CN109914339B - Circular cylindrical breakwater externally connected with cylindrical grating and numerical value calculation method thereof - Google Patents

Circular cylindrical breakwater externally connected with cylindrical grating and numerical value calculation method thereof Download PDF

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CN109914339B
CN109914339B CN201910278777.7A CN201910278777A CN109914339B CN 109914339 B CN109914339 B CN 109914339B CN 201910278777 A CN201910278777 A CN 201910278777A CN 109914339 B CN109914339 B CN 109914339B
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reinforcing mesh
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刘俊
臧全胜
林皋
叶文斌
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Dalian University of Technology
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Abstract

A circular cylindrical breakwater externally connected with a cylindrical grid and a numerical calculation method thereof belong to the technical field of breakwater structures. Comprises an inner side reinforcing mesh, an outer side reinforcing mesh, a porous stone filling layer, a cylindrical grid and a steel pipe beam. The porous stone filling layer is positioned in the cylindrical grid and is clamped and fixed by the inner and outer side reinforcing steel bar nets, and the inner and outer side reinforcing steel bar nets and the cylindrical grid are concentric rings on any horizontal section. The bottoms of the inner and outer reinforcing steel bar nets are fixedly connected with the seabed, and the external cylindrical grid and the inner and outer reinforcing steel bar nets are fixedly connected through a plurality of steel pipe cross beams. And (3) calculating the stress of the circular cylindrical breakwater according to a proportional boundary finite element method, wherein a numerical result shows that the circular cylindrical breakwater has better breakwater performance. The breakwater provided by the invention combines the open pore structure with the porous filling interlayer, integrates the advantages of the open pore structure and the filling coefficient by adjusting the open pore coefficient and the filling coefficient, and has an obvious breakwater effect; and the open-cell grating and the porous stone layer are mutually independent, the design is simple, and the construction is convenient.

Description

Circular cylindrical breakwater externally connected with cylindrical grating and numerical value calculation method thereof
Technical Field
The invention belongs to the technical field of wave-preventing structures, relates to a circular-ring cylindrical breakwater externally connected with a cylindrical grid, and particularly relates to a wave-preventing structure which can absorb partial wave force of seawater through a porous stone filling layer and the cylindrical grid so as to prevent a structure in the surrounded range from being subjected to excessive wave force.
Background
In recent years, in the development of industries such as marine oil and gas, marine transportation, marine fishery, coastal tourism, new marine energy and the like, more and more offshore structures are developed, such as offshore drilling platforms, artificial islands, large-scale sea-crossing bridges and the like, which play a role in economic development and social progress, but due to the particularity of the environment, such structures are more easily damaged compared with land-based structures, various marine disasters, such as disastrous sea waves, storm tides, tsunamis and the like, are great tests for offshore structures, once damage is caused, crude oil leakage can be caused in the marine exploitation field, the marine ecosystem can be damaged, even more serious life and property safety can be caused by explosion, if the prevention measures are unreasonable, the severity of the consequences can be more difficult to estimate, it is therefore necessary to recognize and understand techniques for reducing the wave forces experienced by offshore structures.
One of the effective ways to reduce or prevent these natural marine disasters is to construct offshore engineering facilities at sea or on the coast by using relevant technical equipment. The open pore structure has the characteristics of reducing wave reflection and wave force borne by the open pore structure, and is gradually popularized and applied in ports, seacoasts and offshore engineering, and the open pore structure with the porous filling interlayer is used as an extension of the traditional open pore structure, and is not researched and applied by scholars at home and abroad. Therefore, the invention provides the circular cylindrical breakwater externally connected with the cylindrical grid for the first time, the breakwater combines the open pore structure with the porous filling interlayer, the open pore coefficient and the filling coefficient are adjusted to integrate the advantages of the open pore structure and the open pore structure, and a novel numerical simulation method proportional boundary finite element method is adopted to prove that the breakwater structure has better breakwater performance.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a circular cylindrical breakwater externally connected with a cylindrical grid, in particular to a breakwater structure which can dissipate the wave energy of seawater by means of the circular cylindrical breakwater externally connected with the cylindrical grid so as to protect the structures in the breakwater structure.
