Method for calculating vertical shear and vertical bending moment of a ship in head sea

Abstract

The application relates to a calculation method of vertical shear force and vertical bending moment of a ship facing waves, which comprises the following steps: dividing a rigid ship body into multiple sections along the length direction of the ship; analyzing the stress of the sections by balancing the vertical shear force of the section profile with the balance force system composed of gravity, inertial force and hydrodynamic force acting on the center of gravity of the ship body in front of the section profile, and balancing the vertical bending moment of the section profile with the balance force system composed of gravity moment, inertial force moment and hydrodynamic force moment acting on the center of gravity of the ship body in front of the section profile; obtaining the six-degree-of-freedom motion amplitude, hydrodynamic force at the center of gravity of the rigid ship body and the force and moment at the center of gravity of each section by specifying a hydrodynamic force calculation method; deriving the vertical shear force and the vertical bending moment at each section position according to the d'Alembert principle; and finally obtaining the vertical shear force and the vertical bending moment of the whole ship. The method considers the fluid viscosity problem when solving the wave load of the ship body, realizes the solving problem of the wave load of the rigid ship body, and provides a new prediction method for the wave load design of the ship.

Description

Technical Field

[0001] This invention relates to a ship wave load design technology, and particularly to a method for calculating the vertical shear force and vertical bending moment of a ship facing the waves based on the CFD method. Background Technology

[0002] For ships navigating in waves, methods for calculating the wave loads they experience can be categorized into potential flow methods, finite element methods, meshless particle methods, and computational fluid dynamics methods.

[0003] Potential flow methods are an effective means of solving wave load problems for ships. Based on whether hull deformation is considered, potential flow methods can be divided into rigid body theory and hydroelastic theory. Traditional wave load theory treats the hull as a rigid body when calculating wave loads, neglecting the influence of hull deformation on wave loads; hydroelastic theory can consider the elastic deformation of the hull structure, incorporating the coupling effect of the hull's elastic deformation and fluid into the wave load. Potential flow methods can also be classified according to the dimension of velocity potential into the slice method based on two-dimensional linear potential flow theory, high-speed slender body theory (two-and-a-half-dimensional theory), and three-dimensional potential flow theory.

[0004] (1) The slice method is an approximation theory that assumes the ship hull is slender and approximates the three-dimensional flow around the hull as a two-dimensional flow at each cross section. It introduces the long-wave assumption, transforming the complex diffraction problem into a simple radiation problem. The slice method is only applicable to slender hulls and situations with low speeds or high oscillation frequencies. Its disadvantages are obvious: while simplifying the three-dimensional flow to a two-dimensional flow reduces computation, it neglects the interaction between fluids in different slices. If the hull does not satisfy the "slender body" assumption and the hull motion does not satisfy the "low speed, high frequency" assumption, the slice method is not suitable for solving wave loads.

[0005] (2) The high-speed slender body theory is based on the slice method. The hull must satisfy the "slender body" assumption, and the water waves generated by the cross section of a high-speed vessel mainly propagate downstream. Compared to the slice method, this theory retains the two-dimensional assumption of the flow field around the hull and considers the three-dimensional flow field effect of the free surface. That is, the solved flow field is two-dimensional, while the boundary conditions retain the three-dimensional linear free surface condition; therefore, it is also called the two-and-a-half-dimensional theory. The disadvantage of this method is similar to that of the slice method: it fails to reflect the three-dimensional effect of the flow field. Therefore, when calculating hulls with non-slender body characteristics, the two-and-a-half-dimensional theory cannot accurately predict wave loads.

[0006] (3) The three-dimensional potential flow theory is currently widely used in the prediction of wave loads on ships and can be divided into complex Green's function method and simple Green's function method. The complex Green's function method is suitable for hydrodynamic calculations under linearized free surface conditions, while the simple Green's function method is suitable for hydrodynamic calculations under nonlinear free surface conditions. Its governing equations, surface boundary conditions, and free surface boundary conditions are all three-dimensional, overcoming the shortcomings of two-dimensional theory, breaking through the assumptions of slender bodies and velocity requirements, and thus having a wider range of applications.

[0007] Meshless particle methods describe continuous fluids (or solids) using a group of interacting particles, each carrying its own physical information, including particle type, position, pressure, and velocity. By solving the dynamic equations of the particle group and tracking the trajectory of each particle, the mechanical behavior of the entire system can be obtained. Meshless particle methods can accurately track free surfaces and simulate strongly nonlinear phenomena such as phase interface tumbling and breaking, hydraulic jumps, and jet splashing. However, they have two limitations: first, computational efficiency is significantly reduced when simulating large-scale three-dimensional physical problems; second, there are certain limitations in simulating high Reynolds number viscous flow effects and flow separation effects.

