A method and device for calculating internal forces of shear pin sliding friction pendulum bearings

Abstract

The present application relates to a method for calculating the internal forces of a shear pin type sliding friction pendulum bearing, comprising: obtaining the external load of the structure, the stiffness matrix and the mass matrix, the shear pin state value and the parameters of the shear pin type sliding friction pendulum bearing; establishing an incremental iterative formula for the structural displacement at time t; determining the calculation formula for the internal forces and tangential stiffness of the shear pin type sliding friction pendulum bearing according to the shear pin state value; substituting the calculation formula for the internal forces and tangential stiffness of the shear pin type sliding friction pendulum bearing into the incremental iterative formula for the structural displacement at time t, and performing iterative calculations until the converged internal forces of the shear pin type sliding friction pendulum bearing are calculated; determining whether to update the shear pin state value, and determining the internal forces of the shear pin sliding friction pendulum bearing at that moment. The present application provides a method and device for calculating the internal forces of a shear pin type sliding friction pendulum bearing, determining the internal forces and tangential stiffness of the bearing according to the shear pin failure state, simulating the limiting effect of the shear pin on the bearing when it is not damaged, and the energy dissipation and shock absorption effect of the sliding friction pendulum after the shear pin is damaged.

Description

Technical Field

[0001] The present invention relates to the technical field of structural nonlinear analysis, and in particular to a method and device for calculating the internal force of a shear pin type sliding friction pendulum support. Background Art

[0002] The shear pin type sliding friction pendulum bearing is a unique seismic isolation bearing designed for bridge engineering according to engineering needs. By setting shear pins on the sliding friction pendulum bearing, the shear pins limit the bearing during small earthquakes, and the shear pins are sheared and destroyed during large earthquakes, thereby exerting the shock absorption and energy dissipation function of the sliding friction pendulum bearing.

[0003] Currently, relevant finite element software often uses the Wen plastic constitutive element to simulate all sliding friction pendulum bearings, but cannot accurately simulate shear pin sliding friction pendulum bearings. This is because the Wen plastic constitutive element cannot simulate the limiting effect of the shear pin during small earthquakes, nor can it simulate the sudden change from bearing limiting to energy dissipation and vibration reduction of the sliding friction pendulum after shear pin failure, which in turn affects the dynamic results. Summary of the Invention

[0004] The technical problem to be solved by this application is that the Wen plastic constitutive unit used in the related art to calculate the support cannot simulate the limiting effect of the shear pin of the shear pin type sliding friction pendulum support during a small earthquake and the sudden change from the support limiting to the sliding friction pendulum energy dissipation and shock absorption after the shear pin is damaged.

[0005] The present application provides a method for calculating the internal forces of a shear pin type sliding friction pendulum bearing, comprising the following steps:

[0006] Step S1, obtaining the structural external load F, the stiffness matrix K and the mass matrix M, the shear pin state value, and the shear pin sliding friction pendulum bearing parameters;

[0007] Step S2, establishing an iterative formula for the structural displacement increment at time t;

[0008] Step S3: Determine the internal force F of the shear pin type sliding friction pendulum support according to the shear pin state value. d (t) and tangential stiffness K t The calculation formula of

[0009] Step S4: Substitute the calculation formula of the internal force and tangential stiffness of the shear pin type sliding friction pendulum bearing into the iterative formula of the structural displacement increment at time t, and perform iterative calculation until the convergent internal force F of the shear pin type sliding friction pendulum bearing is calculated. d (t);

[0010] Step S5: Based on the converged shear pin sliding friction pendulum support internal force F d(t) and its corresponding shear pin state value to determine whether to update the shear pin state value, and determine the internal force F of the shear pin sliding friction pendulum support at this moment. d (t).

[0011] In one embodiment, the structural external load F, stiffness matrix K and mass matrix M, shear pin state values, and shear pin type sliding friction pendulum bearing parameters are obtained through a finite element model.

[0012] In one embodiment, the incremental iterative formula for the structural displacement at time t is:

[0013]

[0014] in:

[0015]

[0016] In the formula is the equivalent stiffness, is the equivalent external load at time t, F d (t) is the internal force of the shear pin sliding friction pendulum support at time t, K t is the tangential stiffness of the shear pin sliding friction pendulum support, dx(t) is the displacement increment, x i is the structural displacement of the current iteration step, x(t-Δt), are the displacement, velocity and acceleration of the shear pin sliding friction pendulum support at the previous moment, and Δt is the time interval of step-by-step time analysis.

