Ship body ice force calculation method for ship control motion simulation in layer ice area

Abstract

The invention discloses a ship body ice force calculation method for ship control motion simulation in a layer ice area, and relates to the field of ship control motion simulation, and the method comprises the steps: dividing an ice raft area into a plurality of ice units, and determining the ice unit position information of each ice unit at the current moment; according to the ice unit position information and the ship body waterline position information, determining each contact ice unit in contact with the ship body waterline; determining the contact length between any contact ice unit and the ship body waterline and the ship ice contact speed by combining the ship navigation state parameters; calculating the local acting force of the contact ice unit on the ship body by using an extreme value static ice force formula in which a speed correction term is introduced; and superposing the local acting force of each ice contact unit on the ship body to obtain the ship body ice force at the current moment. According to the method, the ship body ice force can be accurately calculated when special control operations such as backing and large-drift-angle maneuvering of the ship in the layer ice area are simulated, and the accuracy and reliability of control motion simulation of the ship in the layer ice area are effectively improved.

Description

Technical Field

[0001] The present application relates to the field of ship maneuvering motion simulation, and in particular to a method for calculating hull ice force in ship maneuvering motion simulation in an ice floe area. Background Art

[0002] With the increasing attention of countries around the world to the polar regions, ice-going ships, as essential equipment for polar scientific research and exploitation, have also received extensive attention. The navigation performance and maneuvering performance of ships under polar ice area environmental conditions are important factors that need to be considered in the design and manufacture of ice-going ships.

[0003] In order to evaluate and optimize the navigation performance and ice area maneuvering performance of ships, it is necessary to conduct simulation analysis on the maneuvering motion process of ships in the ice floe area during the ship design and R & D process. When simulating the maneuvering navigation process of ships in the ice floe area, it is crucial to accurately obtain the hull ice force load input, which directly determines the accuracy and reliability of the simulation results.

[0004] The current means for quickly obtaining the hull ice force mainly involve direct calculation based on analytical, semi-analytical, or empirical ice force formulas. However, the existing analytical, semi-analytical, and empirical ice force formulas are all established for the bow-forward navigation state of ships, and most of them only focus on the longitudinal ice force of the hull. The hull ice force calculated by such methods is difficult to reflect the actual ice force acting situation during the ship maneuvering motion process, seriously affecting the accuracy of the ship maneuvering motion simulation results in the ice floe area. Summary of the Invention

[0005] In view of the above problems and technical requirements, the present application proposes a method for calculating hull ice force in ship maneuvering motion simulation in an ice floe area. The technical solution of the present application is as follows:

[0006] A method for calculating hull ice force in ship maneuvering motion simulation in an ice floe area, comprising the following steps:

[0007] Divide the ice floe area into multiple ice units and determine the ice unit position information of each ice unit at the current moment;

[0008] Determine each contact ice unit in contact with the hull waterline at the current moment according to the ice unit position information of each ice unit at the current moment and the hull waterline position information;

[0009] Combine the ship navigation state parameters to determine the contact length w between any contact ice unit k and the hull waterline and the ship-ice contact speed. The ship-ice contact speed includes the ship-ice contact speeds caused by the ship's yaw motion, longitudinal surge motion, and transverse sway motion;

[0010] Using the extreme static ice force formula with the introduced speed correction term, and calculating the local force of the contact ice element k on the hull according to the contact length w between the contact ice element k and the hull waterline and the ship-ice contact speed;

[0011] Superimposing the local forces of each contact ice element on the hull to obtain the hull ice force at the current moment.

[0012] A further technical solution thereof is that, determining each contact ice element in contact with the hull waterline at the current moment according to the ice element position information and the hull waterline position information of each ice element at the current moment includes:

[0013] Constructing an outer bounding box of the hull waterline according to the hull waterline position information at the current moment, and extracting the ice elements intersecting with the outer bounding box in combination with the ice element position information of each ice element at the current moment to obtain each neighborhood ice element of the hull waterline;

[0014] Rotating the hull waterline and each neighborhood ice element at the current moment around the projection point G of the center of gravity of the ship in the waterplane to the positive direction of the OX axis of the fixed coordinate system; the positive direction of the OX axis of the fixed coordinate system points to the bow direction at the initial moment, and the positive direction of the OY axis of the fixed coordinate system points to the starboard direction of the ship at the initial moment;

[0015] Constructing an inner rectangular bounding box according to the rotated hull waterline position information, and extracting the neighborhood ice elements intersecting with the inner rectangular bounding box in combination with the ice element position information of each rotated neighborhood ice element to obtain each circumferential ice element of the ship at the current moment, and taking the circumferential ice elements in contact with the hull waterline as contact ice elements; the inner rectangular bounding box is located inside the outer bounding box, the side length direction of the inner rectangular bounding box is the same as the coordinate axis direction of the fixed coordinate system, and the distance between any side of the inner rectangular bounding box and the rotated hull waterline is not less than the longest side length of the ice element.

[0016] A further technical solution thereof is that, the shape of the outer bounding box is rectangular and the side length direction of the outer bounding box is the same as the coordinate axis direction of the fixed coordinate system, determining the neighborhood ice elements of the hull waterline includes:

[0017] According to the ice element position information of the first ice element obtained by partitioning and the corner positions of the outer bounding box, determining the ice element row and column indexes intersecting with each side of the outer bounding box;

[0018] Directly extracting the ice elements intersecting with the outer bounding box from all the ice elements obtained by partitioning according to the ice element row and column indexes, and taking the ice elements intersecting with the outer bounding box as the neighborhood ice elements of the hull waterline.

[0019] A further technical solution thereof is that, the local force includes a normal extrusion force and a tangential friction force, determining the normal extrusion force of the contact ice element k on the hull and tangential frictional force including:

[0020] Determine the ship-ice contact line of the contact ice unit k with the ship's waterline;

[0021] According to the ship-ice contact line and combining with the ship navigation state parameters, determine the component of the ship-ice contact speed of the contact ice unit k with the ship's waterline in the normal direction of the ship-ice contact line and the component of the ship-ice contact speed in the tangential direction of the ship-ice contact line The positive direction of [] is along the normal line at the midpoint c of the ship-ice contact line and points to the outside direction of the ship's waterline, The positive direction of [] is along the tangent line at the midpoint c of the ship-ice contact line and points to the counterclockwise direction of the ship's waterline;

[0022] When Determine the normal extrusion force of the contact ice unit k on the hull at the midpoint c of the ship-ice contact line When Determine the normal extrusion force of the contact ice unit k on the hull at the midpoint c of the ship-ice contact line

[0023] When and Determine the tangential frictional force of the contact ice unit k on the hull at the midpoint c of the ship-ice contact line Otherwise, determine the tangential frictional force of the contact ice unit k on the hull at the midpoint c of the ship-ice contact line

[0024] where h is the sea ice thickness, p G is the effective ice pressure per unit area, λ and η are velocity correction term coefficients, g is the acceleration due to gravity, L w is the length of the ship's waterline, sign() is the sign function, γ is the ship-ice friction coefficient; the direction of the normal extrusion force is opposite to the component of the ship-ice contact speed in the normal direction of the ship-ice contact line The direction of the tangential frictional force is opposite to the component of the ship-ice contact speed in the tangential direction of the ship-ice contact line opposite.

