Rotational rigidity calculation method and system and size design method and system

Abstract

The invention discloses a rotational rigidity calculation method and system and a size design method and system. The rotational rigidity calculation method comprises the following steps that joint planes on the two sides of a concave-convex tenon in a target mortise joint structure serve as a first joint face, and a joint concave-convex face corresponding to the concave-convex tenon serves as a second joint face; in each calculation step, based on the relative rotation angle and the corresponding actual contact length, the contact stress corresponding to the corresponding first joint surface is calculated according to a symmetric triangle contact rule or a symmetric ellipse contact rule, and the contact stress corresponding to the corresponding second joint surface is calculated according to an anti-symmetric triangle contact rule; and calculating corresponding rotational stiffness based on the contact stress corresponding to each first joint surface and each second joint surface. According to the method, the joint planes on the two sides of the concave-convex tenon and the joint concave-convex surface corresponding to the concave-convex tenon are calculated separately, so that the joint flexural rigidity obtained through calculation is closer to engineering practice.

Description

Technical Field

[0001] The invention relates to the field of tongue-and-groove joint structure design, and in particular to a rotational stiffness calculation method and system for tongue-and-groove joint structures, and also to a dimension design method and system for tongue-and-groove joint structures. Background Art

[0002] The integrated pipeline corridor is assembled by multiple components using mortise and tenon joints. Appropriate bending stiffness is an important prerequisite for ensuring the safety and stability of the integrated pipeline corridor, and the geometric dimensions of the mortise and tenon structure are an important factor affecting the bending stiffness of the joint.

[0003] At present, most methods for calculating the bending stiffness of tongue-and-groove joints use the plane section assumption method for analysis and selection, that is, the joint is equivalent to a rectangular joint, and the mechanical properties of the compression and tension sections of the joint are calculated based on the reinforced concrete structure design principle.

[0004] The plane section assumption method is more effective in analyzing the bending stiffness of the tongue and groove joint with slight deformation, but it is not applicable to the joint with obvious deformation. The reason is that the stress mechanism of the concave and convex surface and the plane section of the tongue and groove joint is different, and the failure law under bending is also quite different. Therefore, the plane section assumption method is not accurate and reliable to calculate the bending stiffness of the tongue and groove joint of the comprehensive pipeline corridor. Summary of the invention

[0005] In view of the shortcoming in the prior art that it is difficult to accurately calculate the bending stiffness of a joint with obvious deformation using the plane section assumption method, the present invention provides a rotational stiffness calculation method and system, and also provides a dimension design method and system. By separately calculating the joint planes on both sides of the tenon and the joint concave and convex surfaces corresponding to the tenon, the calculated joint bending stiffness is closer to engineering practice.

[0006] In order to solve the above technical problems, the present invention is solved by the following technical solutions:

[0007] A method for calculating rotational stiffness comprises the following steps:

[0008] Taking the joint planes on both sides of the concave and convex tenon in the target tongue-and-groove joint structure as the first joint surface, taking the concave and convex joint surface corresponding to the concave and convex tenon as the second joint surface, gradually calculating the contact stress between the first joint surface and the second joint surface at each relative rotation angle, and calculating the rotational stiffness of the target tongue-and-groove joint structure based on the obtained contact stress;

[0009] The present invention takes into account the stress characteristics of different joint surfaces, and calculates the joint planes on both sides of the tenon and the joint concave-convex surfaces corresponding to the tenon separately, so that the calculated joint bending stiffness is closer to engineering practice.

[0010] The method for calculating the rotational stiffness of the target tongue-and-groove joint structure at the target relative rotation angle comprises the following steps:

[0011] Obtaining the actual contact lengths corresponding to the current first joint surfaces and the second joint surfaces;

[0012] Based on the target relative rotation angle and the corresponding actual contact length, the contact stress corresponding to each first joint surface is calculated according to the symmetrical triangle contact law or the symmetrical ellipse contact law to obtain the corresponding first contact stress, and the influence of joint damage is considered. When the joint is not damaged, the corresponding contact stress is calculated using the symmetrical triangle law, and when the joint is damaged, the corresponding contact stress distribution is calculated using the symmetrical ellipse contact law;

[0013] Based on the target relative rotation angle and the corresponding actual contact length, the contact stress corresponding to each second joint surface is calculated according to the antisymmetric triangle contact law to obtain the corresponding second contact stress;

[0014] calculating a corresponding rotational stiffness based on each first contact stress and each second contact stress;

[0015] The actual contact lengths corresponding to each first joint surface and each second joint surface are updated based on the target relative rotation angle.

[0016] As an implementable method, based on the target relative rotation angle and the corresponding actual contact length, the contact stress corresponding to the first joint surface is calculated according to the symmetrical triangle contact law or the symmetrical ellipse contact law to obtain the corresponding first contact stress;

[0017] When the symmetric ellipse contact law is used to calculate the contact stress corresponding to the first joint surface in the previous calculation step, the symmetric ellipse contact law is still used to calculate the contact stress corresponding to the first joint surface in this calculation step;

[0018] That is, the previous calculation step performed contact stress calculation based on the condition of joint damage, and this calculation step also performs contact stress calculation based on the condition of joint damage.

