Method and device for calculating frictional resistance of variable-axial-force two-way support

Abstract

The invention relates to a variable-axial-force bidirectional support frictional resistance calculation method which comprises the steps that a structure external load, a rigidity matrix, a mass matrix and support parameters are obtained, and the support parameters comprise support axial elastic rigidity and a support friction coefficient; according to the structure external load, the rigidity matrix and the mass matrix, establishing a t-moment structure deformation increment iterative formula; establishing a variable axial force bidirectional support internal force and tangent stiffness formula according to the support parameters; and substituting the internal force of the variable-axial-force bidirectional support and the tangent stiffness formula into a structural deformation increment iterative formula at the moment t, and calculating the frictional resistance of the variable-axial-force bidirectional support. According to the variable-axial-force two-way support friction resistance calculation method and device, a structural deformation increment iteration formula and a variable-axial-force two-way support internal force and tangent rigidity formula are constructed according to the mechanical characteristics of a friction support, then the variable-axial-force two-way support friction resistance is determined, the influence of support pressure changes on the support friction resistance is fully considered, and the friction resistance calculation accuracy is improved. And iterative calculation is simple and efficient.

Description

Technical Field

[0001] The invention relates to the technical field of structural nonlinear analysis, and in particular to a method and device for calculating the friction resistance of a variable axial force bidirectional support. Background Art

[0002] Bridge engineering structures often use spherical bearings, rubber bearings and other bearings to connect the main beam with the bridge substructure such as piers or bridge towers. When the bearing is compressed, the bearing will also move horizontally with the relative movement between the main beam and the bridge substructure, which will generate tangential friction in the longitudinal and transverse directions of the bridge. Under dynamic loads such as earthquakes, the bearing pressure changes significantly, and its tangential friction will also change, significantly affecting the deformation and internal force of the overall structure. Therefore, in order to improve the safety of the structure, it is very important to accurately calculate the bearing friction.

[0003] At present, the Wen plastic constitutive unit is often used to calculate the bearing friction. This constitutive unit introduces a hysteresis function to characterize the relationship between the friction and the bearing sliding velocity. Due to the introduction of many hysteresis function parameters, the complex hysteresis function causes slow convergence calculation, the stability of the calculation result will be affected by the integral time step, and the change of the maximum bearing friction caused by the change of the bearing pressure cannot be considered, resulting in inaccurate calculation of the bearing friction, and the bearing friction cannot change according to the change of the dynamic load. Summary of the invention

[0004] The technical problem to be solved by the present application is that the use of Wen-plastic units in the related art to calculate bearing friction leads to slow convergence calculation and inaccurate calculation.

[0005] The present application provides a method for calculating the friction resistance of a variable axial force bidirectional bearing, comprising the following steps:

[0006] Obtain the structural external load F, stiffness matrix K and mass matrix M, as well as support parameters, the support parameters include the support axial elastic stiffness K n , bearing friction coefficient μ;

[0007] Establishing an incremental iterative formula for structural deformation at time t according to the structural external load F, stiffness matrix K and mass matrix M;

[0008] According to the support parameters, the internal force F of the variable axial force bidirectional support is established. d and the tangent stiffness K t formula;

[0009] The variable axial force bidirectional support internal force F d and the tangent stiffness K t Substitute the formula into the incremental iterative formula of the structural deformation at time t to calculate the variable axial force bidirectional support friction resistance.

[0010] In one embodiment, the structure applied load F, stiffness matrix K and mass matrix M, and support parameters are obtained through a finite element model.

[0011] In one embodiment, the incremental iterative formula of the structural deformation at time t is:

[0012]

[0013] In the formula,

[0014] Where F is the external load on the structure, du, and are displacement, velocity and acceleration increments, respectively, is the support internal force function with respect to velocity The derivative of du ′ is the derivative of the support internal force function with respect to the displacement u, dF is the load residual, F t is the external load at time t, is the support internal force of the current iteration step, u i is the displacement of the current iteration step, is the current iteration speed, is the acceleration of the current iteration.

