A coordinated deformation full-time-domain fluid-solid coupling analysis method for transporting immersed tubes on a semi-submersible barge

Abstract

The present invention provides a coordinated deformation full-time domain fluid-solid coupling analysis method for semi-submersible barge transport of immersed tubes, which is applicable to the technical field of large-scale pipe segment marine transportation. The present invention includes two main steps: establishing a motion equation and solving the motion equation. Based on the mutual relationship between the semi-submersible barge motion equation, the immersed tube motion equation and the towing cable equation in the force, displacement and deformation in the time domain analysis process, a coordinated deformation full-time domain fluid-solid coupling analysis method for semi-submersible barge transport of immersed tubes is proposed, and the force, displacement and deformation data at every time step during the entire process of immersed tube transportation are obtained, providing data support and theoretical analysis basis for solving the crack control problem in the process of immersed tube segment transportation.

Description

Technical Field

[0001] The invention relates to a coordinated deformation full-time domain fluid-solid coupling analysis method for transporting a submerged pipe by a semi-submersible barge, and is applicable to the technical field of marine transportation of large pipe segments. Background Art

[0002] Semi-submersible barges are an important and commonly used method of transporting large pipe segments at sea. When using semi-submersible barges to transport pipe segments, the piers are first installed on the deck of the semi-submersible barge, and then the immersed pipe segments are placed on the piers, and the immersed pipe segments and semi-submersible barges are connected by towing cables. During the marine transportation process, the deck of the semi-submersible barge will sink into the water, so the immersed pipe will also be partially submerged in the sea water. Under the action of waves, both the semi-submersible barge and the immersed pipe will deform, causing cracks in the immersed pipe segments. The problem of crack control during the transportation of immersed pipe segments is a major difficulty in engineering construction, and there is currently little research on crack control. Therefore, the coordinated deformation full-domain fluid-solid coupling analysis of semi-submersible barges transporting immersed pipes is considered as a basis, and further consideration is given to controlling deformation, reducing or even avoiding problems in the transportation process of immersed pipe segments. Summary of the invention

[0003] The purpose of the present invention is to solve the problem that there is currently no analysis method for deformation during the transportation of immersed tubes by semi-submersible barges. A full-time domain fluid-solid coupling analysis method for coordinated deformation of immersed tubes transported by semi-submersible barges is provided, which provides a basis for the problem of crack control during the transportation of immersed tube segments. The method can be widely used in the field of marine transportation technology for large pipe segments.

[0004] To achieve the above object, the present invention provides the following technical solutions:

[0005] A coordinated deformation full-time domain fluid-solid coupling analysis method for transporting immersed tubes by semi-submersible barges specifically includes the following steps:

[0006] S1 establishes the equation of motion;

[0007] The establishing of the motion equations comprises establishing the semi-submersible barge motion equation (1), the immersed tube motion equation (2) and the towing cable equation (3);

[0008]

[0009] Where, m is the mass of the semi-submersible barge, A ∞ is the additional mass at infinite frequency, X is the displacement of the semi-submersible barge, the first-order and second-order derivatives of X correspond to the semi-submersible barge motion velocity and acceleration respectively, t is the semi-submersible barge motion time, K is the hydrodynamic stiffness, R(t-τ) is the velocity pulse function, F is the wave load, and F c F is the water power of the semi-submersible barge. w is the wind resistance, F g is the gravity of the semi-submersible barge, F m is the cable force, Fe is the additional external force, j is the jth section of the cable, M is the mass, is the acceleration of the cable, T is the tension of the cable, V is the shear force of the cable, W is the weight of the cable, F is the external hydrodynamic force, m d is the mass of the immersed tube, x d is the displacement of the immersed tube in six degrees of freedom, including translation in the directions of three rectangular coordinate axes and rotation around three rectangular coordinate axes, c d is the damping coefficient, k d is the stiffness of the immersed tube, f dm is the weight of the immersed tube, f dn is the immersed tube support load, f de Add external force to the immersed tube;

[0010] Solve the S2 motion equations;

[0011] The solution of the motion equation comprises the following steps:

[0012] 1) Initialize the semi-submersible barge motion equation, immersed tube motion equation and M cable equations according to the preset position initialization parameters;

[0013] 2) Assume that the current time t has passed i time steps, as shown in formula (4),

[0014] t=i×Δt (4)

[0015] Where Δt is a single time step, i starts from 0 and increases by 1 after each calculation iteration;