[0019] When the symmetrical triangle contact law is used to calculate the contact stress corresponding to the first joint surface in the previous calculation step, in this calculation step:

[0020] The contact stress corresponding to the first joint surface is calculated by using the symmetrical triangle contact rule to obtain a candidate contact stress;

[0021] determining whether the candidate contact stress exceeds the corresponding concrete compressive strength;

[0022] When the candidate contact stress does not exceed the corresponding concrete compressive strength, taking the candidate contact stress as the first contact stress;

[0023] When the candidate contact stress exceeds the corresponding concrete compressive strength, the contact stress corresponding to the first joint surface is calculated using the symmetrical ellipse contact law to obtain the corresponding first contact stress.

[0024] Those skilled in the art can determine the concrete compressive strength of the target mortise and tenon joint structure according to the materials used;

[0025] The previous calculation step calculated the contact stress based on the case where the joint was not damaged. This calculation step first calculated the contact stress using the symmetrical triangle contact law based on the case where the joint was not damaged. When the obtained contact stress exceeded the compressive strength of concrete, the symmetrical ellipse contact law was used instead of the symmetrical triangle contact law to make the obtained contact stress calculation result more accurate and more realistic.

[0026] As an implementation method, the contact stress corresponding to the first joint surface is calculated using the symmetrical triangle contact rule as follows:

[0027]

[0028] in:

[0029] β represents the relative rotation angle of the target;

[0030] P e (x) represents the obtained contact stress, i.e., the candidate contact stress;

[0031] x represents the actual contact length of the corresponding surface;

[0032] E j represents the contact modulus;

[0033] v represents the Poisson’s ratio of the target tongue-and-groove joint structure;

[0034] a C1 Indicates the interface length corresponding to the compressed joint plane in the first joint surface.

[0035] As an implementation method, the contact stress corresponding to the first joint surface is calculated using the symmetrical ellipse contact rule, and the calculation formula for the corresponding first contact stress is obtained as follows:

[0036]

[0037] in:

[0038] β represents the relative rotation angle of the target;

[0039] P c1 (x) represents the obtained contact stress, i.e., the corresponding first contact stress;

[0040] represents the radius of the major axis of the corresponding ellipse;

[0041] x represents the actual contact length of the corresponding surface;

[0042] E j represents the contact modulus;

[0043] v represents the Poisson’s ratio of the target tongue-and-groove joint structure;

[0044] a C1 Indicates the interface length corresponding to the compressed joint plane in the first joint surface.

[0045] As an implementable method, based on the target relative rotation angle and the corresponding actual contact length, the contact stress corresponding to each second joint surface is calculated according to the antisymmetric triangle contact law, and the calculation formula for the corresponding second contact stress is obtained as follows:

[0046]

[0047] in:

[0048] β represents the relative rotation angle of the target;

[0049] Ti represents the i-th second joint surface;

[0050] P Ti (x) represents the contact stress corresponding to the second joint surface, that is, the second contact stress;

[0051] x represents the actual contact length of the corresponding surface;

[0052] E j represents the contact modulus;

[0053] a Ti Represents the interface length corresponding to the i-th second joint surface.

[0054] As an implementable method, the specific steps of calculating the corresponding rotational stiffness based on each first contact stress and each second contact stress are:

[0055] Based on each first contact stress, each second contact stress and the axial force on the target tongue and groove joint structure, calculate and obtain the tensile force on the target tongue and groove joint structure;

[0056] The rotational stiffness is calculated based on the first contact stresses, the second contact stresses, and the tensile force.

[0057] As an implementable embodiment, based on a torque balance model, the rotational stiffness is calculated based on each first contact stress, each second contact stress and the tension, and the expression of the torque balance model is:

[0058]

[0059] TL C2i =M T

[0060] M CC +M CT +M T =M

[0061] in:

[0062] The first seam surface is divided into a first edge seam plane C1 and a second edge seam plane C2, and the first edge seam plane C1 contacts the external structure;

[0063] The second seam surface is divided into a first inclined surface T1, a second inclined surface T2 and a third plane T3, wherein the first inclined surface T1 is connected to the first edge seam plane C1, and the second inclined surface T2 is connected to the second edge seam plane C2;

[0064] M CC It represents the bending moment corresponding to the first edge joint plane C1, which is recorded as the first bending moment;

[0065] M CT The bending moment corresponding to the first inclined surface T1 and the second inclined surface T2 is denoted as the second bending moment;

[0066] M T It represents the bending moment corresponding to the third plane T3, denoted as the third bending moment;

[0067] M represents the bending moment corresponding to the target tongue-and-groove joint structure, i.e., the rotational stiffness;