The annular cylindrical breakwater externally connected with the cylindrical grating is provided for the first time. The breakwater combines the open pore structure with the porous filling interlayer, integrates the advantages of the open pore structure and the filling coefficient by adjusting the open pore coefficient and the filling coefficient, and has the effectiveness of reducing the wave force borne by a structure in the protection range by the proportional boundary finite element numerical result.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a circular cylindrical breakwater externally connected with a cylindrical grid comprises an inner side reinforcing mesh 1, a porous stone filling layer 2, an outer side reinforcing mesh 3, the cylindrical grid 4 and a steel pipe beam 5. The porous stone filling layer 2 is positioned in the cylindrical grid 4 and is clamped and fixed by the inner reinforcing mesh 1 and the outer reinforcing mesh 3, and the inner reinforcing mesh 1, the outer reinforcing mesh 3 and the cylindrical grid 4 are concentric rings on any horizontal section. The porosity and the linear resistance coefficient of the porous stone filling layer 2 are uniform, the opening coefficient of the cylindrical grid 4 is uniform, the inner reinforcing mesh 1 and the outer reinforcing mesh 3 only play a role in clamping and fixing the porous stone filling layer between the inner reinforcing mesh and the outer reinforcing mesh, and the influence on the porosity and the linear resistance coefficient of the wave-proof structure is negligible. The inner side reinforcing mesh 1 and the outer side reinforcing mesh 3 are fixedly connected with the seabed 7, the top elevation of the circular cylindrical wave-proof structure of the external cylindrical grid 4 is larger than the elevation of the sea level 6, and the external cylindrical grid 4, the inner side reinforcing mesh 1 and the outer side reinforcing mesh 3 are connected through a plurality of steel pipe cross beams 5 in a welding mode.
The circular ring cylindrical breakwater externally connected with the cylindrical grid absorbs the wave force of the seawater part through the porous stone filling layer and the cylindrical grid, so that the breakwater structure capable of preventing structures in the surrounding range from bearing excessive wave force is achieved. Setting the radius of a cylindrical grid as b, the radius of an outer reinforcing mesh as c, the radius of an inner reinforcing mesh as a, the porosity of a porous stone filling layer as epsilon and the linear resistance coefficient as f; the coefficient of opening of the cylindrical grating is G, the depth of seawater is H, the wave-proof structure is vertical, and the bottom end of the wave-proof structure is fixedly connected with the seabed. In the calculation process, the following parameters are also used: liquid density ρ, gravitational acceleration g, and coefficient of inertia λ.
The method for calculating the wave force borne by the system comprises the following steps:
in a first step, the entire watershed is divided into three sub-calculation domains, i.e. the region Ω surrounded by the inner steel mesh 1ΙThe region omega enclosed by the inner steel bar mesh 1 and the outer steel bar mesh 3ΙΙThe circular column between the outer steel bar net 3 and the cylindrical grid 4Shape region omegaΙΙΙAnd infinite region omega outside the cylindrical grating 4ΙV。
In the second step, for the ideal fluid without rotation and viscosity, the velocity potential function Φ (x, y, z, t) of the fluid in each sub-domain can be decomposed into:
Figure GDA0002418620660000031
in the above formula
Figure GDA0002418620660000032
Omega is angular frequency and satisfies the equation omega2Gktanh (kh), k is the wave number, i is the imaginary unit,
Figure GDA0002418620660000033
satisfying the three-dimensional Laplace equation, and obtaining a two-dimensional Helmholtz equation after simplification:
Figure GDA0002418620660000034
is provided with
Figure GDA0002418620660000035
The normal derivative at the boundary is
Figure GDA0002418620660000036
The normal wave velocity is expressed, a variational principle is adopted, and a proportional boundary finite element (SBFEM) coordinate system is introduced, so that an SBFEM basic control equation and an inner boundary and outer boundary condition expression are obtained:
Figure GDA0002418620660000037
Figure GDA0002418620660000038
Figure GDA0002418620660000039
in the formula (I), the compound is shown in the specification,
Figure GDA00024186206600000310
for using proportional boundary finite element coordinate representation
Figure GDA00024186206600000311
The node value of (1), ζ ═ k0b ξ, s, ξ are the hoop and radial coordinates, respectively, in the proportional boundary finite element coordinates, ξ0As radial coordinates at the center of similarity, ξ1As radial coordinates on the boundary, N being a Lagrangian interpolation shape function, E0、E2、FsIn the form of a matrix of coefficients,
Figure GDA0002418620660000041
are respectively as
Figure GDA0002418620660000042
Second and first derivatives of ζ.
