CN110046400A - A kind of high resolution numerical simulation calculation method carrying out Analysis of Static Force Characteristics to concrete gravity dam based on h-p type FInite Element - Google Patents
A kind of high resolution numerical simulation calculation method carrying out Analysis of Static Force Characteristics to concrete gravity dam based on h-p type FInite Element Download PDFInfo
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Abstract
The present invention relates to a kind of high resolution numerical simulation calculation methods for carrying out Analysis of Static Force Characteristics to concrete gravity dam based on h-p type FInite Element, belong to imitation technology field.This carries out the high resolution numerical simulation calculation method of Analysis of Static Force Characteristics based on h-p type FInite Element to concrete gravity dam, the computation model for sequentially including the following steps: building concrete for hydraulic structure gravity dam, using the displacement and stress fields of h-p type Finite element arithmetic concrete for hydraulic structure gravity dam model；Judge whether obtained displacement and stress fields meet required precision, such as do not meet required precision, the order of refined net and raising interpolation polynomial, steps be repeated alternatively until to obtain satisfied result again.The present invention calculates overlong time for the existing concrete gravity dam model based on conventional finite element static analysis, and error is excessive, and the lower problem of precision gives a kind of finite element method (fem) analysis method of concrete gravity dam novel high-precision.
Description
Technical field
The present invention relates to a kind of high-precisions for carrying out Analysis of Static Force Characteristics to concrete gravity dam based on h-p type FInite Element
Numerical simulation method belongs to imitation technology field.
Background technique
Gravity dam is one of a kind of important dam type that the mankind use earliest, and since it has, design and construction are simple, reliability
By force, good to terrain adaptability, the advantages that durability is high, therefore be widely used.The effective security evaluation of hydraulic structure
Standard General is the displacement and stress situation for dam body each section, and when displacement and stress are more than safety standard, dam body will be sent out
It is raw to destroy, so static analysis (including stress analysis and Displacement Analysis) is analysis of hydraulic aspect unavoidably and has
The project of important meaning.Currently, in hydraulic structure safety analysis the calculation method of static analysis be mainly Finite Element,
Mechanics of materials method and elastic theory parse method, and it is also some that mechanics of materials method and elastic theory parsing method are applied in early days
The analysis of hydro-structure problem is made that contribution, but because of its own intrinsic limitation, it is caused to consume in calculating process
When it is longer, so Development of Novel numerical simulation method is particularly important in Hydraulic Structure Analysis.Conventional finite unit
Method (H type Finite Element), mainly come not by way of gradually decreasing unit grid size h (subdivided meshes i.e. commonly referred to as)
The disconnected precision for promoting finite elements solution is widely used in in terms of the design calculating and security evaluation of hydraulic structure, such as each
All kinds of hydraulic structures such as class earth and rockfill dam, rock, concrete gravity dam, arch dam, floodwater releasing port.
In the correlative study of hydraulic structure, conventional finite elements method has played considerable effect, solves big
The problem of criticizing hydro-structure aspect, but due to the limitation of its calculation method itself, calculated result cannot be completely satisfactory, number
Value simulation calculates that convergence rate is slower, and error is larger, and precision is lower, so studying a kind of novel finite elements method to solve tradition
Finite Element fails to solve the problems, such as just to be particularly important very well.It is mostly to what problem was studied using FInite Element
Traditional H type FInite Element or the development based on conventional finite element, thus there are the following problems:
(1) control of traditional H type FEM calculation precision more relies on the experience of researcher, to obtain preferable meter
Precision is calculated, needs repeatedly to repartition grid；
(2) traditional interpolating function of the H type finite element based on low order, in numerical simulation there are inadequate natural endowment, for obtain compared with
In high precision, a large amount of refined net is needed, pre-treatment and calculating cost are larger.
Conventional finite elements method (H type Finite Element) and p-type Finite Element have been successfully applied to various reality
In engineering field (including in Hydraulic Structure Analysis), in recent years, h-p type Finite Element is rapidly developed, but in water
In work structural analysis, especially in concrete gravity dam static analysis, there are no the correlations of h-p type Finite Element both at home and abroad
Application technology.