[0025] Its further technical solution is to determine the components of the ship-ice contact speed of the contact ice unit k with the ship's waterline and including:

[0026] According to the ship heaving velocity u in the ship navigation state parameters, determine the ship-ice contact speed u caused by the ship heaving motion at the midpoint c of the ship-ice contact line c= u and the velocity direction is along the Gx axis of the moving coordinate system; determine the ship-ice contact velocity v caused by the ship's swaying motion at the midpoint c of the ship-ice contact line according to the ship's swaying velocity v in the ship navigation state parameters c = v and the velocity direction is along the Gy axis of the moving coordinate system; determine the ship-ice contact velocity r caused by the ship's turning motion at the midpoint c of the ship-ice contact line according to the yaw angular velocity r of the ship and the position of the projection point G of the ship's center of gravity on the waterplane c = r|Gc| and the velocity direction is perpendicular to the Gc connection line and points to the ship's turning direction;

[0027] The ship-ice contact velocity u caused by the ship's heaving motion at the midpoint c of the ship-ice contact line c 、the ship-ice contact velocity v caused by the ship's swaying motion c and the ship-ice contact velocity r caused by the ship's turning motion c are decomposed and transformed onto the normal direction and the tangent direction of the ship-ice contact line to obtain:

[0028]

[0029] wherein, ξ is the angle between the tangent line of the ship-ice contact line at the midpoint c and the OX axis of the fixed coordinate system, is the angle between the Gc connection line and the Gx axis of the moving coordinate system, ψ is the angle between the Gx axis of the moving coordinate system and the OX axis of the fixed coordinate system; the positive direction of the Gx axis of the moving coordinate system points to the ship's bow direction at the current moment, and the positive direction of the Gy axis of the moving coordinate system points to the ship's starboard direction at the current moment; the positive direction of the OX axis of the fixed coordinate system points to the ship's bow direction at the initial moment, and the positive direction of the OY axis of the fixed coordinate system points to the ship's starboard direction at the initial moment.

[0030] Its further technical solution is that the local forces of each ice contact unit on the hull are superimposed to obtain the hull ice force at the current moment, including:

[0031] Decompose and transform the normal extrusion force f n k and the tangential friction force f τ k exerted by the ice contact unit k on the hull at the midpoint c of the ship-ice contact line to obtain the components f x k on the Gx axis of the moving coordinate system and the components f y k on the Gy axis:

[0032]

[0033] wherein, ξ is the angle between the tangent line of the ship-ice contact line at its midpoint c and the OX axis of the fixed coordinate system, and ψ is the angle between the Gx axis of the moving coordinate system and the OX axis of the fixed coordinate system; the positive direction of the Gx axis of the moving coordinate system points to the bow direction at the current moment, and the positive direction of the Gy axis of the moving coordinate system points to the starboard direction at the current moment; the positive direction of the OX axis of the fixed coordinate system points to the bow direction at the initial moment, and the positive direction of the OY axis of the fixed coordinate system points to the starboard direction at the initial moment;

[0034] Calculate the local yaw moment of the contact ice element k on the projection point G of the ship's center of gravity in the waterplane Among them, The yaw moment arm about point G The yaw moment arm about point G

[0035] The calculated ship-ice forces at the current moment include longitudinal ice forces Lateral ice forces And yaw ice moments K is the total number of contact ice elements, and the integer parameter K ≥ 1.

[0036] Its further technical solution is that the ship-ice force calculation method further includes:

[0037] For any contact ice element k, determine the failure state of the contact ice element k according to the ice element position information of the contact ice element k and the hull waterline position information at the current moment, and the failure state indicates the degree of damage of the contact ice element k after ship-ice contact;

[0038] Update the contact ice element k according to the failure state of the contact ice element k, and enter the next calculation moment.

[0039] Its further technical solution is that the failure state includes non-failure, partial failure and overall failure. The ice element position information of any contact ice element k includes the position information of each corner point of the contact ice element k and the position information of the initial centroid of the contact ice element k, and the initial centroid is the centroid of the contact ice element k at the initial moment; updating the contact ice element k according to the failure state of the contact ice element k includes:

[0040] When at most one corner point of all the corner points of the contact ice element k is located inside the hull waterline, determine that the failure state is non-failure, and the contact ice element k remains unchanged;

[0041] When a preset number M of corner points of all the corner points of the contact ice element k are located inside the hull waterline, determine that the failure state is partial failure, and change the shape of the contact ice element k;

[0042] When there are more than a preset number M of corner points of the ice unit k in contact located inside the hull waterline, or when the initial centroid of the ice unit k in contact is located inside the hull waterline, it is determined that the failure state is overall failure, and the ice unit k in contact is removed.

[0043] A further technical solution thereof is that dividing the ice floe area into several ice units includes:

[0044] The ice floe area is divided into a rectangular grid. On the basis of keeping the connection relationship between the corner points in the rectangular grid unchanged, the corner points of the rectangular grid are randomly moved within a preset range with their respective positions as the centers to form ice units with irregular shapes.

[0045] A further technical solution thereof is that the ice unit position information of any ship-peripheral ice unit m includes the position information of each corner point of the ship-peripheral ice unit m; detecting the contact state between any ship-peripheral ice unit m and the hull waterline includes:

[0046] According to the position information of each corner point of the ship-peripheral ice unit m at the current moment and the hull waterline position information, it is determined that at least 1 corner point of the ship-peripheral ice unit m is located inside the hull waterline at the current moment, and at least 1 corner point of the ship-peripheral ice unit m is located outside the hull waterline, or, when it is determined that at least 1 discrete point of the hull waterline is located inside the ship-peripheral ice unit m according to the hull waterline position information at the current moment, it is determined that there is contact between the ship-peripheral ice unit m and the hull waterline.

[0047] The beneficial technical effects of the present application are:

[0048] A hull ice force calculation method for ship maneuvering motion simulation in a layered ice area proposed by the present application, by considering the ship-ice contact speed and contact length when the ship sails in the layered ice area, and using the extreme static ice force formula introducing a speed correction term to calculate the local force of the contact ice unit on the hull. This method can calculate the multi-directional hull ice forces of the ice floe on the hull, including longitudinal ice force, lateral ice force and yaw ice moment, effectively solving the problem that the simulation results of ship maneuvering motion response are unreasonable caused by the traditional method only focusing on the longitudinal ice force. At the same time, the method of the present application calculates the multi-directional hull ice forces according to the ship-ice contact state, and can realize the accurate calculation of the hull ice forces when simulating special maneuvering operations such as star-shaped maneuvering, breaking away from the waterway, large drift angle maneuvering and reverse sailing, effectively improving the accuracy and reliability of the ship maneuvering motion simulation results in the layered ice area.

