CN108090268B - Integrated addition method of seismic time-course wave under viscoelastic boundary - Google Patents
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Abstract
The invention provides an integrated adding method of a seismic time-course wave under a viscoelastic artificial power boundary, and relates to the field of automatic design. The method comprises the following steps: (1) establishing a structural finite element base model; (2) calculating the normal and tangential spring stiffness of the spring in the viscoelastic boundary, and the normal and tangential damping coefficient of the damper; (3) integrally adding a three-way spring-damper system at discrete nodes of a rock stratum boundary; (4) automatically calculating the seismic force time course at discrete nodes of a rock layer boundary; (5) automatically inputting seismic force time-travel waves at a boundary node at the bottom of a rock stratum; (6) and (5) carrying out time history analysis on the structure. The invention relies on the programming function of ANSYS software APDL language, solves the difficult problem of node viscoelasticity constraint and integrated input of force type earthquake time-course wave when a great amount of discrete points exist on the rock layer boundary, and can greatly improve the efficiency of calculation analysis.
Description
Field of the method
The invention belongs to the field of automatic design, and particularly relates to an integrated adding method of seismic time-course waves under a viscoelastic boundary.
Background method
With the implementation of national strategies such as 'western development', 'west gas transport from east', 'south water transfer from north' and the like in China, a large number of projects such as tunnels, pipelines, underground plants and the like are vigorously built. They mostly pass through earthquake fortification areas with complex geological conditions, and the earthquake resistance characteristics of the earthquake fortification areas are directly related to the safety of personnel life and facilities.
Finite element time-course analysis is the most effective method for analyzing the seismic response problem of such structures. Based on the dynamic interaction of the structure and the bedrock, an artificial boundary is added at the limited truncation boundary of the rock stratum, and earthquake time-course waves are applied to realize the introduction of earthquake dynamic loads. The viscoelastic artificial boundary simulated by the spring-damper system has outstanding excellent performance in accurately reflecting the elastic recovery capability of bedrock and the scattering of seismic waves because the spring stiffness and the damping coefficient are simultaneously considered. The method specifically comprises the steps of adding a three-way spring-damper element at discrete points of a rock stratum truncation boundary, and inputting a node force time interval considering seismic speed and displacement so as to carry out power time interval analysis.
The strategic engineering projects have the common characteristics of large line length and huge number of discrete points of bedrock. The parameters of the boundary elements at the discrete points are closely related to the attached area, the rock stratum property and the like of each point, and each point is different in nature, and the time consumption of adding boundary constraint and earthquake time course by means of a manual method is extremely long. At present, although the literature discusses the calculation principle of the viscoelastic boundary and the seismic time-course force, the detailed description of the integrated addition operation method of the seismic time-course wave under the viscoelastic boundary in the finite element analysis environment is not provided.
Disclosure of Invention
Aiming at the problems of the method, the invention provides an integrated adding method of the seismic time-course wave under the viscoelastic boundary, which solves the difficult problems of node viscoelastic constraint and integrated input of the force type seismic time-course wave when a large volume structure has a huge number of boundary discrete points by relying on the programming function of an ANSYS software APDL language.
The method scheme of the invention is as follows: an integrated addition method of seismic time-course waves under a viscoelastic boundary comprises the following steps:
s1: establishing a finite element solid structure model according to the characteristics of the size and the material property of the analyzed structure and the surrounding rock;
s2: defining a surrounding rock interface needing applying viscoelastic constraint, and calculating the normal and tangential spring stiffness of a spring in a viscoelastic boundary element in a stratigraphic range and the normal and tangential damping coefficient of a damper according to the material characteristics of layered surrounding rocks;
s3: loading an APDL language-based self-programming program, and automatically applying a three-way spring-damper system to each discrete point of a rock layer boundary one by one;
s4: loading an APDL language-based self-programming program, and calculating a node seismic force time course determined by seismic velocity, a displacement time course and viscoelastic boundary parameters at discrete points of a surrounding rock bottom boundary under three-dimensional seismic motion;
s5: loading an APDL language-based self-programming program, and automatically inputting node seismic force time-travel waves at discrete points of a boundary at the bottom of a rock stratum;
s6: and analyzing the time history of the structure by adopting an ANSYS transient dynamic analysis method.
