CN114091153A - Novel joint model considering joint interface dynamic effect, construction method thereof and numerical value realization method - Google Patents

Novel joint model considering joint interface dynamic effect, construction method thereof and numerical value realization method Download PDF

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CN114091153A
CN114091153A CN202111349567.6A CN202111349567A CN114091153A CN 114091153 A CN114091153 A CN 114091153A CN 202111349567 A CN202111349567 A CN 202111349567A CN 114091153 A CN114091153 A CN 114091153A
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肖明清
龚彦峰
廖少明
孙文昊
邓朝辉
薛光桥
门燕青
徐意志
张靖坤
王少锋
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China Railway Siyuan Survey and Design Group Co Ltd
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Abstract

The invention relates to a novel joint model considering joint interface dynamic effect, a construction method and a numerical value realization method thereof, wherein the novel joint model enables uneven characteristics of microscopic appearance of a rough surface to be equivalent to dynamic physical parameters of flat and homogeneous multi-linear materials on two sides through rough surface dynamic contact rigidity and dynamic contact damping based on a fractal theory, so that the difficulty and the workload of modeling and analysis are reduced; the flat homogeneous virtual material maintains direct contact in the normal direction, the contact dynamic characteristic of the joint and the discontinuity of displacement are not changed, and the elastic multi-linear spring connection is adopted in the tangential direction to simulate the stress tangential nonlinearity of the joint. The method combines a direct contact method, a virtual material method and macro-micro observation, can simultaneously consider normal and tangential stress nonlinearity and displacement discontinuity, is correction of a joint model, and reduces the difficulty and workload of modeling and analysis.

Description

Novel joint model considering joint interface dynamic effect, construction method thereof and numerical value realization method
Technical Field
The invention belongs to the technical field of underground building structure design, and particularly relates to a novel joint model considering joint interface dynamic effect, a construction method thereof and a numerical value realization method.
Background
The joint of the duct piece is physically composed of two rough contact surfaces, and the dynamic response of the joint is largely determined and influenced by the microscopic configuration and physical properties of the two rough contact surfaces. And the current literature is less about the study on the microscopic characteristic of the shield tunnel segment joint. However, in the field of traditional machine tool manufacturing, researches on dynamic contact rigidity and dynamic damping of the splicing surfaces of mechanical components have a long history, and results are rich. In the conventional mechanical part joint research, two rough joint surfaces are mostly equivalent to the contact of a rough contact surface and a smooth surface (namely, only the rough characteristic of one side surface is considered). Compared with mechanical parts, the shield tunnel segment has the characteristics of self, and the core difference is that the shield tunnel segment is manufactured manually and is a multi-phase medium material, compared with the mechanical part manufacturing in the working procedures of mold building, concrete stirring, vibrating, maintenance and the like, the magnitude and difference of the surface roughness of the obtained segment are large.
Based on the reasons, the novel joint nonlinear model considering the joint interface dynamic effect is established, and the modeling of the model on numerical analysis software is realized, so that the model not only has important significance in theory, but also has important practical value for shield tunnel engineering.
From the microscopic contact characteristics of the joint, under the condition that the surface topography of the rough surface on two sides of the joint is not changed, the axial and tangential dynamic contact stiffness of the joint basically increases along with the increase of the contact pressure, which is a remarkable mechanical characteristic after considering the influence of the microscopic topography of the surface of the rough surface of the joint. The rough surface direct contact method has high simulation degree, can reflect the dynamic contact characteristic of the rough contact surface, but has complex modeling, low universality and large trial calculation and calculation amount; the generalized gap method has high universality and high precision, but the physical gap of the joint is difficult to define. The joint model considers the non-continuity characteristic of the joint, but the existing numerical method is difficult to simultaneously consider the characteristics of tangential, normal non-linearity and non-continuity. The application range of the theoretical constitutive model is relatively limited.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a novel joint model considering the dynamic effect of a joint interface, a construction method and a numerical value realization method thereof.
The technical scheme of the invention is realized as follows: the invention discloses a construction method of a novel joint model considering joint interface dynamic effect, which comprises the following steps:
measuring fractal dimension and fractal dimension parameters of pipe piece concrete on two sides of the joint;
calculating the plastic critical contact area a of the microprotrusions on both sides of the seamc1、ac2And the maximum microprotrusion contact area a of the contact surfaceLAccording to the maximum microprotrusion contact area a of the contact surfaceLAnd ac1、ac2The working condition classification is carried out by a plurality of relative relations;
calculating normal contact stiffness and normal contact damping according to the working condition classification condition, and calculating the elastic modulus and the equivalent Poisson ratio of the equivalent homogeneous material to obtain an equivalent homogeneous material constitutive model and a seam normal nonlinear model;
and calculating the tangential contact stiffness and the tangential contact damping according to the working condition classification condition, and calculating the shearing stiffness of the tangential nonlinear spring to obtain the tangential nonlinear spring and a seam tangential nonlinear model.
Further, the fractal dimension D and the fractal dimension parameter G of the pipe piece concrete on the two sides of the joint are measured, and the method specifically comprises the following steps:
scanning a segment test piece by using a surface topography instrument, importing a coordinate point data dat file output by the surface topography instrument into Matlab for programming, wherein a power spectral density function S (omega) and omega are in a linear relation on a log-log coordinate system, the linear slope is related to a fractal dimension D, the intercept is related to a fractal dimension parameter G, and the fractal dimension D and the fractal dimension parameter G are obtained by a method of obtaining the slope and the intercept on the log-log coordinate system.
Further, calculating the plastic critical contact area a of the microprotrusions on the two sides of the seamc1、ac2And the maximum microprotrusion contact area a of the contact surfaceLThe method specifically comprises the following steps:
the concrete of the pipe pieces on two sides of the joint has different surface roughness, wherein fractal dimensions are D1 and D2 respectively, and fractal scale parameters are G1 and G2 respectively;
plastic critical contact area a of micro-convex body on two sides of seamc1、ac2The method comprises the following steps:
Figure BDA0003355406200000021
Figure BDA0003355406200000031
wherein E is the modulus of elasticity, σyIs the yield stress of the steel, and,
Figure BDA0003355406200000032
mu is a connectionThe coefficient of friction of the contact surface material;
the expansion coefficients psi of the two contact surfaces are obtained by solving the following transcendental equation1、Ψ2：
Figure BDA0003355406200000033
Wherein psi is the expansion coefficient of the contact surface;
the two rough contact surfaces on both sides of the joint have the same maximum contact area aLThe following equation is used to obtain:
Figure BDA0003355406200000034
aL＝min(aL1,aL2)
in the formula, Ar1、Ar2The actual contact areas of the two segments, respectively.