[0008] When ships navigate in high-wave environments, waves impact the hull structure instantaneously. Therefore, slamming is a transient, highly nonlinear dynamic phenomenon resulting from the interaction between the hull and waves, representing a fluid-structure interaction. However, existing technologies have the following drawbacks:

[0009] (1) The potential flow method ignores the viscosity of the fluid and is not good at handling problems with strong nonlinear characteristics, which limits its application in the slamming problem.

[0010] (2) The meshless particle method cannot accurately solve the problems of high Reynolds number viscous flow effects and flow separation effects, thus making it difficult to numerically calculate wave loads on ships in complex marine environments.

[0011] (3) Traditional CFD (Computational Fluid Dynamics) methods can only calculate the motion and hydrodynamics at the center of gravity of rigid hulls, but cannot calculate wave loads at the hull profile. Summary of the Invention

[0012] To address the challenge of calculating wave loads on ships navigating in viscous fluids, a method for calculating vertical shear force and vertical bending moment when the ship is facing the wave is proposed.

[0013] The technical solution of this invention is as follows: a method for calculating the vertical shear force and vertical bending moment of a ship facing the waves, comprising subdividing the rigid hull into multiple segments along the length of the ship; performing force analysis on each segment, and balancing the vertical shear force of the segment section with the gravity, inertial force, and hydrodynamic force acting at the center of gravity of the ship at the front of the segment section, and balancing the vertical bending moment of the segment section with the gravity torque, inertial torque, and hydrodynamic torque acting at the center of gravity of the ship at the front of the segment section; by specifying a hydrodynamic calculation method, outputting the six-degree-of-freedom motion amplitude at the center of gravity of the rigid ship, the hydrodynamic force, and the force and torque at the center of gravity of each segment; deriving the vertical shear force and vertical bending moment at each segment position based on d'Alembert's principle; and finally obtaining the vertical shear force and vertical bending moment of the entire ship by traversing all segments of the ship.

[0014] Furthermore, the specific implementation method for performing force analysis on the segments is as follows:

[0015] Weight distribution processing: It is assumed that the weight between each rib of the hull is uniformly distributed, and the center of gravity between each rib can be considered to be located at the center point between the two ribs, thus obtaining the weight curve for subsequent calculations.

[0016] The entire ship is divided into (k+1) segments from stern to bow, numbered 0, 1, 2, ..., i, ..., k, k+1. These segments contain k cross-sections, corresponding to the hull cross-sections in step 1. The mass of the i-th segment is denoted as m. i To calculate the vertical shear force and vertical bending moment at k cross-sections, a variable C cross-section is created. The k cross-sections are traversed, and the weight and center of gravity of the segment from the stern to C cross-section are calculated. The hull between the stern and C cross-section is designated as the forequarter, and the hull between C cross-section and the bow is designated as the aftquarter. The forequarter comprises n segments from the stern to C cross-section, and its mass is:

[0017]

[0018] Taking the moment of each section of the bow hull about section C, and applying the moment theorem of resultant forces in statics, the longitudinal coordinate x of the center of gravity of the bow hull can be determined. cg for:

[0019]

[0020] Where x i Let x be the x-coordinate of the centroid of segment i. c Here is the x-coordinate of the position of section C;

[0021] According to d'Alembert's principle, all external forces acting on a system of particles and the inertial forces virtually applied to each particle form a balanced force system. Taking out the forequarters of the ship, analysis shows that the vertical shear force F at section C is...C And the gravity F acting at the center of gravity of the forward half of the hull (gravity,vertical) Inertial force F (Inertia,vertical) and hydrodynamic F (Hydro,vertical) Formally composed of a balanced force system, with vertical bending moment M C With the gravitational moment M acting at the center of gravity of the forward half of the hull (gravity,vertical) Inertial force and torque M (Inertia,vertical) and hydrodynamic torque M (Hydro,vertical) The system is in equilibrium in form; the forces acting on the first half of the body satisfy formulas (3) and (4):

[0022]

[0023] Where F (gravity,vertical) The weight of the forequarters of the ship; F i(Inertia,vertical) The inertial force for segment i; F i(Hydro,vertical) Hydrodynamics for segment i; F C The vertical shear force at section C;

[0024]

[0025] Where M (gravity,vertical) M is the moment of gravity of the forequarters of the ship; i(Inertia,vertical) The inertial torque for segment i; M i(Hydro,vertical) The hydrodynamic torque is segmented into i; M C Let C be the vertical bending moment at section C.