Further, in S1, basic modeling parameters such as cell type, material properties, real constants, cell mesh shape and size are determined according to the structure and rock formation characteristics, and a structural solid finite element model is established.
Further, the bottom and periphery of the surrounding rock are determined as interfaces for applying viscoelastic constraints in S2, and the viscoelastic constraints are discretized by applying a three-dimensional spring-damper system at each boundary node. According to the material characteristics of the surrounding rock, determining the physical element parameters of the spring-damper system at the artificial boundary node of each layered surrounding rock by utilizing the automatic calculation function of excel:
CN＝(αM+βN)ρcp，CT＝(αM+βN)ρcs (2)
in formulae (1) to (6), KN、KTNormal and tangential spring rates for the nodes; cN、CTNormal and tangential damping coefficients of the node; a is the effective area of the node; g is the medium shear modulus; e is a bed rock elastic mold; mu is Poisson's ratio; r is the distance from the wave source to the artificial boundary point; rho is the mass density of the bedrock; c. Cp、csP wave and S wave velocities of bedrock; m is a mass matrix of the bedrock; n is a rigidity matrix of the bedrock; alpha is an orthogonality factor 1; beta is an orthogonality factor 2; xi is the damping ratio of the bedrock; omega is the natural frequency of the bedrock; lambda is a Lami first parameter; gamma is a Lami second parameter.
Further, in S3, based on the self-programming of the APDL language, the step of automatically adding the formation viscoelastic boundary element is as follows:
(1) inputting K of ith rock stratum in a certain side interface of the surrounding rock by using APDL language parameterizationNi、CNi、KTi、CTi
(2) Selecting all nodes of the ith rock stratum, and defining the total number of the nodes as the number; to m of it0Each node is used for solving three-way coordinates by nx, ny and nz commands and storing the three-way coordinates into an (x, y, z) array;
(3) solving for m by an arnode command0Subsidiary areas A of nodes, and KNi、CNi、KTi、CTiMultiplication to obtain m0Viscoelastic boundary physical element parameter K in node attachment rangemNi、CmNi、KmTi、CmTi；
(4) According to m0Point coordinates in the outer normal direction of the surrounding rock surface and at a distance m0Generating new node m at unit length of node1At m0And m1Establishes a normal combine 14 unit and gives K to the normal combine 14 unitmNiAnd CmNiReal constant of (c) to m1Applying fixed constraint to the nodes and establishing a normal spring-damper unit;
(5) in the same way, at two orthogonal tangents of the surrounding rock face and at a distance m0Respectively generating new nodes m at the unit length of the node2And m3At m0And m2And m0And m3Establishes a two-way bin14 unit and gives K to the binmTiAnd CmTiReal constant of (c) to m2And m3The node is fixedly restrained, and two orthogonal tangential spring-damper units are established;
(6) do circulation is implemented from the node 1 to the number, and all node three-way spring-damper units in the i-rock layer section are added according to the processes from (2) to (5);
(7) implementing do circulation from the layer 1 to the layer i, and realizing the addition of all node three-way spring-damper units on the side interface according to the processes from (1) to (6);
(8) and sequentially selecting the bottom boundary and each side boundary of the surrounding rock, and realizing the addition of three-way spring-damper units of nodes contained in all the boundaries, so as to finish the integrated addition of the viscoelastic boundary of the surrounding rock.
