.

[0129] A novel hydroelastic analytical model for ultra-large double-layer floating structures is established. Assuming the longitudinal length of the structure is much greater than the water depth and the incident wavelength, the velocity potential function Φ(x,z,t) can be expressed as follows for a linear wave problem:

[0130] Φ(x,z,t)=Re[φ(x,z)e -iωt (11)

[0131] Where φ(x,z) is the spatial velocity potential, Re is the real part of the independent variable, and e -iωt The time factor.

[0132] Assuming the structure undergoes simple harmonic motion with small amplitude under wave action, the following expression can be given:

[0133]

[0134] Among them, P b W, S, and M represent the wave pressure, deflection, shear force, and bending moment distributed in the time and space of the double-layer floating structure, respectively; p, w, ... and The wave pressure, deflection, shear force, and bending moment are spatially distributed within the structure.

[0135] S32. Divide the fluid domain in which the structure is located into three regions, and establish the boundary condition equations that the spatial velocity potential of each region needs to satisfy, as well as the end condition equations of the structure.

[0136] like Figure 4 As shown, the fluid domain in which the structure is located is divided into three regions: the left open region 1, the region below the floating body 2, and the right open region 3.

[0137] The open region on the left is defined as follows: region 1: x ≤ -b, –h ≤ z ≤ 0; region 2 below the buoy: -b ≤ x ≤ b, –h ≤ z ≤ 0; and open region 3 on the right: x ≥ b, –h ≤ z ≤ 0.

[0138] Where b is half the width of the float, the origin of the x and z coordinates is located at the midpoint of the float, and h is the water depth.

[0139] For each region, the spatial velocity potential satisfies the Laplace equation, which can be expressed as follows:

[0140]

[0141] Furthermore, the boundary conditions related to the water surface (14), bottom (15), and far field (16) satisfied by the velocity potential can be obtained, and can be expressed as follows:

[0142]

[0143]

[0144]

[0145]

[0146]

[0147] Where h is the water depth, c is the total thickness of the double-layer floating structure, c = t1 + t2, k0 is the wave number, ρ is the seawater density, g is the gravitational acceleration, and ρ b is the equivalent density of the structure, and i is a complex unit.

[0148] For the structural region, the spatial velocity potential satisfies the transverse vibration equation, which can be expressed as follows:

[0149]

[0150] Where c is the thickness of the double-layer floating structure, i.e., c = t1 + t2.

[0151] If the spatial velocity potential function satisfies the Laplace governing equation, then the boundary conditions satisfied by the velocity potential can be listed as follows:

[0152]

[0153]

[0154]

[0155] Where H is the wave height of the incident wave, and R... m (m≥0), A m (m≥-2), B m (m≥-2) and T m (m≥0) represents unknown coefficients to be determined; Z m (z) and Y m (z) is the characteristic function that needs to be solved, and the equation can be written as follows:

[0156]

[0157]

[0158] k0, k m and λ m For wavenumber, the dispersion relation must be satisfied, and the equation can be written as follows:

[0159] ω 2 =gk0 tan h(k0h)=-gk m tank m h,m≥1 (21)

[0160]

[0161] Where g is the acceleration due to gravity, and h is the water depth. ρ is the density of seawater, ρ b The equivalent density of the double-layer floating structure.

[0162] The undetermined coefficients and characteristic functions in the above equations can be obtained by substituting the boundary conditions (23) between adjacent regions and the end conditions (24) of the double-layer floating structure into the solution. The corresponding boundary conditions and end conditions can be expressed as follows:

[0163] φ1=φ2,x=-b,-h≤z≤0 (23a)

[0164]

[0165] φ2=φ3,x=b,-h≤z≤0 (23c)

[0166]

[0167]

[0168]

[0169] Solve R m (m≥0) and T m (m≥0) The reflection coefficient K of the structure can be obtained. r and transmission coefficient K t , can be represented as follows:

[0170] K r =|R0|,K t =|T0|(25)

[0171] S33. Based on the homogenized bending stiffness equation of the structure, the novel hydroelastic model, the boundary condition equations of the region, and the end condition equations of the structure, the spatial deflection equation of the structure is obtained:

[0172] Based on solving the undetermined coefficients and characteristic functions in the velocity potential equation, the spatial deflection of the structure can be further calculated, as shown in the formula:

[0173]

[0174] The bending moment and shear force in a double-layer structure can be calculated using the following formula:

[0175]

[0176]

[0177] S34. Based on the contact surface strain equation and spatial deflection equation of the structure, obtain the contact surface strain equation of the surface layer.

