A Modeling Method for Automatic Transition Mesh Generation

Abstract

The present invention discloses a method for automatically dividing and modeling transition grids, belonging to the technical field of finite element simulation, and is applied to a compact tension specimen with side grooves. The method includes: determining the geometric design parameters of the compact tension specimen with side grooves, and establishing a quarter geometric model based on geometric symmetry and the coordinate description of geometric feature points; determining the mesh division size parameters and generating the coordinates of the key mesh feature points; cutting the original geometric model into a preset number of model components according to the coordinates of the key mesh feature points; setting the mesh division types for the preset number of model components, and sequentially dividing and generating the mesh model of the compact tension specimen with side grooves. It improves the mesh division quality of the compact tension specimen with side grooves model, avoids manual interactive division, takes into account the solution accuracy and solution efficiency of simulation calculations, has regular meshes, strong versatility and is not prone to errors, overcomes the deficiencies of geometrically simplified mesh models and traditional transition mesh models, and thus realizes high-precision automated modeling.

Description

Technical Field

[0001] The present invention belongs to the technical field of finite element simulation, and particularly relates to a method for automatically dividing and modeling transition meshes. Background Art

[0002] The compact tension (CT) specimen with side grooves is one of the common specimen types recommended by the ASTM standard for studying the crack propagation behavior of metallic materials and measuring the fracture toughness of metallic materials. When using computer-aided solutions to solve the mechanical response of the CT specimen with side grooves, due to the drastic change in the stress gradient at the mechanical machining notch and the geometric part of the side groove of the specimen, a finer mesh is usually required to capture the stress change, while in the area far from the above-mentioned area where the stress gradient change is relatively gentle, a coarser mesh is used to save the calculation cost. In order to ensure smooth and uniform connection between the fine and coarse meshes, a transition mesh division method with appropriate size is needed.

[0003] Currently, the mesh models of the compact tension specimen for simulation mechanical calculation can be divided into two categories. The first category is the 2D mesh model that ignores the side groove geometry [1][2][3] or the 3D mesh model that simplifies the side groove geometry [4] . Because these models have been simplified in the side groove geometric details, although the difficulty of mesh division is reduced, it is difficult to explore the influence of the 3D geometric constraint of the side groove on the mechanical response. The second category is the 3D mesh model that considers the complete side groove geometry [5] . This type of geometric model adopts the traditional mesh transition method with a geometric progression node distribution, with a large number of elements and too high a calculation cost. In addition, other studies on the three-point bending specimen with side grooves using transition mesh division [6] lack comparability because they are essentially different from the CT specimen targeted by the present invention in geometric form. However, the above-mentioned existing studies all adopt manual interactive division, and there is generally the drawback of long preprocessing time. To sum up, there is still a lack of a method specifically for automatically dividing the transition mesh of the compact tension specimen with side grooves to generate a high-precision finite element model.

[0004] [1] Wang G Z, Liu X L, Xuan F Z, et al. Effect of constraint induced by crack depth on creep crack-tip stress field in CT specimens [J]. International Journal of solids and structures, 2010, 47(1): 51-57.

[0005] [2]Pericoli V,Lao X,Ziccarelli A,et al.Integration of an adaptivecohesive zone and continuum ductile fracture model to simulate crackpropagation in steel structures[J].Engineering Fracture Mechanics,2021,258:108041.

[0006] [3]Li Tieping, Tian Xinlu, Liu Rui, et al. Research on the influence of specimen size on the fracture toughness of the main steam pipeline in nuclear power plants[J]. Chinese Quarterly of Mechanics, 2016, 37(4): 8.

[0007] [4]Tkach Y, Burdekin F M. A three-dimensional analysis of fracturemechanics test pieces of different geometries–Part 1Stress-state ahead of thecrack tip[J].International Journal of Pressure Vessels and Piping,2012,93:42-50.

[0008] [5]Mao J, Li X, Bao S, et al. Comparative Study of the Geometric Effectson Fracture Behaviors of Side-Grooved and Plain-Sided Compact TensionSpecimens[J].Journal of Materials Engineering and Performance,2019,28(10):6514-6524.

[0009] [6]Chen C, Qian X. A non-contact approach to measure JR curve for side-grooved specimens using digital image correlation[J].Theoretical and AppliedFracture Mechanics,2022,121:103549. Summary of the Invention

[0010] In order to solve the technical problems existing in the prior art that manual interactive division is generally used, the preprocessing link takes a long time, and there is still a lack of a method specifically for automatically dividing and generating a high-precision finite element model for the transition mesh of a compact tension specimen with side grooves, the present invention provides a method for automatically dividing and modeling the transition mesh.

[0011] The present invention provides a method for automatically dividing and modeling the transition mesh, which is applied to a compact tension specimen with side grooves and includes:[[]]

[0012] S1: Determine the geometric design parameters of the compact tension specimen with side grooves, and establish a quarter geometric model based on the geometric symmetry and the coordinate description of geometric feature points;

[0013] S2: Determine the mesh division size parameters and generate the coordinates of the key mesh feature points;

[0014] S3: Cut the original geometric model into a preset number of model components according to the coordinates of the key mesh feature points;

[0015] S4: Set the mesh division types for the preset number of model components, and sequentially divide and generate the mesh model of the compact tension specimen with side grooves.

[0016] In a possible implementation manner, the preset number is 18.

[0017] In a possible implementation manner, the S1 specifically includes:[[]]

[0018] S101: Determine the geometric design parameters of the compact tension specimen with side grooves, where the geometric design parameters include: specimen width W, specimen thickness B, step height h, mechanical machining notch length l n , step width w3, opening width w4, mechanical machining notch finishing angle θ, clamping round hole diameter D, side groove root radius r sg , net thickness B of the specimen N , side groove root transition arc angle

[0019] S102: Determine the mechanical machining side groove width w2 according to the geometric design parameters of the compact tension specimen with side grooves:

[0020]

[0021] S103: Determine the position of the coordinate origin and the direction of the coordinate axes, and establish the overall coordinate system O-xyz;

[0022] S104: Determine the projection characteristic point coordinates of a quarter geometric model of a compact tension specimen without side grooves on the xy plane where z = 0: O(0, 0, 0), O'(h + l n , 0, 0), I(-0.25W, 0.6W, 0), J(W, 0.6W, 0), V(W, 0, 0), K(0, 0.375W, 0),

[0023] S105: Draw a two - dimensional geometric sketch of a quarter of the compact tension specimen without side grooves according to the projection characteristic point coordinates of the quarter geometric model of the compact tension specimen without side grooves;

[0024] S106: Stretch along the thickness direction (positive z - axis direction) of the specimen the length to generate a quarter geometric model of the compact tension specimen without side grooves;

[0025] S107: Draw a two - dimensional geometric sketch of the side groove on the yz plane where x = W;

[0026] S108: Stretch the two - dimensional geometric sketch of the side groove along the x - axis by a length of W and perform cutting to generate a quarter geometric model of the compact tension specimen with side grooves.