Further, calculating normal contact stiffness according to the working condition classification condition, specifically comprising:
the contact rigidity value k of the micro-convex point is only in the part of the area where the elastic deformation occursn，
Figure BDA0003355406200000035
Wherein, PeIs the elastic contact pressure, δ is the contact deformation;
according to the maximum microprotrusion contact area a of the contact surfaceLAnd ac1、ac2Three relative relations exist between the two groups to classify the working conditions;
when in the first operating mode, aL<ac1<ac2When the joint is in a plastic contact state, all the microprotrusions of the first rough surface on one side of the joint and the second rough surface on the other side of the joint are in plastic contact state, and the normal contact stiffness is 0;
when in the second operating mode, ac1<aL<ac2When the micro-convex bodies on the first rough surface at one side of the joint are partially in an all-plastic state and partially in an elastic-plastic state, all the micro-convex bodies on the second rough surface at the other side of the joint are in the all-plastic state, and the normal contact rigidity of the single micro-convex point is integrated on a distribution function to obtain the total normal contact rigidity KnComprises the following steps:
Figure BDA0003355406200000041
when in the third operating mode, ac1<ac2<aLWhen the joint is in use, the first rough surface on one side of the joint and the second rough surface on the other side of the joint are in all-plastic state with partial micro-protrusions and elastic-plastic state, and the total normal contact rigidity KnComprises the following steps:
Figure BDA0003355406200000042
wherein E is the modulus of elasticity, #1、ψ2The expansion coefficients of the first rough surface and the second rough surface are obtained; d1 is the fractal dimension of the first matte and D2 is the fractal dimension of the second matte.
Further, according to the operating condition classification condition, normal contact damping is calculated, and the method specifically comprises the following steps:
the elastic strain energy stored by the microprotrusions in the elastic phase is:
Figure BDA0003355406200000043
whereas the strain energy in the plastic range is:
Figure BDA0003355406200000044
wherein E is the modulus of elasticity, σyIs the yield stress, R is the radius of curvature of the elastic microprotrusions, deltacIs a critical plastic contactAmount of deformation, δLIs the maximum contact deflection;
according to the maximum microprotrusion contact area a of the contact surfaceLAnd ac1、ac2Three relative relations exist between the two groups to classify the working conditions;
when in the first operating mode, aL<ac1<ac2During the process, all the microprotrusions of the first rough surface on one side of the joint and the second rough surface on the other side of the joint are in an all-plastic state, normal contact damping does not exist, and the plastic strain energy of the contact surface is as follows:
Figure BDA0003355406200000051
when in the second operating mode, ac1<aL<ac2During the process, the first rough surface on one side of the joint is provided with a part of micro-convex bodies in an all-plastic state, the other part of the first rough surface is in an elastic-plastic state, all the micro-convex bodies on the second rough surface on the other side of the joint are in the all-plastic state, and the corresponding elastic strain energy of the contact surface is as follows:
Figure BDA0003355406200000052
the plastic strain energy of the contact surface is:
Figure BDA0003355406200000053
the corresponding damping loss factor is then:
Figure BDA0003355406200000054
the dimensionless expression of the above equation is:
Figure BDA0003355406200000055
the normal contact damping of the contact surface is:
Figure BDA0003355406200000056
wherein M is the damping system mass, KnNormal contact stiffness;
when in the third operating mode, ac1<ac2<aLDuring the process, the first rough surface on one side of the joint and the second rough surface on the other side of the joint are all in a full plastic state by a part of micro-convex bodies, and the part of the micro-convex bodies is in an elastic plastic state, and the corresponding elastic strain energy of the contact surface is as follows:
Figure BDA0003355406200000061
the plastic strain energy of the contact surface is:
Figure BDA0003355406200000062
the corresponding damping loss factor is then:
Figure BDA0003355406200000063
the dimensionless expression of the above equation is:
Figure BDA0003355406200000064
the normal contact damping of the contact surface is:
Figure BDA0003355406200000065
wherein M is the damping system mass, KnIs the normal contact stiffness.
Further, calculating the elastic modulus and the equivalent poisson's ratio of the equivalent homogeneous material specifically includes:
the normal contact stiffness is basically equal to
Figure BDA0003355406200000066
Forming a positive linear relation; according to the geometrical relationship of the microprotrusions, the contact area aLAlso positively linear with the microprotrusion deformation delta, for simplicity of analysis, ignoring low order micro-scale, the joint pressure FnThe following power function relationship exists between the normal deformation Δ h of the seam:
Figure BDA0003355406200000071
Figure BDA0003355406200000072
at any stage, the work of the normal load in the equivalent material range satisfies the following relation:
Figure BDA0003355406200000073
wherein h is the thickness of the nonlinear equivalent material, FniIs the joint pressure of the i-th stage, KniIs the approximate normal stiffness of the i-th stage, AaIs the total area of the seam (m) corresponding to the unit loop width2/m), E is the modulus of elasticity;
the equivalent nonlinear material stores strain energy as:
Figure BDA0003355406200000074
wherein E isiFor the equivalent elastic modulus of the generalized gap, since the work done by the external load is equal to the strain energy stored by the equivalent material, then:
Figure BDA0003355406200000075
equivalently, shear modulus G of nonlinear materialiThe values are as follows:
Figure BDA0003355406200000076
wherein, KtiFor the sectional tangential stiffness of the contact surface, the equivalent Poisson ratio of the equivalent material at the i stage is obtained by the two formulas:
Figure BDA0003355406200000077
further, calculating the tangential contact stiffness according to the working condition classification condition specifically comprises:
the tangential stiffness is related to normal load P, tangential load T and contact area, and the tangential stiffness expression of a single micro-convex body in the elastic stage is as follows:
Figure BDA0003355406200000081
wherein,
Figure BDA0003355406200000082
is the shear modulus of the material, v is the Poisson's ratio, and mu is the friction coefficient of the material;
according to the maximum microprotrusion contact area a of the contact surfaceLAnd ac1、ac2Three relative relations exist between the two groups to classify the working conditions;
when in the first operating mode, aL<ac1<ac2When the pipe piece joint is in a full plastic state, all the micro-protrusions on the first rough surface on one side of the joint and the second rough surface on the other side of the joint are in a full plastic state, the tangential contact rigidity is 0, and the shearing rigidity of the pipe piece joint is completely provided by the bolt and the tenon and the mortise;
when in the second operating mode, ac1<aL<ac2During, the first rough surface of seam one side has some microprotrusions to be in the plastic state, has some to be in the plastic state, and all microprotrusions of the second rough surface of seam opposite side all are in the plastic state, and the tangential contact rigidity of segment seam both sides fractal is:
Figure BDA0003355406200000083
when in the third operating mode, ac1<ac2<aLDuring the time, the first rough surface of seam one side and the second rough surface of seam opposite side are that part microprotrusions are in the plastic state, and the part is in the elastoplastic state, and the tangential contact rigidity of segment seam both sides fractal is:
Figure BDA0003355406200000084
wherein,
Figure BDA0003355406200000085
is the shear modulus of the material, v is the Poisson's ratio, mu is the friction coefficient of the material, T is the tangential load, P is the normal load, psi1、ψ2D1 is the fractal dimension of the first rough surface, and D2 is the fractal dimension of the second rough surface.