[0026] Furthermore, the six-degree-of-freedom motion at the rigid ship's center of gravity: the ship will move under the action of external forces, which is regarded as a six-degree-of-freedom rigid body motion, which is decomposed into motion in six directions relative to the Earth coordinate system, including translation: the translational motion in the x, y, z directions are sway, roll, and heave respectively, and rotation: the rotational motion in the x, y, z directions are roll, pitch, and yaw respectively.

[0027] The motion of a ship is described using multiple coordinate systems, typically two right-handed Cartesian coordinate systems: the Earth coordinate system O-xyz and the hull coordinate system O'-x'y'z'. The Earth coordinate system O-xyz can be fixed on the Earth reference frame or move forward relative to the Earth at a constant speed; the hull coordinate system O'-x'y'z' is always fixed on the hull, with its origin at the center of rotation or the ship's center of gravity.

[0028] In the Earth coordinate system, sway, roll, and heave are linear displacements along the x, y, and z coordinate axes, while roll, pitch, and yaw are angular displacements about the x, y, and z coordinate axes. The six degrees of freedom of the ship's motion are defined as follows:

[0029]

[0030] Where (x,y,z) represent the sway, roll, and heave of the ship, respectively, and (φ,θ,ψ) represent the roll, pitch, and yaw of the ship, respectively, and are three Euler angles.

[0031] In the ship's coordinate system, the linear velocities of translational momentum along the coordinate axes—swing, roll, and heave—and the angular velocities of rotation about the coordinate axes—roll, pitch, and yaw—are expressed as:

[0032]

[0033] Where (u,v,w) represent the pitching velocity, swaying velocity, and heave velocity of the ship, respectively, and (p,q,r) represent the roll angular velocity, pitch angular velocity, and heave angular velocity of the ship, respectively; the velocity transformation between the Earth coordinate system and the ship coordinate system is achieved through a transformation matrix based on the Euler angle.

[0034] Furthermore, the calculation of gravity and gravitational torque is as follows:

[0035] The weight F of the bow half of the hull (gravity,vertical) Let m be the weight of the n segments from the stern to section C. i The sum of g, that is:

[0036]

[0037] According to the simplified theorem for planar force systems, the gravitational torque M of the forebody is... (gravity,vertical) This is caused by the gravity of n segments, that is, the gravitational torque caused by the gravity of n segments, which is the product of the gravity between each rib and the distance from the center of gravity of each rib to section C:

[0038]

[0039] Among them, (x c -x i ) is the distance from the centroid of segment i to section C.

[0040] Furthermore, the inertial force and inertial torque are calculated;

[0041] The inertial force on segment i is:

[0042]

[0043] The inertial torque on segment i is:

[0044]

[0045] Where r2y is the radius of inertia of the entire ship about the y-axis passing through the ship's center of gravity; The heave acceleration during the ship's motion; The pitch acceleration of the ship during its motion; (x cog ,y cog ,z cog ) represents the coordinates of the ship's center of gravity.

[0046] Furthermore, the calculation of the vertical hydrodynamic force and vertical hydrodynamic torque is as follows:

[0047] The piecewise hydrodynamics is based on the Earth coordinate system O-xyz, assuming that the components of the hydrodynamic force on segment i along the x, y, and z axes are respectively F i(Hydro,x) F i(Hydro,y) F i(Hydro,z) Based on coordinate transformation, the components of the hydrodynamic forces in the x', y', and z' axes in the ship's coordinate system are obtained as Fi, Fj, Fz, Fj ...z, Fj, Fz, F< i(Hydro,Horizontalx) F i(Hydro,Horizontaly) F i(Hydro,vertical) That is, the vertical hydrodynamic force on segment i along the z' axis can be written as:

[0048] F i(Hydro,vertical) =F i(Hrdro,z) ·cosθ+F i(Hydro,x) ·sinθ (16)

[0049] The vertical hydrodynamic moment experienced by segment i is:

[0050] M i(Hydro,vertical) =(F i(Hrdro,z) ·cosθ+F i(Hydro,x) ·sinθ)·(x c -x i )+M si (17)

[0051] Among them, (F i(Hrdro,z) ·cosθ+F i(Hydro,x) ·sinθ)·(x c -x i M represents the torque caused by hydrodynamic forces. si M is the rotational torque of segment i about the y-axis passing through the centroid of segment i. si Specify the output using hydrodynamic calculation software.

[0052] Furthermore, the calculation of the vertical shear force and vertical bending moment is as follows:

[0053] Substituting the obtained gravity and gravitational torque, inertial force and inertial torque, and vertical hydrodynamic force and vertical hydrodynamic torque into formulas (3) and (4) derived according to d'Alembert's principle, we obtain the vertical shear force F at section C. C and vertical bending moment M C for:

[0054]

[0055]

[0056] Furthermore, the rigid hull is subdivided into multiple segments along the length of the ship: the hull is evenly divided along the length of the ship according to the calculation accuracy requirements to obtain various cross-sections, including typical cross-sections, which are located at one-quarter, one-half, and three-quarters of the ship length.