[0027] In a possible implementation manner, the S105 is specifically: sequentially connect line segment AB’, line segment B’C, line segment CF, line segment FG, line segment GH, line segment HI, line segment IJ, line segment JV, line segment VO’, and draw a clamping round hole with point K as the center and a radius of ;

[0028] The S107 is specifically: sequentially connect line segment OT, line segment TS, arc SQ, and line segment QO to form a closed geometric sketch.

[0029] In a possible implementation manner, the S2 specifically includes:

[0030] S201: Determine that the number of equal - division grids of the side lengths of the geometric components with the bottom surfaces of bcdC and CdGF are N bc , N dC and N CF , and the minimum number of equal - division grids of the side length aB of the geometric component with the bottom surface of abCB is N x1 (which needs to be an integer multiple of 3);

[0031] S202: Determine that the densest number of equal - division grids of the 13th geometric component in the thickness direction is N z1(Must be an integer multiple of 8), determine that the grid equal division size of line segment hV - sU is N1, and the grid equal division size of line segment tU - sU is N2;

[0032] S203: Generate the coordinates of the key feature points of the stepped part:

[0033] S204: Generate the coordinates of the key geometric points required for the grid division of the geometric component with the bottom surface abCB as:

[0034]

[0035] S205: Generate the coordinates of the grid division reference points of the 13th geometric component as:

[0036]

[0037]

[0038] S206: Determine the coordinates of the grid division reference points of the 12th geometric component as: hV(x tT , y A , z rT ), iV(x rT , y e , z rT ), rV(x hV , y e , z rT ), yV(x rT , y tT , z rT ), zV(x rT + ms x1 , y tT , z rT ), aW(x rT + 2ms x1 , y tT , z rT ), eW(x bV , y dW , z rT ), fW(x bV , y bW , z rT ), gW(x A , y bW , z rT ), hW(x zV , y iV , z rT), jW(x cV , y bW , z rT ), iW(x cV , y bW , z rT ), lW(x dV , y dW , z rT ), kW(x dV , y bW , z rT ), mW(x eV , y bW , z rT ), nW(x aW , y iV , z rT ), oW(x fV , y bW , z rT ), pW(x fV , y dW , z rT ), qW(x gV , y bW , z rT ), rW(x gV , y dW , z rT ), sW(x hV , y bW , z rT ), where,

[0039] S207: Determine the coordinates of the meshing reference point of the 10th geometric component as: tW(x B , y B , -z pT ), yU(x A , y A , -z pT ), rU(W, 0, -z pT ), qU(x W , 0, -z pT ), aU(x tW , y tW , z tW + ms z1 ), cU(x tW , y tW , z tW + 2ms z1 ), eU(x tW , y uW , z tW + 2msz1 ), fU(x tW , y tW , z tW + 3ms z1 ), hU(x tW , y tW , z tW + 4ms z1 ), iU(x tW , y uW , z tW + 4ms z1 ), where,

[0040] S208: Determine that the coordinates of the mesh division reference point for the transition section between the machining notch and the side groove are:

[0041] xU(x rU , y rU , z qU ), yU(x A , y A , z qU ), zU(x rT , y A , z qU ), cA(x qU , y qU , z Q ), uU(x hV , y qU , z qU ), tU(x hV , y qU , z cV ), sU(x hV , y S , z S ), dA(x rT , y A , z A ), eA(x tU , y aA , z aA ), fA(x A , y A , z rT ), hA(x uU , y O' , z O' ),

[0042] In a possible implementation manner, the specific content of the S3 includes:

[0043] S301: Cut the geometric model where it is located with the yz plane of x = x C , x = x rT , x = x hV , x = x sW , x = x bW and x = x hV ;

[0044] S302: Cut the geometric model where it is located with the xz plane of y = y G , y = y F , y = y T , y = y e , and ;

[0045] S303: Cut the geometric model where it is located with the xy plane of z = z tW , z = z uW and z = z qU ;

[0046] S304: Cut the geometric model where it is located with the line segments yV - rT, tT - hV, tW - yU, qU - rU.

[0047] In a possible implementation manner, the said S4 specifically includes:

[0048] S401: Set the mesh type of the 15th geometric component to swept mesh, and on the xy plane where it is located, connect the line segments nj, rm, mi, if, sC, rf, Cf, ji, nm, sr, sn, Cj in sequence to draw a 3 - in - 1 transition mesh template, and copy it along the positive x - axis at an interval of 3ms x1 copies, and set the sweeping path to be along the negative z - axis;

[0049] S402: Set the mesh type of the 13th geometric component to swept mesh, and on the yz plane where x = W, connect the line segments fT - gT, kT - lT, lT - mT, nT - oT, pT - qT, gT - lT, lT - oT, aT - fT, fT - kT, kT - nT, nT - pT, Ta - gT, qT - oT in sequence to draw a 2 - in - 1 transition mesh template, and copy it z1 along the negative z - axis at an interval of 8ms copies, and set the sweeping path to be along the negative x - axis;

[0050] S403: Set the mesh type of the 12th geometric component to swept mesh, and on the On the xy plane, successively connect the line segments A-gW, cV-iW, dV-lW, eV-mW, fV-pW, gV-rW, bW-sW, iW-lW, pW-rW, hW-gW, hW-gW, hW-iW, nW-lW, nW-mW, nW-pW, rW-rV to draw a 3-in-1 transition grid template; set the sweeping path to be along the negative z-axis;