Further, in S4, according to the assumption that the seismic waves are vertically incident from the surrounding rock bed boundary, a three-dimensional equivalent seismic load of a certain node of the boundary is calculated by an analytic method:
p-wave incidence equation:
s-wave incidence equation:
in formulae (7) to (8), Fi -yThe subscript of the equivalent seismic load in the i direction of the artificial boundary node under the action of the incident wave represents the component direction, and the superscript represents the outer normal direction of the bottom artificial boundary surface; u shapep(t) and
the displacement time and the speed time of the theoretical seismic wave at the point are obtained; u shapep[max(t)]And
the actual seismic wave displacement time course and the actual seismic wave velocity time course of the point are obtained; where max (t) -t is Δ t, which is the traveling wave delay, in equation (7)
In formula (8)
d is the distance from the node to the bottom surface of the finite element body.
Further, finite element transient analysis setting is carried out in S5, convergence conditions are determined, and sub-steps and damping ratios are analyzed;
based on the self-programming of the APDL language, the steps of automatically inputting node seismic force time-travel waves at discrete points of the bottom boundary of a rock stratum are as follows:
(1) selecting all nodes on the bottom boundary, wherein the total number of the nodes is nbottom;
(2) at a certain time step, do loop is implemented from node 1 to nbottom, and the node force at the time step solved in S4 is calculated
And
sequentially loading by a command F;
(3) and in turn, executing do cycle from time step 1 to step to realize the loading of the bottom boundary three-way node force in all time steps.
Further, all the units of the model are selected in S6, time history analysis is carried out on the structure by adopting an ANSYS transient dynamic analysis method, and the structure deformation and stress results under the action of the three-dimensional earthquake time history based on the viscoelastic artificial boundary are obtained.
Compared with the prior art, the invention has the beneficial effects that: the invention solves the problems of long time consumption and poor precision of manual addition of viscoelastic boundaries and node force type earthquake time courses aiming at large-scale structures with huge number of discrete points. Based on the programming function of the APDL language, a nested program for automatically adding the boundary node spring-damper units is created, and the viscoelastic boundary application to any property rock stratum and any shape boundary unit can be realized; a nesting program of calculation of discrete points of a boundary at the bottom of a rock stratum and input of node force type seismic time-course waves is created, and rapid addition of the seismic time-course considering the elastic restoring force and wave scattering performance of the bedrock can be realized. The method provided by the invention is a secondary development of ANSYS software for large-scale structure earthquake-resistant analysis, fully considers the attribute difference of each discrete point of the model boundary, and adopts an integrated program calling method, thereby greatly improving the efficiency of modeling and calculation. The method can be directly used by engineering method personnel in the anti-seismic analysis of various long-line large-span structures.
Drawings
FIG. 1 is a flow chart of a seismic time-course wave integration adding method under a viscoelastic boundary;
FIG. 2 is a schematic diagram of a finite element solid structure model;
FIG. 3 is a schematic diagram of a boundary node three-dimensional spring-damper system;
FIG. 4 is a schematic representation of a finite element model viscoelastic boundary simulation;
FIG. 5 is a schematic diagram of a time course of the positive stress of an inner node of a base plate of the finite element model.
Detailed Description
The invention is further illustrated with reference to figures 1-5.
As shown in fig. 1, the flow of implementing the present invention using ANSYS software APDL programming language is as follows:
s1: establishing a finite element solid structure model: as shown in fig. 2, according to the characteristics of the analyzed structure, the size and the material property of the surrounding rock and the like, the unit type, the material property, the real constant and the like are sequentially input in the ANSYS pretreatment stage, and an entity model is established and the grids are divided.
S2: calculating the parameters of the spring-damper unit physical elements: defining a surrounding rock interface needing viscoelastic constraint, calculating the normal and tangential spring stiffness K of the spring in the viscoelastic boundary element in the range of the stratigraphic boundary according to the shear modulus of bedrock, elastic modulus, Poisson ratio, the distance from a wave source to an artificial boundary point, the node attachment area, mass density, mass matrix, stiffness matrix, damping ratio, natural frequency, P wave and S wave velocity and other material characteristics of the stratified surrounding rock by equations (1) and (2)NAnd KTNormal and tangential damping coefficient C of damperNAnd CTSee fig. 3.