[0015] In one embodiment, the internal force F d Including the axial pressure of the support and the friction resistance of the support in the horizontal direction.

[0016] In one embodiment, the variable axial force bidirectional support internal force F d The formula is:

[0017]

[0018] In the formula,

[0019]

[0020]

[0021] In the formula, F n is the axial internal force of the support, F tx F is the friction resistance of the support in the horizontal x direction, ty is the friction resistance of the support in the horizontal y direction, u iz is the axial displacement of the support in the current iteration step, k is the support sliding velocity coefficient, Z 0x , Z 0y is the friction coefficient of the support in two directions at the previous moment, Z ix , Z iy is the friction coefficient of the support in two directions in the current iteration step, Δt is the time interval of dynamic analysis, is the horizontal x-direction velocity of the support at the current moment, is the horizontal x-direction velocity of the support at the previous moment, is the horizontal y-direction velocity of the support in the current iteration step, is the horizontal y-direction velocity of the support at the previous moment.

[0022] In one embodiment, the bearing sliding speed coefficient k≥10000.

[0023] In one embodiment, the variable axial force bidirectional support tangent stiffness K t The formula is:

[0024]

[0025] In the formula, when F n <0,

[0026]

[0027] When F n ≥0,

[0028]

[0029] In the formula, K tn is the axial tangential stiffness of the support, K txx K is the tangential stiffness of the support in the horizontal x direction, txy K is the tangential stiffness of the support in the x and y directions. tyy is the tangential stiffness of the support in the horizontal y direction.

[0030] In one embodiment, the variable axial force bidirectional support internal force F d and the tangent stiffness K t The formula is substituted into the incremental iteration formula of the structural deformation at time t in the form of array and matrix.

[0031] In one embodiment, when substituted in array and matrix form,

[0032] F du ′=K tn .

[0033] The present application also provides a variable axial force bidirectional bearing friction calculation device, which includes:

[0034] The parameter acquisition module is used to obtain the structure's external load F, stiffness matrix K and mass matrix M, as well as support parameters, including the support axial elastic stiffness K n , bearing friction coefficient μ;

[0035] The first formula establishment module is used to establish an incremental iterative formula for structural deformation at time t according to the structural external load F, the stiffness matrix K and the mass matrix M;

[0036] The second formula establishment module is used to establish the variable axial force bidirectional support internal force F according to the support parameters. d and the tangent stiffness K t formula;

[0037] A calculation module is used to convert the variable axial force bidirectional support internal force F d and the tangent stiffness K t Substitute the formula into the incremental iterative formula of the structural deformation at time t to calculate the variable axial force bidirectional support friction resistance.

[0038] The beneficial effects brought by the technical solution provided by the embodiments of the present application include:

[0039] The present application provides a method for calculating the friction resistance of a variable axial force bidirectional support. According to the mechanical characteristics of the friction support, an incremental iterative formula for structural deformation, an internal force and tangent stiffness formula for a variable axial force bidirectional support are constructed to further determine the friction resistance of the variable axial force bidirectional support. The influence of the change in support pressure on the support friction resistance is fully considered. The iterative calculation is simple and efficient, and the problems of slow convergence of Wen plastic unit calculation, the stability of the calculation results being affected by the integral time step, and the inaccurate calculation caused by the inability to consider the influence of the change in support pressure on the friction resistance are solved. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0041] Figure 1 The present invention is a flowchart of a method for calculating the friction resistance of a variable axial force bidirectional support in one embodiment of the present invention.

[0042] Figure 2 It is a block diagram of a variable axial force bidirectional support friction calculation device in one embodiment of the present invention.

[0043] Figure 3 It is a schematic diagram of the connection structure model of a single beam and a friction support in one embodiment of the present invention.