[0051] S404: Set the grid type of the 10th geometric component to a swept grid. On the yz plane where x = h, successively connect the line segments aU-bU, bU-uW, bU-dU, cU-dU, dU-eU, dU-gU, fU-gU, gU-iU, iU-hU to draw a 2-in-1 transition grid template; and at an interval of 4 ms along the positive z-axis z1 Copy copies, and set the sweeping path to be along the positive x-axis;

[0052] S405: Respectively set the grid types of the 17th geometric component and the 18th geometric component to swept grids, and set the sweeping paths to be along the positive z-axis and along the positive x-axis respectively;

[0053] S406: Set the grid types of the remaining geometric components to structured grids;

[0054] S407: Select the line segments tW-zU, B-rT, e2B-bW, and set the number of grid equal divisions to 3N rT ;

[0055] S408: Select the line segments A-yU, O'-qU, hA-uU, dA-zU, and set the number of grid equal divisions to

[0056] S409: Select the line segments fA-yU, rU-xU, tU-uU, cA-qU, and set the number of grid equal divisions to

[0057] S410: Select the line segments rU-sU, cA-tU, qU-uU, O'-hA, and set the number of grid equal divisions to 6;

[0058] S411: Select the line segments S-sU, Q-tU, V-hA, rU-uU, and set the grid equal division size to ms x1 ;

[0059] S412: Respectively select the line segment hV-sU and the line segment tU-sU, and respectively set the grid equal division sizes to N1 and N2;

[0060] S413: Select the arc segment and set the grid equal division size to N1;

[0061] S414: Generate the mesh model of the final compact tension specimen with side grooves in the order of 17→14, 16→15→13→5, 6, 7, 12→8, 9, 10, 11→0, 1, 2, 3, 4, 18.

[0062] Compared with the prior art, the present invention has at least the following beneficial effects:

[0063] In the present invention, determine the geometric design parameters of the compact tension specimen with side grooves, and establish a quarter geometric model based on the geometric symmetry and the coordinate description of geometric feature points; determine the mesh division size parameters, and generate the coordinates of the key mesh feature points; according to the coordinates of the key mesh feature points, cut the original geometric model into a preset number of model components; set the mesh division types for the preset number of model components, and divide and generate the mesh model of the compact tension specimen with side grooves in sequence. Improve the mesh division quality of the compact tension specimen with side grooves model, avoid using manual interactive division, balance the solution accuracy and solution efficiency of simulation calculation, the mesh is regular, has strong versatility and is not prone to errors, overcome the deficiencies of the geometric simplified mesh model and the traditional transition mesh model, use mathematical description to accurately express the process of transitional mesh division of the compact tension specimen with side grooves, so as to realize high-precision automatic modeling, and make up for the gap in the method for automatically dividing and generating a high-precision finite element model for the transitional mesh of the compact tension specimen with side grooves. Description of the Drawings

[0064] The following will further illustrate the above characteristics, technical features, advantages and their implementation manners of the present invention in a clear and understandable manner in combination with the drawings.

[0065] Figure 1 is a schematic flow chart of a method for automatically dividing and modeling transitional meshes provided by the present invention;

[0066] Figure 2 is a schematic diagram of the feature points of a quarter geometric model provided by the present invention;

[0067] Figure 3 is a schematic diagram of the component cutting result of a quarter geometric model provided by the present invention;

[0068] Figure 4 is a schematic diagram of the mesh feature points at the intersection of the machined notch and the side groove provided by the present invention;

[0069] Figure 5 is a schematic diagram of the actual effect of a quarter mesh model provided by the present invention. Detailed Embodiments

[0070] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the specific implementation methods of the present invention will be described below with reference to the accompanying drawings. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings and other implementation methods can be obtained based on these drawings without creative work.

[0071] In order to simplify the drawings, only the parts related to the invention are schematically shown in each figure, and they do not represent the actual structure of the product. In addition, in order to simplify the drawings and facilitate understanding, in some figures, only one of the parts with the same structure or function is schematically drawn or marked. In this article, "one" not only means "only one", but also means "more than one".

[0072] It should be further understood that the term "and / or" used in the present description and the appended claims refers to any and all possible combinations of one or more of the associated listed items, and includes these combinations.

[0073] In this document, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0074] In addition, in the description of the present invention, the terms "first", "second", etc. are only used to distinguish the description and cannot be understood as indicating or implying relative importance.

[0075] Reference Manual Attached Figure 1 , a schematic diagram of the flow chart of a transitional grid automatic partitioning and modeling method provided by the present invention.

[0076] Reference Manual Attached Figure 2 , a schematic diagram of characteristic points of a quarter geometric model provided by the present invention;

[0077] Reference Manual Attached Figure 3 , a schematic diagram of component cutting results of a quarter geometric model provided by the present invention;

[0078] Reference Manual Attached Figure 4 , a schematic diagram of grid feature points at the intersection of a machining notch and a side groove provided by the present invention;

[0079] Reference Manual Attached Figure 5, an actual effect diagram of a quarter-grid model provided by the present invention.

[0080] A method for automatically dividing and modeling transition grids provided by the present invention is applied to a compact tension specimen with side grooves, and includes:

[0081] S1: Determine the geometric design parameters of the compact tension specimen with side grooves, and establish a quarter geometric model based on the geometric symmetry and the coordinate description of geometric feature points.

[0082] Among them, the quarter geometric model is the modeling basis of the grid model.

[0083] S2: Determine the grid division size parameters and generate the coordinates of grid key feature points.

[0084] Among them, the key point coordinates may include the coordinates of key feature points for generating the stepped part, the key geometric point coordinates required for grid division of the geometric component with the bottom surface of abCB, the grid division reference point coordinates of the geometric component, and the grid division reference point coordinates of the transition section between the machining notch and the side groove.

[0085] S3: Cut the original geometric model into a preset number of model components according to the coordinates of the grid key feature points.

[0086] In a possible implementation manner, the preset number is 18.

[0087] Among them, the preset number of model components is the basic composition of a compact tension specimen with side grooves. Each compact tension specimen with side grooves can be cut into the preset number of basic model components. Further, the properties of the corresponding compact tension specimen with side grooves can be obtained by analyzing the properties of the preset number of model components.

[0088] S4: Set the grid division type for the preset number of the model components, and sequentially divide and generate the grid model of the compact tension specimen with side grooves.