[0068] n CI Indicates the number of units corresponding to the first edge seam plane C1;

[0069] n T3 Indicates the number of units corresponding to the third plane T3;

[0070] β represents the relative rotation angle of the target;

[0071] P Cli represents the contact stress corresponding to the i-th unit in the first edge joint plane C1;

[0072] A Cli represents the interface area corresponding to the first edge seam plane C1;

[0073] L Cloi represents the total length of the contact force corresponding to the first edge seam plane C1;

[0074] P T3irepresents the contact stress corresponding to the i-th unit in the third plane T3;

[0075] A T3i represents the interface area corresponding to the third plane T3;

[0076] H T3i It represents the vertical sum of the contact forces at the first inclined surface T1 and the second inclined surface T2;

[0077] T represents tension;

[0078] L C2i Represents the total length of the contact force at the third plane T3.

[0079] The present invention also provides a rotational stiffness calculation system for executing any one of the rotational stiffness calculation methods described above.

[0080] The present invention also provides a size design method, comprising the following steps:

[0081] Configure several groups of candidate joint sizes, and calculate the rotational stiffness of the tongue-and-groove joint structure under each candidate joint size according to any of the above-mentioned rotational stiffness calculation methods to obtain corresponding force analysis results;

[0082] Based on the force analysis results, the optimal candidate joint size is selected as the target joint size.

[0083] The present invention also provides a size design system for executing the size design method described above.

[0084] The present invention has significant technical effects due to the adoption of the above technical solution:

[0085] The present invention takes into account the stress characteristics of different joint surfaces, and calculates the joint planes on both sides of the tenon and the joint concave-convex surfaces corresponding to the tenon separately, so that the calculated joint bending stiffness is closer to engineering practice. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0087] Figure 1 It is a schematic diagram of establishing the force model of the joint of the present invention;

[0088] Figure 2 It is a schematic diagram of the contact law of symmetrical triangles;

[0089] Figure 3 is a schematic diagram of the finite contact length modification of a three-dimensional solid;

[0090] Figure 4 This is a schematic diagram of the shape transformation from a triangle to an ellipsoid;

[0091] Figure 5 This is a schematic diagram of the antisymmetric triangle contact law. DETAILED DESCRIPTION

[0092] The present invention is further described in detail below in conjunction with embodiments. The following embodiments are for explanation of the present invention but the present invention is not limited to the following embodiments.

[0093] A method for calculating rotational stiffness comprises the following steps:

[0094] S100, constructing a joint geometry model;

[0095] Reference Figure 1 , the joint geometry model is constructed based on the interface length a of each joint surface and the tongue-and-groove angle γ, Figure 1 Here, a is used to indicate that the marked length is the interface length of the corresponding joint surface, and does not refer to the length value, that is, the interface length a of each joint surface may be different.

[0096] In this embodiment, the tongue-and-groove joint structure uses the joint planes on both sides of the concave and convex tenon in the target tongue-and-groove joint structure as the first joint surface, and uses the joint concave and convex surfaces corresponding to the concave and convex tenon as the second joint surface.

[0097] Reference Figure 1 , the first seam surface is divided into a first edge seam plane C1 and a second edge seam plane C2;

[0098] When there is no contact point on either side of the joint, there is no need to construct a mechanical equilibrium equation, such as Figure 1 As shown, during the stress process, the first edge seam plane C1 is in contact with the external structure; the second edge seam plane C2 is separated from the external structure. At this stage, only the first edge seam plane C1 needs to be subjected to stress analysis.

[0099] Reference Figure 1 The second seam surface is divided into a first inclined plane T1, a second inclined plane T2 and a third plane T3. The third plane T3 is located between the first inclined plane T1 and the second inclined plane T2. The first inclined plane T1 is connected to the first edge seam plane C1, and the second inclined plane T2 is connected to the second edge seam plane C2.

[0100] Figure 1The x marked in the force balance model of the middle joint refers to the actual contact length between the corresponding joint surface and the external solid. During the force process, as the relative rotation angle β changes, the actual contact length of each joint surface and the external solid will also change. Here, x is only used to identify the actual contact surface and does not refer to the length value. The actual contact length of each joint surface is different in the same calculation step.

[0101] S200, constructing joint material model;

[0102] Select the physical parameters of the corresponding material, such as Figure 1 As shown, by assigning corresponding parameters to the geometric model constructed in step S100, the corresponding joint material model can be obtained;

[0103] This step is a prior art and will not be described in detail in this embodiment.

[0104] S300, constructing a joint force balance model;

[0105] The equilibrium equation of the combined node force is established, that is, the sum of the axial force and the bolt prestressing force on the joint is equal to the horizontal stress on the interface.

[0106] The specific steps include:

[0107] S310, contact stress distribution analysis at the first joint surface;

[0108] In this embodiment, a symmetrical triangle interface contact formula is constructed to calculate the contact stress distribution at the first joint surface, and a shape transformation formula and a symmetrical ellipse contact formula are established to correct the contact stress distribution at the first edge joint plane C1 by considering the influence of joint damage.