[0057] The beneficial effects of this invention are as follows: The calculation method for vertical shear force and vertical bending moment of a ship under wave-facing conditions is based on the CFD method. It considers both the fluid viscosity problem when solving for wave loads on the hull and the problem of solving wave loads on rigid hulls, providing a new prediction method for the design of wave loads on ships. Attached Figure Description

[0058] Figure 1 This is a schematic diagram of the hull cross-section of the present invention;

[0059] Figure 2 This is a schematic diagram of the forces acting on the sections of the hull when it is upright and floating according to the present invention;

[0060] Figure 3 This is a schematic diagram of the forces acting on the hull sections after the hull undergoes a change in attitude according to the present invention;

[0061] Figure 4 This is a diagram of the six-degree-of-freedom coordinate system of the present invention;

[0062] Figure 5 This is a diagram showing the vertical bending moment at the cross-sectional location of the hull of the present invention.

[0063] Figures 6A-6D The vertical shear force curve and vertical bending moment curve are given for four moments within one cycle of the present invention. Detailed Implementation

[0064] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0065] A CFD-based method for calculating vertical shear force and vertical bending moment of a ship under wave-heading conditions is proposed: The rigid hull is subdivided into multiple segments along its length; force analysis is performed on the forward half of the hull between the stern and the calculation section; the vertical shear force of the calculation section is combined with the gravity, inertial force, and hydrodynamic force acting at the center of gravity of the forward half of the hull to form a balanced force system; the vertical bending moment of the calculation section is combined with the gravity torque, inertial torque, and hydrodynamic torque acting at the center of gravity of this forward half of the hull to form a balanced force system; by specifying a hydrodynamic calculation method, the method outputs the six-degree-of-freedom motion amplitude at the center of gravity of the rigid hull, the hydrodynamic force, and the forces and moments at the center of gravity of each segment; the vertical shear force and vertical bending moment at each section location are derived based on d'Alembert's principle; by traversing all sections of the entire ship, the vertical shear force and vertical bending moment of the entire ship are finally obtained.

[0066] The specific implementation steps are as follows:

[0067] Step 1, cross-sectional location statistics;

[0068] like Figure 1 The diagram shows the location of the ship's hull cross-section. The hull is divided evenly along its length according to the required calculation accuracy to obtain various cross-sections. The cross-sections include typical cross-sections (generally, the vertical shear force has the maximum value at one-quarter and three-quarters of the ship's length; the vertical bending moment has the maximum value at one-half of the ship's length). The coordinates of each cross-section location along the x-direction of the ship's length are counted, and the cross-sections are numbered sequentially starting from the stern.

[0069] Step 2, weight distribution processing;

[0070] Assuming that the weight is uniformly distributed between each rib of the hull, the center of gravity between each rib can be considered to be located at the center point between the two ribs, thus obtaining the weight curve for subsequent calculations.

[0071] The entire ship is divided into (k+1) segments from stern to bow, numbered 0, 1, 2, ..., i, ..., k, k+1. These segments contain k cross-sections, corresponding to the hull cross-sections in step 1. The mass of the i-th segment is denoted as m. i .

[0072] To calculate the vertical shear force and vertical bending moment at k cross-sections, a variable C cross-section (the calculation cross-section) is created. The k cross-sections are traversed, and the weight and center of gravity of the segment from the stern to C cross-section are calculated for each segment. The hull between the stern and C cross-section is designated as the forequarter, and the hull between C cross-section and the bow is designated as the aftquarter. The forequarter comprises n segments from the stern to C cross-section; therefore, the mass of the forequarter is:

[0073]

[0074] Taking the moment of each segment of the forward half of the hull about section C (segment mass × distance from the center of gravity of the segment to section C), and applying the moment theorem of resultant forces in statics, the longitudinal coordinate x of the center of gravity of the forward half of the hull can be determined. cg for,

[0075]

[0076] Where x i Let x be the x-coordinate of the centroid of segment i. c Let x be the x-coordinate of the position of section C.