[0178] Compared to traditional hydroelastic theory models, the new model couples material composition with structural performance to obtain overall stiffness, and then introduces strain calculation as a primary factor in determining the potential damage zone of floating structures. This can be expressed as follows:

[0179]

[0180] Where W′(x,t)=Re[w′(x)e -iωt ],W″(x,t)=Re[w″(x)e -iωt Considering the small deflection deformation condition of the hydroelastic problem, a constant assumption (1+W′) can be given in the calculation. 2 (x,t)) 3 / 2 ≈1.

[0181] S35. Based on the new hydroelastic model, the contact surface strain equation of the surface layer obtained in step S34 is transformed into a linear equation.

[0182] For a linear harmonic problem, the solution for the strain distribution of the contact surface in the frequency domain can be expressed as follows:

[0183]

[0184] Dimensionless deflection, bending moment, shear force, and contact surface strain can be defined as follows:

[0185]

[0186]

[0187]

[0188]

[0189] It should be noted that the contact surface strain is a dimensionless quantity and has a strong correlation with the amplitude of the wave height.

[0190] S4. Obtain the surface strain of the surface layer based on the structural parameters of the structure and the surface strain equation of the surface layer.

[0191] S5. Compare the contact surface strain of the surface layer with the tensile yield strain of the surface layer. If the contact surface strain of the surface layer is greater than the tensile yield strain, it indicates that the surface layer has a plastic damage area, where the tensile yield strain is ε. tu =σ tu / E f , where σ tu E represents the tensile yield strength of the surface layer. f These are the elastic moduli of the surface layer, and all are obtained from S1.

[0192] To intuitively analyze the impact of design parameters, the wave height can be set to a constant value in the contact surface strain calculation, depending on the specific working conditions of the engineering sea area.

[0193] When the calculated contact surface strain is greater than the yield strain of the corresponding material, the material layer in the contact surface region yields and enters the elastoplastic deformation stage.

[0194] Because EPS foam has strong deformation capacity in actual engineering, UHPC material is prone to cracking after deformation. Therefore, the design mainly considers the plastic cracking of the surface layer, that is, only focuses on the location and magnitude of the plastic area generated in the surface layer.

[0195] The method described in this application can be used for analytical calculations of existing marine double-layer composite structures. Based on the structural parameters of the existing marine double-layer composite structure, its plastic damage area can be calculated. If there is no plastic damage area, it indicates that the structure does not pose a safety risk under the corresponding working condition and meets the design requirements; otherwise, it indicates that the structure poses a safety risk under the corresponding working condition.

[0196] Example 2

[0197] This embodiment provides an optimized design method for a marine double-layer composite structure, which includes the following steps:

[0198] S100. Construct an initial design structure with initial structural parameters and initial microstructure based on the design conditions;

[0199] S200. According to the calculation method described in Example 1, determine whether the structure has a plastic damage area under the design working conditions; if so, proceed to step S300.

[0200] S300: Optimize the structural parameters and / or microstructure of the initial design structure to obtain the optimized structure; and repeat step S200 until there is no plastic damage area.

[0201] The method described in this application can be used in the design of ultra-large floating structures. Based on the structural parameters of the initially designed marine double-layer composite structure, the plastic damage area of ​​the structure can be calculated according to engineering requirements. Then, based on the plastic damage area, the structural parameters (thickness of each material layer) and micro-composition (volume fraction of steel fibers) of the structure can be optimized. Iterative calculations are performed until the structure has no potential damage risk under the design conditions (no plastic damage area), so that the safety of the structure meets the actual engineering requirements.

[0202] The multi-scale analytical calculation method of this invention will be illustrated below using a marine double-layer composite structure of a certain size as an example.

[0203] The length of the marine double-layer composite structure was set to 200m and the width to 50m. The volume fraction of steel fibers in the surface layer was 1%, 2%, 3%, and 4%, respectively, and four surface layer RVE models were established. Displacement loading analysis was performed on the above four surface layer RVE models under periodic boundary conditions. The post-processing analysis results yielded the parametric relationship between the steel fiber volume fraction and the homogenized elastic modulus and homogenized yield strength, and the relevant parameter formulas were fitted. Figure 5 As shown, the RVE model calculation results are in good agreement with the experimental results. Therefore, the parameter fitting formula is substituted into the subsequent calculations.