S3: loading an APDL language-based self-programming program, and automatically applying a three-way spring-damper system at discrete points of a rock layer boundary one by one: a nested do circulation program based on APDL language is adopted, normal and tangential fixed constraint points are created outside discrete points for all side interfaces except for a free surface at the top of a bedrock, a combin14 unit is communicated between the boundary discrete points and the fixed constraint points, the addition of a three-way spring-damper system is realized, and meanwhile, the system is endowed with spring stiffness and damping coefficient after the node attachment area is considered, which is shown in figure 4.
S4: loading an APDL language-based self-programming program, and calculating a node force type earthquake time course at discrete points of a surrounding rock bed boundary: adopting a nested do loop program based on APDL language, calling earthquake displacement and speed time travel waves of bottom boundary nodes, and calculating three-dimensional earthquake equivalent node force of each node on all time steps according to formulas (7) and (8)
And
s5: loading an APDL language-based self-programming program, and automatically inputting node seismic force time-travel waves at discrete points of a boundary at the bottom of a rock stratum: and (3) loading the three-way seismic node force solved in the S4 to all nodes of the bottom boundary in time steps by adopting a nested do loop program based on the APDL language.
S6: and (3) analyzing the time history of the structure by adopting an ANSYS transient dynamic analysis method: as shown in fig. 5, a stress and displacement time-course graph and a cloud graph of the key node are extracted, and the safety performance of the structure is evaluated.
Experimental example:
finite element parametric modeling and mechanical calculation of subsurface structure
S1: and establishing a finite element solid structure model. A150 m underground shallow concrete pipeline structure is used as an analysis object, a solid45 unit is used for simulating a structure and a rock stratum, and a combination 14 unit is used for simulating a bedrock viscoelastic boundary. The mass density, elastic modulus and poisson ratio of the concrete are recorded in sequence by an ansys pretreatment program. The rock stratum is sequentially loam, pebbles and medium sand from top to bottom, and the mass density, the elastic modulus, the Poisson ratio, the natural frequency, the damping ratio, the cohesive force and the internal friction angle of each rock stratum are sequentially recorded by an ANSYS pretreatment program. And establishing a solid model and carrying out mesh grid.
S2: and calculating the parameters of the physical elements of the spring-damper unit. The method is characterized by comprising the following components of rock stratum shear modulus, elastic modulus, Poisson ratio, wave source-artificial boundary point distance, node attachment area, mass density, mass matrix, rigidity matrix, damping ratio,The parameters of the spring-damper unit physical elements, such as the natural frequency, the P wave speed, the S wave speed and the like, are calculated as follows: soil layer KN1＝32867N/m，CN1＝208290N·s/m，KT1＝19133N/m，CT190070N · s/m; pebble bed KN2＝134719N/m，CN2＝312613N·s/m，KT2＝67360N/m，CT2167396N · s/m; middle sand layer KN3＝21056N/m，CN3＝125446N·s/m，KT3＝10528N/m，CT3＝50266N·s/m。
S3: loading an APDL language-based self-programming program, and automatically applying a three-way spring-damper system at discrete points of a rock layer boundary one by one: operating an APDL nested loop program, solving the attached area A of the node for the bedrock boundary node by an arnode command, and comparing the attached area A with K in S2Ni、CNi、KTi、CTiMultiplication to obtain m0Viscoelastic boundary physical element parameter K within nodal attachment areamNi、CmNi、KmTi、CmTi. Sequentially selecting front, back, left, right side surfaces and a bottom surface of the bedrock, and adding three-way spring-damper units with node properties layer by layer point by point.