[0017] In one embodiment, the iterative formula for the structural displacement increment at time t is given by the dynamic formula And Newmark method is established to obtain, where x, and are displacement, velocity, and acceleration respectively.

[0018] In one embodiment, the internal force F of the shear pin type sliding friction pendulum support is determined according to the state value of the shear pin. d (t) and tangential stiffness K t The calculation formula includes:

[0019] The shear pin state value is 0, which means the shear pin is not damaged. At time t, the internal force F of the shear pin sliding friction pendulum support is d (t) and tangential stiffness K t The calculation formula is:

[0020]

[0021] Among them, x i is the structural displacement of the current iteration step, Kq is the elastic stiffness of the shear pin.

[0022] In one embodiment, the internal force F of the shear pin type sliding friction pendulum support is determined according to the state value of the shear pin. d (t) and tangential stiffness K t The calculation formula includes:

[0023] The shear pin state value is 1, which means the shear pin is damaged. At time t, the internal force F of the shear pin sliding friction pendulum support is d (t) and tangential stiffness K t The calculation formula is:

[0024] F d (t) = f1 + f2

[0025]

[0026] Where,

[0027] Where f1 is the restoring force of the shear pin sliding friction pendulum bearing, P is the axial pressure of the shear pin sliding friction pendulum bearing, and x i is the displacement of the structure in the current iteration step, R is the curvature radius of the shear pin sliding friction pendulum bearing, f2 is the friction resistance of the shear pin sliding friction pendulum bearing, μ is the friction coefficient, k is the sliding velocity coefficient of the shear pin sliding friction pendulum bearing, z t-Δt is the friction coefficient of the shear pin sliding friction pendulum support at the previous moment, and x(t-Δt) is the displacement of the shear pin sliding friction pendulum support at the previous moment.

[0028] In one embodiment, the calculation formula of the internal force and tangential stiffness of the shear pin sliding friction pendulum support is substituted into the structural displacement increment iterative formula at time t, and iterative calculation is performed until a convergent shear pin sliding friction pendulum support internal force F is calculated. d (t) include:

[0029] Substituting the calculation formula of the internal force and tangential stiffness of the shear pin sliding friction pendulum support into the incremental iterative formula of the structural displacement at time t;

[0030] Calculate dF for each iteration t , determine dF t Relationship with the iterative convergence limit eps;

[0031] If |dF t |≤eps, the iteration converges, and the output is the structural displacement x of the current iteration step i As the iterative displacement, F of the current iteration step d (t) As the convergent shear pin sliding friction pendulum internal force F d(t), enter step S5;

[0032] If |dF t | > eps, update the iterative displacement, i.e., x i = x i + dx(t), and repeat steps S3 to S4.

[0033] In one embodiment, determining whether to update the shear pin state value according to the converged internal force F d (t) of the shear pin type sliding friction pendulum bearing and its corresponding shear pin state value, and determining the internal force F d (t) of the shear pin sliding friction pendulum bearing at this moment includes:

[0034] When the shear pin state value corresponding to the converged internal force F d (t) of the shear pin type sliding friction pendulum bearing is 1, do not update the shear pin state value;

[0035] Output the converged internal force F d (t) of the shear pin type sliding friction pendulum bearing as the internal force F d (t) of the shear pin type sliding friction pendulum bearing at this moment.

[0036] In one embodiment, determining whether to update the shear pin state value according to the converged internal force F d (t) of the shear pin type sliding friction pendulum bearing and its corresponding shear pin state value, and determining the internal force F d (t) of the shear pin sliding friction pendulum bearing at this moment includes:

[0037] When the shear pin state value corresponding to the converged internal force F d (t) of the shear pin type sliding friction pendulum bearing is 0, determine the magnitude relationship between the converged internal force F d (t) of the shear pin type sliding friction pendulum bearing and the shear pin yield strength Q;

[0038] |F d (t)| < Q, then do not update the shear pin state value, and output the converged internal force F d (t) of the shear pin type sliding friction pendulum bearing as the internal force F d (t) of the shear pin type sliding friction pendulum bearing at this moment;

[0039] |F d (t)| ≥ Q, then update the shear pin state value to 1, the iterative displacement x i = 0, and repeat steps S3 to S4.