[0077] Step 3, segmented force analysis;

[0078] According to d'Alembert's principle, all external forces acting on a system of particles and the inertial forces virtually applied to each particle form a balanced force system. Taking the forequarter of the ship out of the water and analyzing its forces, we can see that the vertical shear force F at section C is... C And the gravity F acting at the center of gravity of the forward half of the hull (gravity,vertical) Inertial force F (Inertia,vertical) and hydrodynamic F (Hydro,vertical) Formally composed of a balanced force system, with vertical bending moment M C With the gravitational moment M acting at the center of gravity of the forward half of the hull (gravity,vertical) Inertial force and torque M (Inertia,vertical) and hydrodynamic torque M (Hydro,vertical) Formally, they form a balanced force system. When the hull is in a state of upright buoyancy, the force distribution of each section is as follows: Figure 2 As shown, after the ship's attitude (heave and pitch) changes, the force distribution of each section is as follows. Figure 3 As shown. Combined with Figure 2 and Figure 3 It can be seen that the force situation of the front half satisfies formulas (3) and (4):

[0079]

[0080] Where F (gravity,vertical) The weight of the forequarters of the ship; F i(Inertia,vertical) The inertial force for segment i; F i(Hydro,vertical) Hydrodynamics for segment i; F C The vertical shear force at section C;

[0081]

[0082] Where M (gravity,vertical) M is the moment of gravity of the forequarters of the ship; i(Inertia,vertical) The inertial torque for segment i; M i(Hydro,vertical) The hydrodynamic torque is segmented into i; M C Let C be the vertical bending moment at section C.

[0083] Step 4: Specify the output results of the hydrodynamic calculation software;

[0084] Ships undergo motion under the influence of external forces, which can be considered as six-degree-of-freedom rigid body motion. This motion can be decomposed into motions in six directions relative to the Earth coordinate system, including translation (swell, sway, and heave in the x, y, and z directions, respectively) and rotation (roll, pitch, and yaw in the x, y, and z directions, respectively). Multiple coordinate systems are used to describe the ship's motion, typically two right-handed Cartesian coordinate systems: the Earth coordinate system O-xyz and the ship's coordinate system O'-x'y'z', as shown below. Figure 4 As shown. The Earth coordinate system O-xyz can be fixed on the Earth reference frame or move forward relative to the Earth at a constant speed; the ship's coordinate system O'-x'y'z' is always fixed on the ship's hull, with its origin at the center of rotation or the ship's center of gravity.

[0085] In the Earth coordinate system, sway, roll, and heave are linear displacements along the x, y, and z coordinate axes, while roll, pitch, and yaw are angular displacements about the x, y, and z coordinate axes. The six degrees of freedom of the ship's motion are defined as follows:

[0086]

[0087] Where (x, y, z) represent the sway, roll, and heave of the ship, respectively, and (φ, θ, ψ) represent the roll, pitch, and yaw of the ship, respectively, and are three Euler angles.

[0088] In the ship's coordinate system, the linear velocities of translational motion (sway, roll, heave) along the coordinate axes and the angular velocities of rotational motion (roll, pitch, yaw) about the coordinate axes are expressed as:

[0089]

[0090] Where (u,v,w) represent the pitching, swaying, and heaving velocities of the ship, respectively, and (p,q,r) represent the roll, pitching, and heave angular velocities of the ship, respectively. The velocity transformation between the Earth coordinate system and the ship's coordinate system is achieved using a transformation matrix based on Euler angles.

[0091] The hull in still water or waves is calculated using hydrodynamic calculation software, and the output is:

[0092] (1) Six-degree-of-freedom motion amplitude and hydrodynamics at the center of gravity of a rigid ship;

[0093] (2) Forces and moments at the center of gravity of each section of the rigid hull.

[0094] The acceleration at the ship's center of gravity can be obtained in the ship's coordinate system using the six-degree-of-freedom rigid body motion equation (7).

[0095]

[0096] It should be noted that all physical quantities in equation (7) are based on the ship's coordinate system. Where m total For the mass of the entire ship; These are the surge acceleration, sway acceleration, and heave acceleration during the ship's motion, respectively. These are the roll acceleration, pitch acceleration, and yaw acceleration, respectively, during the ship's motion. (x) g ,y g ,z g ) is the vector from the ship's center of gravity to the center of rotation, i.e., (x g ,y g ,z g )=(x cog ,y cog ,z cog )-(x rot ,y rot ,z rot ), (x cog ,y cog ,z cog (x) represents the coordinates of the ship's center of gravity. rot ,y rot ,z rot (I) represents the coordinates of the ship's rotation center; x ,I y ,I z Let (x, y, z) be the principal moment of inertia about the center of rotation. (X, Y, Z) are the components of the forces acting on the ship along the x', y', and z' axes, respectively, namely the longitudinal force, lateral force, and vertical force. (K, M, N) are the components of the moments acting on the ship along the x', y', and z' axes, respectively, namely the roll moment, pitch moment, and yaw moment.