[0049] By constructing the outer bounding box of the hull waterline, the direct extraction of neighboring ice elements is achieved using the ice element row and column indices. By rotating the hull waterline and its surrounding neighboring ice elements and constructing the inner rectangular bounding box of the hull waterline with the side length direction the same as the fixed coordinate system direction, the rapid extraction of the ice elements around the ship can be realized through simple logical calculations. This effectively reduces the number of ice elements participating in the ship-ice interaction calculation and improves the efficiency of the hull ice force calculation.

[0050] Considering the damage of the hull to the contacting ice elements after ship-ice contact, the reliability of the hull ice force calculation result at the next moment is further improved by updating the contacting ice elements, thus ensuring the accuracy of the hull ice force calculation result during the entire maneuvering motion simulation process. Description of the Drawings

[0051] Figure 1 is the flowchart of the hull ice force calculation method.

[0052] Figure 2 is the schematic diagram of the fixed coordinate system and the moving coordinate system.

[0053] Figure 3 is the schematic diagram of the discretization of the hull waterline.

[0054] Figure 4 is the schematic diagram of the discretization of the ice floe.

[0055] Figure 5 is the schematic diagram of the random movement of the grid corner points.

[0056] Figure 6 is the schematic diagram of the process of extracting the contacting ice elements.

[0057] Figure 7 is the schematic diagram of ship-ice contact.

[0058] Figure 8 is the schematic diagram of the local coordinate system.

[0059] Figure 9 is the schematic diagram of the angle definition.

[0060] Figure 10 is the schematic diagram of the failure state of the contacting ice elements.

[0061] Figure 11 is the schematic diagram of the local force of the contacting ice elements on the hull. Detailed Implementation Manner

[0062] The following further describes the detailed implementation manner of the present application with reference to the drawings.

[0063] A hull ice force calculation method for ship maneuvering motion simulation in a multi-layer ice region proposed by the present application, please refer to Figure 1 the flowchart shown, and the specific steps are as follows:

[0064] Step 1: Divide the ice floe area into multiple ice cells and determine the ice cell position information of each ice cell at the current moment.

[0065] To clearly represent the positions of the ice cells for calculating the hull ice force and the hull waterline, first, define the coordinate system used in the hull ice force calculation process. Please refer to Figure 2 , pre - establish a fixed coordinate system O - XY. The fixed coordinate system is fixedly connected to the earth. It takes any point outside the hull waterplane as the origin O, the positive direction of the OX axis is from the origin O to the bow direction of the ship at the initial moment, and the positive direction of the OY axis is from the origin O to the starboard direction of the ship at the initial moment. Pre - establish a moving coordinate system G - xy. The moving coordinate system moves with the ship. It takes the projection point G of the ship's center of gravity on the waterplane as the coordinate origin, the positive direction of the Gx axis is from the origin G to the bow direction of the ship at the current moment, and the positive direction of the Gy axis is from the origin G to the starboard direction of the ship at the current moment. The angle ψ between the Gx axis of the moving coordinate system and the OX axis of the fixed coordinate system is the heading angle, and the heading angle ψ is positive when the Gx axis is in the clockwise direction of the OX axis.

[0066] Under the fixed coordinate system, discretize the hull waterline into multiple discrete points and determine the hull waterline position information. The hull waterline position information includes the positions of each discrete point. Specifically, take a finite number of discrete points at a certain interval on the hull waterline. Where the shape of the hull waterline changes violently, the interval between adjacent discrete points should be appropriately reduced. The number of discrete points should be sufficient to accurately represent the geometric shape of the hull waterline. Then the hull waterline can be represented by a series of continuous line segments formed between adjacent discrete points, and the closed polyline formed by all continuous line segments is as Figure 3 shown.

[0067] Under the fixed coordinate system, divide the ice floe area into multiple ice cells. The division method adopted in this application is rectangular grid division. For the sake of simplicity in calculation, square grids can also be used, as Figure 4 (a) shown. However, in practical applications, whether it is a rectangular grid or a square grid, this type of grid arrangement form of regular quadrilaterals with obvious directional orientation has certain defects in describing the randomness of sea ice damage and fracture. Therefore, it is necessary to perform a certain degree of randomization processing on the grid shape.

[0068] In one embodiment, when dividing the ice floe area into a rectangular grid, while keeping the connection relationship between the corner points in the rectangular grid unchanged, randomly move the corner points of the rectangular grid within a preset range centered on their respective positions to form ice cells with irregular shapes. Specifically, as Figure 4As shown in (b), the four corner points of each grid are randomly moved within a certain range centered on their positions to form irregular quadrilateral grid cells, and each irregular quadrilateral grid cell is an ice cell that constitutes the whole ice floe.

[0069] The random movement process of each corner point is as Figure 5 shown. It is set that the random movement range of each corner point is within a circle with its position as the center and radius R. In a fixed coordinate system, if the original position coordinates of any corner point i are (X i , Y i ), its position coordinates (X i ′, Y i ′) after random movement are:

[0070] R′ = rand[1]R

[0071] θ′ = 2rand[1]π

[0072] X i ′ = X i + R′cosθ′

[0073] Y i ′ = Y i + R′sinθ′

[0074] where rand[1] represents a function of random numbers within 0 to 1; for rectangular grids, the integer parameter 1≤ i ≤ 4. After randomly moving each corner point of the rectangular grid, the non-uniform grid discretization of the ice floe area can be completed. It should be noted that when randomly moving the corner points of the rectangular grid obtained by dividing the ice floe area, in order to improve the moving efficiency of the rectangular grid corner points, only the shapes of several rectangular grids can be changed, but in order to improve the accuracy of ice force calculation, the shapes of all rectangular grids can be changed so that each ice cell is an irregular quadrilateral grid. At the same time, when moving each corner point of the rectangular grid, it should be ensured that the position offsets of the shared corner points of adjacent rectangular grids are the same. In order to further improve the moving efficiency of the ice grid corner points, if a corner point is shared by more than one rectangular grid, only one random movement is required, and its position coordinates after random movement are the position coordinates after random movement of the corresponding corner points of the other rectangular grids sharing this corner point.

[0075] Taking the centroid of the irregular quadrilateral ice cell obtained at the initial moment as the initial centroid of each irregular quadrilateral ice cell, the calculation formula for the position coordinates (X0, Y0) of the initial centroid of each irregular quadrilateral ice cell is as follows:

[0076]

[0077] Step 2: Determine the contact ice cells that are in contact with the hull waterline at the current moment based on the ice cell position information and the hull waterline position information of each ice cell at the current moment.