Further, according to the operating condition classification condition, calculating the tangential contact damping specifically comprises:
under the action of tangential force, the tangential contact damping energy consumption of a single microprotrusion body in one vibration period is as follows:
Figure BDA0003355406200000091
wherein,
Figure BDA0003355406200000092
as shears for materialShear modulus, μ is the friction system, t is fnShear force and normal force applied to the micro convex body;
assuming that the shear force and the normal force applied to each asperity are proportional to the size of the contact area, the above equation can be expressed as:
Figure BDA0003355406200000093
wherein A isrFor actual contact area, T and FnTotal tangential force and normal force on the contact surface, respectively;
according to the maximum microprotrusion contact area a of the contact surfaceLAnd ac1、ac2Three relative relations exist between the two groups to classify the working conditions;
when in the first operating mode, aL<ac1<ac2During the process, all the microprotrusions of the first rough surface on one side of the joint and the second rough surface on the other side of the joint are in an all-plastic state, and the integral of tangential damping energy consumption on the area is as follows:
Figure BDA0003355406200000094
when in the second operating mode, ac1<aL<ac2During the process, the first rough surface on one side of the joint has part of the micro-protrusions in the all-plastic state, the other part of the first rough surface is in the elastic-plastic state, all the micro-protrusions on the second rough surface on the other side of the joint are in the all-plastic state, and the integral of the tangential damping energy consumption on the area can be expressed as:
Figure BDA0003355406200000101
when in the third operating mode, ac1<ac2<aLWhen the energy-saving steel plate is used, the first rough surface on one side of the joint and the second rough surface on the other side of the joint are in a full plastic state with partial micro-protrusions and in an elastic plastic state with tangential damping energy consumption on the surfacesThe product integral can be expressed as:
Figure BDA0003355406200000102
wherein,
Figure BDA0003355406200000103
is the shear modulus of the material, mu is the friction system, ArFor actual contact area, T and FnTotal tangential and normal forces on the contact surfaces, psi1、ψ2The expansion coefficients of the first rough surface and the second rough surface are shown, D1 is the fractal dimension of the first rough surface, and D2 is the fractal dimension of the second rough surface;
the loss factor of the tangential contact damping is:
ηT＝Wd/(Wd-We)
and the damping form belongs to hysteresis damping, the tangential damping coefficient is as follows:
CT＝ηTKt，
wherein, KtIs the tangential contact stiffness.
Further, calculating the shear stiffness of the tangential nonlinear spring specifically comprises:
(1-T/(μ P))1/3Performing Taylor series expansion, neglecting high-order trace, obtaining,
Figure BDA0003355406200000111
if the above equation does not take into account the influence of the normal contact pressure variation, i.e. P is taken as a constant value or as an initial contact pressure, then there is a linear relationship between the tangential stiffness and the shear force,
KT＝AT-BTT
will KTWritten shear force T and shear displacement deltaTThe above formula is converted into:
Figure BDA0003355406200000112
solving the first-order linear non-homogeneous differential equation to obtain T relative to deltaTThe general solution of the linear differential equation is:
Figure BDA0003355406200000113
it can be seen that shear is exponentially related to shear displacement, where AT、BTAs a seam characteristic parameter, CTThen a constant having a relationship to the initial state of the seam tangential static force; shear deformation delta due to the larger shear T in the usual caseTThe larger the size, the less difficult it is to obtain CTShould be a negative value, the asymptote height A of the exponential curve of the seam tangent multi-linear constitutive modelTThe physical meaning of (A) is the ultimate shear strength of the joint, AT+CTReflecting the shear strength of the seam prior to elastic slippage.
The invention also discloses a numerical realization method of the novel joint model considering the dynamic effect of the joint interface, which comprises the following steps:
establishing an equivalent homogeneous material constitutive and seam normal nonlinear model, a tangential nonlinear spring and a seam tangential nonlinear model by adopting the construction method of the novel seam model considering the dynamic effect of the seam interface;
for normal behavior: simulating an equivalent homogeneous material by adopting a multi-linear follow-up strengthening model, and determining the thickness of an equivalent homogeneous material layer and a multi-linear curve of the material according to the constitutive of the equivalent homogeneous material and a seam normal nonlinear model;
for tangential behavior: and determining a material constitutive model by adopting a multi-linear spring model according to the tangential nonlinear spring and the joint tangential nonlinear model.
The invention also discloses a novel joint model considering the dynamic effect of the joint interface, the model enables the unevenness characteristic of the microscopic appearance of the rough surface to be equivalent to the dynamic physical parameters of the flat and homogeneous multi-linear materials at the two sides of the joint through the rough surface dynamic contact rigidity and the dynamic contact damping based on the fractal theory, the flat and homogeneous virtual materials are kept in direct contact in the normal direction, the contact dynamic characteristic and the displacement discontinuity of the joint are not changed, and the elastic multi-linear springs are connected in the tangential direction to simulate the stress tangential nonlinearity of the joint.
The invention has at least the following beneficial effects: the invention provides a dynamic contact model combining a direct contact method, a spring damping method and a virtual material method and combining macro and micro observation, which can simultaneously consider normal and tangential stress nonlinearity and displacement discontinuity, is correction of a joint model and is convenient for numerical calculation and application.
The rough surface dynamic contact stiffness and dynamic contact damping based on the fractal theory are equivalent to dynamic physical parameters of a smooth and homogeneous multi-linear material on two sides by the rough surface dynamic contact stiffness and dynamic contact damping of the rough surface, so that the difficulty and workload of modeling and analysis are reduced; essentially, the model is a nonlinear contact model, i.e. the basic characteristic of maintaining discontinuous contact of the seam, the contact nonlinearity in the axial direction is considered by nonlinear equivalent homogeneous materials, and the tangential direction is considered by nonlinear springs.
The equivalent homogeneous material is normally used in the constitutive model, the problem that the initial distance of the joint points on two sides of the joint contact surface is set when the normal spring is applied is solved, and the problem does not exist in the tangential direction of the joint, so that the nonlinear spring is tangentially used.
The model of the invention is convenient for numerical calculation and application, and the calculation result has high simulation degree, high universality and high precision.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a schematic diagram of a novel seam model considering dynamic effects of a seam interface according to an embodiment of the present invention;
FIG. 2 is a flowchart of a method for constructing a novel joint model considering dynamic effects of a joint interface according to an embodiment of the present invention;
FIG. 3 is a flow chart of a numerical implementation method of a novel joint model considering dynamic effects of a joint interface according to an embodiment of the present invention;
fig. 4 is a flowchart of a method for acquiring fractal parameters D and G according to an embodiment of the present invention;
FIG. 5 is a seam normal multi-linear constitutive model provided by an embodiment of the present invention;
FIG. 6 is a seam tangent multi-linear constitutive model provided by an embodiment of the invention;
FIG. 7 is a schematic diagram illustrating a thickness value of an equivalent homogeneous material according to an embodiment of the present invention;
fig. 8 shows a combination 39 nonlinear spring structure according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature.
The invention considers the possible larger difference of the roughness of the rough surfaces on the two sides of the concrete segment joint, further discusses and considers the mesoscopic dynamic contact characteristic of the rough surfaces on the two sides of the segment joint on the basis of the existing research of the joint surface in the mechanical field, and provides a numerical value realization method of the corresponding macroscopic mechanical parameters (normal direction and tangential direction rigidity) of the joint.
The invention provides a dynamic contact model combining a direct contact method, a spring damping method and a virtual material method and combining macro and micro observation, which can simultaneously consider normal and tangential stress nonlinearity and displacement discontinuity, is correction of a joint model and is convenient for numerical calculation and application. The principle of the model is shown in figure 1.