[0097] Step 5, calculate gravity and gravitational torque;

[0098] The weight F of the bow half of the hull (gravity,vertical) Let mig be the sum of the gravity mig of the n segments from the stern to section C, i.e.:

[0099]

[0100] According to the simplified theorem for planar force systems, the gravitational torque M of the forebody is... (gravity,vertical) This is caused by the gravity of n segments, that is, the gravitational torque caused by the gravity of n segments, which is the product of the gravity between each rib and the distance from the center of gravity of each rib to section C:

[0101]

[0102] Among them, (x c -xi) is the distance from the centroid of segment i to section C.

[0103] Step 6: Calculation of inertial force and inertial torque;

[0104] The inertial force system of a rigid body is simplified to a force (inertial force) and a couple (inertial torque) in this plane. The derivation of the inertial force and the inertial torque are both based on the six-degree-of-freedom motion equations.

[0105] The physical quantities in the six-degree-of-freedom rigid body motion equations satisfied by the entire ship are solved in the ship's coordinate system. Therefore, the forebody, composed of various segments, can be considered as moving about a rotational axis passing through the rigid ship's center of gravity, and thus also satisfies the six-degree-of-freedom rigid body motion equations. The acceleration of the forebody is the coupled acceleration of the six degrees of freedom of the ship, that is, it satisfies the six-degree-of-freedom rigid body motion equation (7). The acceleration at the center of gravity of segment i is denoted as:

[0106]

[0107] in Let x, y, z be the components of the acceleration of segment i along the x', y', and z' axes, respectively. Let x, y, z be the components of the acceleration about the x', y', and z' axes, respectively, for segment i. i ,Y i Z i ) represent the components of the force acting on the segment along the x', y', and z' axes, respectively. (K) i M i N i ) are the components of the torque acting on the segment along the x', y', and z' axes, respectively. cog ,y cog ,z cog (x) represents the coordinates of the ship's center of gravity. i ,y i ,z i (x) represents the centroid coordinates of segment i, and (x) represents the centroid coordinates of segment i. cog -x i ,y cog –y i ,z cog –z i ) represents the distance from the center of gravity of segment i to the center of gravity of the ship.

[0108] In equation (10), the external force X i ,Y i Z i ,K i M i N i Move to the left side of the equals sign:

[0109]

[0110] According to d'Alembert's principle, the inertial force passes through the center of gravity of the rigid body. The inertial force is related to the acceleration generated by the coupling of the ship's six degrees of freedom. The magnitude of the inertial force is equal to the product of the mass of segment i and the acceleration of the center of gravity of segment i, and its direction is opposite to the acceleration at the center of gravity of the first half of the body. According to equation (11), the acceleration along the z-axis at the center of gravity of segment i is:

[0111]

[0112] Therefore, the inertial force on segment i is:

[0113]

[0114] Since the y and z coordinates of the centroid of segment i are equal to the y and z coordinates of the centroid of the entire ship, i.e. (x cog -x i ,y cog –y i ,z cog –z i ) is written as (x cog -x i Therefore, the inertial force simplifies to:

[0115]

[0116] The inertial force system of a rigid body can be simplified to a force and a couple in this plane. The inertial torque consists of two parts: ① the torque caused by the inertial force; ② the torque of the couple obtained by simplifying the inertial force system. The magnitude of this couple is equal to the product of the moment of inertia about the y-axis passing through the center of gravity of segment i and the pitch acceleration. Since the hull is rigid, the radius of inertia is equal at different positions throughout the ship. The moment of inertia of segment i is equal to the product of the mass of segment i and the square of the radius of inertia. The inertial torque on segment i is:

[0117]

[0118] Where r2y is the radius of inertia of the entire ship around the y-axis passing through the ship's center of gravity.

[0119] Step 7, Calculation of vertical hydrodynamic forces and vertical hydrodynamic moments

[0120] Hydrodynamics refers to the forces generated by the interaction between the ship's hull and the fluid. Since the flow field is solved in the Earth coordinate system, the piecewise hydrodynamic output of the hydrodynamic calculation software is based on the Earth coordinate system O-xyz. It is assumed that the components of the hydrodynamic force on segment i along the x, y, and z axes are F... i(Hydro,x) F i(Hydro,y) F i(Hydro,z)Based on coordinate transformation, the components of the hydrodynamic forces along the x', y', and z' axes in the ship's coordinate system can be obtained as Fi. i(Hydro,Horizontalx) F i(Hydro,Horizontaly) F i(Hydro,vertical) That is, the vertical hydrodynamic force on segment i along the z' axis can be written as:

[0121] F i(Hydro,vertical) =F i(Hrdro,z) ·cosθ+F i(Hydro,x) ·sinθ (16)