[0204] See Figure 5 The design thickness of the surface layer t2 is 0.15m, and the thickness of the bottom layer t1 is 2m; according to the "Technical Requirements for Ultra-High Performance Concrete (UHPC)" (T / CECS10107-2020), the density of UHPC material is set at 2500kg / m³. 3 The Poisson's ratio is 0.19. It should be noted that the density and Poisson's ratio of UHPC are almost unaffected by changes in the volume fraction of steel fibers. Assuming the initial volume fraction of steel fibers in the UHPC material is 2%, the homogenized elastic modulus and tensile yield strength of the surface layer can be determined based on... Figure 5 The parameters shown were obtained by fitting the formula and were 49850 MPa and 11.2 MPa, respectively.

[0205] According to the EPS foam material industry standard "Standard Specification for Rigid Geosynthetic Polystyrene Foam" (ASTM D6817), the density of the EPS base material is set at 14.4 kg / m³. 3 Its elastic modulus is 2.5 MPa and its Poisson's ratio is 0.12.

[0206] Based on the aforementioned basic parameters, and using the dynamic equivalent method of the floating double-layer structure, a novel hydroelastic coupling analytical model is further established through homogenization calculation of the overall performance of the double-layer structure.

[0207] Figure 6 The reflection coefficient K r and transmission coefficient K t Curve showing the variation of wavenumber k0h; Figure 7 The spatial distribution characteristics of deflection, bending moment, shear force, and contact surface strain of the initial design floating structure under typical wave frequencies (wave number k0h = 4, 6, 8) are shown. In the strain calculation, the wave height H is set to 0.65m, and the other variables (deflection, bending moment, and shear force) are dimensionless.

[0208] according to Figure 7 (d) The maximum strain at the contact surface in the initially designed floating structure can be obtained as 2.31 × 10⁻⁶. -4The yield strain is greater than that of UHPC material (2% steel fiber volume fraction) 2.25 × 10⁻⁶. -4 If the wave conditions (H = 0.65m, k0h = 6) are observed, the floating structure is predicted to have a plastic zone, requiring further adjustment of structural parameters or material proportions.

[0209] The surface layer thicknesses were adjusted to 0.25m and 0.35m respectively, which is to enhance the thickness of the high-stiffness layer. Other structural parameters remained unchanged. The initial design and the model after subsequent parameter adjustments were designated as Model 1, Model 2 and Model 3 respectively.

[0210] Figure 8 The spatial distribution characteristics of deflection, bending moment, and shear force of each floating body model as a function of wave frequency (wave number k0h); Figure 9 (a) shows the variation characteristics of strain on the contact surface of each floating body model in the frequency domain (wave number k0h) and spatial distribution. Figure 9 (b) The variation characteristics of the time and space distribution of the contact surface strain of each floating body model when the wave number k0h corresponds to the maximum contact surface strain amplitude.

[0211] See Figure 9 When the wave height is set to 0.65m, both floating body model 1 and model 2 have plastic distribution areas at a specific wave frequency, indicating that the structural safety of this model is at risk under this working condition. However, when the thickness of the UHPC layer increases to 0.35m, that is, for floating body model 3, there is no plastic area at any wave frequency, and there is no potential risk of damage.

[0212] Further adjustments were made to the steel fiber content in the surface layer of the above-mentioned floating body models with different structural parameters, thereby providing an application example for the hydrodynamic structure-material coupling analysis model.

[0213] See Figure 10 Using a multi-scale coupled analytical model, based on interfacial strain calculation, the optimal solution for the volume fraction of steel fiber in the surface layer of each floating body model was discussed. The wave height H was kept constant at 0.65m, and the wave number met the condition k0h≤20.

[0214] Figure 10 The maximum interfacial strain of each floating body model is shown as the volume fraction of steel fiber in the surface layer increases. The gradually rising curves represent the yield strain of UHPC materials with different steel fiber volume percentages.

[0215] Considering practical engineering applications, the maximum interfacial strain should be controlled below the yield strain of the surface layer to avoid plastic damage. When the surface layer thickness t2 = 0.35m (Model 3) and the steel fiber volume fraction is ≥2%, it can be ensured that no plastic zone will appear in the floating body model under appropriate wave frequency and wave height (H = 0.65m).