[0040] The embodiment of the present application further provides a device for calculating the internal force of a shear pin type sliding friction pendulum bearing, which includes:

[0041] A parameter acquisition module is used to obtain the external load F, stiffness matrix K and mass matrix M of the structure, the state value of the shear pin, and the parameters of the shear pin sliding friction pendulum support;

[0042] The first formula establishment module is used to establish an incremental iterative formula for structural displacement at time t;

[0043] The second formula building module is used to determine the internal force F of the shear pin sliding friction pendulum support according to the shear pin state value. d (t) and tangential stiffness K t The calculation formula of

[0044] The first calculation module is used to substitute the calculation formula of the internal force and tangential stiffness of the shear pin sliding friction pendulum bearing into the structural displacement increment iterative formula at time t, and perform iterative calculation until the converged shear pin sliding friction pendulum bearing internal force F is calculated. d (t);

[0045] The second calculation module is used to calculate the internal force F of the shear pin sliding friction pendulum support according to the convergence d (t) and its corresponding shear pin state value to determine whether to update the shear pin state value, and determine the internal force F of the shear pin sliding friction pendulum support at this moment. d (t).

[0046] The beneficial effects of the technical solutions provided in the embodiments of the present application include:

[0047] This application provides a method for calculating the internal forces of a shear pin-type sliding friction pendulum bearing. The method uses the shear pin's state value to determine the shear pin's failure state in real time, thereby obtaining the internal forces and tangential stiffness of the shear pin-type sliding friction pendulum bearing at each moment based on its failure state. This application determines the bearing internal forces and tangential stiffness based on the shear pin's failure state in real time, simulating the shear pin's limiting effect on the bearing when it is intact, as well as the energy dissipation and shock absorption effect of the sliding friction pendulum after the shear pin is damaged. This method addresses the problem that related technologies using Wen plastic units are unable to simulate the shear pin's limiting effect during small earthquakes, nor can they simulate the sudden change from bearing limiting to energy dissipation and shock absorption of the sliding friction pendulum after the shear pin is damaged. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following briefly introduces the drawings required for use in the description of the embodiments. 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 any creative work.

[0049] Figure 1Flowchart of a method for calculating the internal forces of a shear pin type sliding friction pendulum support according to one embodiment of the present invention.

[0050] Figure 2 1 is a block diagram of an internal force calculation device for a shear pin type sliding friction pendulum support according to an embodiment of the present invention.

[0051] Figure 3 Schematic diagram of a shear pin sliding friction pendulum support model with a single degree of freedom structure in one embodiment of the present invention.

[0052] In the figure: 1. Upper node of single degree of freedom unit; 2. Lower node of single degree of freedom unit; 3. Lower node of shear pin sliding friction pendulum support unit; 4. Shear pin component; 5. Sliding surface of friction pendulum. DETAILED DESCRIPTION

[0053] In order to enable those skilled in the art to better understand the present invention, the following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0054] like Figure 1 As shown, Figure 1 Flowchart of a method for calculating the internal forces of a shear pin type sliding friction pendulum support according to one embodiment of the present invention.

[0055] This embodiment provides a method for calculating the internal forces of a shear pin type sliding friction pendulum bearing, comprising the following steps:

[0056] Step S1, obtaining the structural external load F, the stiffness matrix K and the mass matrix M, the shear pin state value, and the shear pin sliding friction pendulum bearing parameters;

[0057] Step S2, establishing an iterative formula for the structural displacement increment at time t;

[0058] Step S3: Determine the internal force F of the shear pin sliding friction pendulum support according to the shear pin state value. d (t) and tangential stiffness K t The calculation formula of

[0059] Step S4: Substitute the calculation formula of the internal force and tangential stiffness of the shear pin sliding friction pendulum bearing into the structural displacement increment iterative formula at time t, and perform iterative calculation until the convergent shear pin sliding friction pendulum bearing internal force F is calculated. d (t);

[0060] Step S5: Based on the converged shear pin sliding friction pendulum bearing internal force F d(t) and its corresponding shear pin state value to determine whether to update the shear pin state value, and determine the internal force F of the shear pin sliding friction pendulum support at that moment d (t).