[0078] During the actual navigation of a ship in an ice floe area, only the ice cells in contact with the hull in the entire ice floe area will exert a direct force on the hull. Therefore, in order to reduce unnecessary computational effort, it is only necessary to extract the ice cells in contact with the hull in the ice floe area. In one embodiment, the specific method for determining the contact ice cells that are in contact with the hull waterline at the current moment is as follows:

[0079] (1) Construct an outer bounding box of the hull waterline based on the hull waterline position information at the current moment, and extract the ice cells that intersect with the outer bounding box in combination with the ice cell position information of each ice cell at the current moment to obtain the neighboring ice cells of the hull waterline.

[0080] Constructing the outer bounding box is a relatively large range divided to be able to extract all the ice cells in contact with the hull waterline, playing a role of preliminary screening. The shape of the outer bounding box can be any shape. For the sake of simplicity and efficiency in calculation, the shape of the outer bounding box in this application is a rectangle and the side length direction of the outer bounding box is the same as the coordinate axis direction of the fixed coordinate system. Then, determining the neighboring ice cells of the hull waterline includes:

[0081] Determine the ice cell row and column indices that intersect with each side of the outer bounding box based on the ice cell position information of the first ice cell obtained by division and the corner positions of the outer bounding box.

[0082] Specifically, if there are I rows and J columns of ice cells in the discretized ice floe, and in the fixed coordinate system, the original position coordinates of the upper left corner point of the ice cell in the first row and the first column are (X i,min , Y i,min ), and at the same time, the minimum horizontal and vertical coordinates of the 4 corner points of the outer bounding box of the hull waterline constructed in the fixed coordinate system are (X b,min , Y b,min ), and the maximum horizontal and vertical coordinates are (X b,max , Y b,max ).

[0083] If (X b,min ≥X i,max ) || (X b,max ≤X i,min ) || (Y b,min ≥Y i,max ) || (Y b,max ≤Y i,min) indicates that there is no intersection between the outer bounding box and the ice floes. At this time, it can be directly determined that there are no ice elements around the ship, and the ice elements cannot interact with the hull, that is, the ice force on the hull is 0. Conversely, the row and column indices of the ice elements that intersect with the sides of the outer bounding box are calculated according to the following formula:

[0084]

[0085] ii = min{1 + ceil[(Y b,min - Y i,min ) / w i , I}

[0086]

[0087] ii = min{1 + ceil[(X b,min - X i,min ) / l i , J}

[0088] Among them, ceil() represents the ceiling function (rounding up), mod() represents the modulo function, max() represents the maximum value function, and min() represents the minimum value function; w i represents the width of the rectangular ice element before the random movement of the corner points; l i represents the length of the rectangular ice element before the random movement of the corner points; for the case of the discrete ice floe area with a square grid, w i is equal to l i ; i, ii, j, jj represent the row and column indices of the ice elements that intersect with the sides of the outer bounding box. The ice elements in the i-th to ii-th rows and the j-th to jj-th columns of the ice elements that make up the ice floes intersect with the outer bounding box.

[0089] Extract the ice elements that intersect with the outer bounding box directly from all the ice elements obtained by the division according to the row and column indices of the ice elements, and use the ice elements that intersect with the outer bounding box as the neighboring ice elements of the hull waterline, as shown in Figure 6 (a).

[0090] (2) Rotate the hull waterline and each neighboring ice element at the current moment around the projection point G of the ship's center of gravity on the waterplane to make the bow point to the positive direction of the OX axis of the fixed coordinate system.

[0091] In the fixed coordinate system, rotate the neighboring ice elements and the hull waterline counterclockwise by an angle ψ around point G so that the bow direction after the counterclockwise rotation is consistent with the bow direction at its initial moment, that is, the coordinate axes of the moving coordinate system after rotation are parallel to those of the earth coordinate system.

[0092] (3) Construct an inner rectangular bounding box based on the position information of the hull waterline after rotation, and extract the neighboring ice elements that intersect with the inner rectangular bounding box by combining the ice element position information of each neighboring ice element after rotation, to obtain the ice elements around the ship at the current moment, and regard the ice elements around the ship that are in contact with the hull waterline as the contact ice elements.

[0093] The inner rectangular bounding box is located inside the outer bounding box. The side length direction of the inner rectangular bounding box is the same as the coordinate axis direction of the fixed coordinate system, and the distance between any side of the inner rectangular bounding box and the hull waterline after rotation is not less than the longest side length of the ice element. For example, in the case of a square grid discrete ice floe area, the distance between the inner rectangular bounding box and the hull waterline after rotation is not less than the side length of the square grid, as shown in Figure 6 (b).

[0094] Since the four sides of the inner rectangular bounding box are consistent with the coordinate axis direction of the fixed coordinate system, the extraction of the ice elements around the ship can be realized through simple logical judgment. The specific method is as follows: Denote the minimum horizontal and vertical coordinates of the 4 corner points of the inner rectangular bounding box as (X b ′ ,min , Y b ′ ,min ), and the maximum horizontal and vertical coordinates as (X b ′ ,max , Y b ′ ,max ). At this time, traverse each neighboring ice element after rotation. If the coordinates (X0′, Y0′) of the centroid position at its initial moment after rotation satisfy the following logical judgment formula, then it is a non-ice element around the ship, otherwise it is an ice element around the ship. The logical judgment formula is:

[0095] (X0′ < X b ′ ,min ) || (X0′ > X b ′ ,max ) || (Y0′ < Y b ′ ,min ) || (Y0′ > Y b ′ ,max )

[0096] In one embodiment, the ice element position information of any ice element m around the ship includes the position information of each corner point of the ice element m around the ship and the position information of its initial centroid. Detecting the contact state between any ice element m around the ship and the hull waterline includes:

[0097] When it is determined according to the position information of each corner point of the ship's circumferential ice unit m at the current moment and the hull waterline position information that at least one corner point of the ship's circumferential ice unit m is located inside the hull waterline at the current moment, and at least one corner point of the ship's circumferential ice unit m is located outside the hull waterline, or when it is determined according to the position information of the hull waterline at the current moment that at least one discrete point of the hull waterline is located inside the ship's circumferential ice unit m, it is determined that there is contact between the ship's circumferential ice unit m and the hull waterline.