[0109] S311, symmetrical triangle contact law;

[0110] Reference Figure 1 , the contact behavior corresponding to the first edge joint plane C1 is characterized by: the closer to the outer edge, the greater the compression; in order to highlight this feature, the geometric model assumes that the upper component is an elastic half-space entity and the lower component is a rigid entity, that is, the upper elastic solid and the lower rigid solid are in contact, and the actual contact length is equal to the interface length, where the upper part is the side of the first edge joint plane C1 away from the tenon, and the lower part is the side of the first edge joint plane C1 close to the tenon.

[0111] Assume that the interface of the lower solid is a triangle when under pressure, such as Figure 2 As shown, the angle β corresponds to the relative rotation angle of the assembly joint during the bending process. It should be noted that due to the solid discontinuity, the assembly joint may have a different angle β from the adjacent continuous section.

[0112] Considering that the two sides of the first edge joint plane C1 interface have similar solid morphology, the interface morphology is similar and completely in contact, therefore, a symmetrical triangle is used to represent the first edge joint plane C1 interface contact characteristics and its deformation mode, and the relevant displacement formula is as follows:

[0113] u z =xtan(β) (1)

[0114] in:

[0115] β represents the relative rotation angle of the target;

[0116] x represents the actual contact length of the corresponding surface, which is the actual contact length corresponding to the first edge seam plane C1;

[0117] Z refers to the vertical downward direction, where u z is the displacement of the solid in the Z direction;

[0118] It is assumed that the contact stress distribution of the solid is determined by the contact mode, that is, the contact stress generated by the integral of the distributed contact stress at point s is equal to the contact pressure generated by the solid contact at s.

[0119] The solid contact modulus represents the mechanical properties of the interface. The compression modulus of the solids on both sides of the interface is used to represent the contact modulus. The relevant meanings are as follows:

[0120]

[0121] in:

[0122] p(s) is the distributed contact stress at point s;

[0123] a is the corresponding interface length;

[0124] E j is the contact modulus;

[0125] E1 and E2 are the compression moduli corresponding to adjacent contact solids;

[0126] v1 and v2 are the Poisson’s ratios corresponding to adjacent contacting solids;

[0127] v refers to the Poisson’s ratio of the target tongue and groove joint structure.

[0128] The normal contact stress distribution of any shape on the interface corresponding to the first edge seam plane C1 is as follows:

[0129]

[0130] in:

[0131] N is the axial force;

[0132] Substituting equations (2) and (3) into equation (4), the contact stress distribution of the symmetrical triangular solid is shown in the following equation (5):

[0133]

[0134] Wherein, p(x) is the contact stress distribution corresponding to the first edge joint plane C1.

[0135] Considering that in the actual three-dimensional case, the length of the C1 interface is finite and the outer edge is unconstrained, the contact on the outer edges of the two solids can be regarded as the contact of two cylinders with a diameter of R. For an almost planar interface, R can be regarded as infinite, such as Figure 3 shown.

[0136] Reference Figure 3 , the outer edges are free and unconstrained in the x-direction, while the solid is in a plane strain state along the y-axis.

[0137] Assume that the free area at the outer edge is in a plane stress state; a y and the compressive contact stress p at the free outer edge e The relationship between (x) is shown as follows:

[0138]

[0139] in:

[0140] a y is the contact length of the outer edge of the solid in the Y-axis direction;

[0141] p(x) is the contact stress distribution.

[0142] R is the diameter of the cylinder;

[0143] E is the elastic modulus of concrete.

[0144] The contact stress at the outer edge of finite length can be expressed as:

[0145] p e (x) = (1-v 2 )p(x) (8)

[0147] By substitution, the expression of the contact distribution stress, that is, the symmetrical triangle contact formula used in this embodiment is as follows:

[0148]

[0149] in:

[0150] β represents the relative rotation angle of the target;

[0151] P e (x) represents the compressive contact stress at the free outer edge, which is denoted as the candidate contact stress;

[0152] a C1 represents the interface length of the first edge seam plane C1;

[0153] x represents the actual contact length of the corresponding surface, which is the actual contact length corresponding to the first edge seam plane C1;

[0154] E j represents the contact modulus;

[0155] v represents the Poisson’s ratio of the target tongue-and-groove joint structure.

[0156] S312, shape conversion formula;

[0157] Considering that the joint will cause the corners of the mortise and tenon to break during the later deformation process, the triangular contact model needs to be adjusted to improve the calculation accuracy.

[0158] Depend on Figure 4 It can be seen that the C1 interface will experience stress redistribution at the outer edge and allow the steep contact stress to be released. In order to reflect this phenomenon, the interface morphology can be adjusted to make the outer edge present a gentle slope. Therefore, an ellipse is selected as the imaginary entity at the bottom, and the arc length is assumed to be equal to the length of the hypotenuse corresponding to the corner of the triangle.