[0061] This embodiment provides a method for calculating the internal forces of a shear pin-type sliding friction pendulum bearing. This method uses the shear pin's state value to determine the shear pin's failure state in real time, thereby obtaining the internal forces and tangential stiffness of the shear pin-type sliding friction pendulum bearing at each moment based on its failure state. This embodiment determines the bearing internal forces and tangential stiffness based on the shear pin's failure state in real time. This method can simulate the shear pin's limiting effect on the bearing when it is intact, as well as the energy dissipation and vibration reduction effect of the sliding friction pendulum after the shear pin has failed. This method addresses the problem that related technologies using Wen plastic units are unable to simulate the shear pin's limiting effect during small earthquakes, nor can it simulate the sudden change from bearing limiting to energy dissipation and vibration reduction of the sliding friction pendulum after the shear pin has failed.

[0062] Each step is described and explained in detail below.

[0063] In one embodiment, in step S1, the structural external load F, the stiffness matrix K and the mass matrix M, the shear pin state value, and the shear pin type sliding friction pendulum bearing parameters are obtained through a finite element model.

[0064] 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 x(t-Δt) and velocity of the structure at the previous moment and acceleration The friction coefficient z of the shear pin sliding friction pendulum support at the previous moment t-Δt , the state value of the shear pin at the previous moment state.

[0065] The parameters of the shear pin sliding friction pendulum bearing include the friction coefficient μ, the bearing axial pressure P, the friction pendulum bearing curvature radius R, the shear pin elastic stiffness K q , shear pin yield strength Q, set the iteration convergence limit eps.

[0066] In one embodiment, in step S2, the iterative formula for the structural displacement increment at time t is:

[0067]

[0068] in:

[0069]

[0070] In the formula is the equivalent stiffness, is the equivalent external load at time t, F d (t) is the internal force of the shear pin sliding friction pendulum support at time t, Kt is the tangential stiffness of the shear pin sliding friction pendulum support, dx(t) is the displacement increment, x i is the structural displacement of the current iteration step, x(t-Δt), are the displacement, velocity and acceleration of the shear pin sliding friction pendulum support at the previous moment, and Δt is the time interval of step-by-step time analysis.

[0071] In one embodiment, the iterative formula for the structural displacement increment at time t is given by the dynamic formula And the Newmark method is established to obtain x, and are displacement, velocity, and acceleration respectively.

[0072] The Newmark method is a numerical technique for solving structural dynamics. This method discretizes the motion equations of the structure into a set of ordinary differential equations and uses a step-by-step integration scheme to numerically solve them. It is suitable for simulating the dynamic behavior of structures under various load conditions. The Newmark method can handle nonlinear and damping effects and is suitable for the analysis of complex structural systems. The Newmark method is widely used in structural dynamics and is particularly suitable for solving the motion equations of structures subjected to earthquakes or transient loads. Its characteristics include unconditional stability and high numerical efficiency, which can accurately and effectively simulate the dynamic behavior of structures. The Newmark method has a wide range of application examples in different fields. For example, in earthquake engineering, the Newmark method is used to analyze the stability of structures; in bridge engineering, it is used to analyze the dynamic response of bridges; and in impact problems, it is used to solve the dynamic response of structures. This method belongs to the prior art and will not be described in detail here.

[0073] In one embodiment, step S3, determining the internal force F of the shear pin type sliding friction pendulum support according to the shear pin state value d (t) and tangential stiffness K t The calculation formula includes:

[0074] Step S31: If the shear pin state value is 0, the shear pin is not damaged. At time t, the internal force F of the shear pin sliding friction pendulum support is d (t) and tangential stiffness K t The calculation formula is:

[0075]

[0076] Among them, x i is the structural displacement of the current iteration step, K q is the elastic stiffness of the shear pin.

[0077] In one embodiment, step S3, determining the internal force F of the shear pin type sliding friction pendulum support according to the shear pin state value d (t) and tangential stiffness Kt The calculation formula includes:

[0078] Step S32: If the shear pin state value is 1, the shear pin is damaged. At time t, the internal force F of the shear pin sliding friction pendulum support is d (t) and tangential stiffness K t The calculation formula is:

[0079] F d (t) = f1 + f2

[0080]

[0081] Where,

[0082] Where f1 is the restoring force of the shear pin sliding friction pendulum bearing, P is the axial pressure of the shear pin sliding friction pendulum bearing, when the bearing axial direction is tensile, P is taken to be zero, x i is the displacement of the structure in the current iteration step, R is the curvature radius of the shear pin sliding friction pendulum bearing, f2 is the friction resistance of the shear pin sliding friction pendulum bearing, μ is the friction coefficient, k is the sliding velocity coefficient of the shear pin sliding friction pendulum bearing, z t-Δt is the friction coefficient of the shear pin sliding friction pendulum support at the previous moment, and x(t-Δt) is the displacement of the shear pin sliding friction pendulum support at the previous moment.