[0016] 3) Calculate the motion and velocity of the cable mooring point at time t according to the motion of the center of gravity of the semi-submersible barge, and provide them to the cable equation as parameter input. Calculate the cable force according to the motion and velocity of the cable mooring point, and include them in the cable force F m and the additional external force f de ;

[0017] 4) The finite element model is used to solve the deformation of the reference points on the top and bottom surfaces of the pier. The pier load at time t is calculated based on the deformation of the pier, and the additional external force F is taken into account in the motion equations of the semi-submersible barge and the immersed tube. e and immersed tube support load f dn ;

[0018] 5) Use numerical methods to simultaneously solve the motion equations of the semi-submersible barge, immersed tube and M cable equations to obtain the motion and velocity of each particle of the semi-submersible barge, immersed tube and cable at time t;

[0019] 6) Calculate the pressure of the current semi-submersible barge surface unit according to all external loads of the semi-submersible barge at time t and output it;

[0020] 7) The immersed tube support load acts on the top reference surface of the pier in the form of surface pressure, and the sum of the immersed tube support load and the pier gravity acts on the bottom reference surface in the form of surface pressure;

[0021] 8) According to the load conditions in 6) and 7), the finite element model is further used to solve and obtain the force and deformation data of the semi-submersible barge and immersed tube at time t;

[0022] 9) Update the number of time steps passed by the current time, as shown in formula (5),

[0023] i=i+1 (5)

[0024] Repeat steps 2) to 8) until the number of time steps reaches the preset value;

[0025] 10) Output the motion response and speed of all semi-submersible barges, immersed tubes and cables, and the force and deformation data of immersed tubes and semi-submersible barges.

[0026] Furthermore, the movement of the center of gravity of the semi-submersible barge is obtained in real time by a monitoring device, in which the translation of the center of gravity of the semi-submersible barge in the directions of the three rectangular coordinate axes and the rotation around the three rectangular coordinate axes in the three-dimensional rectangular coordinate system are obtained, and then a relationship between the coordinates of any point on the structure and the coordinates of the center of gravity position is established, thereby obtaining the movement and speed of any point on the semi-submersible barge.

[0027] Furthermore, the method of using the finite element model to solve the deformation of the reference points on the top and bottom surfaces of the buttress comprises the following steps:

[0028] 1) Establish a finite element model of a semi-submersible barge with beams, plates and solid units, establish a finite element model of an immersed tube with a solid model, establish the pressure of the finite element unit of the semi-submersible barge and the pressure surface correlation relationship of the motion equation model, realize the transmission of surface pressure to the surface pressure of the finite element unit, and establish the relationship between the reference points of the top and bottom surfaces of the pier in the form of average pressure;

[0029] 2) The pressure on the top and bottom surfaces of the pier is used as the load input, and the surface pressure of the semi-submersible barge obtained by the motion equation solution process is used as the input of the semi-submersible barge finite element model;

[0030] 3) Solve the structural stress and deformation of the current time step by solving the structural dynamics time domain equation;

[0031] 4) Calculate the deformation of all finite element grid points on the reference surface of the pier (including immersed tubes and semi-submersible barges), calculate the average deformation of the finite element grid points near each reference point on the top and bottom surfaces of the pier, and use the change relative to the center of gravity as the deformation of the point (du, dv, dw).

[0032] The beneficial effects of the present invention are as follows: based on the relationship among the semi-submersible barge motion equation, the immersed tube motion equation and the cable equation in the process of force, displacement and deformation in the time domain analysis, a coordinated deformation full-time domain fluid-solid coupling analysis method for semi-submersible barge transport of immersed tubes is proposed, which can obtain the force, displacement and deformation data at every time step during the whole process of immersed tube transportation, and provide data support and theoretical analysis basis for solving the problem of crack control in the process of immersed tube segment transportation. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a flow chart of the coordinated deformation full-time domain fluid-solid coupling analysis method of the semi-submersible barge transporting immersed tubes of the present invention. DETAILED DESCRIPTION

[0034] The specific embodiments of the present invention are described in detail below in conjunction with the accompanying drawings. It should be understood that the specific embodiments given here are only used to illustrate and explain the present invention and cannot be used to limit the present invention. It should be noted that many specific details are set forth in the following description to facilitate a full understanding of the present invention, but the present invention may also have other embodiments and variations thereof, and therefore, the protection scope of the present invention is not limited by the specific embodiments disclosed below.