The present invention is based on state natural sciences funds (grant numbers: 51769011), to propose and answer h-p type FInite Element
For hydraulic and hydroelectric engineering field.
Summary of the invention
For the above-mentioned problems of the prior art and deficiency, the present invention provides one kind based on h-p type FInite Element to mixed
Solidifying soil gravity dam carries out the high resolution numerical simulation calculation method of Analysis of Static Force Characteristics.Technical problem solved by the present invention is existing
There is the simulation computing technique being applied in Hydraulic Structure Analysis based on conventional finite elements method, due to the office of its calculation method itself
Limit, calculated result are not able to satisfy practical implementation needs, for example when carrying out numerical simulation calculation to Practical Project problem, receive
It is slower to hold back speed, error is larger, and precision is lower.
The core concept of h-p type Finite Element of the invention is exactly H type Finite Element and p-type Finite Element
Advantage combines, i.e., reduces unit grid size h (subdivided meshes) simultaneously and improve the order of interpolation polynomial on unit
P can more quickly improve the convergence rate and precision of finite elements solution, during solution, h-p type Finite Element
Faster, computational solution precision is higher for convergence rate, and error is smaller, has the advantages that its uniqueness.Traditional low-order finite element scheme be with
Low order interpolation polynomial constructs Finite-Element Solution, and h-p type FInite Element is constructed using high-order (non-linear) interpolation polynomial
Finite-Element Solution is high-order nonlinear FInite Element, and h-p type FInite Element is the new development of FInite Element, it is able to achieve higher
Precision and faster convergence rate.
The invention is realized by the following technical scheme.
It is a kind of by h-p type FInite Element to concrete gravity dam carry out Analysis of Static Force Characteristics high resolution numerical simulation based on
Calculation method, sequentially includes the following steps:
Step 1, the computation model for constructing concrete for hydraulic structure gravity dam, comprising steps of
Step 1.1 geometrical model is established: control Practical Project figure carries out two-dimensional structure model foundation, two-dimensional structure model knot
Structure is made of dam body part and dam foundation part；
Step 1.2 grid dividing: FEM meshing is carried out using quadrilateral mesh, avoids elongated quadrilateral mesh
And it must be simulated in borderline region encryption grid division so as to more preferable；
Step 1.3 sets material properties: simulating operating condition with linear elastic materials, sets corresponding material category for grid cell
Property, wherein the setting for elasticity modulus are as follows: the elasticity modulus of setting concrete gravity dam main part and dam foundation part takes
Value is static modulus of elasticity value corresponding to the practical rock mass of the actually used material of concrete gravity dam main part and dam foundation part；
Boundary condition is arranged in step 1.4: vertical constraint is arranged to dam foundation bottom, on dam foundation part along river width direction
Two sides side Normal Constraint is respectively set；
Load is arranged in step 1.5: simulation Water quality hydrostatic pressure, silt pressure, uplift pressure；
Step 2, using the displacement and stress fields of h-p type Finite element arithmetic concrete gravity dam model, comprising steps of
Step 2.1, solution obtain displacement structure array a
According to equation: Ka=F (1),
Wherein K=∑eGTKeG, structure Bulk stiffness matrix, KeFor element stiffness matrix；F=∑eGTfe, structural junction load column
Battle array；G is the transition matrix of the unit degree of freedom on a node basis and structure node freedom degree, GTFor the transposition of G, subscript T representing matrix turns
It sets；E indicates individual unit；A is displacement structure array；
Further according to formula cells stiffness matrix Ke=∫ΩBTDBd Ω (2),
Unit equivalent node load column
Unit internal node power
External node power
Into (5), Ω is indicated inside unit above-mentioned formula (2)；B=LNI, L is differential operator, NIFor interpolating function square
Battle array or form function matrix, I are the label of unit, ΓtFor the outer boundary of unit；D is stress matrix, and b is physical strength,For load
Boundary condition, respectively by step 1 material properties and load and displacement boundary conditions determine；
By formula (2) to (5) and NIInterpolation polynomial for h-p type FInite Element is updated in (1), by solving line
Property equation group (1) obtains displacement structure array a；