[0089] Among them, the grid division types include swept grids and structured grids. In the case where the model component is a swept grid, the sweep path is also an important parameter. The grid model of the compact tension specimen with side grooves can be finally generated according to the preset number of model components.

[0090] Compared with the prior art, the present invention has at least the following beneficial effects:

[0091] In the present invention, the geometric design parameters of the compact tensile specimen with side grooves are determined, and a quarter geometric model is established based on the geometric symmetry and the coordinate description of the geometric feature points; the meshing size parameters are determined to generate the coordinates of the key feature points of the mesh; according to the coordinates of the key feature points of the mesh, the original geometric model is cut into a preset number of model components; the meshing type is set for the preset number of model components, and the mesh model of the compact tensile specimen with side grooves is divided and generated in sequence. The meshing quality of the compact tensile specimen with side grooves is improved, manual interactive division is avoided, and the solution accuracy and solution efficiency of the simulation calculation are taken into account. The mesh is regular, versatile and not prone to errors, and the shortcomings of the geometric simplified mesh model and the traditional transition mesh model are overcome. The transition meshing process of the compact tensile specimen with side grooves is accurately expressed by mathematical description, thereby realizing high-precision automatic modeling, making up for the lack of a method specifically for automatic division of transition meshes for compact tensile specimens with side grooves to generate high-precision finite element models.

[0092] In a possible implementation manner, the S1 specifically includes:

[0093] S101: Determine the geometric design parameters of the compact tensile test piece with side grooves, wherein the geometric design parameters include: the test piece width is W, the test piece thickness is B, the step height is h, the machining notch length is l n , step width is w3, opening width is w4, machining notch end angle is θ, clamping hole diameter is D, side groove root radius is r sg , Net thickness of the specimen B N , Transition arc angle of side groove root

[0094] For example, Figure 2 The geometric design parameters of the compact tensile specimen in the experiment can be: specimen width W = 60 mm, specimen thickness B = 15 mm, step height h = 4.5 mm, and machining notch length l n =29.5mm, step width w3 = 10mm, opening width w4 = 18mm, machining notch ending angle The diameter of the clamping hole is D = 15mm, and the radius of the side groove root is r sg =0.4mm, net thickness of the sample B N =12mm, transition arc angle of side groove root

[0095] S102: Determine the machining side groove width w2 according to the geometric design parameters of the compact tensile test piece with side grooves:

[0096]

[0097] Specifically, according to the calculation results, the width w2 of the machined side groove is approximately 2.194 mm.

[0098] S103: Determine the position of the coordinate origin and the direction of the coordinate axes, and establish the overall coordinate system O-xyz.

[0099] S104: Determine the coordinates of the projection feature points of a quarter of the geometric model of the compact tension specimen without side grooves on the xy plane where z = 0: O(0, 0, 0), O'(h + l n , 0, 0), I(-0.25W, 0.6W, 0), J(W, 0.6W, 0), V(W, 0, 0), K(0, 0.375W, 0),

[0100] Specifically, according to the calculation results, the coordinates of the projection feature points of the geometric model can be: O(0, 0, 0), O1(32.903, 0, 0), O'(34, 0, 0), A(32.903, 1.097, 0), B'(4.5, 1.097, 0), C(4.5, 5, 0), F(0, 5, 0), G(0, 9, 0), H(-15, 9, 0), I(-15, 36, 0), J(60, 36, 0), V(60, 0, 0), K(0, 22.5, 0), N(7.5, 22.5, 0), P(-7.5, 22.5, 0), T(60, 1.097, 7.5), S(60, 0.346, 6.2), Q(60, 0, 6), O V (60, 0, 6.4).

[0101] S105: Draw a two-dimensional geometric sketch of a quarter of the compact tension specimen without side grooves according to the coordinates of the projection feature points of the quarter geometric model of the compact tension specimen without side grooves.

[0102] In a possible implementation, S105 is specifically: Connect the line segments AB', B'C, CF, FG, GH, HI, IJ, JV, and VO' in sequence, and draw a clamping round hole with a radius of centered at point K. According to the calculation, it can specifically be to draw a clamping round hole with a radius of 7.5 mm.

[0103] S106: Stretch along the thickness direction (positive z-axis direction) of the specimen by a length based on the two-dimensional geometric sketch of a quarter of the compact tension specimen without side grooves to generate a quarter geometric model of the compact tension specimen without side grooves.

[0104] Specifically, according to the calculation results, it can be to stretch 7.5 mm in length along the thickness direction of the specimen.

[0105] S107: Draw a two-dimensional geometric sketch of the side groove in the yz plane where x = W.

[0106] In a possible implementation, the S107 is specifically: Connect the line segment OT, the line segment TS, the arc SQ, and the line segment QO in sequence to form a closed geometric sketch.

[0107] S108: Stretch the two-dimensional geometric sketch of the side groove along the x-axis by a length of W and perform cutting to generate a quarter geometric model of the compact tensile specimen with a side groove.

[0108] Specifically, according to the calculation results, it can be to stretch 60 mm in length along the x-axis.

[0109] In the present invention, by determining the geometric design parameters of the compact tensile specimen with a side groove and establishing a quarter geometric model based on the geometric symmetry and the coordinate description of geometric feature points, high-precision automated modeling can be achieved, filling the gap in the method for automatically generating a high-precision finite element model specifically for the transition grid division of the compact tensile specimen with a side groove.

[0110] In a possible implementation, the S2 specifically includes:

[0111] S201: Determine that the number of equal divisions of the side length grid of the geometric components with the bottom surfaces of bcdC and CdGF are N bc , N dC and N CF , and the minimum number of equal divisions of the side length aB of the geometric component with the bottom surface of abCB is N x1 (which needs to be an integer multiple of 3).

[0112] Specifically, it can be determined that the number of equal divisions of the side length grid of the geometric components with the bottom surfaces of bcdC and CdGF are N bc = 20, N dC = 2, and N CF = 2, and the minimum number of equal divisions of the side length aB of the geometric component with the bottom surface of abCB is N x1 = 60.

[0113] S202: Determine that the densest number of equal divisions of the 13th geometric component in the thickness direction is N z1 (which needs to be an integer multiple of 8), determine that the grid equal division size of the line segment hV - sU is N1, and the grid equal division size of the line segment tU - sU is N2.