[0098] For the case where the ship's circumferential ice unit is an irregular quadrilateral, since the hull waterline is a closed polyline composed of a series of continuous line segments formed between adjacent discrete points, when all 4 corner points of the ship's circumferential ice unit m are located inside the hull waterline, there is no contact between the ship's circumferential ice unit m and the hull waterline. However, for the ship's circumferential ice unit m located at the front and rear tips of the hull waterline, when all 4 corner points of the ship's circumferential ice unit m are located outside the hull waterline, but there are discrete points of the hull waterline located inside the ship's circumferential ice unit m, there is contact between the ship's circumferential ice unit m and the hull waterline. When there are corner points of the ship's circumferential ice unit m all located inside the hull waterline, but the intersecting part of the hull waterline and the ship's circumferential ice unit m is between two discrete points, at this time there are no discrete points located inside the ship's circumferential ice unit m, but there is still contact between the ship's circumferential ice unit m and the hull waterline. Therefore, it is necessary to use both the positional relationship between the corner points of the ship's circumferential ice unit m and the hull waterline and the positional relationship between the discrete points of the hull waterline and the ship's circumferential ice unit m as the basis for judging the contact state. When only one corner point of the 4 corner points of the ship's circumferential ice unit m is located on the hull waterline, it indicates that the ship's circumferential ice unit m is in single-point contact with the hull waterline. At this time, the contact length is 0, and this ship's circumferential ice unit does not exert a force on the hull.

[0099] Step 3: Combine the ship's navigation state parameters to determine the contact length w between any contact ice unit k and the hull waterline and the ship-ice contact speed. The ship-ice contact speed includes the ship-ice contact speed caused by the ship's yaw motion, longitudinal surge motion, and transverse sway motion.

[0100] Use the extreme value static ice force formula with a velocity correction term and calculate the local force exerted by the contact ice unit k on the hull according to the contact length w between the contact ice unit k and the hull waterline and the ship-ice contact speed.

[0101] Loop through all the extracted contact ice units, and calculate the local force exerted by any contact ice unit k on the hull. In one embodiment, the local force includes the normal extrusion force and the tangential friction force, and determine the normal extrusion force exerted by the contact ice unit k on the hull and the tangential friction force The specific steps are as follows:

[0102] (1) Determine the ship-ice contact line between the contact ice unit k and the hull waterline.

[0103] Such as Figure 7As shown in the figure, the dotted line represents the hull waterline, the irregular quadrilateral is the ice contact unit k, point a and point b are the intersection points of the ice contact unit k and the hull waterline respectively, and point c is the midpoint of the line segment ab. The coordinates of point a in the fixed coordinate system are (X a , Y a ), the coordinates of point b in the fixed coordinate system are (X b , Y b ), the connecting part between a and b is the ship-ice contact line, and the length of the ship-ice contact line is the contact length w between the ice contact unit k and the hull waterline.

[0104] The ship-ice contact line is the connecting line between a and b. According to the actual situation of the interaction between the laminated ice and the hull in this application, the straight line segment between a and b is used as the ship-ice contact line, which can simplify the calculation on the basis of ensuring the accuracy of the calculation results to improve the calculation efficiency. Thus, the contact length w can be determined according to the length of the straight line segment ab. The specific calculation formula is:

[0105]

[0106] (2) Determine the component of the ship-ice contact velocity between the ice contact unit k and the hull waterline in the normal direction of the ship-ice contact line in combination with the ship navigation state parameters and the component of the ship-ice contact velocity in the tangential direction of the ship-ice contact line The positive direction of which is along the normal line of the ship-ice contact line at the midpoint c and points to the outside of the hull waterline, The positive direction of which is along the tangent line of the ship-ice contact line at the midpoint c and points to the counterclockwise direction of the hull waterline.

[0107] Take the midpoint c of the ship-ice contact line as the force application point of the local force of the ice contact unit k on the hull. To facilitate the expression of the direction of the local force, a local coordinate system o e -τn is established in advance. As Figure 8 shown, take the midpoint c of the ship-ice contact line as the origin o e of the local coordinate system, take the tangent line of the ship-ice contact line and point to the counterclockwise direction of the hull waterline as the positive direction of the o e τ axis of the local coordinate system, and take the normal line of the ship-ice contact line and point to the outside of the hull waterline as the positive direction of the o e n axis of the local coordinate system. Since the line segment ab is a straight line segment, the tangent line of the ship-ice contact line is along the line segment ab, and the normal line of the ship-ice contact line is perpendicular to the line segment ab.

[0108] The relationship between the local coordinate system and the fixed coordinate system and the moving coordinate system is as Figure 9 shown, the included angle between the line segment Gc and the Gx axis of the moving coordinate system is As Figure 9(a), the positive direction is defined as the clockwise direction of the Gc line with respect to the Gx axis; the angle between the o e τ axis of the local coordinate system and the OX axis of the fixed coordinate system is ξ, as shown in Figure 9 (b), where the positive direction is defined as the clockwise direction of the o e τ axis with respect to the OX axis. Since the tangent line of the ship-ice contact line at its midpoint c is in the same direction as the o e τ axis of the local coordinate system, the angle between the tangent line of the ship-ice contact line at its midpoint c and the OX axis of the fixed coordinate system is also ξ.

[0109] In one embodiment, the method for determining the components of the ship-ice contact velocity of the ice-contact unit k with the ship's waterline and is as follows:

[0110] According to the ship's surge velocity u in the ship navigation state parameters, determine the ship-ice contact velocity u c = u caused by the ship's surge motion at the midpoint c of the ship-ice contact line, and the velocity direction is along the Gx direction of the moving coordinate system; according to the ship's sway velocity v in the ship navigation state parameters, determine the ship-ice contact velocity v c = v caused by the ship's sway motion at the midpoint c of the ship-ice contact line, and the velocity direction is along the Gy direction of the moving coordinate system; according to the yaw angular velocity r of the ship and the position of the projection point G of the ship's center of gravity on the waterplane, determine the ship-ice contact velocity r c = r|Gc| caused by the ship's yaw motion at the midpoint c of the ship-ice contact line, and the velocity direction is perpendicular to the Gc line and points to the ship's yaw direction; where the directions of the ship's surge velocity u, the ship's sway velocity v, and the yaw angular velocity r are as shown in Figure 7 . If the position coordinates of point G in the fixed coordinate system are (X G , Y G ), and in addition, the position coordinates of point c are denoted as (X c , Y c ), then the length of the Gc line

[0111] Decompose and transform the ship-ice contact velocity u c caused by the ship's surge motion at the midpoint c of the ship-ice contact line, the ship-ice contact velocity v c caused by the ship's sway motion, and the ship-ice contact velocity r c caused by the ship's yaw motion onto the normal direction and the tangent direction of the ship-ice contact line. The specific process is as follows:

[0112] Decompose the ship-ice contact velocity u c caused by the ship's surge motion at the midpoint c of the ship-ice contact line, the ship-ice contact velocity v cand the ship-ice contact velocity r caused by the ship's turning motion c Decomposed onto the Gx-axis direction of the moving coordinate system, the component of the ship-ice contact velocity in the Gx-axis direction of the moving coordinate system is obtained And decomposed onto the Gy-axis direction of the moving coordinate system, the component of the ship-ice contact velocity in the Gy-axis direction of the moving coordinate system is obtained