Example one
Referring to fig. 1, the embodiment of the invention discloses a novel joint model considering a joint interface dynamic effect, which equates the unevenness characteristic of the microscopic appearance of a rough surface to dynamic physical parameters of a smooth and homogeneous multi-linear material on two sides through rough surface dynamic contact rigidity and dynamic contact damping based on a fractal theory, and reduces the difficulty and workload of modeling and analysis; the flat homogeneous virtual material maintains direct contact in the normal direction (without considering the initial microscopic gap of the joint), does not change the contact dynamic characteristic of the joint and the discontinuity of displacement, and adopts elastic multi-linear spring connection in the tangential direction to simulate the stress tangential nonlinearity of the joint.
Essentially, the model is a nonlinear contact model, i.e. the basic characteristic of maintaining discontinuous contact of the seam, the contact nonlinearity in the axial direction is considered by nonlinear equivalent homogeneous materials, and the tangential direction is considered by nonlinear springs.
Example two
Referring to fig. 2, an embodiment of the present invention provides a method for constructing a novel seam model considering a dynamic effect of a seam interface, including the following steps:
s1, measuring fractal dimension and fractal dimension parameters of the segment concrete on the two sides of the joint;
s2, calculating the plastic critical contact area a of the microprotrusions on the two sides of the seamc1、ac2And the maximum microprotrusion contact area a of the contact surfaceLAccording to the maximum microprotrusion contact area a of the contact surfaceLAnd ac1、ac2Between areClassifying the working conditions according to the relative relations;
s3, calculating normal contact stiffness and normal contact damping according to the working condition classification conditions, and calculating the elastic modulus and the equivalent Poisson ratio of the equivalent homogeneous material to obtain the constitutive of the equivalent homogeneous material and a seam normal nonlinear model;
and S4, calculating the tangential contact stiffness and the tangential contact damping according to the working condition classification condition, and calculating the shearing stiffness of the tangential nonlinear spring to obtain the tangential nonlinear spring and a seam tangential nonlinear model.
Further, step S3 specifically includes:
1. normal contact stiffness model considering fractal on two sides of segment joint
The shield tunnel concrete pipe sheet is different from conventional metal mechanical parts, the manufacturing and maintenance processes are multiple and complex, the automation degree is low, the uniformity of materials is not high, the roughness of two sides of a joint is likely to have larger difference, and the probability that the two concrete pipe sheets have the same fractal dimension D and fractal parameter G is extremely low. It is therefore necessary to investigate the effect of different roughness on the two sides of the seam (fractal on both sides) on the contact characteristics. And for the segment contact surface with the same concrete material on both sides, the factors influencing the plastic critical contact area of the microprotrusions are mainly fractal dimension D and fractal dimension parameter G,
assuming that the concrete of the segment at two sides of the joint has different surface roughness, the fractal dimensions are D1 and D2 respectively, and the fractal dimension parameters are G1 and G2 respectively.
Plastic critical contact area a of two-sided microprotrusionsc1，ac2The method comprises the following steps:
Figure BDA0003355406200000151
Figure BDA0003355406200000152
wherein E is the modulus of elasticity, σyIs the yield stress.
Figure BDA0003355406200000153
Wherein mu is the friction coefficient of the contact surface material, and for the concrete material, when no measured data exists, the value of mu is generally 0.55. Then press the above formula kμIs 0.62.
According to the M-B fractal theory, the relation between the distribution density n of contact points and the contact area a is as follows:
Figure BDA0003355406200000154
Figure BDA0003355406200000155
psi is the expansion coefficient of the contact surface, and the expansion coefficient psi of the two contact surfaces can be calculated by solving the following transcendental equation1、Ψ2For calculation of contact rigidity and the like:
Figure BDA0003355406200000156
the two rough contact surfaces have the same maximum contact area aLThe following formula was used to obtain,
Figure BDA0003355406200000157
aL＝min(aL1,aL2) (8)
in the formula, wherein Ar1、Ar2The actual contact areas of the two segments, respectively.
The micro-convex points only have contact rigidity values in the part of the area where elastic deformation occurs.
Figure BDA0003355406200000161
Wherein, PeIs the elastic contact pressure and δ is the contact deformation.
The maximum microprotrusion contact area a of the contact surfaceLAnd ac1And ac2There are three relative relationships between them: operating regime (1): aL<ac1<ac2
For rough surface 1 and rough surface 2, all the microprotrusions were in plastic contact with a normal contact stiffness of 0. The total contact pressure P is:
Figure BDA0003355406200000162
operating regime (2): ac1<aL<ac2
The rough surface 1 has a part of micro-convex bodies in an all-plastic state and a part in an elastic-plastic state. All the microprotrusions of the rough surface 2 are in an all plastic state.
And integrating the normal contact stiffness of the single micro-bump on a distribution function to obtain the total normal contact stiffness as follows:
Figure BDA0003355406200000163
Figure BDA0003355406200000164
Ψ1、Ψ2is an expansion coefficient.
Operating regime (3): ac1<ac2<aL
The rough surface 1 and the rough surface 2 are both partially in a full plastic state by virtue of the micro-protrusions, and partially in a plastic state.
Figure BDA0003355406200000171
The relationship of the pressure is:
Figure BDA0003355406200000172
wherein E is the modulus of elasticity, σyIs the yield stress, wherein1、ψ2The expansion coefficients of the first rough surface and the second rough surface are respectively; d1 is the fractal dimension of the first rough surface, D2 is the fractal dimension of the second rough surface, G1 is the fractal dimension parameter of the first rough surface, and G2 is the fractal dimension parameter of the second rough surface.
2. Normal dynamic damping model analysis considering fractal on two sides of segment joint
From a microscopic perspective, elastic deformation of the contact surface is primarily used to store deformation energy, but not to dissipate energy. The energy consumption is mainly the plastic deformation portion.
The elastic strain energy stored by the microprotrusions in the elastic phase is:
Figure BDA0003355406200000173
wherein R is the radius of curvature of the elastic microprotrusions.
While the strain energy in the plastic range,
Figure BDA0003355406200000174
likewise, δcIs the critical plastic contact deformation, deltaLIs the maximum contact deformation.
Operating regime (1): aL<ac1<ac2，
All the microprotrusions of the rough surface 1 and the rough surface 2 are in an all-plastic state.
The plastic strain energy of the contact surface is:
Figure BDA0003355406200000181
operating regime (2): ac1<aL<ac2
The rough surface 1 has a part of micro-convex bodies in an all-plastic state and a part in an elastic-plastic state. All the microprotrusions of the rough surface 2 are in an all plastic state.
The corresponding elastic strain energy of the contact surface is as follows:
Figure BDA0003355406200000182
the plastic strain energy of the contact surface is:
Figure BDA0003355406200000183
the corresponding damping loss factor is then:
Figure BDA0003355406200000184
the dimensionless expression of the above equation is:
Figure BDA0003355406200000185
the normal contact damping of the contact surface is:
Figure BDA0003355406200000186
wherein M is the damping system mass.
