CN108595893A - A kind of three-dimensional mechanical Modal Analysis analogy method based on three layers of pretreatment - Google Patents
A kind of three-dimensional mechanical Modal Analysis analogy method based on three layers of pretreatment Download PDFInfo
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Abstract
The invention belongs to three-dimensional mechanical vibration analysis numerical technology fields, are related to a kind of three-dimensional mechanical Modal Analysis analogy method based on three layers of pretreatment.The present invention carries out finite element modeling to target aircraft first, it introduces displacement or stress boundary condition establishes corresponding geometric model, and domain is solved using tetrahedron mesh generation, then by selecting scalar hierarchical basis functions, and the finite element eigen[value of Flight Vehicle Structure is obtained with standard finite element Eigenanalysis method, carry out the implicit efficiency restarted Arnoldi alternative manners and solve the equation in accelerating ARP ACK software packages finally by three layers of pretreatment of construction, finally obtain characteristic value and feature vector, that is vibration modal frequency and the vibration vibration shape, to realize quick model analysis.
Description
Technical field
The invention belongs to three-dimensional mechanical vibration analysis numerical technology field, it is related to a kind of based on three layers of pretreatment
Three-dimensional mechanical Modal Analysis analogy method.
Background technology
Chatter can occur when by various incentive actions for aircraft, such as subsonic speed leads to full machine vibration；Low supersonic speed
Shi Yinqi rudders and vertical fin vibration；Complete machine oscillation when gear down etc..Aircraft meeting under the action of above-mentioned excitation
Stress is unbalance, material failure, even structure are disintegrated, this designs gas-operated integratedization for being unfavorable for aircraft.Solve or reduce machine
All kinds of vibration problems of body structure, be frequently not it is simple increase the rigidity of structure, intensity can gather effect, be also possible to sometimes it is suitable its
Instead, because structural vibration problem is all related with the eigenfrequncies and vibration models of fuselage and its partial structurtes, aircraft is carried out
Vibration-mode analysis is very important.Model analysis can obtain the vibration characteristics of aircraft, be the important of its structure design
Can link avoid resonating when main check structure bears various load effects.Therefore quickly and effectively modal analysis technique is
The key of Flight Vehicle Design.General experimental test procedures are since its is with high costs, and the period, which is grown, is difficult to large-scale application, and Numerical-Mode
Quasi- method is since its is at low cost, the period is short, is easy to implement to obtain large-scale application.
All it is to use currently, when carrying out Modal Analysis analysis to Flight Vehicle Structure using various mechanics numerical computation methods
Finite element Eigenanalysis method, and most structural analysis business software is also using finite element method, such as
ANSYS, ABAQUS etc..Finite element analysis generally comprises, modeling, mesh generation, unit calculates, matrix is integrated, introduce boundary and
Excitation solves several steps such as generalized eigen equation, post-processing.In above process, it is most to consume to solve generalized eigen equation
Calculate the time and the step of memory, therefore it is crucial to seek a kind of efficient solution technique.
Widely used at present is that one kind implicitly restarting Arnoldi alternative manners to solve, and is needed in this course anti-
A linear equation is solved again.Preconditioning conjugate gradient is widely used in the solution of linear equation, and for eigenvalue problem,
Linear equation coefficient matrix is constant when due to each intrinsic iteration, only needs to do primary pretreatment, be considerably improved in this way
Computational efficiency.However the thought of preconditioning conjugate gradient is that original linear equation is transformed to one by pre-processing son
It is easy the new linear equation solved, importance of good pretreatment of this explanation to entire Arnoldi processes.Especially work as
When Flight Vehicle Structure complexity, mesh generation is more, and linear equation often reaches ten million rank, and general pretreatment is calculating the time
With it is often very huge on memory consumption, this will be unable to the model analysis that Flight Vehicle Structure is rapidly completed.Therefore construction one is needed
A efficient pretreatment improves the solution efficiency of preconditioning conjugate gradient, to improve the speed of the intrinsic iteration of Arnoldi
Degree, the final quick model analysis for realizing Flight Vehicle Structure.
Invention content
For above-mentioned there are problem or deficiency, to solve to construct high-efficiency pretreatment in finite element modal analysis, realize
The quick model analysis of Flight Vehicle Structure；The present invention provides a kind of three-dimensional mechanical Modal Analysis moulds based on three layers of pretreatment
Quasi- method.