[0114] Specifically, it can be determined that the densest number of equal divisions of the 13th geometric component in the thickness direction is N z1= 24, determine that the grid equal division size of line segment hV - sU is N1 = 12, and the grid equal division size of line segment tU - sU is N2 = 4.

[0115] S203: Generate the key feature point coordinates of the step part:

[0116] Specifically, according to the calculation results, the key feature point coordinates of the step part can be determined as: a(60, 1.097, 0), b(60, 5, 0), c(60, 9, 0), d(4.5, 9, 0), W(34, 0.346, 0).

[0117] S204: The key geometric point coordinates required for generating the grid division of the geometric component with the bottom surface abCB are:

[0118]

[0119] Specifically, according to the calculation results, the key geometric point coordinates required for generating the grid division of the geometric component with the bottom surface abCB can be determined as: e(4.5, 1.747, 0), f(4.5, 3.048, 0), g(5.425, 1.097, 0), h(5.425, 1.747, 0), i(5.425, 3.048, 0), j(5.425, 4.024, 0), k(6.35, 1.097, 0), l(6.35, 1.747, 0), m(6.35, 3.048, 0), n(6.35, 4.024, 0), p(7.275, 1.097, 0), q(7.275, 1.747, 0), r(7.275, 3.048, 0), s(7.275, 5, 0).

[0120] S205: Generate the grid division reference point coordinates of the 13th geometric component as:

[0121]

[0122]

[0123] Specifically, according to the calculation results, the coordinates of the mesh division reference points for generating the 13th geometric component can be determined as: aT(60, 1.747, -7.5), Ta(60, 3.048, -7.5), bT(60, 1.097, -7.188), cT(60, 1.422, -7.188), dT(60, 1.097, -6.875), eT(60, 1.422, -6.875), fT(60, 1.747, -6.875), gT(60, 2.398, -6.875), hT(60, 1.097, -6.563), iT(60, 1.422, -6.563), jT(60, 1.097, -6.25), kT(60, 1.747, -6.25), lT(60, 2.398, -6.25), mT(60, 3.048, -6.25), nT(60, 1.747, -5.625), oT(60, 2.398, -5.625), pT(60, 1.747, -5.0), qT(60, 3.048, -5.0).

[0124] S206: Determine the coordinates of the mesh division reference points for the 12th geometric component as: hV(x tT , y A , z rT ), iV(x rT , y e , z rT ), rV(x hV , y e , z rT ), yV(x rT , y tT , z rT ), zV(x rT + ms x1 , y tT , z rT ), aW(x rT + 2ms x1 , y tT , z rT ), eW(x bV , y dW , z rT ), fW(x bV , y bW , z rT ), gW(x A , y bW , z rT ), hW(xzV , y iV , z rT ), jW(x cV , y bW , z rT ), iW(x cV , y bW , z rT ), lW(x dV , y dW , z rT ), kW(x dV , y bW , z rT ), mW(x eV , y bW , z rT ), nW(x aW , y iV , z rT ), oW(x fV , y bW , z rT ), pW(x fV , y dW , z rT ), qW(x gV , y bW , z rT ), rW(x gV , y dW , z rT ), sW(x hV , y bW , z rT ), where,

[0125] Specifically, according to the calculation results, the coordinates of the mesh division reference points for generating the 12th geometric component can be determined as: rT(32.25, 1.097, 7.5), tT(35.025, 3.048, 7.5), aV(32.468, 1.097, 7.5), bV(32.685, 1.097, 7.5), cV(33.257, 1.097, 7.5), dV(33.61, 1.097, 7.5), eV(33.964, 1.097, 7.5), fV(34.318, 1.097, 7.5), gV(34.671, 1.097, 7.5), hV(35.025, 1.097, 7.5)), iV(32.25, 1.747, 7.5)), rV(35.025, 1.747, 7.5), yV(32.25, 3.048, 7.5), zV(33.175, 3.048, 7.5), aW(34.1, 3.048, 7.5), bW(32.25, 1.422, 7.5), cW(32.468, 1.422, 7.5), dW(32.468, 1.531, 7.5), eW(32.685, 1.531, 7.5), fW(32.685, 1.422, 7.5), gW(32.903, 1.422, 7.5), hW(33.175, 1.747, 7.5), jW(33.257, 1.422, 7.5), iW(33.257, 1.531, 7.5), lW(33.610, 1.531, 7.5), kW(33.610, 1.422, 7.5), mW(33.964, 1.422, 7.5), nW(34.1, 1.747, 7.5), oW(34.318, 1.422, 7.5), pW(34.318, 1.531, 7.5), qW(34.671, 1.422, 7.5), rW(34.671, 1.531, 7.5), sW(35.025, 1.422, 7.5), where, N rT = 10, ms x1 = 0.925 mm.

[0126] S207: Determine the coordinates of the mesh division reference points for the 10th geometric component as: tW(x B , y B , -z pT ), yU(x A , y A , -z pT ), rU(W, 0, -z pT ), qU(x W , 0, -z pT ), aU(xtW , y tW , z tW + ms z1 ), cU(x tW , y tW , z tW + 2ms z1 ), eU(x tW , y uW , z tW + 2ms z1 ), fU(x tW , y tW , z tW + 3ms z1 ), hU(x tW , y tW , z tW + 4ms z1 ), iU(x tW , y uW , z tW + 4ms z1 ), where,

[0127] Specifically, according to the calculation results, the grid division reference point coordinates for generating the 10th geometric component can be determined as: tW(4.5, 1.097, 5), yU(32.903, 1.097, 5), rU(33.944, 0.346, 6.2), qU(34, 0, 5), uW(4.5, 1.422, 5), aU(4.5, 1.097, 5.313), bU(4.5, 1.26, 5.313), cU(4.5, 1.097, 5.625), dU(4.5, 1.26, 5.6), eU(4.5, 1.422, 5.625), fU(4.5, 1.097, 5.938), gU(4.5, 1.26, 5.938), hU(4.5, 1.097, 6.25), iU(4.5, 1.422, 6.25), where, ms z1 = 0.3125 mm.