Operating regime (3): ac1<ac2<aL
The rough surface 1 and the rough surface 2 are both partially in a full plastic state by virtue of the micro-protrusions, and partially in a plastic state.
The corresponding elastic strain energy of the contact surface is as follows:
Figure BDA0003355406200000191
the plastic strain energy of the contact surface is:
Figure BDA0003355406200000192
the corresponding damping loss factor is then:
Figure BDA0003355406200000193
the dimensionless expression of the above equation is:
Figure BDA0003355406200000194
the normal contact damping of the contact surface is:
Figure BDA0003355406200000195
in summary, normal contact damping of the contact surface can be obtained.
3. Equivalent homogeneous material constitutive model and seam normal nonlinear analysis
From equation (14), it can be seen that the axial and tangential dynamic contact stiffness of the joint increases substantially with increasing contact pressure, with the asperity surface topography on both sides of the joint being constant, a significant mechanical feature after taking into account the microscopic topography effects of the asperity surface of the joint.
The normal contact stiffness is basically equal to
Figure BDA0003355406200000201
Forming a positive linear relation; according to the geometrical relationship of the microprotrusions, the contact area aLAlso positively linear with the microprotrusion deformation delta, for simplicity of analysis, ignoring low order micro-scale, the joint pressure FnThe following power function relationship exists between the normal deformation deltah of the seam,
Figure BDA0003355406200000202
at any stage, the work of the normal load in the equivalent material range satisfies the following relationship,
Figure BDA0003355406200000203
wherein h is the thickness of the nonlinear equivalent material, FniIs the joint pressure of the i-th stage, KniIs the approximate normal stiffness of the i-th stage, AaIs the total area of the seam (m) corresponding to the unit loop width2/m)。
The equivalent nonlinear material stores strain energy as:
Figure BDA0003355406200000204
wherein EiIs the equivalent modulus of elasticity of the generalized gap.
Since the work done by the external load is equal to the strain energy stored by the equivalent material, then,
Figure BDA0003355406200000205
equivalently, shear modulus G of nonlinear materialiThe values are taken as follows,
Figure BDA0003355406200000206
wherein KtiIs the piecewise tangential stiffness of the interface.
Through the two formulas, the equivalent Poisson ratio of the equivalent material at the i stage is obtained as follows:
Figure BDA0003355406200000207
in conclusion, the elastic modulus of the equivalent homogeneous material and the equivalent Poisson's ratio can be obtained.
Further, step S4 specifically includes:
1. tangential contact rigidity model considering fractal on two sides of segment seam
The tangential stiffness is related to normal load P, tangential load T and contact area, and the tangential stiffness expression of a single micro-convex body in the elastic stage is as follows:
Figure BDA0003355406200000211
wherein,
Figure BDA0003355406200000212
is the shear modulus of the material, v is the Poisson's ratio, and mu is the friction coefficient of the material;
operating regime (1): aL<ac1<ac2All the microprotrusions of the rough surface 1 and the rough surface 2 are in an all-plastic state, and the tangential contact stiffness is 0. The shear stiffness of the segment joint at this point is provided entirely by the bolts and rebates.
Operating regime (2): ac1<aL<ac2The rough surface 1 has a part of micro-protrusions in an all-plastic state and a part in an elastic-plastic state. All the microprotrusions of the rough surface 2 are in an all plastic state.
Figure BDA0003355406200000213
Operating regime (3): ac1<ac2<aL，
The rough surfaces 1 and 2 are partially in a full plastic state and partially in an elastic plastic state.
Figure BDA0003355406200000214
2. Tangential dynamic damping model considering fractal on two sides of segment joint
Under the action of tangential force, the tangential contact damping energy consumption of a single microprotrusion body in one vibration period is as follows:
Figure BDA0003355406200000221
wherein,
Figure BDA0003355406200000222
is the shear modulus of the material, mu is the friction system, t is fnShear force and normal force applied to the micro convex body;
assuming that the shear force and the normal force applied to each asperity are proportional to the size of the contact area, the above equation can be expressed as:
Figure BDA0003355406200000223
wherein A isrFor actual contact area, T and FnTotal tangential force and normal force on the contact surface, respectively;
operating regime (1): aL<ac1<ac2All the microprotrusions of the rough surface 1 and the rough surface 2 are in an all-plastic state. The integral of the tangential damping energy consumption on the area is as follows:
Figure BDA0003355406200000224
wherein A isrFor actual contact area, T and FnTotal tangential force and normal force on the contact surface, respectively;
operating regime (2): ac1<aL<ac2The rough surface 1 has a part of micro-protrusions in an all-plastic state and a part in an elastic-plastic state. All the microprotrusions of the rough surface 2 are in an all plastic state. Cutting machineThe integral over the area of the dissipation energy to the damping can be expressed as:
Figure BDA0003355406200000231
wherein A isrFor actual contact area, T and FnTotal tangential force and normal force on the contact surface, respectively; operating regime (3): ac1<ac2<aL
The rough surfaces 1 and 2 are partially in a full plastic state and partially in an elastic plastic state. The tangential damping energy consumption is integrated in area,
Figure BDA0003355406200000232
wherein A isrFor actual contact area, T and FnTotal tangential force and normal force on the contact surface, respectively;
accordingly, the loss factor of tangential contact damping is:
ηT＝Wd/(Wd-We)
(42)
and the damping form belongs to hysteresis damping, the tangential damping coefficient is as follows:
CT＝ηTKt (43)
3. tangential nonlinear spring constitutive model and joint tangential nonlinear analysis
(1-T/(μ P))1/3Performing Taylor series expansion, neglecting high-order trace, obtaining,
Figure BDA0003355406200000233
if the above equation does not take into account the influence of the normal contact pressure variation, i.e. P takes a constant value (or takes the initial contact pressure), then there is a linear relationship between the tangential stiffness and the shear force,
KT＝AT-BTT
(45)
will KTWritten shear force T and shear displacement deltaTThe above formula is converted into:
Figure BDA0003355406200000241
solving the first-order linear non-homogeneous differential equation to obtain T relative to deltaTThe general solution of the linear differential equation is:
Figure BDA0003355406200000242
it can be seen that shear is exponentially related to shear displacement, where AT、BTAs a seam characteristic parameter, CTThen a constant having a relationship to the initial state of the seam tangential static force; shear deformation delta due to the larger shear T in the usual caseTThe larger the size, the less difficult it is to obtain CTShould be a negative value. Exponential curve asymptote height A of seam tangential multi-linear constitutive modelTThe physical meaning of (A) is the ultimate shear strength of the joint, AT+CTReflected by the shear strength of the joint before elastic slippage (where CTNegative), both of which are related by the macroscopic physical structure of the seam.
In summary, the shear stiffness of the tangential nonlinear spring can be obtained by dividing the shear force by the shear displacement.
According to the above calculation formula, equivalent homogeneous material constitutive and seam normal nonlinear models, tangential nonlinear springs and seam tangential nonlinear models can be obtained. The numerical method of the novel seam model is realized, and the specific flow is shown in fig. 3.