[0216] However, when the steel fiber volume fraction of the UHPC exceeds 2%, the improvement trend of structural performance slows down significantly with the increase of steel fiber content. Considering both material cost and engineering effect, for the marine double-layer composite structure designed in this embodiment, Model 3 with a corresponding UHPC layer steel fiber volume fraction of 2% is the optimal design scheme under the assumed wave conditions (k0h≤20, H=0.65m).

[0217] Example 3

[0218] This application provides a marine double-layer composite structure, which is optimized and designed using the method described in Example 2, wherein the volume fraction of steel fibers in the surface layer is 1% to 4%.

[0219] This application first establishes a surface layer RVE model, and performs displacement loading analysis on the surface layer RVE model under periodic boundary conditions. After post-processing the analysis results, the parameterized relationship between the material's micro-composition and homogenized elastoplastic characteristics is obtained. Based on the continuity condition of the non-homogeneous interface of the laminated structure, a dynamic equivalent model of the floating double-layer structure is established, in which the micro-composition characteristics of the high-stiffness surface layer are introduced through parameterized relationships. Through this dynamic equivalent model analysis, a novel hydroelastic analytical model coupling macroscopic wave action, mesoscopic laminated structure, and microscopic material composition is established. Based on this novel hydroelastic analytical model of the floating double-layer structure, the relationships between multi-scale characteristics are substituted into the hydroelastic-structural coupling calculation. The hydrodynamic-structural response coupling equation, including internal deformation, can be solved. By calculating the hydrodynamic response and quasi-plastic zone, structural and material design optimization can be performed to meet engineering requirements. This application can perform multi-scale hydrodynamic-structural-material calculation analysis of offshore double-layer composite structures and effectively achieve safety optimization design of offshore double-layer composite structures.

[0220] This application introduces ultra-high performance concrete material with added steel fibers into ultra-large floating body laminated structures, which improves the strength, stiffness and ductility of the floating body structure and delays the failure of the floating body structure. At the same time, through the method in this application, the application of steel fiber reinforced high performance concrete surface layer in engineering will no longer rely entirely on a large number of material performance tests. The material proportions and structural dimensional parameters in production and construction can be adjusted and optimized through basic analytical calculations.

[0221] In this application, unless otherwise expressly specified and limited, the terms "connected," "linked," "fixed," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0222] Numerous specific details are set forth in this specification. However, it will be understood that embodiments of the invention may be practiced without these specific details. In some instances, well-known methods, systems, and techniques have not been shown in detail so as not to obscure the understanding of this specification.

[0223] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, system, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, systems, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0224] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered within the scope of the claims and specification of the present invention.

Claims

1. An analytical calculation method for a marine double-layer composite structure, characterized in that, The marine double-layer composite structure consists of a top layer and a bottom layer. The top layer is composed of a UHPC matrix and steel fibers embedded in the UHPC matrix, and the bottom layer is EPS material. The calculation method includes the following steps: S1. Establish surface layer RVE models for multiple structures, and obtain the functional relationship between the macroscopic mechanical performance parameters and microscopic components of the surface layer based on the surface layer RVE models; S2. Establish a dynamic equivalent model of the structure. Based on the dynamic equivalent model and the functional relationship between the macroscopic mechanical performance parameters and microscopic components of the surface layer, obtain the contact surface strain equation and the homogenized bending stiffness equation of the structure. S3. Establish a novel hydroelastic analytical model for structures under waves. Based on the novel hydroelastic analytical model, the contact surface strain equation and the homogenized bending stiffness equation of the structure, obtain the contact surface strain equation of the surface layer. S4. Obtain the contact surface strain of the surface layer based on the structural parameters of the structure and the contact surface strain equation of the surface layer; S5. Compare the contact surface strain of the surface layer with the tensile yield strain. If the contact surface strain of the surface layer is greater than the tensile yield strain, it indicates that the surface layer has a plastic damage area.

2. The analytical calculation method for marine double-layer composite structures according to claim 1, characterized in that, In step S1, multiple surface layer RVE models are established, specifically including the following steps: S11. Establish a UHPC matrix model based on the performance parameters of the UHPC matrix material; S12. Based on the volume fraction of steel fibers, establish multiple randomly distributed steel fiber units; S13. Embed the steel fiber unit into the UHPC matrix model to complete the surface assembly; S14. Mesh the UHPC matrix and steel fiber separately to form surface layer RVE models with different microstructures.