And thirdly, introducing boundary conditions to solve the proportional boundary finite element control equation. Is provided with
Figure GDA0002418620660000043
Figure GDA0002418620660000044
Respectively represent the domain omegaΙ，ΩΙΙ、ΩΙΙΙAnd ΩΙVThe coupling boundary condition should be satisfied between sub-fields: inside reinforcing bar net interface
Figure GDA0002418620660000045
Outer steel bar mesh interface
Figure GDA0002418620660000046
Cylindrical grid interface
Figure GDA0002418620660000047
In addition, ΩΙVIt is also necessary to satisfy the Sommerfeld boundary condition at infinity, i.e.：
Figure GDA0002418620660000048
Wherein the content of the first and second substances,
Figure GDA0002418620660000049
and
Figure GDA00024186206600000410
the normal derivative of the velocity potential, r, is the distance between the node and the center of proportion.
The fourth step is to
Figure GDA00024186206600000411
And
Figure GDA00024186206600000412
after the calculation, the total field velocity potential phi can be calculated, and further the wave surface height η and the dynamic pressure p can be calculated,
Figure GDA00024186206600000413
p＝-ρΦ,t(ii) a The total force exerted by the domain is calculated as follows:
Figure GDA00024186206600000414
wherein the first to third terms in the brackets are the inner reinforcing mesh (filling inner wall) and the outer reinforcing mesh (filling outer wall), respectively, the wave force applied on the structure unit length at the cylindrical grid (outer wall), and R represents the distance from the calculation interface to the central axis.
Compared with the prior art, the invention has the following advantages: 1) the wave prevention effect is remarkable; 2) the open-cell grating and the porous stone layer are mutually independent, the design is simple, and the construction is convenient; 3) the circular cylindrical wave-proof structure layer is filled with stone materials, and the material source is wide and economical.
Drawings
FIG. 1 is a schematic view of an annular cylindrical breakwater circumscribing a cylindrical grid;
fig. 2 is a model simplified diagram.
Figure 3 is a graph of the wave forces experienced at different locations of the structure as a function of the different porosities epsilon of the porous stone fill layer.
FIG. 4 is a graph showing the total wave force of a structure with dimensionless wave number kb under different void ratios epsilon of a porous stone filling layer.
FIG. 5 is a graph of the wave force at different locations of the structure as a function of different linear resistance coefficients f of the porous stone fill layer.
FIG. 6 is a graph showing the variation of the wave force applied to different parts of the structure with the coefficient G of the opening of the cylindrical grating.
Fig. 7 and 8 are schematic diagrams of amplitudes of the regions in which the structures are located in a certain range when the aperture ratio G of the cylindrical grating is 0.1 and G is 1.0, respectively.
Fig. 9 and 10 are schematic diagrams of the amplitudes of the areas where the structures are located in the case where the radii c of the outer tendons are 6 and 8, respectively.
Fig. 11 and 12 are schematic diagrams of the amplitudes of the regions where the structures are located in the case where the radii a of the inner mesh reinforcements are 2 and 4, respectively.
In the figure: 1 is an inner reinforcing mesh; 2 is a porous stone filling layer; 3 is an outer reinforcing mesh; 4 is a cylindrical grid; 5 is a steel pipe beam, 6 is sea level; and 7 is the sea bottom.
Detailed Description
The application of the principles of the present invention will now be further described with reference to the accompanying drawings and simulation examples. It should be understood that the simulation examples described herein are merely illustrative of the present invention and are not intended to limit the present invention.