[0128] S208: Determine the grid division reference point coordinates for the transition section between the machining notch and the side groove as:

[0129] xU(x rU , y rU , z qU ), yU(x A , y A , zqU ), zU(x rT , y A , z qU ), cA(x qU , y qU , z Q ), uU(x hV , y qU , z qU ), tU(x hV , y qU , z cV ), sU(x hV , y S , z S ), dA(x rT , y A , z A ), eA(x tU , y aA , z aA ), fA(x A , y A , z rT ), hA(x uU , y O' , z O' ),

[0130] Specifically, according to the calculation results, the coordinates of the reference points for the mesh division of the transition section between the machining notch and the side groove can be determined as: aA(33.944, 0.2, 6.054), rU(33.944, 0.346, 6.2), xU(33.944, 0.346, 5), yU(32.903, 1.097, 5), zU(32.25, 1.097, 5), vU(33.423, 0.722, 6.85), cA(34, 0, 6), uU(35.025, 0, 5), tU(35.025, 0, 7.5), sU(35.025, 0.346, 6.2), wU(33.423, 0.722, 5.0), dA(32.25, 1.097, 0), bA(33.972, 0.173, 5), eA(35.025, 0.2, 6.054), fA(32.903, 1.097, 7.5), hA(35.025, 0, 0), iA(33.679, 0.776, 0.0), e2B(4.5, 1.422, 0).

[0131] In the present invention, the mesh division size parameters are determined, and the coordinates of the key feature points of the mesh are generated. Then, the original geometric model can be cut into basic model components according to the coordinates of the key feature points of the mesh. The mesh division quality of the compact tension specimen model with side grooves is improved, manual interactive division is avoided, and both the solution accuracy and solution efficiency of the simulation calculation are taken into account. The mesh is regular, has strong versatility and is not prone to errors, overcoming the deficiencies of the geometric simplified mesh model and the traditional transition mesh model. The mathematical description is used to accurately express the process of the transition mesh division of the compact tension specimen with side grooves.

[0132] In a possible implementation manner, the S3 specifically includes:

[0133] S301: Cut the geometric model where it is located by using the yz planes of x = x C 、x = x rT 、x = x hV 、x = x sW 、x = x bW 、and x = x hV respectively.

[0134] Specifically, according to the calculation results, the geometric model where it is located can be cut by using the yz planes of x = 4.5 mm, x = 32.25 mm, and x = 35.025 mm respectively.

[0135] S302: Cut the geometric model where it is located by using the xz planes of y = y G 、y = y F 、y = y T 、y = y e 、 、and respectively.

[0136] Specifically, according to the calculation results, the geometric model where it is located can be cut by using the xz planes of y = 9 mm, y = 5 mm, y = 1.097 mm, y = 1.747 mm, y = 1.422 mm, and y = 6.097 mm respectively.

[0137] S303: Cut the geometric model where it is located by using the xy planes of z = z tW 、z = z uW 、and z = z qU respectively.

[0138] Specifically, according to the calculation results, the geometric model where it is located can be cut by using the xy plane of z = 5 mm.

[0139] S304: Cut the geometric model where it is located by using the line segments yV - rT, tT - hV, tW - yU, and qU - rU.

[0140] In the present invention, according to the coordinates of the grid key feature points, the original geometric model is cut into a preset number of model components. The quality of the mesh division of the side-grooved compact tension specimen model is improved, manual interactive division is avoided, the solution accuracy and solution efficiency of the simulation calculation are taken into account, the mesh is regular, has strong versatility and is not prone to errors, overcoming the deficiencies of the geometric simplified mesh model and the traditional transition mesh model. A mathematical description is used to accurately express the process of the transition mesh division of the side-grooved compact tension specimen, so as to achieve high-precision automated modeling.

[0141] In a possible implementation manner, the S4 specifically includes:

[0142] S401: Set the mesh type of the 15th geometric component to swept mesh. On the xy plane located at Connect the line segments nj, rm, mi, if, sC, rf, Cf, ji, nm, sr, sn, Cj in sequence to draw a 3-in-1 transition mesh template, and copy it x1 Copy for a number of copies along the positive x-axis at an interval of 3ms. The sweeping path is set to be along the negative z-axis.

[0143] Specifically, according to the calculation results, on the xy plane where z = 7.5 mm, connect the line segments nj, rm, mi, if, sC, rf, Cf, ji, nm, sr, sn, Cj in sequence to draw a 3-in-1 transition mesh template, and copy it 20 times along the positive x-axis at an interval of 2.775 mm.

[0144] S402: Set the mesh type of the 13th geometric component to swept mesh. On the yz plane where x = W, connect the line segments fT-gT, kT-lT, lT-mT, nT-oT, pT-qT, gT-lT, lT-oT, aT-fT, fT-kT, kT-nT, nT-pT, Ta-gT, qT-oT in sequence to draw a 2-in-1 transition mesh template, and copy it z1 Copy for a number of copies along the negative z-axis at an interval of 8ms. The sweeping path is set to be along the negative x-axis.

[0145] Specifically, according to the calculation results, on the yz plane where x = 60 mm, connect the line segments fT-gT, kT-lT, lT-mT, nT-oT, pT-qT, gT-lT, lT-oT, aT-fT, fT-kT, kT-nT, nT-pT, Ta-gT, qT-oT in sequence to draw a 2-in-1 transition mesh template, and copy it 3 times along the negative z-axis at an interval of 2.5 mm.

[0146] S403: Set the mesh type of the 12th geometric component to swept mesh. On the plane located at On the xy plane, connect the line segments A-gW, cV-iW, dV-lW, eV-mW, fV-pW, gV-rW, bW-sW, iW-lW, pW-rW, hW-gW, hW-gW, hW-iW, nW-lW, nW-mW, nW-pW, rW-rV in sequence to draw a 3-in-1 transition grid template. The sweeping path is set to be along the negative z-axis.

[0147] Specifically, according to the calculation results, on the xy plane located at z = 7.5 mm, connect the line segments A-gW, cV-iW, dV-lW, eV-mW, fV-pW, gV-rW, bW-sW, iW-lW, pW-rW, hW-gW, hW-gW, hW-iW, nW-lW, nW-mW, nW-pW, rW-rV in sequence to draw a 3-in-1 transition grid template.

[0148] S404: Set the grid type of the 10th geometric component to a swept grid. On the yz plane located at x = h, connect the line segments aU-bU, bU-uW, bU-dU, cU-dU, dU-eU, dU-gU, fU-gU, gU-iU, iU-hU in sequence to draw a 2-in-1 transition grid template. And the interval along the positive z-axis is 4 ms z1 Copy copies, and the sweeping path is set to be along the positive x-axis.