[0113] Decompose the component u′ of the ship-ice contact velocity in the Gx-axis direction and the component v′ in the Gy-axis direction of the moving coordinate system onto the OX-axis direction of the fixed coordinate system, and the component U′ = u′cosψ - v′sinψ of the ship-ice contact velocity in the OX-axis direction of the fixed coordinate system is obtained. And decompose it onto the OY-axis direction of the fixed coordinate system, and the component V′ = u′sinψ + v′cosψ of the ship-ice contact velocity in the OY-axis direction of the fixed coordinate system is obtained. ψ is the angle between the Gx-axis of the moving coordinate system and the OX-axis of the fixed coordinate system

[0114] Decompose the component U′ of the ship-ice contact velocity in the OX-axis direction and the component V′ in the OY-axis direction of the fixed coordinate system onto the normal direction of the ship-ice contact line at the midpoint c of the ship-ice contact line, and the component u of the ship-ice contact velocity between the contact ice element k and the ship's waterline in the normal direction of the ship-ice contact line is obtained n k = U′cosξ + V′sinξ, and decompose it onto the tangent direction of the ship-ice contact line at the midpoint c of the ship-ice contact line, and the component u of the ship-ice contact velocity between the contact ice element k and the ship's waterline in the tangent direction of the ship-ice contact line is obtained τ k = -U′sinξ + V′cosξ; ξ is the angle between the tangent of the ship-ice contact line and the OX-axis of the fixed coordinate system

[0115] (3) The normal squeezing force of the contact ice element k on the hull can be calculated according to the component of the ship-ice contact velocity in the normal direction Calculate the normal squeezing force of the contact ice element k on the hull The specific calculation method is as follows

[0116] Take the midpoint c of the ship-ice contact line as the acting point of the normal squeezing force f n k When Determine the normal squeezing force of the contact ice element k on the hull Since Taking its direction pointing outside the ship's waterline as positive, so when The hull does not squeeze the ice element, but has a tendency to move away from the ice element. Therefore, there is no squeezing force between the ship-ice element at this time

[0117] When When the contact ice unit k exerts a normal extrusion force f on the hull at the midpoint c of the ship-ice contact line, n =p G wh, where h is the sea ice thickness, p G is the effective ice pressure per unit area; p G It can be calculated by the extreme static ice force formula C R is the ice strength coefficient, h1 is the reference ice thickness, which is generally 1 meter; β is an empirical coefficient, which is set to -0.16 in this application; α is also an empirical coefficient, and when h<1 meter, α=-0.5+h / 5, and when h≥1 meter, α=-0.3.

[0118] Since the ship's ice contact speed is closely related to the ice force when the ship is actually sailing in the ice layer, the speed correction term is introduced into the extreme static ice force formula to improve the applicability of the extreme static ice force formula in calculating the ice force on the hull of the ship sailing in the ice layer. n k The direction points to the inner normal direction of the ship-ice contact line, then the normal extrusion force f is calculated based on the extreme static ice force formula with the introduction of the velocity correction term. n k The calculation expression is as follows:

[0119]

[0120] Among them, λ and η are velocity correction coefficients, and their specific values ​​can be set according to the actual application situation. g is the gravitational acceleration, L w is the hull waterline length, normal extrusion pressure The direction of the ship-ice contact velocity is the component of the ship-ice contact velocity in the normal direction of the ship-ice contact line. On the contrary, that is, along the normal of the ship-ice contact line at the midpoint c and pointing to the inside of the hull waterline.

[0121] (4) The normal extrusion force of the contact ice unit k on the hull can be and the component of the ship-ice contact velocity in the tangent direction of the ship-ice contact line Calculate the tangential friction force f of the contact ice unit k on the hull τ k , the specific calculation method is:

[0122] Since the friction force is generated by the relative motion between the hull and the contact ice unit in the tangential direction of the ship-ice contact line and its value is proportional to the magnitude of the extrusion force of the ship-ice unit, the friction force is generated only when the tangential relative speed between the hull and the contact ice unit is not 0 and there is an extrusion force between the hull and the contact ice unit. and When the midpoint c of the ship-ice contact line is taken as the tangential friction force The acting point of the force is used to determine the tangential frictional force of the ice contact element k on the hull. Otherwise, determine the tangential frictional force of the ice contact element k on the hull at the midpoint c of the ship-ice contact line.

[0123] Among them, sign() is the sign function. It means taking the sign of, γ is the ship-ice friction coefficient, and the tangential frictional force is along the tangent of the ship-ice contact line at the midpoint c and is opposite to the component of the ship-ice contact velocity in the tangent direction of the ship-ice contact line. in the opposite direction.

[0124] Since the ship will damage the ice element when it actually sails in the layer ice area and collides with the ice element, according to the different degrees of contact, the damage degrees of the ice elements are different. The ice elements with less damage will still exert forces on the hull subsequently, while the ice elements with greater damage will no longer exert forces on the hull subsequently. To ensure the accuracy of the entire maneuvering motion simulation calculation results, during the ship navigation simulation process, after calculating the local acting forces of the ship-ice interaction at each calculation moment, it is necessary to judge the failure state of the ice contact element according to the relative position relationship between the ice contact element and the hull waterline, and further update the ice contact element.

[0125] In one embodiment, for any ice contact element k, determine the failure state of the ice contact element k according to the ice element position information and the hull waterline position information of the ice contact element k at the current moment. The failure state indicates the damage degree of the ice contact element k after the ship-ice contact; update the ice contact element k according to the failure state of the ice contact element k, and enter the next calculation moment.

[0126] The failure state includes non-failure, partial failure, and overall failure. The ice element position information of any ice contact element k includes the position information of each corner point of the ice contact element k and the position information of the initial centroid of the ice contact element k. The initial centroid is the centroid of the ice contact element k at the initial moment; updating the ice contact element k according to the failure state of the ice contact element k includes:

[0127] When at most one corner point of all the corner points of the ice contact element k is located inside the hull waterline, determine that the failure state is non-failure, and the ice contact element k remains unchanged.

[0128] When there are a preset number M of corner points of the ice contact element k located inside the hull waterline, determine that the failure state is partial failure, and change the shape of the ice contact element k. Specifically, the part of the ice contact element k located inside the hull waterline is deleted, and the part located outside the hull waterline is retained and together with the ship-ice contact line ab forms a new ice element shape.

[0129] When there are more than a preset number M of corner points of the ice contact unit k located inside the ship's waterline among all the corner points, or when the initial centroid of the ice contact unit k is located inside the ship's waterline, it is determined that the failure state is overall failure, and the ice contact unit k is removed so that the ice contact unit k falls off the ice floe, and it will no longer participate in the calculation of ship-ice interaction subsequently, that is, it will no longer exert ice force on the ship hull subsequently.