The three-dimensional mechanical Modal Analysis analogy method based on three layers of pretreatment, includes the following steps：
A. target aircraft structure is subjected to finite element modeling, introduces displacement boundary conditions or stress boundary condition is established
Corresponding geometric model；
B. tetrahedron mesh generation is used to solve domain；
C. second order scalar hierarchical basis functions are selected, and target aircraft is obtained with the finite element Eigenanalysis method of standard
The finite element eigen[value of structure；
D. the implicit finite element restarted Arnoldi alternative manners solution step C and obtained in ARPACK software packages is used
Eigen[value, obtains eigenvalue λ and corresponding feature vector α, that is, amplitude vecotr, and Arnoldi alternative manners are produced per single-step iteration
Raw linear equation uses the preconditioning conjugate gradient based on three layers of pretreatment to solve, the specific configuration of three layers of pretreatment
Method is as follows：
It needs to solve following linear equation repeatedly during implicitly restarting Arnoldi iteration
Px=Myj (1)
Wherein matrix P is matrix to be pre-treated, and M is mass of system matrix, and x is intermediate vector to be asked, yjFor iteration to
Amount solves (1) formula using preconditioned conjugate gradient method, needs to solve following pretreatment system in preconditioning conjugate gradient
Nz=r (2)
Wherein N is pretreatment, and z waits seeking pretreatment vector, and r is residual vector；
First matrix P according to x, tri- direction block sortings of y, z obtain following matrix in block form form
Wherein PxxFor the matrix in the directions x, PyyFor the matrix in the directions y, PzzFor the matrix in the directions z, PxyAnd PyxFor the directions x and
The coupling matrix in the directions y, PxzAnd PzxFor the coupling matrix in the directions x and the directions z, PyzAnd PzyFor the coupling moment in the directions y and the directions z
Battle array, the form for taking first layer pretreatment sub are
To the block diagonal matrix P in (4) formulaxx, Pyy, PzzIt is pre- that the second layer is constructed using the property based on hierarchical basis functions
Processing：P is constructed firstxxThe second layer pretreatment son, according to single order basic function, the P that puts in order of second order basic functionxxIt writes
At following block form
Wherein P11For the matrix that single order basic function is formed, P22For the matrix that second order basic function is formed, P12And P21For single order base
Coupling matrix between function and second order basic function, it is following form to take second layer pretreatment
Matrix Pyy, PzzThe building method and matrix P of corresponding second layer pretreatmentxxThe second layer pretreatment son
Building method is the same, is named as N to the second layer pretreatment corresponding to them respectivelyy, Nz。
For the block diagonal matrix P in (6) formula11And P22It is decomposed using the incomplete cholesky of more wavefront to construct third
Layer pretreatment, matrix P11And P22Corresponding third layer pretreatment is respectively NlAnd Nh：First to matrix P11Carry out more waves
Preceding incomplete cholesky is decomposed, and obtains the form of following third layer pretreatment
Nl=(D0P0)-1LLT(P0TD0 T)-1. (7)
Wherein D0For diagonal matrix, P0Attach most importance to ordinal matrix, L is matrix P11Cholesky decompose lower triangular matrix, Nh's
Building method and NlBuilding method it is the same, complete three layers pretreatment son constructions；
E. the characteristic value to the acquisition of D steps and character pair vector carry out post-processing acquisition vibration modal frequency and correspondence is shaken
The dynamic vibration shape.
In conclusion the three-dimensional mechanical Modal Analysis analogy method for three layers of pretreatment that the present invention constructs can greatly improve
The solving speed of Arnoldi alternative manners realizes quick model analysis.
Description of the drawings
Fig. 1 is that the present invention is based on the flow charts of the three-dimensional mechanical Modal Analysis analogy method of three layers of pretreatment；
Fig. 2 is the finite element model figure of embodiment；
Fig. 3 is the calculated performance comparison diagram of embodiment and ANSYS softwares.
Specific implementation mode
Carry out the technical solution that the present invention will be described in detail with reference to the accompanying drawings and examples.
Referring to Fig.1, a kind of three-dimensional mechanical Modal Analysis analogy method based on three layers of pretreatment, includes the following steps：
A. target aircraft structure is subjected to finite element modeling, introduces displacement boundary conditions or stress boundary condition is established
Corresponding geometric model.
According to the characteristic of aircraft, introduces displacement boundary conditions and establish corresponding geometric model emulation total
Vibration Characteristics, as shown in Figure 2.
B. tetrahedron mesh generation is used to solve domain.
Solution domain after subdivision is artificially divided into multiple three-dimensional tetrahedral grids, thus by continuous geometry space
It is converted into discrete mesh space.
C. second order scalar hierarchical basis functions are selected, and target aircraft is obtained with the finite element Eigenanalysis method of standard
The finite element eigen[value of structure.