[0035] A coordinated deformation full-time domain fluid-solid coupling analysis method for transporting immersed tubes by semi-submersible barges specifically includes the following steps:

[0036] S1 establishes the equation of motion;

[0037] The establishing of the motion equations comprises establishing the semi-submersible barge motion equation (1), the immersed tube motion equation (2) and the cable equation (3);

[0038]

[0039]

[0040] Where, m is the mass of the semi-submersible barge, A ∞ is the additional mass at infinite frequency, X is the displacement of the semi-submersible barge, the first-order and second-order derivatives of X correspond to the semi-submersible barge motion velocity and acceleration respectively, t is the semi-submersible barge motion time, K is the hydrodynamic stiffness, R(t-τ) is the velocity pulse function, F is the wave load, and F c F is the water power of the semi-submersible barge. w is the wind resistance, F g is the gravity of the semi-submersible barge, F m is the cable force, F e To add external force;

[0041]

[0042] In the formula, m d is the mass of the immersed tube, xd is the displacement of the immersed tube in six degrees of freedom, including translation in the directions of three rectangular coordinate axes and rotation around three rectangular coordinate axes, c d is the damping coefficient, k d is the stiffness of the immersed tube, f dm is the weight of the immersed tube, f dn is the immersed tube support load, f de Add external force to the immersed tube;

[0043]

[0044] Where j is the jth section of cable, M is the mass, is the acceleration of the cable, T is the tension of the cable, V is the shear force of the cable, W is the weight of the cable, F is the external hydrodynamic force, E is the elastic modulus of the cable, d is the cable diameter, and L j is the length of the jth segment of the cable, L is the total length of the cable, C is the damping coefficient, ρ is the cable density, ρ w is the water density, I is the unit matrix, C1 is the lateral additional mass coefficient, C2 is the tangential additional mass coefficient, B is the additional force, D dn Lateral drag coefficient, D dt Tangential drag coefficient, I j is the stiffness of the j-th cable unit, q' j is the distributed load acting on the jth segment;

[0045] The hydrodynamic stiffness matrix is ​​shown in formula (12):

[0046]

[0047] In the formula, each element can be expressed as:

[0048]

[0049] Where ρ is water density, g is gravitational acceleration, (X, Y, Z) is the coordinate of a certain point of the crane ship, (X B ,Y B ,Z B ) is the buoyancy center of the crane vessel, (X G ,Y G ,Z G ) is the center of gravity of the crane vessel, S0 is the area of ​​the tangent plane, and A is the water retaining area. In addition, the system stiffness matrix of the crane vessel includes a hydrodynamic stiffness matrix. In addition, the system stiffness matrix of the crane vessel also includes a custom additional stiffness matrix, which is the stiffness matrix of the auxiliary structure of the crane vessel;

[0050] Solve the S2 motion equations;

[0051] The solution of the motion equation comprises the following steps:

[0052] 1) Initialize the semi-submersible barge motion equation, immersed tube motion equation and M cable equations according to the preset position initialization parameters;

[0053] 2) Assume that the current time t has passed i time steps, as shown in formula (21),

[0054] t=i×Δt (21)

[0055] Where Δt is a single time step, i starts from 0 and increases by 1 after each calculation iteration;

[0056] 3) Calculate the motion and velocity of the cable mooring point at time t according to the motion of the center of gravity of the semi-submersible barge, and provide them to the cable equation as parameter input. Calculate the cable force according to the motion and velocity of the cable mooring point, and include them in the cable force F m and the additional external force f de ;

[0057] 4) The finite element model is used to solve the deformation of the reference points on the top and bottom surfaces of the pier. The pier load at time t is calculated based on the deformation of the pier, and the additional external force F is taken into account in the motion equations of the semi-submersible barge and the immersed tube. e and immersed tube support load f dn ;

[0058] 5) Use numerical methods to simultaneously solve the motion equations of the semi-submersible barge, immersed tube and M cable equations to obtain the motion and velocity of each particle of the semi-submersible barge, immersed tube and cable at time t;

[0059] 6) Calculate the pressure of the current semi-submersible barge surface unit according to all external loads of the semi-submersible barge at time t and output it;

[0060] 7) The immersed tube support load acts on the top reference surface of the pier in the form of surface pressure, and the sum of the immersed tube support load and the pier gravity acts on the bottom reference surface in the form of surface pressure;

[0061] 8) According to the load conditions in 6) and 7), the finite element model is further used to solve and obtain the force and deformation data of the semi-submersible barge and immersed tube at time t;

[0062] 9) Update the number of time steps elapsed at the current time, as shown in formula (22),

[0063] i=i+1 (22)

[0064] Repeat steps 2) to 8) until the number of time steps reaches the preset value;

[0065] 10) Output the motion response and speed of all semi-submersible barges, immersed tubes and cables, and the force and deformation data of immersed tubes and semi-submersible barges.