[0083] Through this scheme, the shear pin state value is set as an intermediate judgment value based on the mechanical properties of the shear pin sliding friction pendulum bearing. This allows the calculation of internal forces and tangential stiffness based on the mechanical properties of the shear pin. The constructed formulas for calculating the internal forces and tangential stiffness of the shear pin sliding friction pendulum bearing are simple, require few parameters, and enable efficient and simple iterative calculations.

[0084] In one embodiment, step S4, the calculation formula of the internal force and tangential stiffness of the shear pin type sliding friction pendulum bearing is substituted into the structural displacement increment iterative formula at time t, and iterative calculation is performed until the convergent shear pin type sliding friction pendulum bearing internal force F is calculated. d (t) include:

[0085] Step S41, substituting the calculation formula of the internal force and tangential stiffness of the shear pin sliding friction pendulum support into the incremental iterative formula of the structural displacement at time t;

[0086] Step S42: Calculate dF for each iteration t , determine dF t Relationship with the iterative convergence limit eps;

[0087] Step S43: If |dF t |≤eps, the iteration converges and the structural displacement x of the current iteration step is output. iAs the iterative displacement and the F at the current iteration step d (t) as the internal force F of the converged shear pin type sliding friction pendulum d (t), enter step S5;

[0088] Step S44: If |dF t | > eps, update the iterative displacement, that is, x i = x i + dx(t), and repeat steps S3 to S4.

[0089] In one embodiment, step S5: Determine whether to update the shear pin state value according to the converged internal force F d (t) of the shear pin type sliding friction pendulum support and its corresponding shear pin state value, and determine the internal force F d (t) of the shear pin sliding friction pendulum support at this moment includes:

[0090] Step S51: When the shear pin state value corresponding to the converged internal force F d (t) of the shear pin type sliding friction pendulum support is 1, do not update the shear pin state value;

[0091] Step S52: Output the converged internal force F d (t) of the shear pin type sliding friction pendulum support as the internal force F d (t) of the shear pin type sliding friction pendulum support at this moment.

[0092] In one embodiment, step S5: Determine whether to update the shear pin state value according to the converged internal force F d (t) of the shear pin type sliding friction pendulum support and its corresponding shear pin state value, and determine the internal force F d (t) of the shear pin sliding friction pendulum support at this moment includes:

[0093] Step S53: When the shear pin state value corresponding to the converged internal force F d (t) of the shear pin type sliding friction pendulum support is 0, judge the magnitude of the converged internal force F d (t) of the shear pin type sliding friction pendulum support and the shear pin yield strength Q;

[0094] Step S54: When |F d (t)| < Q, do not update the shear pin state value, keep the shear pin state value as 0, and output the converged internal force F d (t) of the shear pin type sliding friction pendulum support as the internal force F d (t) of the shear pin type sliding friction pendulum support at this moment;

[0095] Step S55: When |F d (t)| ≥ Q, update the shear pin state value to 1, and the iterative displacement x i=0, repeat steps S3 to S4.

[0096] like Figure 2 As shown, Figure 2 1 is a block diagram of an internal force calculation device for a shear pin type sliding friction pendulum support according to an embodiment of the present invention.

[0097] The present application also provides a device for calculating the internal forces of a shear pin type sliding friction pendulum support, which includes:

[0098] A parameter acquisition module is used to obtain the external load F, stiffness matrix K and mass matrix M of the structure, the state value of the shear pin, and the parameters of the shear pin sliding friction pendulum support;

[0099] The first formula establishment module is used to establish an incremental iterative formula for structural displacement at time t;

[0100] The second formula building module is used to determine the internal force F of the shear pin sliding friction pendulum support according to the shear pin state value. d (t) and tangential stiffness K t The calculation formula of

[0101] The first calculation module is used to substitute the calculation formula of the internal force and tangential stiffness of the shear pin sliding friction pendulum bearing into the structural displacement increment iterative formula at time t, and perform iterative calculation until the converged shear pin sliding friction pendulum bearing internal force F is calculated. d (t);

[0102] The second calculation module is used to calculate the internal force F of the shear pin sliding friction pendulum support according to the convergence d (t) and its corresponding shear pin state value to determine whether to update the shear pin state value, and determine the internal force F of the shear pin sliding friction pendulum support at that moment d (t).