[0159] The arc length of the ellipsoid is equal to the hypotenuse of the triangle when the relative rotation angle is β, that is:

[0160]

[0161] in:

[0162] β represents the relative rotation angle of the target;

[0163] R0 represents the radius of curvature of the ellipse;

[0164] x refers to the length of the corresponding actual contact surface, which is the actual contact length corresponding to the first edge seam plane C1; assuming x = a / R0, the above equation (10) can be simplified to:

[0165]

[0166] Applying Taylor expansion, the above formula can be transformed into:

[0167]

[0168] Then the transformation formula from triangle to ellipsoid, that is, the shape transformation formula can be expressed as:

[0169]

[0170] S313, Symmetrical ellipse contact law;

[0171] The corresponding contact stress of the symmetric elliptical solid can be obtained by substituting the shape transformation formula (15) into formula (5), and the specific formula is:

[0172]

[0173] The contact stress within a finite length is:

[0174]

[0175] Based on the above formula, the symmetrical ellipse contact formula in this embodiment is:

[0176]

[0177] in:

[0178] β represents the relative rotation angle of the target;

[0179] P c1 (x) represents the obtained contact stress, that is, the pressure corresponding to the C1 interface, which is recorded as the first contact stress;

[0180] x represents the actual contact length of the corresponding surface, which is the actual contact length corresponding to the first edge seam plane C1;

[0181] E j represents the contact modulus;

[0182] v represents the Poisson’s ratio of the target tongue-and-groove joint structure;

[0183] a C1 Indicates the interface length corresponding to the compressed joint plane in the first joint surface.

[0184] S320, contact stress distribution analysis at the second joint surface;

[0185] Depend on Figure 5 It can be seen that the stress characteristics of the second joint surface and the C1 interface are quite different. When the corner of the outer edge of the second joint surface contacts the lower interface, the contact stress increases sharply. Therefore, an antisymmetric triangular solid contact model can be established to represent the mechanical properties at the tenon-mortise interface.

[0186] The displacement of an antisymmetric triangular solid can be expressed as:

[0187] u z = -tan(β) (20)

[0188]

[0189] Same as above:

[0190] β represents the relative rotation angle of the target;

[0191] Z refers to the vertical downward direction, where u z is the displacement of the solid in the Z direction;

[0192] p(s) is the distributed contact stress at point s;

[0193] x represents the actual contact length of the corresponding surface, which here is the actual contact length of the corresponding second joint surface;

[0194] E is the elastic modulus of concrete;

[0195] v refers to the Poisson's ratio of the target tongue-and-groove joint structure;

[0196] p(x) is the corresponding contact stress distribution;

[0197] E j is the contact modulus;

[0198] a is the corresponding interface length.

[0199] Considering the boundary condition that p(x) = 0 when x = 0, the contact stress of the antisymmetric triangular solid can be expressed as:

[0200]

[0201] In this embodiment, the antisymmetric triangle contact formula is:

[0202]

[0203] in:

[0204] β represents the relative rotation angle of the target;

[0205] P Ti (x) represents the contact stress corresponding to the second joint surface, that is, the pressure corresponding to the Ti interface;

[0206] x represents the actual contact length of the corresponding surface, that is, the actual contact length corresponding to the Ti interface;

[0207] E j represents the contact modulus;

[0208] a Ti It represents the interface length corresponding to the i-th second joint surface, that is, the interface length corresponding to the Ti interface.

[0209] S330, contact force, tension;

[0210] The formula is as follows:

[0211]

[0212] in:

[0213] F C is the contact force;

[0214] N is the axial force;

[0215] T is the tension;

[0216] γ is the mortise angle;

[0217] A C1i and A Ti is the corresponding interface area; n C1i and n Ti is the number of corresponding interface units. This embodiment divides the corresponding interface into a number of geometric units based on the prior art;

[0218] a C11 and a Ti is the length of the corresponding interface.

[0219] P Cli It refers to the pressure when the edge plane section unit is i, that is, the pressure corresponding to the i-th unit of the C1 interface;

[0220] P T3i It refers to the pressure when the plane section unit at the mortise and tenon is i, that is, the pressure corresponding to the i-th unit of the T3 interface;

[0221] P T1i It refers to the pressure when the upper unit of the inclined section at the mortise is i, that is, the pressure corresponding to the i-th unit of the T1 interface;

[0222] P T2i is the pressure at the lower unit of the inclined section at the mortise and tenon when it is i, that is, the pressure corresponding to the i-th unit of the T2 interface;

[0223] ∑ is the summation series;

[0224] β is the rotation angle of the mortise and tenon due to force.