S4: loading an APDL language-based self-programming program, and calculating a node force type earthquake time course at discrete points of a surrounding rock bed boundary:
and 3, seismic fortification is carried out on the area where the structure is located according to VII degrees, and the seismic acceleration peak value is 0.10 g. Operating an APDL language nested loop program, calling the Elcentro three-dimensional seismic displacement and velocity time-course wave of the bottom boundary node, parameterizing and inputting the attachment area, the spring stiffness and the damping coefficient of the node, the distance from the node to the bottom surface of the finite element body, the bedrock density, the P wave and the S wave velocity according to the formulas (7) and (8), and calculating the three-dimensional seismic equivalent node force of each node of the bottom boundary on all time steps
And
s5: loading an APDL language-based self-programming program, and automatically inputting node seismic force time-travel waves at discrete points of a boundary at the bottom of a rock stratum: and (4) running an APDL language nested loop program, and repeatedly calling an F command to load the three-way node force solved in the S4 to all nodes of the bottom boundary in time step.
S6: and (3) analyzing the time history of the structure by adopting an ANSYS transient dynamic analysis method: and carrying out power time course analysis on the structure, extracting a stress and displacement time course graph and a cloud graph of the key node by an ANSYS post-processing function, and evaluating the safety performance of the structure.
In the invention, the setting of the calculation conditions is specifically specified in NB 35047-.
Based on the invention, the integrated addition of node force type earthquake time-course waves under a viscoelastic boundary can be realized, and the illustrated boundary processing and earthquake force addition method aiming at the large-scale structure earthquake-resistant state with a huge amount of discrete points is not possessed by other analysis methods. The above examples are merely examples for clarity of illustration and are not intended to limit the scope of the embodiments. Modifications may be made without departing from the principles of the invention and these modifications are to be considered within the scope of the invention and all such implementations are not necessarily or exclusively exhaustive.
Claims (3)
1. An integrated addition method of seismic time-course waves under a viscoelastic boundary is characterized by comprising the following steps:
s1: establishing a finite element solid structure model according to the characteristics of the size and the material property of the analyzed structure and the surrounding rock;
s2: defining a surrounding rock interface needing applying viscoelastic constraint, and calculating the normal and tangential spring stiffness of a spring in a viscoelastic boundary element in a stratigraphic range and the normal and tangential damping coefficient of a damper according to the material characteristics of layered surrounding rocks;
s3: loading an APDL language-based self-programming program, and automatically applying a three-way spring-damper system to each discrete point of a rock layer boundary one by one;
s4: loading an APDL language-based self-programming program, and calculating a node seismic force time course determined by seismic velocity, a displacement time course and viscoelastic boundary parameters at discrete points of a surrounding rock bottom boundary under three-dimensional seismic motion;
s5: loading an APDL language-based self-programming program, and automatically inputting node seismic force time-travel waves at discrete points of a boundary at the bottom of a rock stratum;
s6: analyzing the time history of the structure by adopting an ANSYS transient dynamic analysis method;
determining the bottom surface and the periphery of the surrounding rock as interfaces applying viscoelastic constraint in S2, dispersing the viscoelastic constraint into applying a three-dimensional spring-damper system on each boundary node, and determining the physical element parameters of the spring-damper system at each layered artificial boundary node of the surrounding rock by utilizing the automatic calculation function of excel according to the material characteristics of the surrounding rock:
CN＝(αM+βN)ρcp，CT＝(αM+βN)ρcs (2)
in formulae (1) to (6), KN、KTNormal and tangential spring rates for the nodes; cN、CTNormal and tangential damping coefficients of the node; a is the effective area of the node; g is the medium shear modulus; e is a bed rock elastic mold; mu is Poisson's ratio; r is the distance from the wave source to the artificial boundary point; rho is the mass density of the bedrock; c. Cp、csP wave and S wave velocities of bedrock; m is a mass matrix of the bedrock; n is a rigidity matrix of the bedrock; alpha is an orthogonality factor 1; beta is an orthogonality factor 2; xi is the damping ratio of the bedrock; omega is the natural frequency of the bedrock; lambda is a Lami first parameter; gamma is a second parameter of Lami;