EXAMPLE III
Referring to fig. 3, the embodiment of the invention discloses a numerical implementation method of a novel seam model considering a dynamic effect of a seam interface, which comprises the following steps:
establishing an equivalent homogeneous material constitutive and seam normal nonlinear model, a tangential nonlinear spring and a seam tangential nonlinear model by adopting the construction method of the novel seam model considering the dynamic effect of the seam interface as described in the second embodiment;
for normal behavior: and simulating by adopting a multi-linear follow-up strengthening model, and determining the thickness of the equivalent homogeneous material layer and the multi-linearity of the material according to the constitutive of the equivalent homogeneous material and the seam normal nonlinear model.
For tangential behavior: and determining a material constitutive model by adopting a multi-linear spring model according to the tangential nonlinear spring and the seam tangential nonlinear model.
Therefore, a contact model combining a direct contact method, a virtual material method and a macro-micro view is established, normal and tangential stress nonlinearity and displacement discontinuity can be considered simultaneously by the contact model, and the contact model is a correction of a joint model and can be used for various numerical calculation applications.
The specific method flow for obtaining the fractal parameters D and G is as shown in fig. 4, and the fractal parameters D and G are imported into Matlab for programming processing according to the coordinate point data dat file output by the scanner. Because the power spectral density function S (omega) and omega are in a linear relation on the log-log coordinate system, the slope of the linear line is related to D, and the intercept is related to G, the D and G can be obtained by a method of solving the slope and the intercept on the log-log coordinate system, and the maximum microprotrusion contact area a of the contact surface is calculatedLAnd ac1And ac2. Further, according to a calculation formula in the key technology, an equivalent homogeneous material constitutive model and a seam normal nonlinear model, such as the tangential nonlinear spring and the seam tangential nonlinear model shown in fig. 5, can be obtained, such as the seam tangential nonlinear model shown in fig. 6. The model parameters are now input into the finite element analysis software to implement the numerical method.
The numerical method realization of the novel joint model provided by the invention is explained by taking large-scale general finite element software ANSYS as an example.
(1) Multi-linear equivalent homogeneous material and thickness value thereof
In ANSYS, there are various nonlinear material models such as a bilinear follow-up enhancement model BKIN, a multilinear follow-up enhancement model MKIN and KINH, a nonlinear follow-up enhancement model CHAB, a bilinear isotropic enhancement model BISO, a multilinear isotropic enhancement model MISO, a nonlinear isotropic enhancement model NLISO and the like.
And simulating the equivalent homogeneous material by adopting a multi-linear follow-up strengthening model MKIN or KINH. The thickness of the equivalent homogeneous material layer may be determined according to the division size of the structural unit, and may be one unit wide, as shown in fig. 7. And inputting stress-strain data points according to the relation between the equivalent homogeneous material constitutive and the seam normal nonlinear model, and determining the multi-linear curve of the material.
(2) Tangential nonlinear spring model selection
In ANSYS, the Combin39 is a multi-linear spring model that allows up to 20 sets of force-deflection curve data points to be entered, and the material structure can be determined from the tangential nonlinear spring shear stiffness as shown in FIG. 8.
Therefore, a contact model combining a direct contact method, a virtual material method and a macro-micro view is established, normal and tangential stress nonlinearity and displacement discontinuity can be considered simultaneously by the contact model, and the contact model is a correction of a joint model and can be used for various numerical calculation applications.
The method combines a direct contact method, a virtual material method and macro-micro observation, can simultaneously consider normal and tangential stress nonlinearity and displacement discontinuity, and is the correction of a joint model.
The equivalent homogeneous material is normally used in the constitutive model, and the problem of setting the initial distance of the nodes on two sides of the joint contact surface in the application of the normal spring is solved. The seam tangent does not present this problem and therefore a non-linear spring is used tangentially.
The invention is convenient for numerical calculation application, and has high simulation degree, high universality and high precision of the calculation result.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (10)

1. A construction method of a novel joint model considering joint interface dynamic effect is characterized by comprising the following steps:
measuring fractal dimension and fractal dimension parameters of pipe piece concrete on two sides of the joint;
calculating the plastic critical contact area a of the microprotrusions on both sides of the seamc1、ac2And the maximum microprotrusion contact area a of the contact surfaceLAccording to the maximum microprotrusion contact area a of the contact surfaceLAnd ac1、ac2The working condition classification is carried out by a plurality of relative relations;
calculating normal contact stiffness and normal contact damping according to the working condition classification condition, and calculating the elastic modulus and the equivalent Poisson ratio of the equivalent homogeneous material to obtain an equivalent homogeneous material constitutive model and a seam normal nonlinear model;
and calculating the tangential contact stiffness and the tangential contact damping according to the working condition classification condition, and calculating the shearing stiffness of the tangential nonlinear spring to obtain the tangential nonlinear spring and a seam tangential nonlinear model.
2. The method of constructing a novel joint model considering dynamic effects of joint interfaces according to claim 1, wherein: calculating the plastic critical contact area a of the microprotrusions on both sides of the seamc1、ac2And the maximum microprotrusion contact area a of the contact surfaceLThe method specifically comprises the following steps:
the concrete of the pipe pieces on two sides of the joint has different surface roughness, wherein fractal dimensions are D1 and D2 respectively, and fractal scale parameters are G1 and G2 respectively;
plastic critical contact area a of micro-convex body on two sides of seamc1、ac2The method comprises the following steps:
Figure FDA0003355406190000011
Figure FDA0003355406190000012
wherein E is the modulus of elasticity, σyIs the yield stress of the steel, and,
Figure FDA0003355406190000013
mu is the friction coefficient of the contact surface material;
the expansion coefficients psi of the two contact surfaces are obtained by solving the following transcendental equation1、Ψ2：
Figure FDA0003355406190000014
Wherein Ψ is an expansion coefficient of the contact surface;
the two rough contact surfaces on both sides of the joint have the same maximum contact area aLThe following equation is used to obtain:
Figure FDA0003355406190000021
aL＝min(aL1,aL2)。
in the formula, Ar1、Ar2The actual contact areas of the two segments, respectively.
3. The method of constructing a novel joint model considering dynamic effects of joint interfaces according to claim 1, wherein: calculating normal contact stiffness according to the working condition classification conditions, and specifically comprising the following steps:
the contact rigidity value k of the micro-convex point is only in the part of the area where the elastic deformation occursn，
Figure FDA0003355406190000022
Wherein, PeIs the elastic contact pressure, δ is the contact deformation;
according to maximum contact surfaceMicroprotrusion contact area aLAnd ac1、ac2Three relative relations exist between the two groups to classify the working conditions;
when in the first operating mode, aL<ac1<ac2When the joint is in a plastic contact state, all the microprotrusions of the first rough surface on one side of the joint and the second rough surface on the other side of the joint are in plastic contact state, and the normal contact stiffness is 0;
when in the second operating mode, ac1<aL<ac2When the joint is in use, part of the first rough surface on one side of the joint is in an all-plastic state, and part of the first rough surface is in an elastic-plastic state;
integrating the normal contact stiffness of the single micro-convex point on a distribution function to obtain the total normal contact stiffness KnComprises the following steps:
Figure FDA0003355406190000023
when in the third operating mode, ac1<ac2<aLWhen the joint is in use, the first rough surface on one side of the joint and the second rough surface on the other side of the joint are in all-plastic state with partial micro-protrusions and elastic-plastic state, and the total normal contact rigidity KnComprises the following steps:
Figure FDA0003355406190000031
wherein E is the modulus of elasticity, #1、ψ2The expansion coefficients of the first rough surface and the second rough surface are obtained; d1 is the fractal dimension of the first matte and D2 is the fractal dimension of the second matte.