[0130] Among them, the preset number M is set according to the shape of the ice contact unit. For an ice contact unit in the shape of an irregular quadrilateral, such as Figure 10 As shown, if among the 4 corner points of the ice contact unit k, no corner point or only 1 corner point is located inside the ship's waterline, the failure state of the ice contact unit k is non-failure; if 2 corner points are located inside the ship's waterline, the failure state of the ice contact unit k is partial failure; if 3 or more corner points are located inside the ship's waterline, the failure state of the ice contact unit k is overall failure; for the ice contact unit k in contact with the front and rear tip positions of the ship's waterline, when the initial centroid of the ice contact unit k is located inside the ship's waterline, but there is no corner point or less than 3 corner points are located inside the ship's waterline, the failure state of the ice contact unit k is also overall failure.

[0131] Step 4, superimpose the local forces of each ice contact unit on the ship hull to obtain the ship hull ice force at the current moment.

[0132] When calculating the overall ice force, the midpoint c of the ship-ice contact line is used as the force application point, and the normal extrusion force and tangential friction force of each ice contact unit k on the ship hull are superimposed to obtain the overall ice force exerted by the ice floe on the ship hull. In one embodiment, the specific process of superimposing the local forces of each ice contact unit on the ship hull to obtain the ship hull ice force at the current moment is as follows:

[0133] Using the midpoint c of the ship-ice contact line as the force application point, the normal extrusion force and the tangential friction force of the ice contact unit k on the ship hull are decomposed and transformed to obtain their components on the OX axis of the fixed coordinate system and their components

[0134]

[0135] on the OY axis: The component of the force of the ice contact unit k on the ship hull on the OX axis of the fixed coordinate system and the component on the OY axis are decomposed and transformed to obtain their components

[0136]

[0137] Calculate the local pitch moment of the ice contact unit k on the projection point G of the ship's center of gravity in the waterline plane in, Bow rocker arm at point G Bow rocker arm at point G represents the Gc vector, represents the Gx vector, represents the Gy vector, represents the modulus of the Gx vector, Represents the magnitude of the Gy vector.

[0138] The component of the force exerted by the contact ice unit k on the hull on the Gx axis of the motion coordinate system as well as The component of the bow rocking arm at point G on the Gy axis of the motion coordinate system as well as For the bow rocker arm at point G, please refer to Figure 11 .

[0139] The calculated hull ice force at the current moment includes the longitudinal ice force along the longitudinal direction of the hull. Transverse ice force along the transverse direction of the hull and bow ice moment K is the total number of contact ice units, an integer parameter K ≥ 1.

[0140] The above is only a preferred embodiment of the present application, and the present application is not limited to the above embodiments. It is understood that other improvements and changes directly derived or associated by those skilled in the art without departing from the spirit and concept of the present application should be considered to be included in the scope of protection of the present application.

Claims

1. A method for calculating ice forces on a hull for simulation of ship maneuvering motion in ice areas, characterized in that: The hull ice force calculation method comprises: Dividing the ice row area into a plurality of ice units and determining ice unit position information of each ice unit at a current moment; Determine each contact ice unit that is in contact with the hull waterline at the current moment according to the ice unit position information of each ice unit at the current moment and the hull waterline position information; The contact length w between any contact ice unit k and the hull waterline and the ship-ice contact speed are determined in combination with the ship's navigation state parameters. The ship-ice contact speed includes the ship-ice contact speed caused by the ship's bow turning motion, the ship's longitudinal motion and the ship's transverse motion. The local force of the contact ice unit k on the hull is calculated by using the extreme static ice force formula with the velocity correction term introduced and according to the contact length w between the contact ice unit k and the hull waterline and the ship-ice contact speed. The local forces of each contact ice unit on the hull are superimposed to obtain the hull ice force at the current moment.

2. The method for calculating hull ice forces according to claim 1, characterized in that: The step of determining each contacting ice unit that is in contact with the hull waterline at the current moment according to the ice unit position information of each ice unit at the current moment and the hull waterline position information comprises: According to the current position information of the hull waterline, an outer bounding box of the hull waterline is constructed, and the ice units intersecting with the outer bounding box are extracted in combination with the ice unit position information of each ice unit at the current moment, so as to obtain each neighborhood ice unit of the hull waterline; Rotate the hull waterline and each neighboring ice unit around the projection point G of the hull gravity center in the waterline plane until the bow points to the positive direction of the OX axis of the fixed coordinate system; the positive direction of the OX axis of the fixed coordinate system points to the bow direction at the initial moment, and the positive direction of the OY axis of the fixed coordinate system points to the starboard direction of the ship at the initial moment; An inner rectangular bounding box is constructed according to the position information of the rotated hull waterline, and the neighboring ice units intersecting with the inner rectangular bounding box are extracted in combination with the ice unit position information of each rotated neighboring ice unit to obtain each ship surrounding ice unit at the current moment, and the ship surrounding ice units in contact with the hull waterline are taken as contact ice units; the inner rectangular bounding box is located inside the outer bounding box, the side length direction of the inner rectangular bounding box is the same as the coordinate axis direction of the fixed coordinate system, and the distance between any side of the inner rectangular bounding box and the rotated hull waterline is not less than the longest side length of the ice unit.

3. The method for calculating hull ice forces according to claim 2, characterized in that: The shape of the outer bounding box is rectangular and the length direction of the outer bounding box is the same as the coordinate axis direction of the fixed coordinate system. The neighborhood ice unit for determining the hull waterline includes: According to the ice unit position information of the first ice unit obtained by the division and the positions of each corner point of the outer bounding box, the row and column indexes of the ice units intersecting with each edge of the outer bounding box are determined; Ice cells intersecting with the outer bounding box are directly extracted from all ice cells obtained by division according to the ice cell row and column indexes, and the ice cells intersecting with the outer bounding box are used as neighborhood ice cells of the hull waterline.