in S3, based on the self-programming of the APDL language, the step of automatically adding the formation viscoelastic boundary element is as follows:
(1) inputting K of ith rock stratum in a certain side interface of the surrounding rock by using APDL language parameterizationNi、CNi、KTi、CTi；
(2) Selecting all nodes of the ith rock stratum, and defining the total number of the nodes as the number; to m of it0Each node is used for solving three-way coordinates by nx, ny and nz commands and storing the three-way coordinates into an (x, y, z) array;
(3) solving for m by an arnode command0Subsidiary areas A of nodes, and KNi、CNi、KTi、CTiMultiplication to obtain m0Viscoelastic boundary physical element parameter K in node attachment rangemNi、CmNi、KmTi、CmTi；
(4) According to m0Point coordinates in the outer normal direction of the surrounding rock surface and at a distance m0Generating new node m at unit length of node1At m0And m1Establishes a normal combine 14 unit and gives K to the normal combine 14 unitmNiAnd CmNiReal constant of (c) to m1Applying fixed constraint to the nodes and establishing a normal spring-damper unit;
(5) in the same way, at two orthogonal tangents of the surrounding rock face and at a distance m0Respectively generating new nodes m at the unit length of the node2And m3At m0And m2And m0And m3Establishes a two-way bin14 unit and gives K to the binmTiAnd CmTiReal constant of (c) to m2And m3The node is fixedly restrained, and two orthogonal tangential spring-damper units are established;
(6) do circulation is implemented from the node 1 to the number, and all node three-way spring-damper units in the i-rock layer section are added according to the processes from (2) to (5);
(7) implementing do circulation from the layer 1 to the layer i, and realizing the addition of all node three-way spring-damper units on the side interface according to the processes from (1) to (6);
(8) sequentially selecting a surrounding rock bottom boundary and each side boundary to realize the addition of three-way spring-damper units of nodes contained in all the boundaries, thereby finishing the integrated addition of the surrounding rock viscoelastic boundary;
in S4, according to the assumption that seismic waves are vertically incident from the boundary of the surrounding rock bottom, the anisotropic equivalent seismic load of the l node of the boundary is calculated by an analytic method:
p-wave incidence equation:
s-wave incidence equation:
in the formulae (7) to (8),
and
the method is characterized in that equivalent seismic loads along the x direction and the y direction at a node l of an artificial boundary under the action of incident waves are represented, the subscript represents the component direction, and the superscript represents the outer normal direction of a bottom artificial boundary surface; u shapep(t-. DELTA.t) and
the displacement time and the speed time of the seismic wave at the point are obtained; wherein,Δ t is traveling wave delay, in equation (7)
In formula (8)
d is the distance from the node to the bottom surface of the finite element body;
performing finite element transient analysis setting in S5, determining a convergence condition, analyzing sub-steps and a damping ratio;
based on the self-programming of the APDL language, the steps of automatically inputting node seismic force time-travel waves at discrete points of the bottom boundary of a rock stratum are as follows:
(1) selecting all nodes on the bottom boundary, wherein the total number of the nodes is nbottom;
(2) at a certain time step, do loop is implemented from the node 1 to nbottom, and the anisotropic force of the node l at the time step solved in S4 is calculated
And
sequentially loading by a command F;
(3) and in turn, executing do cycle from time step 1 to step to realize the loading of the bottom boundary three-way node force in all time steps.
2. The method of claim 1, wherein the step of S1 comprises determining basic modeling parameters such as element type, material properties, real constants, element mesh shape and size from the structural and formation characteristics to create a solid finite element model of the structure.
3. The method for integrated addition of seismic time history waves under a viscoelastic boundary as claimed in claim 1, wherein, in S6, all the units of the model are selected, and the time history analysis is performed on the structure by using ANSYS transient dynamic analysis method to obtain the structure deformation and stress results under the action of the three-way seismic time history based on the viscoelastic artificial boundary.
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