[0225] S340, actual contact length x update formula;

[0226] x cl (β) = a Cl -a Cl tan(β) (27)

[0227]

[0228] in:

[0229] xcl (β) is the actual contact length of the first edge seam plane C1 after updating based on the target relative rotation angle β, that is, the length of the plane section corresponding to C1 after the update;

[0230] x T1 (β) is the actual contact length of the first slope T1 after updating based on the target relative rotation angle of β;

[0231] x T2 (β) is the actual contact length of the second inclined surface T2 after updating based on the target relative rotation angle of β;

[0232] x T3 (β) is the actual contact length of the third plane T3 after being updated based on the target relative rotation angle of β.

[0233] a cl is the interface length of the first edge seam plane C1, a T1 is the interface length of the first inclined surface T1, a T2 is the interface length of the second inclined surface T2 and the interface length of the third plane T3, that is, the actual contact length in the initial state is equal to the interface length.

[0234] S350, constructing a moment balance model;

[0235] The bending moment of the joint includes the sum of the C1, C2, T1, T2, and T3 sides, that is, each contact surface has a bending moment toward the center of the joint. The moment-relative rotation relationship (M-β) is formed by increasing the β value (until failure).

[0236] Considering the influence of the axial force, the moment balance model in this embodiment is expressed as:

[0237]

[0238] TL C2i =M T (33)

[0239] M CC +M CT +M T =M (34)

[0240] in:

[0241] M CC It represents the bending moment corresponding to the first edge joint plane C1, which is recorded as the first bending moment;

[0242] M CT The bending moment corresponding to the first inclined surface T1 and the second inclined surface T2 is denoted as the second bending moment;

[0243] M TIt represents the bending moment corresponding to the third plane T3, denoted as the third bending moment;

[0244] M represents the bending moment corresponding to the target tongue-and-groove joint structure, i.e., the rotational stiffness;

[0245] n cI Indicates the number of units corresponding to the first edge seam plane C1;

[0246] n T3 Indicates the number of units corresponding to the first plane T3;

[0247] β represents the relative rotation angle of the target;

[0248] P Cli represents the contact stress corresponding to the i-th unit in the first edge joint plane C1;

[0249] A Cli represents the interface area corresponding to the first edge seam plane C1;

[0250] L Cloi represents the total length of the contact force corresponding to the first edge seam plane C1;

[0251] P T3i represents the contact stress corresponding to the i-th unit in the third plane T3;

[0252] A T3i represents the interface area corresponding to the third plane T3;

[0253] H T3i It represents the vertical sum of the contact forces at the first inclined surface T1 and the second inclined surface T2;

[0254] T represents tension;

[0255] L C2i Represents the total length of the contact force at the third plane T3.

[0256] S400, failure process simulation;

[0257] The relative rotation angle β is gradually increased, the contact stress of each first joint surface and the second joint surface under the relative rotation angle β is iteratively calculated, and the rotational stiffness of the target tongue and groove joint structure is calculated based on the obtained contact stress.

[0258] The relative rotation angle β refers to the relative rotation angle of the assembled joint during the bending process.

[0259] The method for calculating the rotational stiffness of a target tongue-and-groove joint structure at a target relative rotation angle in an iteration step comprises the following steps:

[0260] S410, obtaining actual contact lengths corresponding to each current first joint surface and each second joint surface;

[0261] The initial calculation of the actual contact length uses the interface length corresponding to the configured geometric dimensions;

[0262] The actual contact length updated based on the relative rotation angle in the previous iteration is then used.

[0263] S420, based on the target relative rotation angle and the corresponding actual contact length, calculate the contact stress corresponding to each first joint surface according to the symmetrical triangle contact law or the symmetrical ellipse contact law to obtain the corresponding first contact stress;

[0264] When the symmetric ellipse contact law (i.e., the above symmetric ellipse contact formula) is used to calculate the contact stress corresponding to the first joint surface in the previous calculation step, the symmetric ellipse contact law is still used to calculate the contact stress corresponding to the first joint surface in this calculation step;

[0265] When the symmetrical triangle contact rule (i.e., the symmetrical triangle contact formula) is used to calculate the contact stress corresponding to the first joint surface in the previous calculation step, in this calculation step:

[0266] The contact stress corresponding to the first joint surface is calculated by using the symmetrical triangle contact rule to obtain a candidate contact stress;

[0267] determining whether the candidate contact stress exceeds the corresponding concrete compressive strength;

[0268] When the candidate contact stress does not exceed the corresponding concrete compressive strength, taking the candidate contact stress as the first contact stress;

[0269] When the candidate contact stress exceeds the corresponding concrete compressive strength, the contact stress corresponding to the first joint surface is calculated using the symmetrical ellipse contact law to obtain the corresponding first contact stress.

[0270] S430, based on the target relative rotation angle and the corresponding actual contact length, calculating the contact stress corresponding to each second joint surface according to the antisymmetric triangle contact rule to obtain the corresponding second contact stress;

[0271] That is, the contact stress corresponding to the interface from T1 to T3 is calculated based on the above-mentioned antisymmetric triangle contact formula.