4. The method of constructing a novel joint model considering dynamic effects of joint interfaces according to claim 1, wherein: calculating normal contact damping according to the working condition classification condition, and specifically comprising the following steps:
the elastic strain energy stored by the microprotrusions in the elastic phase is:
Figure FDA0003355406190000032
whereas the strain energy in the plastic range is:
Figure FDA0003355406190000033
wherein E is the modulus of elasticity, σyIs the yield stress, R is the radius of curvature of the elastic microprotrusions, deltacIs the critical plastic contact deformation, deltaLIs the maximum contact deflection;
according to the maximum microprotrusion contact area a of the contact surfaceLAnd ac1、ac2Three relative relations exist between the two groups to classify the working conditions;
when in the first operating mode, aL<ac1<ac2During the process, all the microprotrusions of the first rough surface on one side of the joint and the second rough surface on the other side of the joint are in an all-plastic state, normal contact damping does not exist, and the plastic strain energy of the contact surface is as follows:
Figure FDA0003355406190000041
when in the second operating mode, ac1<aL<ac2During the process, the first rough surface on one side of the joint is provided with a part of micro-convex bodies in an all-plastic state, the other part of the first rough surface is in an elastic-plastic state, all the micro-convex bodies on the second rough surface on the other side of the joint are in the all-plastic state, and the corresponding elastic strain energy of the contact surface is as follows:
Figure FDA0003355406190000042
the plastic strain energy of the contact surface is:
Figure FDA0003355406190000043
the corresponding damping loss factor is then:
Figure FDA0003355406190000044
the dimensionless expression of the above equation is:
Figure FDA0003355406190000045
the normal contact damping of the contact surface is:
Figure FDA0003355406190000046
wherein M is the damping system mass, KnNormal contact stiffness;
when in the third operating mode, ac1<ac2<aLDuring the process, the first rough surface on one side of the joint and the second rough surface on the other side of the joint are all in a full plastic state by a part of micro-convex bodies, and the part of the micro-convex bodies is in an elastic plastic state, and the corresponding elastic strain energy of the contact surface is as follows:
Figure FDA0003355406190000051
the plastic strain energy of the contact surface is:
Figure FDA0003355406190000052
the corresponding damping loss factor is then:
Figure FDA0003355406190000053
the dimensionless expression of the above equation is:
Figure FDA0003355406190000054
the normal contact damping of the contact surface is:
Figure FDA0003355406190000055
wherein M is the damping system mass, KnIs the normal contact stiffness.
5. The method of constructing a novel joint model considering dynamic effects of joint interfaces according to claim 1, wherein: calculating the elastic modulus and the equivalent Poisson's ratio of the equivalent homogeneous material, specifically comprising:
the normal contact stiffness is basically equal to
Figure FDA0003355406190000056
Forming a positive linear relation; according to the geometrical relationship of the microprotrusions, the contact area aLAlso positively linear with the microprotrusion deformation delta, for simplicity of analysis, ignoring low order micro-scale, the joint pressure FnThe following power function relationship exists between the normal deformation Δ h of the seam:
Figure FDA0003355406190000061
Figure FDA0003355406190000062
at any stage, the work of the normal load in the equivalent material range satisfies the following relation:
Figure FDA0003355406190000063
wherein h is the thickness of the nonlinear equivalent material, FniIs the joint pressure of the i-th stage, KniIs the approximate normal stiffness of the i-th stage, AaIs the total area of the seam (m) corresponding to the unit loop width2/m), E is the modulus of elasticity;
the equivalent nonlinear material stores strain energy as:
Figure FDA0003355406190000064
wherein E isiFor the equivalent elastic modulus of the generalized gap, since the work done by the external load is equal to the strain energy stored by the equivalent material, then:
Figure FDA0003355406190000065
equivalently, shear modulus G of nonlinear materialiThe values are as follows:
Figure FDA0003355406190000066
wherein, KtiFor the sectional tangential stiffness of the contact surface, the equivalent Poisson ratio of the equivalent material at the i stage is obtained by the two formulas:
Figure FDA0003355406190000067
6. the method of constructing a novel joint model considering dynamic effects of joint interfaces according to claim 1, wherein: calculating the tangential contact stiffness according to the working condition classification condition, and specifically comprising the following steps:
the tangential stiffness is related to normal load P, tangential load T and contact area, and the tangential stiffness expression of a single micro-convex body in the elastic stage is as follows:
Figure FDA0003355406190000071
wherein,
Figure FDA0003355406190000072
is the shear modulus of the material, v is the poisson's ratio, and mu is the friction coefficient of the material;
according to the maximum microprotrusion contact area a of the contact surfaceLAnd ac1、ac2Three relative relations exist between the two groups to classify the working conditions;
when in the first operating mode, aL<ac1<ac2When the welding seam is used, all the microprotrusions of the first rough surface on one side of the welding seam and the second rough surface on the other side of the welding seam are in an all-plastic state, and the tangential contact rigidity is 0;
when in the second operating mode, ac1<aL<ac2During, the first rough surface of seam one side has some microprotrusions to be in the plastic state, has some to be in the plastic state, and all microprotrusions of the second rough surface of seam opposite side all are in the plastic state, and the tangential contact rigidity of segment seam both sides fractal is:
Figure FDA0003355406190000073
when in the third operating mode, ac1<ac2<aLDuring the time, the first rough surface of seam one side and the second rough surface of seam opposite side are that part microprotrusions are in the plastic state, and the part is in the elastoplastic state, and the tangential contact rigidity of segment seam both sides fractal is:
Figure FDA0003355406190000074
wherein,
Figure FDA0003355406190000075
is the shear modulus of the material, v is the Poisson's ratio, mu is the friction coefficient of the material, T is the tangential load, P is the normal load, psi1、ψ2D1 is the fractal dimension of the first rough surface, and D2 is the fractal dimension of the second rough surface.