[0044] In the figure: 1. upper node of the first unit; 2. lower node of the first unit; 3. upper node of the second unit; 4. friction support unit (second unit). DETAILED DESCRIPTION

[0045] In order to enable those skilled in the art to better understand the solution of the present application, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0046] like Figure 1 As shown, Figure 1 The present invention is a flowchart of a method for calculating the friction resistance of a variable axial force bidirectional support in one embodiment of the present invention.

[0047] This embodiment provides a method for calculating the friction resistance of a variable axial force bidirectional support, comprising the following steps:

[0048] Step S1, obtain the structure external load F, stiffness matrix K and mass matrix M, and support parameters, the support parameters include the support axial elastic stiffness K n , bearing friction coefficient μ;

[0049] Step S2, establishing an incremental iterative formula for structural deformation at time t according to the structural external load F, the stiffness matrix K and the mass matrix M;

[0050] Step S3: Establish the variable axial force bidirectional bearing internal force F according to the bearing parameters d and the tangent stiffness K t formula;

[0051] Step S4: convert the variable axial force bidirectional support internal force F d and the tangent stiffness K t Substitute the formula into the incremental iteration formula of the structural deformation at time t to calculate the friction resistance of the bidirectional support with variable axial force.

[0052] The present embodiment provides a method for calculating the friction resistance of a variable axial force bidirectional support. According to the mechanical characteristics of the friction support, an incremental iterative formula for structural deformation, an internal force and tangent stiffness formula for the variable axial force bidirectional support are constructed to further determine the friction resistance of the variable axial force bidirectional support. The influence of the support pressure change on the support friction resistance is fully considered. The iterative calculation is simple and efficient, and the problems of slow convergence of Wen plastic unit calculation, the stability of the calculation result being affected by the integral time step, and the inaccurate calculation caused by the inability to consider the influence of the support pressure change on the friction resistance are solved.

[0053] Each step is described and explained in detail below.

[0054] In one embodiment, in step S1 , the structure applied load F, the stiffness matrix K and the mass matrix M, and the support parameters are obtained through a finite element model.

[0055] Of course, in addition to the above parameters, the external load F at the current time t can also be obtained through the finite element model t , obtain the displacement, velocity and acceleration of the structure at the previous moment, and the friction coefficient Z in both directions of the horizontal plane of the support at the previous moment 0x and Z 0y .

[0056] In one embodiment, the incremental iterative formula of the structural deformation at time t in step S2 is:

[0057]

[0058] In the formula,

[0059] Where F is the external load on the structure, du, and are displacement, velocity and acceleration increments, respectively, is the support internal force function with respect to velocity The derivative of du ′ is the derivative of the support internal force function with respect to the displacement u, i.e., the tangent stiffness, dF is the load residual, F t is the external load at time t, is the support internal force of the current iteration step, u i is the displacement of the current iteration step, is the current iteration speed, is the acceleration of the current iteration step. The initial values ​​of displacement, velocity and acceleration at time 0 are all zero.

[0060] Specifically, the incremental iterative formula of the structural deformation at time t is based on the mechanical characteristics of the friction support and is obtained through the dynamic formula get.

[0061] Where u, and are displacement, velocity and acceleration, is the internal force of the variable axial force bidirectional friction support, which is the displacement u and velocity function.

[0062] In one embodiment, the internal force F in step S3 d It includes the axial pressure of the bearing and the frictional resistance of the bearing in the horizontal direction. The frictional resistance of the friction bearing will only be generated when the friction bearing is under axial pressure.

[0063] In one embodiment, the variable axial force bidirectional support internal force F d The formula is:

[0064]

[0065] In the formula,

[0066]

[0067]

[0068] In the formula, F n is the axial internal force of the support, F tx F is the friction resistance of the support in the horizontal x direction, ty is the friction resistance of the support in the horizontal y direction, u iz is the axial displacement of the support in the current iteration step, k is the support sliding velocity coefficient, Z 0x , Z 0y is the friction coefficient of the support in two directions at the previous moment, Z ix , Z iy is the friction coefficient of the support in two directions in the current iteration step, Δt is the time interval of dynamic analysis, is the horizontal x-direction velocity of the support at the current moment, is the horizontal x-direction velocity of the support at the previous moment, is the horizontal y-direction velocity of the support in the current iteration step, is the horizontal y-direction velocity of the support at the previous moment.