[0103] The functions of each module correspond to the steps of the aforementioned method and will not be repeated here.

[0104] A specific embodiment is provided below for illustration.

[0105] like Figure 3 As shown, Figure 3 Schematic diagram of a shear pin sliding friction pendulum support model with a single degree of freedom structure in one embodiment of the present invention.

[0106] The single-degree-of-freedom structural shear pin sliding friction pendulum support model is taken as the analysis object. The structural model contains single-degree-of-freedom elements and shear pin sliding friction pendulum elements.

[0107] This embodiment provides a method for calculating the internal forces of a shear pin type sliding friction pendulum bearing, comprising the following steps:

[0108] Step S1, obtaining the structural external load F, the stiffness matrix K and the mass matrix M, the shear pin state value and the shear pin type sliding friction pendulum bearing parameters.

[0109] Specifically, a single degree of freedom structural finite element model is established, and the structural stiffness matrix K is 100000 kN / m, the mass matrix M is 100 kg, and the external load F at the current moment is t is 500kN, the displacement, velocity and acceleration at the previous moment are all 0, and the friction coefficient of the shear pin sliding friction pendulum support at the previous moment is z t-Δt The friction coefficient μ of the shear pin sliding friction pendulum bearing is 0.01, the axial pressure P of the bearing is 10000 kN, the curvature radius R of the friction pendulum bearing is 2 m, and the elastic stiffness K of the shear pin is 0. q The shear pin yield strength Q is 100 kN, and the iteration convergence limit eps = 1e-4 is set.

[0110] Step S2: Establish an iterative formula for the structural displacement increment at time t.

[0111] Specifically, the incremental iterative formula of the structural displacement at time t is:

[0112]

[0113] in:

[0114]

[0115] Where, is the equivalent stiffness, is the equivalent external load at time t, F d (t) is the internal force of the shear pin sliding friction pendulum support at time t, K t is the tangential stiffness of the shear pin sliding friction pendulum support, dx(t) is the displacement increment, x i is the displacement of the structure in the current iteration step, the initial displacement x i =0, x(t-Δt), are the displacement, velocity and acceleration of the shear pin sliding friction pendulum support at the previous moment, respectively; Δt is the time interval of step-by-step time analysis, which is taken as 0.02s.

[0116] Step S3: Determine the internal force F of the shear pin sliding friction pendulum support according to the shear pin state value. d (t) and tangential stiffness K t The calculation formula of .

[0117] Specifically, the shear pin state value is 0, which means the shear pin is not damaged. At time t, the internal force F d (t) and tangential stiffness K tThe calculation formula is:

[0118]

[0119] Step S4: Substitute the calculation formula of the internal force and tangential stiffness of the shear pin sliding friction pendulum bearing into the structural displacement increment iterative formula at time t, and perform iterative calculation until the convergent shear pin sliding friction pendulum bearing internal force F is calculated. d (t).

[0120] Specifically, in step S3, the shear pin state state = 0, the initial displacement x0 = 0, and the internal force F of the shear pin sliding friction pendulum bearing is calculated. d (t) = 0, tangent stiffness K t =1000000; Substituting it into the incremental displacement formula of the structure at time t, we can obtain: dx(t)=2.3809524e-4, x1=x0+dx(t)=2.3809524e-4, F d (t) = 238.095 kN. Calculate dF t =4e-6, |dF(t)|≤eps=1e-4, then the iteration converges, F d (t) = 238.095 kN as the internal force F of the convergent shear pin sliding friction pendulum d (t), the corresponding shear pin state value is 0, and the process goes to step S5.

[0121] Step S5: Based on the converged shear pin sliding friction pendulum bearing internal force F d (t) and its corresponding shear pin state value to determine whether to update the shear pin state value, and determine the internal force F of the shear pin sliding friction pendulum support at that moment d (t).