3. The analytical calculation method for marine double-layer composite structures according to claim 2, characterized in that, In step S1, obtaining the functional relationship between the macroscopic mechanical property parameters and microscopic components of the surface layer based on the surface layer RVE model specifically includes the following steps: S15. Perform displacement loading analysis on each surface layer RVE model under periodic boundary conditions to obtain the macroscopic mechanical performance parameters of each surface layer RVE model. S16. Based on the macroscopic mechanical property parameters and microscopic composition of each surface layer RVE model, obtain the functional relationship between the macroscopic mechanical property parameters and microscopic composition of the surface layer.

4. The analytical calculation method for marine double-layer composite structures according to claim 1, characterized in that, Step S2 specifically includes the following steps: S21. Construct the bending moment-curvature equation of the structure during the elastic deformation stage; S22. Assuming the structure is a perfectly fitted homogeneous double-layer composite structure, construct the deflection differential equation of the structure during the elastic deformation stage. S23. Construct the continuity equation of the non-uniform interface of the structure during the elastic deformation stage; S24. Construct the equation for the total bending moment of the structure during the elastic deformation stage; S25. Based on the moment-curvature relationship equation, the deflection differential equation, the non-uniform interface continuity equation, and the total moment equation, the strain equation of the overall structure at the contact surface and the homogenized bending stiffness equation of the double-layer structure are obtained.

5. The analytical calculation method for marine double-layer composite structures according to claim 4, characterized in that, The strain equation for the contact surface of the structure in step S2 is: Where, ε int E1 is the strain at the contact surface, E2 is the elastic modulus of the first layer material, E2 is the elastic modulus of the second layer material, t1 is the thickness of the first layer, t2 is the thickness of the second layer, R is the radius of curvature of the structure under external bending moment, and W is the deflection generated when the structure bends.

6. The analytical calculation method for marine double-layer composite structures according to claim 4, characterized in that, The homogenized bending stiffness equation of the structure in step S2 is: Among them, K b For the homogenized bending stiffness of marine double-layer composite structures, E b It refers to the homogenized equivalent elastic modulus of the double-layer structure, I b It refers to the homogenized equivalent cross-sectional moment of inertia of a double-layer structure, where v1 is the Poisson's ratio of the first layer material and v2 is the Poisson's ratio of the second layer material.

7. The analytical calculation method for marine double-layer composite structures according to claim 1, characterized in that, Step S3 specifically includes the following steps: S31. Establish a novel hydroelastic analytical model for structures under waves; S32. Divide the fluid domain in which the structure is located into three regions, and establish the boundary condition equations that the spatial velocity potential of each region needs to satisfy, as well as the end condition equations of the structure. S33. Based on the homogenized bending stiffness equation of the structure, the new hydroelastic model, the boundary condition equation of the region, and the end condition equation of the structure, the spatial deflection equation of the double-layer floating structure is obtained. S34. Based on the contact surface strain equation and spatial deflection equation of the structure, obtain the contact surface strain equation of the surface layer; S35. Based on the new hydroelastic model, the contact surface strain equation of the surface layer obtained in step S34 is transformed into a linear equation.

8. The analytical calculation method for marine double-layer composite structures according to claim 1, characterized in that, In step S3, the strain function of the contact surface of the surface layer is: Where, ε int (x,t) is the strain function of the contact surface of the surface layer, W′(x,t)=Re[w′(x)e -iωt ],W″(x,t)=Re[w″(x)e -iωt ].

9. An optimized design method for a marine double-layer composite structure, characterized in that, Includes the following steps: S100. Construct an initial design structure with initial structural parameters and initial microstructure based on the design conditions; S200. According to the calculation method of any one of claims 1 to 8, determine whether the structure has a plastic damage area under the design working conditions; If so, proceed to step S300; S300: Optimize the structural parameters and / or microstructure of the initial design structure to obtain the optimized structure; and repeat step S200 until there is no plastic damage area.

10. A marine double-layer composite structure, characterized in that, The steel fiber is designed using the optimization design method described in claim 9, and the volume fraction of the steel fiber is 1% to 4%.

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