NIUsing the interpolation polynomial of h-p type FInite Element, typical two dimension h-p type finite element shape function is based on Legendre
Orthogonal polynomial, by taking two-dimentional quadrilateral units as an example (shown in attached drawing 1), at coordinate system (η, ξ), point p1、p2、p3And p4It is divided into
Four vertex of unit, Γ1、Γ2、Γ3And Γ4It is divided into the four edges of unit, the structural form of shape function is as follows:
P >=1, it is consistent when dot pattern basic function is with conventional Lagrangian type basic function, with four node unit of quadrangle
For by following expansion:
P >=2, edge mode basic function:
In formula:
Here, Pn(t) be order be n >=0 Legnedre polynomial
Similar, it can be as given a definition and side Γk(2≤k≤4) associated shape function:
Internal schema basic function when p >=4:
The h-p type FInite Element that the present invention uses, the order of interpolation polynomial can successively be gradually increased from p=1, be promoted
The stiffness matrix of low order can continue to continue to use after interpolation polynomial order, only need to calculate high order part, avoid stiffness matrix low order
Partial computes repeatedly, and has good inheritedness, has saved calculating cost；
Step 2.2, according to formula aI=Ga solves to obtain element displacement array aI；
Step 2.3, according to displacement field formula u=NIaI, stress field formula σ=D ε=DBaI, solve and obtain displacement field u, answer
Field of force σ；
Whether the displacement and stress fields that step 3, judgment step 2 obtain meet required precision, such as do not meet required precision,
Continue refined net simultaneously and improves the order of interpolation polynomial, return step 2.
Grid dividing uses quadrilateral mesh in the step 1.2: the apex angle of quadrilateral units is quadrilateral units
Apex angle be 5 °~175 °, be preferably close to 90 °.Since shape function is using high-order interpolation function, thus compared with conventional finite
First method can effectively accelerate convergence rate and improve computational accuracy, obtain high-precision Finite-Element Solution.
To non-standard model, in the case that no Theory Solution or experimental result compare, while refined net, and according to
Secondary raising interpolation polynomial order, then displacement field is obtained by Static Calculation.What whether the result obtained after observation calculated with front
Within an acceptable range whether result error.
Precision be unsatisfactory for requiring or the direct deviation of acquired results not within an acceptable range.Step 2 is again returned to, again
Displacement and stress fields are calculated until numerical result meets required precision.
There is no the label of specific explanations to be well known to those skilled in the art the label of its meaning in above-mentioned formula.
The beneficial effects of the present invention are:
The present invention calculates convergence speed for the existing concrete gravity dam model based on conventional finite element Analysis of Static Force Characteristics
Degree is slower, and error is excessive, the lower problem of precision, gives a kind of FEM calculation point of concrete gravity dam novel high-precision
Analysis method: this method has grid division number few, and computational efficiency is high, fast convergence rate, the lesser feature of error.
Detailed description of the invention
Fig. 1 is the schematic diagram of standard quadrilateral mother unit of the present invention；
Fig. 2 is the structural model figure of 1 concrete gravity dam of the embodiment of the present invention；
Fig. 3 is the position in the embodiment of the present invention 1 through using H type Finite element arithmetic finite element model to obtain after step 1.5
Move field cloud atlas；
Fig. 4 is the displacement field cloud atlas that embodiment 1 of the present invention is obtained using h-p type Finite element arithmetic finite element model.
Specific embodiment
With reference to the accompanying drawings and detailed description, the invention will be further described.
Embodiment 1
Some hydropower station using dam-type develop, central hub by barrage, flood and sand discharging building, become water power generation system,
The part such as ship machine, alternation power station is vertically moved up or down to form.Gear sill may material is compaction type concrete gravity dam, and entire crest elevation is high
Up to 622m, entire maximum height of dam is 108m.Reservoir operation scheme is located at 612m.The performances of rock parameter used in calculating is such as
Under:
Mass density: 2.8t/m3, Poisson's ratio: 0.25, elasticity modulus: 10000MPa；Concrete parameters used in gravity dam are such as
Under: mass density: 2.4, Poisson's ratio: 0.2, elasticity modulus: 22000MPa；Parameter used in workshop is as follows: mass density: 2.50t/
m3, Poisson's ratio: 0.167, elasticity modulus: 25500MPa.