Referring to the attached drawings 1-12, the invention discloses a circular cylindrical wave-preventing structure externally connected with a cylindrical grid. Comprises an inner steel bar mesh 1, a porous stone filling layer 2, an outer steel bar mesh 3, a cylindrical grid 4 and a steel pipe beam 5. The porous stone filling layer 2 is positioned in the cylindrical grid 4 and is clamped and fixed by the inner reinforcing mesh 1 and the outer reinforcing mesh 3, and the inner reinforcing mesh 1, the outer reinforcing mesh 3 and the cylindrical grid 4 are concentric rings on any horizontal section. The porosity and the linear resistance coefficient of the porous stone filling layer 2 are uniform, the opening coefficient of the cylindrical grid 4 is uniform, the inner reinforcing mesh 1 and the outer reinforcing mesh 3 only play a role in clamping and fixing the porous stone filling layer between the inner reinforcing mesh and the outer reinforcing mesh, and the influence on the porosity and the linear resistance coefficient of the wave-proof structure is negligible. The inner side reinforcing mesh 1 and the outer side reinforcing mesh 3 are fixedly connected with the seabed 7, the top elevation of the circular cylindrical wave-proof structure of the external cylindrical grid 4 is larger than the elevation of the sea level 6, and the external cylindrical grid 4, the inner side reinforcing mesh 1 and the outer side reinforcing mesh 3 are connected through a plurality of steel pipe cross beams 5 in a welding mode.
In the invention, the correlation calculation follows the linear potential flow theory, and the adopted numerical calculation method is a proportional boundary finite element method.
The whole flow field is divided into three sub-calculation domains, namely an area omega surrounded by the inner steel bar mesh 1 and the wall surface of the inner structure 4ΙThe region omega enclosed by the inner steel bar mesh 1 and the outer steel bar mesh 3ΙΙInfinite omega outside of the outer steel bar net 3ΙΙΙ。
For an ideal fluid without spin or viscosity, the velocity potential function Φ (x, y, z, t) of the fluid in each sub-domain can be decomposed into:
Figure GDA0002418620660000061
in the above formula
Figure GDA0002418620660000062
ω is angular frequency, k is wave number, i is imaginary unit,
Figure GDA0002418620660000063
and (3) obtaining a two-dimensional Helmholtz equation after the three-dimensional Laplace equation is simplified:
Figure GDA0002418620660000064
is provided with
Figure GDA0002418620660000065
The normal derivative at the boundary is
Figure GDA0002418620660000066
Expressing normal wave velocity, adopting variation principle and introducing proportional boundary finite element (SBFEM) coordinate system to obtain SBFEM basic equation and inner and outer boundary condition expression:
Figure GDA0002418620660000067
Figure GDA0002418620660000068
Figure GDA0002418620660000069
the boundary condition is introduced to solve the finite element control equation of the solution ratio boundary, and the solution ratio boundary can be obtained
Figure GDA0002418620660000071
Further, the total field velocity potential phi can be obtained, and the liquid velocity, the wave surface height and the dynamic pressure are respectively determined by the following expressions:
Figure GDA0002418620660000072
p＝-ρΦ,t(ii) a The total x-axis force on the domain is calculated as follows:
Figure GDA0002418620660000073
wherein the first to third items in brackets are the force applied to the unit length of the structure at the inner steel bar net, the outer steel bar net and the cylindrical grid respectively.
In the related example, b is 10m, H is 15m, in the figure, k represents wave number, η represents liquid level height (taking z as a reference), and | F represents liquid level height (taking z as a reference)xAbsolute value of | wave force.
The porosity epsilon and the linear resistance coefficient f are related to the compactness of the porous stone filling layer, the more compact the filling, the smaller the porosity epsilon, the larger the linear resistance coefficient f, and on the contrary, the larger the porosity epsilon, the smaller the linear resistance coefficient f.
Referring to figure 3, it can be seen that the wave forces experienced by the cylindrical grid are hardly affected by the porosity epsilon of the porous stone fill. Along with the increase of the porosity epsilon, the wave force borne by the interface of the inner reinforcing mesh is greatly increased and then tends to be balanced, the wave force borne by the interface of the outer reinforcing mesh and the total wave force borne by the system are both gradually reduced along with the increase of the porosity epsilon, and the total force of the system is obviously smaller and larger than the wave force borne by the mesh surface of the outer reinforcing mesh, which shows that along with the reduction of the compactness degree of the porous stone filling layer, the wave energy absorbed by the wave-proof structure is gradually reduced, and the energy dissipation characteristic of the cylindrical grid is basically not influenced by the filling coefficient of the stone filling layer, so that the filling coefficient of the porous stone filling layer can be independently designed independently from the opening coefficient of the outer cylindrical grid, the more the wave energy is absorbed by the more the porous stone filling layer is filled, but the greater the total wave force is borne by the system, and the compactness of the filling layer is properly increased in order to, but also the overall stability of the system.