[0272] S440, calculating corresponding rotational stiffness based on each first contact stress and each second contact stress;

[0273] Based on the above formula for calculating the tension, based on the obtained first contact stresses, the obtained second contact stresses and the axial force on the target tongue and groove joint structure, the tension on the target tongue and groove joint structure is calculated;

[0274] Based on the torque balance model constructed above, the rotational stiffness is calculated based on each first contact stress, each second contact stress and the tension.

[0275] S450: Update the actual contact lengths corresponding to each first joint surface and each second joint surface based on the target relative rotation angle.

[0276] Based on the actual contact length update formula, the actual contact length corresponding to each interface is corrected based on the target relative rotation angle to obtain an updated actual contact length for use in the next iteration step.

[0277] As an embodiment, a rotational stiffness calculation system is also provided, which is used to execute the rotational stiffness calculation method corresponding to the above step S400.

[0278] As an embodiment, a size design method is also provided, comprising the following steps:

[0279] Configure several groups of candidate joint sizes, and calculate the rotational stiffness of the tongue-and-groove joint structure under each candidate joint size according to the rotational stiffness calculation method corresponding to step S400 to obtain corresponding force analysis results;

[0280] Based on the force analysis results, the optimal candidate joint size is selected as the target joint size.

[0281] As an embodiment, a size design system is also provided for executing the size design method described above.

[0282] As for the device embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment.

[0283] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0284] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, devices, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0285] The present invention is described with reference to the flowcharts and / or block diagrams of the method, terminal device (system), and computer program product according to the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of the processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing terminal device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing terminal device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0286] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing terminal device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce a manufactured product including an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0287] These computer program instructions can also be loaded onto a computer or other programmable data processing terminal device so that a series of operating steps are executed on the computer or other programmable terminal device to produce a computer-implemented process, thereby providing instructions for implementing the process in the computer or other programmable terminal device. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0288] It should be noted that:

[0289] The "one embodiment" or "embodiment" mentioned in the specification means that the specific features, structures or characteristics described in conjunction with the embodiment are included in at least one embodiment of the present invention. Therefore, the phrases "one embodiment" or "embodiment" appearing in various places throughout the specification do not necessarily refer to the same embodiment.

[0290] Although the preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0291] In addition, it should be noted that the shapes and names of the parts and components of the specific embodiments described in this specification may be different. Any equivalent or simple changes made based on the structure, features and principles described in the patent concept of the present invention are included in the protection scope of the patent of the present invention. The technicians in the technical field of the present invention can make various modifications or supplements to the specific embodiments described or replace them in a similar manner, as long as they do not deviate from the structure of the present invention or exceed the scope defined by the claims, they should all fall within the protection scope of the present invention.

Claims

1. A method for calculating rotational stiffness, applied to a tongue-and-groove joint structure, characterized in that: The following steps are involved: Taking the joint planes on both sides of the concave and convex tenon in the target tongue-and-groove joint structure as the first joint surface, taking the concave and convex joint surface corresponding to the concave and convex tenon as the second joint surface, gradually calculating the contact stress between the first joint surface and the second joint surface at each relative rotation angle, and calculating the rotational stiffness of the target tongue-and-groove joint structure based on the obtained contact stress; The method for calculating the rotational stiffness of the target tongue-and-groove joint structure at the target relative rotation angle comprises the following steps: Obtaining the actual contact lengths corresponding to the current first joint surfaces and the second joint surfaces; Based on the target relative rotation angle and the corresponding actual contact length, the contact stress corresponding to each first joint surface is calculated according to the symmetrical triangle contact law or the symmetrical ellipse contact law to obtain the corresponding first contact stress; Based on the target relative rotation angle and the corresponding actual contact length, the contact stress corresponding to each second joint surface is calculated according to the antisymmetric triangle contact law to obtain the corresponding second contact stress; calculating a corresponding rotational stiffness based on each first contact stress and each second contact stress; The actual contact lengths corresponding to each first joint surface and each second joint surface are updated based on the target relative rotation angle.

2. The method for calculating rotational stiffness according to claim 1, characterized in that: Based on the target relative rotation angle and the corresponding actual contact length, the contact stress corresponding to the first joint surface is calculated according to the symmetrical triangle contact law or the symmetrical ellipse contact law to obtain the corresponding first contact stress; When the symmetric ellipse contact law is used to calculate the contact stress corresponding to the first joint surface in the previous calculation step, the symmetric ellipse contact law is still used to calculate the contact stress corresponding to the first joint surface in this calculation step; When the symmetrical triangle contact law is used to calculate the contact stress corresponding to the first joint surface in the previous calculation step, in this calculation step: The contact stress corresponding to the first joint surface is calculated by using the symmetrical triangle contact rule to obtain a candidate contact stress; determining whether the candidate contact stress exceeds the corresponding concrete compressive strength; When the candidate contact stress does not exceed the corresponding concrete compressive strength, taking the candidate contact stress as the first contact stress; When the candidate contact stress exceeds the corresponding concrete compressive strength, the contact stress corresponding to the first joint surface is calculated using the symmetrical ellipse contact law to obtain the corresponding first contact stress.