[0069] In one embodiment, the bearing sliding speed coefficient k≥10000, preferably 10000.

[0070] In one embodiment, the tangential stiffness K of the variable axial force bidirectional support t The formula is:

[0071]

[0072] In the formula, when F n <0,

[0073]

[0074] When F n ≥0,

[0075]

[0076] In the formula, K tn is the axial tangential stiffness of the support, K txx K is the tangential stiffness of the support in the horizontal x direction, txy K is the tangential stiffness of the support in the x and y directions. tyy is the tangential stiffness of the support in the horizontal y direction.

[0077] Through the above scheme, the variable axial force bidirectional support internal force F is constructed. d and the tangent stiffness K tThe formula has a simple form, fewer input parameters and clear physical meaning. The structural displacement and velocity are input to determine the support internal force and support tangent stiffness, which solves the drawback of related technologies that use Wen shaping units for calculation.

[0078] In one embodiment, in step S4, the internal force F of the variable axial force bidirectional support d and the tangent stiffness K t The formula is substituted into the incremental iteration formula of structural deformation at time t in the form of array and matrix.

[0079] In one embodiment, when substituted in array and matrix form,

[0080] F du ′=K tn .

[0081] like Figure 2 As shown, Figure 2 It is a block diagram of a variable axial force bidirectional support friction calculation device in one embodiment of the present invention.

[0082] The present application also provides a variable axial force bidirectional bearing friction calculation device, which includes:

[0083] The parameter acquisition module is used to obtain the structure's external load F, stiffness matrix K and mass matrix M, as well as support parameters. The support parameters include the support axial elastic stiffness K n , bearing friction coefficient μ;

[0084] The first formula establishment module is used to establish the incremental iterative formula of the structural deformation at time t according to the structural external load F, the stiffness matrix K and the mass matrix M;

[0085] The second formula establishment module is used to establish the variable axial force bidirectional support internal force F according to the support parameters d and the tangent stiffness K t formula;

[0086] The calculation module is used to convert the internal force F of the variable axial force bidirectional support d and the tangent stiffness K t Substitute the formula into the incremental iteration formula of the structural deformation at time t to calculate the friction resistance of the bidirectional support with variable axial force.

[0087] The functions of each module correspond to the steps of the aforementioned method and will not be repeated here.

[0088] A specific embodiment is provided below for illustration.

[0089] like Figure 3 As shown, Figure 3 It is a schematic diagram of the connection structure model of a single beam and a friction support in one embodiment of the present invention.

[0090] The structure connected by a single beam and a friction support is taken as the analysis object. The structural model contains a single degree of freedom unit and a friction support unit. 1, 2, and 3 represent the upper node of the first unit, the lower node of the first unit, and the lower node of the second unit, respectively. 4 represents the friction support unit (the second unit).

[0091] This embodiment provides a method for calculating the friction resistance of a variable axial force bidirectional support, comprising the following steps:

[0092] Step S1, obtain the structure external load F, stiffness matrix K and mass matrix M, and support parameters, the support parameters include the support axial elastic stiffness K n , bearing friction coefficient μ.

[0093] The finite element model of the connection structure of a single beam and a friction support is established to obtain the stiffness matrix K and mass matrix M of the single beam structure. At the current moment, an external load of 100 kN is applied to the three translation directions of the structure. The external load array is F t , and the speed at the previous moment is 0, the friction coefficient Z of the support in both directions on the horizontal plane at the previous moment 0x and Z 0y Is 0. The axial elastic stiffness K of the friction bearing n It is 100000 kN / m, the friction coefficient μ is 0.03, and Δt is 0.02.