Referring to fig. 4, it can be seen that the wave numbers of the first-order and second-order resonances of the system are gradually reduced with the increase of the void ratio epsilon, that is, the frequency of the system generating resonance is gradually advanced, and the peak value of the wave force is gradually increased, which again corroborates the conclusion referring to fig. 3, but when the external excitation relative wave number is smaller, the larger the void ratio epsilon is, the smaller the total wave force of the system is, so the design of the circular cylindrical wave-preventing structure also considers the range of the external excitation wave number which may appear in the environment.
Referring to fig. 5, it can be seen that the wave force applied to the cylindrical grating is slightly reduced but less influenced as the linear damping coefficient f of the porous stone filler layer is increased. Along with the increase of the linear damping coefficient f, the total wave force borne by the system is firstly reduced and then steadily increased, the wave forces borne by the inner and outer steel bar mesh surfaces show an increasing trend, and the difference value of the wave forces borne by the outer side steel bar mesh interface and the inner side steel bar mesh interface is gradually increased, which shows that the wave energy consumed by the porous stone filling layer is more and more increased along with the increase of the compactness of the porous stone filling layer (the increase of the linear damping coefficient f), so the wave prevention capability of the wave prevention structure can be improved by increasing the compactness of the filling layer, but the wave force borne by the structure is also increased, and the stability of the structure is considered in the design of the wave prevention structure filling layer.
Referring to the attached figure 6, with the increase of the aperture coefficient G of the cylindrical grid, the total wave force of the system is firstly sharply reduced and then tends to be balanced, the wave force borne by the cylindrical grid is gradually reduced until the cylindrical grid approaches to zero, the wave force borne by the outer side reinforcing mesh interface and the inner side reinforcing mesh interface are both sharply increased and then tend to be unchanged, and the difference value of the two wave forces also presents a similar law, which indicates that with the increase of the aperture coefficient G of the cylindrical grid, the wave energy consumed by the porous stone filling layer is more and finally tends to a fixed value, and the wave energy shared by the cylindrical grid is gradually reduced until the cylindrical grid approaches to zero. Therefore, the design of the circular cylindrical wave-preventing structure externally connected with the cylindrical grating provided by the invention should select a proper grating opening coefficient so as to reasonably distribute wave energy consumed by each part of the structure.
Referring to fig. 7 and 8, it can be seen that when the aperture ratio of the cylindrical grid is small (G ═ 0.1), the amplitude of the annular region defined by the cylindrical grid and the outer reinforcing meshes changes sharply, while the amplitude of the region within the outer reinforcing meshes does not change substantially, which indicates that the smaller aperture ratio G enables the cylindrical grid to consume most of the wave energy, and when the aperture ratio of the cylindrical grid is slightly larger (G ═ 1.0), the amplitude of the annular region defined by the cylindrical grid and the inner reinforcing meshes changes sharply, and the amplitude of the region within the inner reinforcing meshes tends to be gentle, which indicates that the appropriate aperture ratio G enables the cylindrical grid and the porous stone filling layer to distribute the wave energy consumption, so that the wave-proof structure can play a more stable role.
Referring to fig. 9-12, it can be seen that the radius and thickness (c-a) of the porous stone filling layer have a significant influence on the wave height inside the breakwater, and the amplitude at the center of the breakwater structure is significantly lower than that when the filling layer is thinner for a larger thickness of the porous stone filling layer, and is significantly lower than that when the filling layer is smaller for a larger radius of the porous stone filling layer.

Claims (2)

1. The circular cylindrical breakwater externally connected with the cylindrical grid is characterized by comprising an inner steel bar mesh (1), a porous stone filling layer (2), an outer steel bar mesh (3), the cylindrical grid (4) and a steel pipe cross beam (5); the porous stone filling layer (2) is positioned inside the cylindrical grid (4) and is clamped and fixed by the inner reinforcing mesh (1) and the outer reinforcing mesh (3), the inner reinforcing mesh (1), the outer reinforcing mesh (3) and the cylindrical grid (4) are of circular ring structures and are concentric in any horizontal section; the porosity and the linear resistance coefficient of the porous stone filling layer (2) are uniform, and the aperture coefficient of the cylindrical grating (4) is uniform; the bottom of the inner reinforcing mesh (1) and the bottom of the outer reinforcing mesh (3) are fixedly connected with the seabed (7); the external cylindrical grid (4), the inner side reinforcing mesh (1) and the outer side reinforcing mesh (3) are connected through a plurality of steel pipe cross beams (5) in a welding manner; the top elevation of the circular cylindrical wave-preventing structure externally connected with the cylindrical grating (4) is greater than the elevation of the sea level (6).