[0149] Specifically, according to the calculation results, on the yz plane located at x = h, connect the line segments aU-bU, bU-uW, bU-dU, cU-dU, dU-eU, dU-gU, fU-gU, gU-iU, iU-hU in sequence to draw a 2-in-1 transition grid template; and copy 2 copies at an interval of 1.25 mm along the positive z-axis.

[0150] S405: Set the grid types of the 17th geometric component and the 18th geometric component to swept grids respectively, and the sweeping paths are set to be along the positive z-axis and along the positive x-axis respectively.

[0151] S406: Set the grid types of the remaining geometric components to structured grids.

[0152] S407: Select the line segments tW-zU, B-rT, e2B-bW, and set the number of grid equal divisions to 3N rT .

[0153] Specifically, according to the calculation results, the number of grid equal divisions can be set to 30.

[0154] S408: Select the line segments A-yU, O'-qU, hA-uU, dA-zU, and set the number of grid equal divisions to

[0155] Specifically, according to the calculation results, the number of equal divisions of the grid can be set to 8.

[0156] S409: Select line segments fA-yU, rU-xU, tU-uU, cA-qU, and set the number of equal divisions of the grid to

[0157] Specifically, according to the calculation results, the number of equal divisions of the grid can be set to 8.

[0158] S410: Select line segments rU-sU, cA-tU, qU-uU, O'-hA, and set the number of equal divisions of the grid to 6.

[0159] S411: Select line segments S-sU, Q-tU, V-hA, rU-uU, and set the equal division size of the grid to ms x1 。

[0160] Specifically, according to the calculation results, the equal division size of the grid can be set to 0.925.

[0161] S412: Select line segment hV-sU and line segment tU-sU respectively, and set the equal division sizes of the grid to N1 and N2 respectively.

[0162] Specifically, according to the calculation results, the equal division sizes of the grid can be set to 12 and 4 respectively.

[0163] S413: Select the arc segment and set the equal division size of the grid to N1.

[0164] Specifically, according to the calculation results, the equal division size of the grid can be set to 12.

[0165] S414: Generate the grid model of the final side-grooved compact tension specimen in the order of 17→14, 16→15→13→5, 6, 7, 12→8, 9, 10, 11→0, 1, 2, 3, 4, 18.

[0166] In the present invention, the grid division types of a preset number of the model components are set, and the grid model of the side-grooved compact tension specimen is sequentially divided and generated. The quality of the grid division of the side-grooved compact tension specimen model is improved, manual interactive division is avoided, the solution accuracy and solution efficiency of the simulation calculation are taken into account, the grid is regular, has strong versatility and is not prone to errors, the deficiencies of the geometric simplified grid model and the traditional transition grid model are overcome, and the process of the transition grid division of the side-grooved compact tension specimen is accurately expressed by using mathematical descriptions, so as to realize high-precision automatic modeling, and fill the gap in the method for automatically dividing and generating a high-precision finite element model specifically for the transition grid of the side-grooved compact tension specimen.

[0167] The technical features of the above embodiments can be combined arbitrarily. For the sake of concise description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope recorded in this specification.

[0168] The above embodiments only express several implementation manners of the present invention, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the invention patent. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can still be made, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the invention patent should be subject to the appended claims.

Claims

1. A method for automatically dividing and modeling a transition grid, characterized in that, Applied to a compact tension specimen with side grooves, including: S1: Determine the geometric design parameters of the compact tension specimen with side grooves, and establish a quarter geometric model based on geometric symmetry and the coordinates of geometric feature points; S2: Determine the mesh division size parameters and generate the coordinates of the key mesh feature points; S3: Cut the original geometric model into a preset number of model components according to the coordinates of the key mesh feature points; S4: Set the mesh division types for the preset number of model components, and sequentially divide and generate the mesh model of the compact tension specimen with side grooves; Among them, the specific steps of S1 include: S101: Determine the geometric design parameters of the notched compact tension specimen with side grooves, where the geometric design parameters include: specimen width W, specimen thickness B, step height h, machined notch length l n , step width w3, opening width w4, machined notch finishing angle θ, clamping round hole diameter D, side groove root radius r sg , net thickness B of the specimen N , side groove root transition arc angle φ sg ; S102: Determine the width w2 of the machined side groove according to the geometric design parameters of the compact tension specimen with side grooves; S103: Determine the position of the coordinate origin and the direction of the coordinate axes, and establish the overall coordinate system O-xyz; S104: Determine the projected characteristic point coordinates of a quarter geometric model of a compact tension specimen without side grooves on the xy plane where z = 0: O(0, 0, 0), O'(h + l n , 0, 0), S105: Draw a two-dimensional geometric sketch of a quarter of the compact tension specimen without side grooves according to the coordinates of the projection feature points of the quarter geometric model of the compact tension specimen without side grooves; S106: According to the two-dimensional geometric sketch of a quarter compact tension specimen without side grooves, stretch along the thickness direction (positive z-axis direction) of the specimen length to generate a quarter geometric model of the compact tension specimen without side grooves; S107: Draw a two-dimensional geometric sketch of the side groove in the yz plane where x = W; S108: Stretch the two-dimensional geometric sketch of the side groove along the x-axis by a length of W and perform cutting to generate a quarter geometric model of the compact tension specimen with side grooves.

2. The automatic meshing modeling method for transitional grids according to claim 1, wherein The preset number is 18.

3. The automatic meshing modeling method for the transition grid according to claim 1, wherein The specific steps of S105 are as follows: successively connect line segment AB’, line segment B’C, line segment CF, line segment FG, line segment GH, line segment HI, line segment IJ, line segment JV, and line segment VO’, and draw a clamping round hole with point K as the center and a radius of ; The specific step of S107 is: sequentially connect the line segment OT, the line segment TS, the arc SQ, and the line segment QO to form a closed geometric sketch.