It is as follows in the primary load that concrete gravity dam design calculating uses.
Various static load thresholds are as follows:
(1) dam body is self-possessed
The self weight of gravity dam dam concrete, is applied by one-stage completion.The self weight of basement rock will be certainly within the scope of computation modeling
After being converted into basement rock self-weight stress field again, it is applied on computation model by initial self-weight stress field.
(2) hydrostatic pressure
The water pressure generated due to the upstream and downstream depth of water.Water capacity weight: 9.81kN/m3, upstream inpoundment position: 602.00m, downstream
Water level: 535.735m.
(3) silt pressure
Silt buoyant unit weight: 8.1kN/m3, internal friction angle: 24 °.Silt elevation before dam: (siltation is limited to 40 in year to EL560.00m
Year).
(4) uplift pressure
Concrete uplift pressure on dam foundation is designed according to pump drainage antihypertensive effect and is calculated.Determine upstream and downstream curtain and drain in dam foundation
The position in hole.The calculating figure and coefficient of uplift pressure, which are chosen, presses " hydraulic structure load design specification ".Concrete gravity dam dam
Internal portion osmotic pressure strength factor takes 0.2, and the uplift pressure strength factor before main drainage hole takes 0.2.
Using the concrete gravity dam of above-mentioned parameter, static(al) is carried out to the concrete gravity dam based on h-p type FInite Element
The high resolution numerical simulation calculation method of analysis, sequentially includes the following steps:
Step 1, the computation model for constructing concrete for hydraulic structure gravity dam, comprising steps of
Step 1.1 geometrical model is established: control Practical Project figure carries out two-dimensional structure model foundation, two-dimensional structure model knot
Structure is made of dam body part and dam foundation part, and the structural model figure obtained using CAD is as shown in Figure 2；
Step 1.2 grid dividing: FEM meshing is carried out using quadrilateral mesh, avoids elongated quadrilateral mesh
And it must be simulated in borderline region encryption grid division so as to more preferable；Grid dividing uses quadrangle in the step 1.2
Grid: the apex angle of quadrilateral units is that the apex angle of quadrilateral units is 5 °~175 °, is preferably close to 90 °；Grid is divided into
356,1424,3204,5696,8900,12816 units；
Step 1.3 sets material properties: simulating operating condition with linear elastic materials, sets corresponding material category for grid cell
Property, wherein the setting for elasticity modulus are as follows: the elasticity modulus of setting concrete gravity dam main part and dam foundation part takes
Value is static modulus of elasticity value corresponding to the practical rock mass of the actually used material of concrete gravity dam main part and dam foundation part；
Boundary condition is arranged in step 1.4: vertical constraint is arranged to dam foundation bottom, on dam foundation part along river width direction
Two sides side Normal Constraint is respectively set；
Load is arranged in step 1.5: simulation Water quality hydrostatic pressure, silt pressure, uplift pressure；
Step 2, using the displacement and stress fields of h-p type Finite element arithmetic finite element model；
The displacement field cloud atlas such as Fig. 4 obtained in conjunction with step 1 and step 2 using h-p type Finite element arithmetic finite element model
It is shown, along river direction (X-direction) displacement field UxCalculated result is as shown in table 1:
Table 1
From table 1 it follows that two-dimentional concrete gravity dam be self-possessed, hydraulic pressure behind hydraulic pressure, silt pressure, dam before dam
In the case where being combined with base loads such as uplift pressure, the calculated result of X-direction maximum displacement Ux.When using based on H type finite element
For method when solving two-dimentional concrete gravity dam limited element calculation model, specific computation model is as shown in figure 3, when dividing 20023
When a grid, the calculated result of obtained X-direction maximum displacement Ux are as follows: X-direction maximum displacement Ux=7.012mm, and make
With based on h-p type FInite Element FInite Element when calculating concrete gravity dam model, in the case where dividing 1424 grids
When the X-direction maximum displacement that can reach, i.e. X-direction maximum displacement Ux=7.015mm, the two the result is that close
, but the number of grid that h-p type finite element method (fem) analysis is divided at this time is than grid that H type finite element method (fem) analysis is divided
Few more of quantity, this illustrates h-p type FInite Element by improving polynomial order and simultaneously refined net, in grid dividing phase
In the case where less, precision of the H type FInite Element when grid dividing is more can be reached.