[0066] The semi-submersible barge center of gravity movement is obtained in real time by a monitoring device, and the translation of the semi-submersible barge center of gravity in the three rectangular coordinate axis directions and the rotation around the three rectangular coordinate axes in a three-dimensional rectangular coordinate system, and then a relationship between the coordinates of any point on the structure and the coordinates of the center of gravity position is established, thereby obtaining the movement and speed of any point on the semi-submersible barge.

[0067] The method of using the finite element model to solve the deformation of the reference points on the top and bottom surfaces of the buttress comprises the following steps:

[0068] 1) Establish a finite element model of a semi-submersible barge with beams, plates and solid units, establish a finite element model of an immersed tube with a solid model, establish the pressure of the finite element unit of the semi-submersible barge and the pressure surface correlation relationship of the motion equation model, realize the transmission of surface pressure to the surface pressure of the finite element unit, and establish the relationship between the reference points of the top and bottom surfaces of the pier in the form of average pressure;

[0069] 2) The pressure on the top and bottom surfaces of the pier is used as the load input, and the surface pressure of the semi-submersible barge obtained by the motion equation solution process is used as the input of the semi-submersible barge finite element model;

[0070] 3) Solve the structural stress and deformation of the current time step by solving the structural dynamics time domain equation;

[0071] 4) Calculate the deformation of all finite element grid points on the reference surface of the pier (including immersed tubes and semi-submersible barges), calculate the average deformation of the finite element grid points near each reference point on the top and bottom surfaces of the pier, and use the change relative to the center of gravity as the deformation of the point (du, dv, dw).

[0072] The new coordinates of each reference point are calculated according to the deformation of the pier. The three reference points at the center of the bottom surface of the pier and 3 reference points on the top surface This includes two reference points: the bottom and top center of the pier. Each point is represented by (x n,i ,y n,i ,z n,i ) in vector form, where n indicates the current time step is the nth time step, i is the pier number,

[0073]

[0074] In the formula, (X g ,Y g ,Z g ) is the centroid coordinate. The base bottom surface is established with the bottom surface of the pier, and the surface normal vector is the unit vector The bottom surface normal vector during the movement is dynamically calculated based on the three reference points at the center of the bottom surface of the pier.

[0075]

[0076] Real-time calculation of the vector between the two reference points at the bottom and top centers The original axial direction of the pier changes in real time.

[0077]

[0078] The pier load is calculated according to equations (33) to (35):

[0079] F x,i =K x,i (Δx, Δy, Δz, h 0,i )(33)

[0080] F y,i =K y,i (Δx, Δy, Δz, h 0,i )(34)

[0081] F z,i =K z,i (Δx, Δy, Δz, h 0,i )(35)

[0082] In the formula, h 0,i is the original height of the pier.

[0083] In summary, based on the relationship between the semi-submersible barge motion equation, immersed tube motion equation and cable equation in the force, displacement and deformation in the time domain analysis process, a coordinated deformation full-time domain fluid-solid coupling analysis method for semi-submersible barge transport of immersed tubes was proposed. The force, displacement and deformation data at every time step during the entire immersed tube transportation process were obtained, which provided data support and theoretical analysis basis for solving the crack control problem in the transportation process of immersed tube sections.

[0084] It should be understood that the above-mentioned embodiments are one or more embodiments of the present invention, and there are many other embodiments and variations thereof based on the present invention; the variations and modifications made by ordinary technicians in this industry through the present invention without making pioneering innovations all fall within the scope of protection of the present invention.