7. The method of constructing a novel joint model considering dynamic effects of joint interfaces according to claim 1, wherein: calculating tangential contact damping according to the working condition classification condition, and specifically comprising the following steps:
under the action of tangential force, the tangential contact damping energy consumption of a single microprotrusion body in one vibration period is as follows:
Figure FDA0003355406190000081
wherein,
Figure FDA0003355406190000082
is the shear modulus of the material, mu is the friction system, t is fnShear force and normal force applied to the micro convex body;
assuming that the shear force and the normal force applied to each asperity are proportional to the size of the contact area, the above equation can be expressed as:
Figure FDA0003355406190000083
wherein A isrFor actual contact area, T and FnTotal tangential force and normal on the contact surface, respectivelyA directional force;
according to the maximum microprotrusion contact area a of the contact surfaceLAnd ac1、ac2Three relative relations exist between the two groups to classify the working conditions;
when in the first operating mode, aL<ac1<ac2During the process, all the microprotrusions of the first rough surface on one side of the joint and the second rough surface on the other side of the joint are in an all-plastic state, and the integral of tangential damping energy consumption on the area is as follows:
Figure FDA0003355406190000084
when in the second operating mode, ac1<aL<ac2During the process, the first rough surface on one side of the joint has part of the micro-protrusions in the all-plastic state, the other part of the first rough surface is in the elastic-plastic state, all the micro-protrusions on the second rough surface on the other side of the joint are in the all-plastic state, and the integral of the tangential damping energy consumption on the area can be expressed as:
Figure FDA0003355406190000091
when in the third operating mode, ac1<ac2<aLWhen the damping energy consumption is measured, the first rough surface on one side of the joint and the second rough surface on the other side of the joint are both partially convex bodies and partially in an elastic-plastic state, and the integral of the tangential damping energy consumption on the area can be expressed as:
Figure FDA0003355406190000092
wherein,
Figure FDA0003355406190000093
is the shear modulus of the material, mu is the friction system, ArFor actual contact area, T and FnRespectively on the contact surfaceTangential and normal forces,. psi1、ψ2The expansion coefficients of the first rough surface and the second rough surface are shown, D1 is the fractal dimension of the first rough surface, and D2 is the fractal dimension of the second rough surface;
the loss factor of the tangential contact damping is:
ηT＝Wd/(Wd-We)
and the damping form belongs to hysteresis damping, the tangential damping coefficient is as follows:
CT＝ηTKt，
wherein, KtIs the tangential contact stiffness.
8. The method of constructing a novel joint model considering dynamic effects of joint interfaces according to claim 1, wherein: calculating the shear stiffness of the tangential nonlinear spring, which specifically comprises the following steps:
(1-T/(μ P))1/3Performing Taylor series expansion, neglecting high-order trace, obtaining,
Figure FDA0003355406190000101
if the above equation does not take into account the influence of the normal contact pressure variation, i.e. P is taken as a constant value or as an initial contact pressure, then there is a linear relationship between the tangential stiffness and the shear force,
KT＝AT-BTT
will KTWritten shear force T and shear displacement deltaTThe above formula is converted into:
Figure FDA0003355406190000102
solving the first-order linear non-homogeneous differential equation to obtain T relative to deltaTThe general solution of the linear differential equation is:
Figure FDA0003355406190000103
it can be seen that shear is exponentially related to shear displacement, where AT、BTAs a seam characteristic parameter, CTThen a constant having a relationship to the initial state of the seam tangential static force; shear deformation delta due to the larger shear T in the usual caseTThe larger the size, the less difficult it is to obtain CTShould be a negative value, the asymptote height A of the exponential curve of the seam tangent multi-linear constitutive modelTThe physical meaning of (A) is the ultimate shear strength of the joint, AT+CTReflecting the shear strength of the seam prior to elastic slippage.
9. A numerical realization method of a novel joint model considering joint interface dynamic effect is characterized by comprising the following steps:
establishing an equivalent homogeneous material constitutive and seam normal nonlinear model and a tangential nonlinear spring and seam tangential nonlinear model by adopting the construction method of the novel seam model considering the dynamic effect of the seam interface as claimed in any one of claims 1 to 8;
for normal behavior: simulating an equivalent homogeneous material by adopting a multi-linear follow-up strengthening model, and determining the thickness of an equivalent homogeneous material layer and a multi-linear curve of the material according to the constitutive of the equivalent homogeneous material and a seam normal nonlinear model;
for tangential behavior: and determining a material constitutive model by adopting a multi-linear spring model according to the tangential nonlinear spring and the joint tangential nonlinear model.
10. A novel joint model considering joint interface dynamic effect is characterized in that: the model enables uneven characteristics of the microscopic appearance of a rough surface to be equivalent to dynamic physical parameters of flat and homogeneous multi-linear materials on two sides of a joint through rough surface dynamic contact stiffness and dynamic contact damping based on a fractal theory, the flat and homogeneous virtual materials are in direct contact in a normal direction, contact dynamic characteristics and displacement discontinuity of the joint are not changed, and elastic multi-linear springs are connected in a tangential direction to simulate stress tangential nonlinearity of the joint.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115438446A (en) * 2022-07-01 2022-12-06 上海交通大学 Interface tangential contact stiffness prediction method considering macro-micro topography characteristics

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN1997999A (en) * 2004-03-29 2007-07-11 彼德·T·杰尔曼 Systems and methods to determine elastic properties of materials
US20180128710A1 (en) * 2016-11-09 2018-05-10 Beijing University Of Technology Device and Method for measuring three-dimensional contact stiffness of spur gear based on rough surface
CN109960883A (en) * 2019-03-28 2019-07-02 北京工业大学 A kind of calculation method of joint surface contact stiffness containing inclination angle based on fractal theory
CN111177842A (en) * 2020-01-03 2020-05-19 中铁第四勘察设计院集团有限公司 Method and device for determining dynamic characteristics of shield tunnel segment contact surface and storage medium
CN111781134A (en) * 2020-07-09 2020-10-16 中国人民解放军国防科技大学 Measuring method and measuring system for normal contact parameter of joint surface
CN112364451A (en) * 2020-11-08 2021-02-12 太原科技大学 Modeling method for normal stiffness of rough surface considering elastic-plastic contact continuous monotony

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN1997999A (en) * 2004-03-29 2007-07-11 彼德·T·杰尔曼 Systems and methods to determine elastic properties of materials
US20180128710A1 (en) * 2016-11-09 2018-05-10 Beijing University Of Technology Device and Method for measuring three-dimensional contact stiffness of spur gear based on rough surface
CN109960883A (en) * 2019-03-28 2019-07-02 北京工业大学 A kind of calculation method of joint surface contact stiffness containing inclination angle based on fractal theory
CN111177842A (en) * 2020-01-03 2020-05-19 中铁第四勘察设计院集团有限公司 Method and device for determining dynamic characteristics of shield tunnel segment contact surface and storage medium
CN111781134A (en) * 2020-07-09 2020-10-16 中国人民解放军国防科技大学 Measuring method and measuring system for normal contact parameter of joint surface
CN112364451A (en) * 2020-11-08 2021-02-12 太原科技大学 Modeling method for normal stiffness of rough surface considering elastic-plastic contact continuous monotony

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
徐宁: "舰用燃气轮机非连续转子热致变形及振动特性研究", 《中国博士学位论文全文数据库 工程科技Ⅱ辑》, 15 January 2018 (2018-01-15), pages 036 - 3 *
潘五九;李小彭;李木岩;王雪;高建卓;闻邦椿;: "机械结合面切向接触刚度的三维分形理论建模", 振动工程学报, no. 04, 15 August 2017 (2017-08-15) *
肖明清;封坤;张力;何川: "盾构隧道管片接头抗弯承载力计算模型研究", 《土木工程学报》, 15 November 2019 (2019-11-15) *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115438446A (en) * 2022-07-01 2022-12-06 上海交通大学 Interface tangential contact stiffness prediction method considering macro-micro topography characteristics
CN115438446B (en) * 2022-07-01 2024-05-28 上海交通大学 Interface tangential contact stiffness prediction method considering macro-micro morphology features

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