As can be known from Fig. 3, the displacement using H type Finite Element, under conditions of 20023 grids, in dam body X-direction
UxSize is 7.012mm；With displacement U of the h-p type finite element in Fig. 4 under 1424 gridsxSize 7.015mm is close, and says
The result that obtains in the case where grid number is less of h-p type finite element is illustrated than result of the H type in the more situation of grid number
Accurately.
Whether the displacement and stress fields that step 3, judgment step 2 obtain meet required precision, such as do not meet required precision,
The order of refined net and raising interpolation polynomial simultaneously, return step 2；
Above the embodiment of the present invention is explained in detail, but the present invention is not limited to concrete gravities
Dam, within the knowledge of a person skilled in the art, can also without departing from the purpose of the present invention by
H-p type FInite Element is applied in the numerical simulation calculation of other hydro-structures.
Claims (2)
1. a kind of high resolution numerical simulation calculating side for carrying out static analysis to concrete gravity dam based on h-p type FInite Element
Method, it is characterised in that: sequentially include the following steps:
Step 1, the computation model for constructing concrete for hydraulic structure gravity dam, include the following steps:
Step 1.1 geometrical model establish: control Practical Project figure carry out two-dimensional structure model foundation, two-dimensional structure model structure by
Dam body part and dam foundation part composition；
Step 1.2 grid dividing: FEM meshing is carried out using quadrilateral mesh；
Step 1.3 sets material properties: simulating operating condition with linear elastic materials；
Boundary condition is arranged in step 1.4: vertical constraint is arranged to dam foundation bottom, on dam foundation part along the two of river width direction
Normal Constraint is respectively set in side side；
Load is arranged in step 1.5: simulation Water quality hydrostatic pressure, silt pressure, uplift pressure；
Step 2, using the displacement and stress fields of h-p type Finite element arithmetic finite element model, comprising steps of
Step 2.1, solution obtain displacement structure array a
According to equation: Ka=F (1),
Wherein K=∑eGTKeG is structure Bulk stiffness matrix, KeFor element stiffness matrix；F=∑eGTfeFor structural junction load
Array；G is the transition matrix of the unit degree of freedom on a node basis and structure node freedom degree, GTFor the transposition of G, subscript T representing matrix
Transposition；E indicates individual unit；A is displacement structure array；
Computing unit stiffness matrix K againe=∫ΩBTDBd Ω (2),
Unit equivalent node load column
Unit internal node power
External node power
Into (5), Ω is indicated inside unit above-mentioned formula (2)；B=LNI, L is differential operator, NIFor interpolating function matrix or
Form function matrix, I are the label of unit, ΓtFor the outer boundary of unit；D is stress matrix, and b is physical strength,For load boundaries
Condition, respectively by step 1 material properties and load and displacement boundary conditions determine；
By formula (2) to (5) and NIIt is updated in (1) for FInite Element interpolation polynomial, by solving system of linear equations (1)
Obtain displacement structure array a；
Step 2.2, according to formula aI=Ga solves to obtain element displacement array aI；
Step 2.3, according to displacement field formula u=NIaI, stress field formula σ=D ε=DBaI, solve and obtain displacement field u, stress field
σ；
Whether the displacement and stress fields that step 3, judgment step 2 obtain meet required precision, such as do not meet required precision, again
The order of refined net and raising interpolation polynomial simultaneously, return step 2.
2. the height according to claim 1 for carrying out Analysis of Static Force Characteristics to concrete gravity dam based on h-p type FInite Element
Accurate values simulation method, it is characterised in that: grid dividing uses quadrilateral mesh: quadrangle list in the step 1.2
The apex angle of member is 5 °~175 °.
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| CN110852013A (en) * | 2019-11-14 | 2020-02-28 | 中国水利水电科学研究院 | New and old concrete load sharing calculation method for heightened gravity dam based on structural mechanics method |
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