[0122] Hydrodynamic moment is the torque caused by the interaction between the ship and the fluid. It comprises two parts: ① the torque caused by hydrodynamic forces; ② the rotational torque of the segment's external forces about an axis passing through the segment's center of gravity. The vertical hydrodynamic moment acting on segment i is:

[0123] M i(Hydro,vertical) =(F i(Hrdro,z) ·cosθ+F i(Hydro,x) ·sinθ)·(x c -x i )+M si (17)

[0124] Among them, (F i(Hrdro,z) ·cosθ+F i(Hydro,x) ·sinθ)·(x c -x i M represents the torque caused by hydrodynamic forces. si M is the rotational torque of segment i about the y-axis passing through the centroid of segment i. si The output can be specified using hydrodynamic calculation software.

[0125] Step 8, Calculation of vertical shear force and vertical bending moment

[0126] Substituting the gravity and gravitational torque, inertial force and inertial torque, and vertical hydrodynamic force and vertical hydrodynamic torque obtained in steps 5, 6, and 7 into formulas (3) and (4) derived in step 4 based on d'Alembert's principle, we can obtain the vertical shear force and vertical bending moment at section C as follows:

[0127]

[0128]

[0129] According to formulas (18) and (19), by sequentially traversing the k sections of the entire ship through section C, the vertical shear force and vertical bending moment of the entire ship can be obtained.

[0130] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A method for calculating the vertical shear force and vertical bending moment of a ship facing the waves, characterized in that, The rigid hull is subdivided into multiple sections along its length. Force analysis is performed on each section, balancing the vertical shear force of the section with the gravity, inertial force, and hydrodynamic force acting at the ship's center of gravity in the front part of that section. Similarly, the vertical bending moment of the section is balanced with the gravity torque, inertial torque, and hydrodynamic torque acting at the ship's center of gravity in the front part of that section. A specified hydrodynamic calculation method is used to output the six-degree-of-freedom motion amplitude at the rigid hull's center of gravity, hydrodynamic forces, and the weight of each section. The forces and moments at the center are derived using d'Alembert's principle to obtain the vertical shear force and vertical bending moment at each section location. This process is repeated across all sections of the entire ship to obtain the final vertical shear force and vertical bending moment for the whole ship. The specific implementation method for the force analysis of each section is as follows: Weight distribution processing: Assuming the weight between each hull frame is uniformly distributed, the center of gravity between each hull frame can be considered as the center point between two hull frames, thus obtaining a weight curve for subsequent calculations. The entire ship is subdivided from the stern to the bow into sections 0, 1, 2, ... i, …, k , k +1 total ( k+ 1) Segment number, containing a total of k The first section, corresponding sequentially to the hull section in step 1, the second... i The mass of each segment is denoted as m i For calculation k Vertical shear force and vertical bending moment at each section, create variable C section, and iterate through... k For each section, the weight and center of gravity of the hull from the stern to section C are calculated. The section from the stern to section C is designated as the forward hull, and the section from section C to the bow is designated as the aft hull. The forward hull includes the section from the stern to section C. n The hull is divided into sections, and the mass of the fore section is: (1) Calculate the moment of each segment of the bow section about section C. By applying the moment theorem of resultant forces in statics, the longitudinal coordinate of the center of gravity of the bow section can be determined. x cg for: (2), of which x i for i The position of the center of gravity of the segment x Direction coordinates x c For section C x Directional coordinates; According to d'Alembert's principle, all external forces acting on a system of particles and the inertial forces virtually applied to each particle form a balanced force system. Taking out the forequarter of the hull, analysis shows that the vertical shear force at section C is... F C and the force of gravity acting at the center of gravity of the forward half of the hull F (gravity,vertical) Inertial force F (Inertia,vertical) and hydrodynamics F (Hydro,vertical) Formally composed of a balanced force system, with vertical bending moment M C With the gravitational torque acting at the center of gravity of the forward half of the hull M (gravity,vertical) Inertial force and torque M (Inertia,vertical) and hydrodynamic torque M (Hydro,vertical) The system is in equilibrium in form; the forces acting on the first half of the body satisfy formulas (3) and (4): (3), of which F (gravity,vertical) The weight of the forward half of the hull; F i(Inertia,vertical) for i Segmented inertial forces; F i(Hydro,vertical) for i Segmented hydrodynamics; FC represents the vertical shear force at section C; (4), of which M (gravity,vertical) The moment of gravity of the forequarters of the ship; for i Segmented inertial force and torque; for i Segmented hydrodynamic torque; Let C be the vertical bending moment at section C.