[0122] Specifically, due to F d (t)=238.095kN, the corresponding shear pin state value state=0, judge F d (t)|≥Q=100kN, then update the shear pin state value state=1, iterate the displacement x i =0, repeat steps S3 to S4, the process is as follows:

[0123] ① After updating, return to step S3, the shear pin state value state = 1, the shear pin is destroyed, and the internal force and tangential stiffness of the shear pin sliding friction pendulum support are calculated. Iterative displacement x i = 0, the internal force F of the shear pin sliding friction pendulum bearing is calculated d (t) = 0, tangent stiffness K t= 50005000. Step S4: Substitute the calculation formulas of the tangent stiffness and internal force into the structural displacement increment iteration formula at time t, and obtain dx(t) = 9.78378e-6, x1 = x0 + dx(t) = 9.78378e-6, and calculate dF t = 389.1889 kN, |dF(t)| > eps, and repeat steps S3 to S4 again.

[0124] ② The displacement x1 = 9.78378e-6. Step S3: Calculate the internal force F d (t) of the shear pin type sliding friction pendulum bearing to be 100.04892 kN, and the tangent stiffness K t = 5000. Step S4: Substitute the calculation formulas of the tangent stiffness and internal force into the structural displacement increment iteration formula at time t, and obtain dx(t) = 3.52207e-4, x2 = x1 + dx(t) = 3.61991e-4, F d (t) = 101.81 kN, and calculate dF t = -5.5e-5, |dF(t)| < eps, then the iteration converges, and F d (t) = 101.81 kN is used as the converged internal force F d (t) of the shear pin type sliding friction pendulum, and the corresponding shear pin state value is 1, and enter step S5.

[0125] ③ Step S5: Since the shear pin state value state = 1, the shear pin state value is not updated, and directly output the converged internal force F d (t) of the shear pin type sliding friction pendulum bearing at this moment, that is, F d (t) = 101.81 kN.

[0126] In the description of the present application, it should be noted that the orientation or positional relationship indicated by terms such as "upper" and "lower" is based on the orientation or positional relationship shown in the drawings, and is 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 to 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 directly connected or indirectly connected through an intermediate medium, and it can be the connection inside 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 specific situations.

[0127] It should be noted that, in this application, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises", "includes" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device comprising 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, an element defined by the sentence "comprises a ..." does not exclude the presence of other identical elements in the process, method, article or device comprising the element.

[0128] In the description of the embodiments of the present application, unless otherwise specified, “ / ” means or, for example, A / B can mean A or B; “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.

[0129] The above are merely specific embodiments of the present application to enable those skilled in the art to 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 may 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 rather is intended to conform to the widest scope consistent with the principles and novel features of the present application.

Claims

1. A method for calculating the internal forces of a shear pin sliding friction pendulum bearing, characterized in that: The following steps are involved: Step S1: Obtaining the external load of the structure F , stiffness matrix K and mass matrix M , shear pin state values ​​and shear pin sliding friction pendulum bearing parameters; Step S2: Establish t Iterative formula for structural displacement increment at a certain moment; Step S3: Determine the internal force of the shear pin type sliding friction pendulum support according to the shear pin state value. and tangential stiffness The calculation formula of Step S4: Substitute the calculation formula of the internal force and tangential stiffness of the shear pin sliding friction pendulum support into the t The iterative calculation formula of the structural displacement increment at each moment is performed until the convergent internal force of the shear pin sliding friction pendulum support is calculated. ; Step S5: Based on the converged shear pin sliding friction pendulum bearing internal force The corresponding shear pin state value determines whether to update the shear pin state value, and determines the internal force of the shear pin sliding friction pendulum support at this moment. ; The internal force of the shear pin type sliding friction pendulum support is determined according to the state value of the shear pin and tangential stiffness The calculation formula includes: If the shear pin state value is 0, the shear pin is not damaged. t Internal force of shear pin sliding friction pendulum support at the moment and tangential stiffness The calculation formula is: ； in, is the structural displacement of the current iteration step, K q is the elastic stiffness of the shear pin; If the shear pin state value is 1, the shear pin is destroyed. t Internal force of shear pin sliding friction pendulum support at the moment and tangential stiffness The calculation formula is: Where, ; in, is the restoring force of the shear pin sliding friction pendulum bearing, P is the axial pressure of the shear pin sliding friction pendulum bearing, is the structural displacement of the current iteration step, R is the curvature radius of the shear pin sliding friction pendulum support, is the friction resistance of the shear pin sliding friction pendulum support, μ is the friction coefficient, k is the sliding velocity coefficient of the shear pin sliding friction pendulum bearing, is the friction coefficient of the shear pin sliding friction pendulum support at the previous moment, is the displacement of the shear pin sliding friction pendulum support at the previous moment.