Claims

1. A coordinated deformation full-time domain fluid-solid coupling analysis method for semi-submersible barge transport of immersed tubes, characterized in that The following steps are involved: S1 establishes the equation of motion; The establishing of the motion equations comprises establishing the semi-submersible barge motion equation (1), the immersed tube motion equation (2) and the towing cable equation (3); Where, m is the mass of the semi-submersible barge, A ∞ is the additional mass at infinite frequency, X is the displacement of the semi-submersible barge, the first-order and second-order derivatives of X correspond to the semi-submersible barge motion velocity and acceleration respectively, t is the semi-submersible barge motion time, K is the hydrodynamic stiffness, R(t-τ) is the velocity pulse function, F is the wave load, and F c F is the water power of the semi-submersible barge. w is the wind resistance, F g is the gravity of the semi-submersible barge, F m is the cable force, F e is the additional external force, j is the jth section of the cable, M is the mass, is the acceleration of the cable, T is the tension of the cable, V is the shear force of the cable, W is the weight of the cable, F is the external hydrodynamic force, m d is the mass of the immersed tube, x d is the displacement of the immersed tube in six degrees of freedom, including translation in the directions of three rectangular coordinate axes and rotation around three rectangular coordinate axes, c d is the damping coefficient, k d is the stiffness of the immersed tube, f dm is the weight of the immersed tube, f dn is the immersed tube support load, f de Add external force to the immersed tube; Solve the S2 motion equations; The solution of the motion equation comprises the following steps: 1) Initialize the semi-submersible barge motion equation, immersed tube motion equation and M cable equations according to the preset position initialization parameters; 2) Assume that the current time t has passed i time steps, as shown in formula (4), t=i×Δt (4) Where Δt is a single time step, i starts from 0 and increases by 1 after each calculation iteration; 3) Calculate the motion and velocity of the cable mooring point at time t according to the motion of the center of gravity of the semi-submersible barge, and provide it to the towing cable equation as parameter input. Calculate the cable force according to the motion and velocity of the towing cable mooring point, and include it in the cable force F m and the additional external force f de ; 4) The finite element model is used to solve the deformation of the reference points on the top and bottom surfaces of the pier. The pier load at time t is calculated based on the deformation of the pier, and the additional external force F is taken into account in the motion equations of the semi-submersible barge and the immersed tube. e and immersed tube support load f dn ; 5) Use numerical methods to simultaneously solve the motion equations of the semi-submersible barge, immersed tube and M cable equations to obtain the motion and velocity of each particle of the semi-submersible barge, immersed tube and cable at time t; 6) Calculate the pressure of the current semi-submersible barge surface unit according to all external loads of the semi-submersible barge at time t and output it; 7) The immersed tube support load acts on the top reference surface of the pier in the form of surface pressure, and the sum of the immersed tube support load and the pier gravity acts on the bottom reference surface in the form of surface pressure; 8) According to the load conditions in 6) and 7), the finite element model is further used to solve and obtain the force and deformation data of the semi-submersible barge and immersed tube at time t; 9) Update the number of time steps passed by the current time, as shown in formula (5), i=i+1 (5) Repeat steps 2) to 8) until the number of time steps reaches the preset value; 10) Output the motion response and speed of all semi-submersible barges, immersed tubes and cables, and the force and deformation data of immersed tubes and semi-submersible barges.

2. The coordinated deformation full-time domain fluid-solid coupling analysis method for transporting immersed tubes by semi-submersible barge according to claim 1 is characterized by: The semi-submersible barge center of gravity movement is obtained in real time by a monitoring device, and the translation of the semi-submersible barge center of gravity in the three rectangular coordinate axis directions and the rotation around the three rectangular coordinate axes in a three-dimensional rectangular coordinate system, and then a relationship between the coordinates of any point on the structure and the coordinates of the center of gravity position is established, thereby obtaining the movement and speed of any point on the semi-submersible barge.

3. The coordinated deformation full-time domain fluid-solid coupling analysis method for transporting immersed tubes by semi-submersible barge according to claim 1 is characterized by: The method of using the finite element model to solve the deformation of the reference points on the top and bottom surfaces of the buttress comprises the following steps: 1) Establish a finite element model of a semi-submersible barge with beams, plates and solid units, establish a finite element model of an immersed tube with a solid model, establish the pressure of the finite element unit of the semi-submersible barge and the pressure surface correlation relationship of the motion equation model, realize the transmission of surface pressure to the surface pressure of the finite element unit, and establish the relationship between the reference points of the top and bottom surfaces of the pier in the form of average pressure; 2) The pressure on the top and bottom surfaces of the pier is used as the load input, and the surface pressure of the semi-submersible barge obtained by the motion equation solution process is used as the input of the semi-submersible barge finite element model; 3) Solve the structural stress and deformation of the current time step by solving the structural dynamics time domain equations; 4) Calculate the deformation of all finite element grid points on the reference surface of the pier (including immersed tubes and semi-submersible barges), calculate the average deformation of the finite element grid points near each reference point on the top and bottom surfaces of the pier, and use the change relative to the center of gravity as the deformation of the point (du, dv, dw).

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