2. The method for calculating the vertical shear force and vertical bending moment of a ship facing the waves according to claim 1, characterized in that, The six-degree-of-freedom motion at the rigid ship's center of gravity: The ship will move under the action of external forces, which can be regarded as six-degree-of-freedom rigid body motion, decomposed into motion in six directions relative to the Earth coordinate system, including translation: x , y , z Translational motions in different directions include swaying, transverse swaying, heave, and rotation: x , y , z Rotational motions in different directions are represented by roll, pitch, and bow; ship motion is described using multiple coordinate systems, typically two right-handed Cartesian coordinate systems: Earth coordinate system O- xyz And the ship's coordinate system O'- x ' y ' z Earth coordinate system O- xyz It can be fixed in the Earth's reference frame, or move forward relative to the Earth at a constant speed; the ship's coordinate system O'- x ' y ' z 'Always fixed to the hull, its origin is at the center of rotation or the ship's center of gravity; in the Earth coordinate system, sway, roll, and heave are along...' x , y , z The linear displacement of the coordinate axes, namely roll, pitch, and yaw, is about... x , y , z Angular displacement of the coordinate axes, defining the six degrees of freedom motion of the ship as: (5), of which ( x , y , z These represent the three phases of ship motion: sway, roll, and heave. ,θ,ψ Let be the roll, pitch, and heave angles, representing the ship's motion. In the ship's coordinate system, the linear velocities of translational motion along the coordinate axes (the velocities of pitch, heave, and sway) and the angular velocities of rotational motion about the coordinate axes (the angular velocities of roll, pitch, and heave) are expressed as: (6), of which, ( u , v , w These are the pitching speed, swaying speed, and heave speed of the ship, respectively. p,q,r The values ​​are the roll angular velocity, pitch angular velocity, and bow angular velocity, respectively, in the ship's motion. The velocity transformation between the Earth coordinate system and the ship's coordinate system is achieved through a transformation matrix based on the Euler angle.

3. The method for calculating the vertical shear force and vertical bending moment of a ship facing the waves according to claim 2, characterized in that, The calculation of gravity and gravitational moment: gravity of the forequarters of the ship. F (gravity,vertical) Section from stern to C n Gravity of each segment m i g The sum is: (8) According to the simplification theorem of planar force systems, the gravitational torque of the forebody is... M (gravity,vertical) for n Caused by the gravity of each segment, i.e. n The gravitational moment caused by the gravity of each segment is the product of the gravity between each rib and the distance from the center of gravity of each rib to section C: (9), where, ( x c - x i )for i The distance from the centroid of the segment to section C.

4. The method for calculating the vertical shear force and vertical bending moment of a ship facing the waves according to claim 2 or 3, characterized in that, The calculation of the inertial force and inertial moment; i The inertial forces on the segment are: (14), i The inertial torque experienced by the segment is: (15), of which r y The entire ship passes around the ship's center of gravity. y The radius of inertia of the axis; w· The heave acceleration during the ship's motion; q· The pitch acceleration of the ship during its motion; x cog , y cog , z cog ) represents the coordinates of the ship's center of gravity.

5. The method for calculating the vertical shear force and vertical bending moment of a ship facing the waves according to claim 4, characterized in that, Vertical hydrodynamics and vertical hydrodynamic moment calculation: Segmented hydrodynamics based on the Earth coordinate system O- xyz ,assumed i The hydrodynamic force on the segment is x , y , z The components on the axis are respectively F i(Hydro,x) , F i(Hydro,y) , F i(Hydro,z) Based on coordinate transformation, the hydrodynamics in the ship's coordinate system are obtained. x ', y ', z The components of the axis are respectively F i(Hydro,Horizontalx) , F i(Hydro, Horizontaly) , F i(Hydro,vertical) Right now i Segmented along z The vertical hydrodynamic force acting on the axis can be written as: (16), i The vertical hydrodynamic moment experienced by the segment is: (17), where, The torque caused by hydrodynamic forces, M si for i Segmented around the centroid of segment. y The rotational torque of the shaft, M si The output is specified by the hydrodynamic calculation software; the calculation of vertical shear force and vertical bending moment is as follows: the obtained gravity and gravitational moment, inertial force and inertial moment, and vertical hydrodynamic force and vertical hydrodynamic moment are substituted into the formulas (3) and (4) derived according to d'Alembert's principle to obtain the vertical shear force at section C. F C and vertical bending moment M C for: (18), (19).

6. The method for calculating the vertical shear force and vertical bending moment of a ship facing the waves according to claim 1, characterized in that, The rigid hull is subdivided into multiple sections along the length of the ship: the hull is evenly divided along the length of the ship according to the calculation accuracy requirements to obtain various cross-sections, including typical cross-sections, which are located at one-quarter, one-half, and three-quarters of the ship length.

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