[0094] Single beam structural stiffness matrix

[0095] Mass Matrix

[0096] External load array

[0097] Step S2: establishing an incremental iterative formula for structural deformation at time t according to the structural external load F, the stiffness matrix K and the mass matrix M.

[0098]

[0099] In the formula,

[0100] Where F is the external load on the structure, du, and are displacement, velocity and acceleration increments, respectively, is the support internal force function with respect to velocity The derivative of du ′ is the derivative of the support internal force function with respect to the displacement u, i.e., the tangent stiffness, dF is the load residual, F t is the external load at time t, is the support internal force of the current iteration step, ui is the displacement of the current iteration step, is the current iteration speed, is the acceleration of the current iteration step. The initial values ​​of displacement, velocity and acceleration at time 0 are all zero, that is, u i =0,

[0101] Step S3: Establish the variable axial force bidirectional bearing internal force F according to the bearing parameters d and the tangent stiffness K t formula.

[0102] Internal force F of bidirectional support with variable axial force n The formula is:

[0103]

[0104] In the formula,

[0105]

[0106]

[0107] In the formula, F n is the axial internal force of the support, F tx F is the friction resistance of the support in the horizontal x direction, ty is the friction resistance of the support in the horizontal y direction, u iz is the axial displacement of the support in the current iteration step, k is the support sliding velocity coefficient, which is 10000, Z 0x , Z 0y is the friction coefficient of the support in two directions at the previous moment, Z ix , Z iy is the friction coefficient of the support in two directions in the current iteration step, Δt is the time interval of dynamic analysis, is the horizontal x-direction velocity of the support at the current moment, is the horizontal x-direction velocity of the support at the previous moment, is the horizontal y-direction velocity of the support in the current iteration step, is the horizontal y-direction velocity of the support at the previous moment.

[0108] Tangential stiffness K of bidirectional support with variable axial force t The formula is:

[0109]

[0110] In the formula, when F n <0,

[0111]

[0112] When F n ≥0,

[0113]

[0114] In the formula, K tn is the axial tangential stiffness of the support, K txx K is the tangential stiffness of the support in the horizontal x direction, txy K is the tangential stiffness of the support in the x and y directions. tyy is the tangential stiffness of the support in the horizontal y direction.

[0115] Step S4: convert the variable axial force bidirectional support internal force F d and the tangent stiffness K t The formula is substituted into the incremental iteration formula of the structural deformation at time t in the form of array and matrix to calculate the friction resistance of the bidirectional support with variable axial force.

[0116]

[0117]

[0118] In the description of the present application, it should be noted that the terms "upper", "lower", etc. indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present application and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present application. Unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be an indirect connection through an intermediate medium, or it can be a connection between the two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present application can be understood according to the specific circumstances.

[0119] It should be noted that, in this application, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the presence of other identical elements in the process, method, article or device including the elements.

[0120] In the description of the embodiments of the present application, unless otherwise specified, “ / ” means or, for example, A / B can mean A or B; the “and / or” in the text is merely a description of the association relationship of associated objects, indicating that three relationships may exist, for example, A and / or B can mean: A exists alone, A and B exist at the same time, and B exists alone. In addition, in the description of the embodiments of the present application, “multiple” refers to two or more than two.

[0121] The above is only a specific implementation of the present application, so that those skilled in the art can understand or implement the present application. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest range consistent with the principles and novel features applied for herein.

Claims

1. A method for calculating the friction resistance of a bidirectional bearing with variable axial force, characterized in that: The following steps are involved: Obtain the structural external load F, stiffness matrix K and mass matrix M, as well as support parameters, the support parameters include the support axial elastic stiffness K n , bearing friction coefficient μ; An incremental iterative formula for structural deformation at time t is established according to the structural external load F, stiffness matrix K and mass matrix M; According to the support parameters, the internal force F of the variable axial force bidirectional support is established. d and the tangent stiffness K t formula; The variable axial force bidirectional support internal force F d and the tangent stiffness K t Substitute the formula into the incremental iterative formula of the structural deformation at time t to calculate the variable axial force bidirectional support friction resistance.