4. The automatic meshing modeling method for the transition grid according to claim 1, characterized in that, The specific steps of S2 include: S201: Determine that the number of equal divisions of the side length grids of the geometric components with bottom surfaces bcdC and CdGF are N bc , N dC and N CF , and the minimum number of equal divisions of the side length aB of the geometric component with the bottom surface abCB is N x1 (which must be an integer multiple of 3); S202: Determine that the number of equally divided grids with the densest density in the thickness direction of the 13th geometric component is N z1 (which needs to be an integer multiple of 8), determine that the grid equal division size of the line segment hV-sU is N1, and the grid equal division size of the line segment tU-sU is N2; S203: Generate the coordinates of the key feature points of the stepped part: S204: The coordinates of the key geometric points required for the mesh division of the geometric component with the bottom surface abCB are: S205: The coordinates of the mesh division reference points for generating the 13th geometric component are: S206: Determine the coordinates of the mesh division reference points for the 12th geometric component are: iV(x rT ,y e ,z rT )、rV(x hV ,y e ,z rT )、yV(x rT ,y tT ,z rT )、zV(x rT +ms x1 ,y tT ,z rT )、aW(x rT +2ms x1 ,y tT ,z rT )、 eW(x bV ,y dW ,z rT )、fW(x bV ,y bW ,z rT )、gW(x A ,y bW ,z rT )、hW(x zV ,y iV ,z rT )、jW(x cV ,y bW ,z rT )、iW(x cV ,y bW ,z rT )、lW(x dV ,y dW ,z rT )、kW(x dV ,y bW ,z rT )、mW(x eV ,y bW ,z rT )、nW(x aW ,y iV ,z rT )、oW(x fV ,y bW ,z rT )、pW(x fV ,y dW ,z rT )、qW(x gV ,y bW ,z rT )、rW(x gV ,y dW ,z rT ), sW(x hV , y bW , z rT ), where S207: Determine that the coordinates of the meshing reference points of the 10th geometric component are: tW(x B , y B , -z pT ), yU(x A , y A , -z pT ), rU(W, 0, -z pT ), qU(x W , 0, -z pT ), aU(x tW , y tW , z tW + ms z1 ), cU(x tW , y tW , z tW + 2ms z1 ), eU(x tW , y uW , z tW + 2ms z1 ), fU(x tW , y tW , z tW + 3ms z1 ), hU(x tW , y tW , z tW + 4ms z1 ), iU(x tW , y uW , z tW + 4ms z1 ), where, S208: Determine the coordinates of the mesh division reference points for the transition section between the machined notch and the side groove; xU(x rU ,y rU ,z qU )、yU(x A ,y A ,z qU )、zU(x rT ,y A ,z qU )、 cA(x qU ,y qU ,z Q )、uU(x hV ,y qU ,z qU )、tU(x hV ,y qU ,z cV )、sU(x hV ,y S ,z S )、 dA(x rT ,y A ,z A )、 eA(x tU ,y aA ,z aA )、fA(x A ,y A ,z rT )、hA(x uU ,y O' ,z O' )、 5. The automatic meshing modeling method for the transition grid according to claim 4, wherein The specific steps of S3 include: S301: Use the yz plane of x = x C , x = x rT , x = x hV , x = x sW , x = x bW , and x = x hV to cut the geometric model where it is located; S302: Use y = y G , y = y F , y = y T , y = y e , and to cut the geometric model where it is located in the xz plane; S303: Use the xy planes of z = z tW , z = z uW and z = z qU to cut the geometric model where they are located; S304: Cut the geometric model where the line segments yV-rT, tT-hV, tW-yU, and qU-rU are located.

6. The automatic meshing modeling method for the transition grid according to claim 5, wherein The specific steps of S4 include: S401: Set the mesh type of the 15th geometric component to swept mesh. Connect the line segments nj, rm, mi, if, sC, rf, Cf, ji, nm, sr, sn, and Cj in sequence on the xy plane located at to draw a 3-in-1 transition mesh template, and copy it x1 along the positive x-axis at an interval of 3 ms for times. Set the sweeping path to be along the negative z-axis; S402: Set the mesh type of the 13th geometric component to swept mesh. On the yz plane where x = W, sequentially connect line segments fT - gT, kT - lT, lT - mT, nT - oT, pT - qT, gT - lT, lT - oT, aT - fT, fT - kT, kT - nT, nT - pT, Ta - gT, qT - oT to draw a 2 - to - 1 transition mesh template, and space it at an interval of 8 ms along the negative z - axis z1 Duplicate copies, and set the sweeping path to be along the negative x - axis; S403: Set the mesh type of the 12th geometric component to swept mesh. On the xy plane located at , connect the line segments A-gW, cV-iW, dV-lW, eV-mW, fV-pW, gV-rW, bW-sW, iW-lW, pW-rW, hW-gW, hW-gW, hW-iW, nW-lW, nW-mW, nW-pW, rW-rV in sequence to draw a 3-in-1 transition mesh template; set the sweeping path to be along the negative z-axis; S404: Set the mesh type of the 10th geometric component to swept mesh. Connect the line segments aU-bU, bU-uW, bU-dU, cU-dU, dU-eU, dU-gU, fU-gU, gU-iU, iU-hU in sequence on the yz plane where x = h to draw a 2-in-1 transition mesh template; and space it at intervals of 4 ms along the positive z-axis direction. z1 Copy copies, and set the sweeping path to be along the positive x-axis direction. S405: Set the mesh types of the 17th geometric component and the 18th geometric component as swept meshes respectively, and set the sweeping paths as along the positive z-axis and along the positive x-axis respectively; S406: Set the mesh types of the remaining geometric components as structured meshes; S407: Select line segments tW-zU, B-rT, e2B-bW, and set the number of grid equal divisions to 3N rT ; S408: Select line segments A-yU, O'-qU, hA-uU, dA-zU, and set the number of grid equal divisions to S409: Select line segments fA-yU, rU-xU, tU-uU, cA-qU, and set the number of equal divisions of the grid to S410: Select the line segments rU-sU, cA-tU, qU-uU, O'-hA, and set the number of mesh equal divisions to 6; S411: Select line segments S-sU, Q-tU, V-hA, rU-uU, and set the grid equal division size to ms x1 ; S412: Select the line segments hV-sU and tU-sU respectively, and set the mesh equal division sizes as N1 and N2 respectively; S413: Select arc segment and set the grid equal division size to N1; S414: Generate the mesh model of the final compact tension specimen with side grooves in the order of 17→14, 16→15→13→5, 6, 7, 12→8, 9, 10, 11→0, 1, 2, 3, 4, 18.

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