2. The internal force calculation method of the shear pin type sliding friction pendulum support according to claim 1 is characterized in that: The external load of the structure F , stiffness matrix K and mass matrix M , shear pin state values ​​and shear pin sliding friction pendulum bearing parameters are obtained through the finite element model.

3. The internal force calculation method of the shear pin sliding friction pendulum support according to claim 1 is characterized in that: described t The incremental iterative formula of the structural displacement at time is: ； in: ; ； In the formula is the equivalent stiffness, for t Equivalent external load at time for t Internal force of shear pin sliding friction pendulum support at all times, is the tangential stiffness of the shear pin sliding friction pendulum support, is the displacement increment, is the structural displacement of the current iteration step, 、 、 are the displacement, velocity and acceleration of the shear pin sliding friction pendulum support at the previous moment, Δt is the time interval for stepwise time analysis, F t for t External loads on the structure at all times.

4. The internal force calculation method of the shear pin type sliding friction pendulum support according to claim 3 is characterized in that: The incremental iterative formula of the structural displacement at time t is given by the dynamic formula And Newmark method is established to obtain, among which, 、 and are displacement, velocity, and acceleration respectively.

5. The internal force calculation method of the shear pin type sliding friction pendulum support according to claim 3 is characterized in that: Substitute the calculation formula of the internal force and tangential stiffness of the shear pin sliding friction pendulum support into the t The iterative calculation formula of the structural displacement increment at each moment is performed until the convergent internal force of the shear pin sliding friction pendulum support is calculated. include: Substitute the calculation formula of the internal force and tangential stiffness of the shear pin sliding friction pendulum support into the t Iterative formula for structural displacement increment at a certain moment; Calculate each iteration ,judge and iterative convergence limit eps relationship; like , the iteration converges, and the output is the structural displacement of the current iteration step As the iterative displacement, the current iteration step Internal forces of a shear pin sliding friction pendulum as a convergence , proceed to step S5; like , update the iterative displacement, that is , repeat steps S3 to S4.

6. The internal force calculation method of the shear pin sliding friction pendulum support according to claim 1 is characterized in that: The internal force of the shear pin sliding friction pendulum support according to the convergence The corresponding shear pin state value determines whether to update the shear pin state value, and determines the internal force of the shear pin sliding friction pendulum support at this moment. include: The internal force of the convergent shear pin sliding friction pendulum support When the corresponding shear pin state value is 1, the shear pin state value is not updated; Output the convergent shear pin sliding friction pendulum bearing internal force As the internal force of the shear pin sliding friction pendulum support at this moment .

7. The internal force calculation method of the shear pin sliding friction pendulum support according to claim 1 is characterized in that: The internal force of the shear pin sliding friction pendulum support according to the convergence The corresponding shear pin state value determines whether to update the shear pin state value, and determines the internal force of the shear pin sliding friction pendulum support at this moment. include: The internal force of the convergent shear pin sliding friction pendulum support When the corresponding shear pin state value is 0, the internal force of the convergent shear pin sliding friction pendulum support is determined to be and shear pin yield strength Q size; When the shear pin state value is not updated, the converged shear pin sliding friction pendulum bearing internal force is output. As the internal force of the shear pin sliding friction pendulum support at this moment ; When the shear pin state value is updated to 1, the iterative displacement , repeat steps S3 to S4.

8. A device for calculating the internal forces of a shear pin type sliding friction pendulum bearing using the internal force calculation method of a shear pin type sliding friction pendulum bearing according to any one of claims 1 to 7, characterized in that: It includes: Parameter acquisition module, which is used to obtain external loads of the structure F , stiffness matrix K and mass matrix M , shear pin state values ​​and shear pin sliding friction pendulum bearing parameters; The first formula building module is used to build t Iterative formula for structural displacement increment at a certain moment; The second formula establishment module is used to determine the internal force of the shear pin type sliding friction pendulum support according to the shear pin state value and tangential stiffness The calculation formula of The first calculation module is used to substitute the calculation formula of the internal force and tangential stiffness of the shear pin sliding friction pendulum support into the t The iterative calculation formula of the structural displacement increment at each moment is performed until the convergent internal force of the shear pin sliding friction pendulum support is calculated. ; The second calculation module is used to calculate the internal force of the shear pin sliding friction pendulum support according to the convergence The corresponding shear pin state value determines whether to update the shear pin state value, and determines the internal force of the shear pin sliding friction pendulum support at this moment. .

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