2. The method for calculating the friction resistance of a bidirectional bearing with variable axial force according to claim 1, characterized in that: The structure's external load F, stiffness matrix K and mass matrix M, as well as support parameters are obtained through a finite element model.

3. The method for calculating the friction resistance of a bidirectional bearing with variable axial force according to claim 1, characterized in that: The incremental iteration formula of the structural deformation at time t is: In the formula, Where F is the external load on the structure, du, and are displacement, velocity and acceleration increments, respectively, is the support internal force function with respect to velocity The derivative of du ′ is the derivative of the support internal force function with respect to the displacement u, dF is the load residual, F t is the external load at time t, is the support internal force of the current iteration step, u i is the displacement of the current iteration step, is the current iteration speed, is the acceleration of the current iteration.

4. The method for calculating the friction resistance of a bidirectional bearing with variable axial force according to claim 1, characterized in that: The internal force F d Including the axial pressure of the support and the friction resistance of the support in the horizontal direction.

5. The method for calculating the friction resistance of a bidirectional bearing with variable axial force according to claim 3, characterized in that: The variable axial force bidirectional support internal force F d The formula is: In the formula, In the formula, F n is the axial internal force of the support, F tx F is the friction resistance of the support in the horizontal x direction, ty is the friction resistance of the support in the horizontal y direction, u iz is the axial displacement of the support in the current iteration step, k is the support sliding velocity coefficient, Z 0x , Z 0y is the friction coefficient of the support in two directions at the previous moment, Z ix , Z iy is the friction coefficient of the support in two directions in the current iteration step, Δt is the time interval of dynamic analysis, is the horizontal x-direction velocity of the support at the current moment, is the horizontal x-direction velocity of the support at the previous moment, is the horizontal y-direction velocity of the support in the current iteration step, is the horizontal y-direction velocity of the support at the previous moment.

6. The method for calculating the friction resistance of a bidirectional bearing with variable axial force according to claim 5, characterized in that: The bearing sliding speed coefficient k is ≥10000.

7. The method for calculating the friction resistance of a bidirectional bearing with variable axial force according to claim 5, characterized in that: The variable axial force bidirectional support tangent stiffness K t The formula is: In the formula, when F n <0, When F n ≥0, In the formula, K tn is the axial tangential stiffness of the support, K txx K is the tangential stiffness of the support in the horizontal x direction, txy K is the tangential stiffness of the support in the x and y directions. tyy is the tangential stiffness of the support in the horizontal y direction.

8. The method for calculating the friction resistance of a bidirectional bearing with variable axial force according to claim 7 is characterized in that: The variable axial force bidirectional support internal force F d and the tangent stiffness K t The formula is substituted into the incremental iteration formula of the structural deformation at time t in the form of array and matrix.

9. The method for calculating the friction resistance of a bidirectional bearing with variable axial force according to claim 8, characterized in that: When substituting in array and matrix form, F du ′=K tn .

10. A variable axial force bidirectional bearing friction calculation device, characterized in that: It includes: The parameter acquisition module is used to obtain the structure's external load F, stiffness matrix K and mass matrix M, as well as support parameters, including the support axial elastic stiffness K n , bearing friction coefficient μ; The first formula establishment module is used to establish an incremental iterative formula for structural deformation at time t according to the structural external load F, the stiffness matrix K and the mass matrix M; The second formula establishment module is used to establish the variable axial force bidirectional support internal force F according to the support parameters. d and the tangent stiffness K t formula; A calculation module is used to convert the variable axial force bidirectional support internal force F d and the tangent stiffness K t Substitute the formula into the incremental iterative formula of the structural deformation at time t to calculate the variable axial force bidirectional support friction resistance.

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