4. The method for calculating hull ice force according to claim 1, characterized in that: The local forces include normal extrusion force and tangential friction force, and the normal extrusion force of the contact ice unit k on the hull is determined. and tangential friction include: Determine the ship-ice contact line between the contact ice unit k and the hull waterline; According to the ship-ice contact line and the ship's navigation state parameters, the component of the ship-ice contact velocity of the contact ice unit k and the hull waterline in the normal direction of the ship-ice contact line is determined. and the component of the ship-ice contact velocity in the tangent direction of the ship-ice contact line The positive direction is along the normal of the ship-ice contact line at the midpoint c and points to the outside of the hull waterline. The positive direction is along the tangent line of the ship-ice contact line at the midpoint c and points counterclockwise to the hull waterline; when When the contact ice unit k exerts a normal pressure on the hull at the midpoint c of the ship-ice contact line, when When the contact ice unit k exerts a normal pressure on the hull at the midpoint c of the ship-ice contact line, when and When the contact ice unit k exerts a tangential friction force on the hull at the midpoint c of the ship-ice contact line, Otherwise, determine the tangential friction force of the contact ice unit k on the hull at the midpoint c of the ship-ice contact line: Where h is the thickness of sea ice, p G is the effective ice pressure per unit area, g is the acceleration due to gravity, L w is the waterline length of the hull, λ and η are the speed correction coefficients, sign() is the sign function, γ is the ship-ice friction coefficient; normal extrusion force The direction of the ship-ice contact velocity is the component of the ship-ice contact velocity in the normal direction of the ship-ice contact line. In contrast, tangential friction The direction of the ship-ice contact velocity is the component of the tangent direction of the ship-ice contact line on the contrary.

5. The method for calculating hull ice forces according to claim 4, characterized in that: Determine the component of the ship ice contact velocity between the contact ice unit k and the hull waterline and include: According to the ship's longitudinal sway speed u in the ship's navigation state parameters, the ship-ice contact speed u caused by the ship's longitudinal sway motion at the midpoint c of the ship-ice contact line is determined. c =u and the speed direction is along the Gx axis direction of the motion coordinate system; the ship ice contact speed v caused by the ship swaying motion at the midpoint c of the ship ice contact line is determined according to the ship swaying speed v in the ship navigation state parameters c =v and the speed direction is along the Gy axis of the motion coordinate system; according to the bow angular velocity r in the ship's navigation state parameters and the position of the projection point G of the ship's center of gravity in the waterline, the ship ice contact speed r caused by the ship's bow turning motion at the midpoint c of the ship-ice contact line is determined c =r|Gc| and the speed direction is perpendicular to the Gc line and points to the bow turning direction of the ship; The ship-ice contact speed u caused by the ship's longitudinal motion at the midpoint c of the ship-ice contact line c , ship ice contact speed v caused by ship swaying motion c and the ship ice contact speed r caused by the ship's bow motion c Decomposing and converting to the normal direction and tangent direction of the ship-ice contact line, we get: in, ξ is the angle between the tangent line of the ship-ice contact line at the midpoint c and the OX axis of the fixed coordinate system, is the angle between the Gc line and the Gx axis of the moving coordinate system, ψ is the angle between the Gx axis of the moving coordinate system and the OX axis of the fixed coordinate system; the positive direction of the Gx axis of the moving coordinate system points to the bow direction of the ship at the current moment, and the positive direction of the Gy axis of the moving coordinate system points to the starboard direction of the ship at the current moment; the positive direction of the OX axis of the fixed coordinate system points to the bow direction of the ship at the initial moment, and the positive direction of the OY axis of the fixed coordinate system points to the starboard direction of the ship at the initial moment.

6. The method for calculating hull ice forces according to claim 4, characterized in that: The ice force on the hull at the current moment obtained by superimposing the local forces of each contact ice unit on the hull includes: The normal extrusion force of the contact ice unit k on the hull at the midpoint c of the ship-ice contact line is and tangential friction Decompose the transformation to obtain the components of the Gx axis in the motion coordinate system and Gy-axis components in, ξ is the angle between the tangent of the ship-ice contact line at its midpoint c and the OX axis of the fixed coordinate system, ψ is the angle between the Gx axis of the moving coordinate system and the OX axis of the fixed coordinate system; the positive direction of the Gx axis of the moving coordinate system points to the bow direction of the ship at the current moment, and the positive direction of the Gy axis of the moving coordinate system points to the starboard direction of the ship at the current moment; the positive direction of the OX axis of the fixed coordinate system points to the bow direction of the ship at the initial moment, and the positive direction of the OY axis of the fixed coordinate system points to the starboard direction of the ship at the initial moment; Calculate the local pitch moment of the ice contact unit k on the projection point G of the ship's center of gravity in the waterline plane in, Bow rocker arm at point G Bow rocker arm at point G The calculated ice force on the hull at the current moment includes the longitudinal ice force Horizontal ice force and bow ice moment K is the total number of contact ice units, an integer parameter K ≥ 1.

7. The method for calculating hull ice forces according to claim 1, characterized in that: The hull ice force calculation method further comprises: For any contact ice unit k, the failure state of the contact ice unit k is determined according to the ice unit position information of the contact ice unit k at the current moment and the hull waterline position information, wherein the failure state indicates the degree of damage to the contact ice unit k after the ship contacts the ice; The contact ice unit k is updated according to the failure state of the contact ice unit k, and enters the next calculation moment.

8. The method for calculating hull ice forces according to claim 7, characterized in that: The failure state includes non-failure, partial failure and overall failure. The position information of any ice unit contacting the ice unit k includes the position information of each corner point of the ice unit contacting the ice unit k and the position information of the initial centroid of the ice unit contacting the ice unit k, wherein the initial centroid is the centroid of the ice unit contacting the ice unit k at the initial moment. Updating the ice unit contacting the ice unit k according to the failure state of the ice unit contacting the ice unit k includes: When at most one corner point among all corner points of the contact ice unit k is located inside the hull waterline, the failure state is determined to be not failed, and the contact ice unit k remains unchanged; When a preset number M of corner points of all corner points of the contact ice unit k are located inside the hull waterline, or the initial centroid of the contact ice unit k is located inside the hull waterline, the failure state is determined to be partial failure, and the shape of the contact ice unit k is changed; When more than a preset number M of corner points of all the corner points of the contact ice unit k are located inside the hull waterline, the failure state is determined to be an overall failure, and the contact ice unit k is removed.

9. The method for calculating hull ice forces according to claim 1, characterized in that: The ice bank area is divided into several ice units including: The ice area is divided into rectangular grids. On the basis of keeping the connection relationship between the corner points in the rectangular grid unchanged, the corner points of the rectangular grid are randomly moved within a preset range with their respective positions as the center to form irregular ice units.

10. The method for calculating hull ice forces according to claim 2, characterized in that: The hull waterline position information includes the position information of each discrete point, and the ice unit position information of any ice unit m around the ship includes the position information of each corner point of the ice unit m around the ship; Detecting the contact state between any ice unit m around the ship and the hull waterline includes: When it is determined according to the position information of each corner point of the ship surrounding ice unit m and the position information of the hull waterline at the current moment that at least one corner point of the ship surrounding ice unit m is located inside the hull waterline and at least one corner point of the ship surrounding ice unit m is located outside the hull waterline, or when it is determined according to the position information of the hull waterline at the current moment that at least one discrete point of the hull waterline is located inside the ship surrounding ice unit m, it is determined that the ship surrounding ice unit m is in contact with the hull waterline.

Images