2. The method for calculating the stress of the circular cylindrical breakwater externally connected with the cylindrical grating according to claim 1, characterized by comprising the following steps:
setting the radius of a cylindrical grid as b, the radius of an outer reinforcing mesh as c, the radius of an inner reinforcing mesh as a, the porosity of a porous stone filling layer as epsilon and the linear resistance coefficient as f; the aperture coefficient of the cylindrical grating is G, the seawater depth is H, the wave-proof structure is upright, and the bottom end of the wave-proof structure is fixedly connected with the seabed; in the calculation process, the following parameters are also used: liquid density rho, gravity acceleration g and inertia coefficient lambda;
the method for calculating the wave force borne by the system comprises the following steps:
in a first step, the whole watershed is divided into three sub-calculation domains, namely a region omega surrounded by the inner reinforcing mesh (1)ΙThe inside reinforcing steel bar net (1) and the outside reinforcing steel bar net (3) are wrappedEnclosed region omegaIIThe circular cylindrical area omega between the outer steel bar net (3) and the cylindrical grid (4)IIIAnd an infinite region omega outside the cylindrical grating (4)IV；
In the second step, for the ideal fluid without rotation and viscosity, the velocity potential function phi (x, y, z, t) of the fluid in each sub-domain is decomposed into:
Figure FDA0002418620650000011
in the formula
Figure FDA0002418620650000012
Omega is angular frequency and satisfies the equation omega2Gk tanh (kH), k is the wave number, i is the imaginary unit,
Figure FDA0002418620650000021
satisfying the three-dimensional Laplace equation, and obtaining a two-dimensional Helmholtz equation after simplification:
Figure FDA0002418620650000022
is provided with
Figure FDA0002418620650000023
The normal derivative at the boundary is
Figure FDA0002418620650000024
Figure FDA0002418620650000025
Expressing normal wave velocity, adopting variation principle and introducing proportional boundary finite element SBFEM coordinate system to obtain SBFEM basic control equation and inner and outer boundary condition expression:
Figure FDA0002418620650000026
Figure FDA0002418620650000027
Figure FDA0002418620650000028
in the formula (I), the compound is shown in the specification,
Figure FDA0002418620650000029
for using proportional boundary finite element coordinate representation
Figure FDA00024186206500000210
The node value of (1), ζ ═ k0b ξ, s, ξ are the hoop and radial coordinates, respectively, in the proportional boundary finite element coordinates, ξ0As radial coordinates at the center of similarity, ξ1As radial coordinates on the boundary, N being a Lagrangian interpolation shape function, E0、E2、FsIs a coefficient matrix;
thirdly, introducing boundary conditions to solve the proportional boundary finite element control equation; is provided with
Figure FDA00024186206500000211
Figure FDA00024186206500000212
Respectively represent the domain omegaI，ΩII、ΩIIIAnd ΩIVThe coupling boundary condition should be satisfied between sub-fields: inside reinforcing bar net interface
Figure FDA00024186206500000213
Outer steel bar mesh interface
Figure FDA00024186206500000214
Cylindrical grid interface
Figure FDA00024186206500000215
In addition, ΩIVThe Sommerfeld boundary conditions at infinity need to be satisfied, namely:
Figure FDA00024186206500000216
wherein the content of the first and second substances,
Figure FDA00024186206500000217
and
Figure FDA00024186206500000218
is the normal derivative of the velocity potential, r is the distance between the node and the proportional center;
the fourth step is to
Figure FDA0002418620650000031
And
Figure FDA0002418620650000032
after the calculation, the total field velocity potential phi can be calculated, and further the wave surface height η and the dynamic pressure p can be calculated,
Figure FDA0002418620650000033
p＝-ρΦ,t(ii) a The total force exerted by the domain is calculated as follows:
Figure FDA0002418620650000034
wherein the first to third terms in the brackets are the wave force applied to the structure unit length at the inner side reinforcing mesh filling inner wall, the outer side reinforcing mesh filling outer wall and the cylindrical grid outer wall respectively, and R represents the distance from the calculation interface to the central axis.
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