3. The method for calculating rotational stiffness according to claim 2, characterized in that: The calculation formula for calculating the contact stress corresponding to the first joint surface using the symmetrical triangle contact rule is: in: β represents the relative rotation angle of the target; P e (x) represents the obtained contact stress, i.e., the candidate contact stress; a C1 It represents the interface length corresponding to the compressed joint plane in the first joint surface; x represents the actual contact length of the corresponding surface; E j represents the contact modulus; v represents the Poisson’s ratio of the target tongue-and-groove joint structure.

4. The method for calculating rotational stiffness according to claim 2, characterized in that: The contact stress corresponding to the first joint surface is calculated using the symmetrical ellipse contact law, and the calculation formula for the corresponding first contact stress is obtained as follows: in: β represents the relative rotation angle of the target; P c1 (x) represents the obtained contact stress, i.e., the corresponding first contact stress; represents the radius of the major axis of the corresponding ellipse; a C1 It represents the interface length corresponding to the compressed joint plane in the first joint surface; x represents the actual contact length of the corresponding surface; E j represents the contact modulus; v represents the Poisson’s ratio of the target tongue-and-groove joint structure.

5. The method for calculating rotational stiffness according to claim 1, characterized in that: Based on the target relative rotation angle and the corresponding actual contact length, the contact stress corresponding to each second joint surface is calculated according to the antisymmetric triangle contact law, and the calculation formula for the corresponding second contact stress is obtained as follows: in: β represents the relative rotation angle of the target; Ti represents the i-th second joint surface; a Ti represents the interface length corresponding to the i-th second joint surface; P Ti (x) represents the contact stress corresponding to the second joint surface, that is, the second contact stress; x represents the actual contact length of the corresponding surface; E j represents the contact modulus.

6. The method for calculating rotational stiffness according to any one of claims 1 to 5, characterized in that: The specific steps of calculating the corresponding rotational stiffness based on each first contact stress and each second contact stress are: Based on each first contact stress, each second contact stress and the axial force on the target tongue and groove joint structure, calculate and obtain the tensile force on the target tongue and groove joint structure; The rotational stiffness is calculated based on the first contact stresses, the second contact stresses, and the tensile force.

7. The method for calculating rotational stiffness according to claim 6, characterized in that: Based on the moment balance model, the rotational stiffness is calculated based on each first contact stress, each second contact stress and the tension. The expression of the moment balance model is: TL C2i =M M CC ,+M CT +M T =M in: The first joint surface is divided into a first edge joint plane C1 and a second edge joint plane C2. During the force-bearing process, the first edge joint plane C1 is compressed; The second seam surface is divided into a first inclined surface T1, a second inclined surface T2 and a third plane T3, wherein the first inclined surface T1 is connected to the first edge seam plane C1, and the second inclined surface T2 is connected to the second edge seam plane C2; M CC It represents the bending moment corresponding to the first edge joint plane C1, which is recorded as the first bending moment; M CT The bending moment corresponding to the first inclined surface T1 and the second inclined surface T2 is denoted as the second bending moment; M T It represents the bending moment corresponding to the third plane T3, denoted as the third bending moment; M represents the bending moment corresponding to the target tongue-and-groove joint structure, i.e., the rotational stiffness; n CI Indicates the number of units corresponding to the first edge seam plane C1; n T3 Indicates the number of units corresponding to the third plane T3; β represents the relative rotation angle of the target; P Cli represents the contact stress corresponding to the i-th unit in the first edge joint plane C1; A Cli represents the interface area corresponding to the first edge seam plane C1; L Cloi represents the total length of the contact force corresponding to the first edge seam plane C1; P T3i represents the contact stress corresponding to the i-th unit in the third plane T3; A T3i represents the interface area corresponding to the third plane T3; H T3i It represents the vertical sum of the contact forces at the first inclined surface T1 and the second inclined surface T2; T represents tension; L C2i Represents the total length of the contact force at the third plane T3.

8. A rotational stiffness calculation system, applied to a tongue-and-groove joint structure, characterized in that: Used to execute the rotational stiffness calculation method as described in any one of claims 1 to 7.

9. A dimension design method, applied to a tongue-and-groove joint structure, characterized in that: The steps include: Configure several groups of candidate joint sizes, and calculate the rotational stiffness of the tongue-and-groove joint structure under each candidate joint size according to the rotational stiffness calculation method according to any one of claims 1 to 7, to obtain corresponding force analysis results; Based on the force analysis results, the optimal candidate joint size is selected as the target joint size.

10. A dimensioning system, applied to a tongue-and-groove joint structure, characterized in that: Used to perform the dimensioning method as claimed in claim 9.

Images