Final finite element Eigenanalysis equation
(-ω2M+K) α=0 (8)
Wherein M is mass matrix, K is eigenmatrix that stiffness matrix is referred to as system, and α is displacement amplitude to be asked vector,
ω is natural frequency to be asked.Above-mentioned M and K matrix is the eigenmatrix of system, matrix element and unit basic function and list
Member is discrete related, we are using second order hierarchical basis functions, basic function form here：
WhereinFor divalent radical function space, Dim refers to space dimensionality, λ1, λ2, λ3, λ4For volume coordinates function.From above formula
It can be seen that second order basic function includes single order basic function.
D. the implicit intrinsic side restarted Arnoldi alternative manners solution step C and obtained in ARPACK software packages is used
Journey, obtains eigenvalue λ and corresponding feature vector α, that is, amplitude vecotr, Arnoldi alternative manners per single-step iteration caused by line
Property equation use based on three layers pretreatment son preconditioning conjugate gradient solve.
To the eigenvalue problem of formula (8), we restart the following deformation equation of Arnoldi alternative manners solution using implicit
Wherein ω0To estimate minimum modal frequency.It is implicit restart Arnoldi iteration during need to solve repeatedly with
Lower equation
Px=Myj (11)
Wherein matrixX is intermediate vector to be asked, yjIt is iterative vectorized.We are using preconditioned conjugate ladder
Degree method solves (11) formula, needs to solve following pretreatment system in preconditioning conjugate gradient
Nz=r (12)
Wherein N is pretreatment, and z waits seeking pretreatment vector, and r is residual vector.
The solution of equation (12) formula is dependent on the property for pre-processing sub- N, here it is proposed that a kind of three layers pre-process son
Method constructs：First matrix P according to x, tri- direction block sortings of y, z obtain following matrix in block form form
Wherein PxxFor the matrix in the directions x, PyyFor the matrix in the directions y, PzzFor the matrix in the directions z, PxyAnd PyxFor the directions x and
The coupling matrix in the directions y, PxzAnd PzxFor the coupling matrix in the directions x and the directions z, PyzAnd PzyFor the coupling moment in the directions y and the directions z
Battle array.We take first layer to pre-process sub form
This is first layer pretreatment, for the block diagonal matrix P in (14) formulaxx, Pyy, PzzWe are using based on lamination
The property of basic function pre-processes son, matrix P to construct the second layerxx, Pyy, PzzThe corresponding second layer pre-processes sub- building method
It is the same, we are named as N to the second layer pretreatment corresponding to them respectivelyx, Ny, Nz, here with matrix PxxFor
Explanation.First, in accordance with single order basic function, the P that puts in order of second order basic functionxxIt is written as block form
Wherein P11For the matrix that single order basic function is formed, P22For the matrix that second order basic function is formed, P12And P21For single order base
Coupling matrix between function and second order basic function.It is following form that we, which take second layer pretreatment,
For the block diagonal matrix P in (16) formula11And P22We decompose to construct using the incomplete cholesky of more wavefront
Third layer pretreatment, matrix P11And P22Corresponding third layer pretreatment is respectively NlAnd Nh, their building method is
The same, equally we are with P11For illustrate.We are matrix P11It is decomposed to carrying out the incomplete cholesky of more wavefront, then
The form of following third layer pretreatment can be obtained
Wherein D0For diagonal matrix, P0Attach most importance to ordinal matrix, L is matrix P11Cholesky decompose lower triangular matrix.This
Three layers of pretreatment son construction of sample finish.Solutions of the sub- N applied to (12) formula is pre-processed, we can quickly solve in this way
(11) formula realizes quick model analysis to accelerate implicitly to restart the convergence rate of Arnoldi iteration.Pass through ARPACK softwares
Implicit in packet restarts Arnoldi alternative manners, and we finally find out series of features value λi(i=1,2 ..., n) and it is corresponding
Feature vector αi=(i=1,2 ..., n) i.e. amplitude vecotr, wherein n are mode number of concern.
E. the characteristic value to the acquisition of D steps and character pair vector carry out post-processing acquisition vibration modal frequency and correspondence is shaken
The dynamic vibration shape.
Eigenvalue λ is obtained to D stepsiIt is handled, corresponding vibration modal frequency is
According to corresponding feature vector αi, carrying out FEM post-processing in conjunction with basic function property can obtain solving in domain
Displacements Distribution, here it is the vibration vibration shapes of corresponding vibration modal frequency.
Fig. 2 is the finite element model figure for embodiment；Fig. 3 shows the embodiment and ANSYS software meters of the present invention program
The comparison of performance is calculated, as a result can be seen that fast 2 times of the calculating speed ratio ANSYS softwares of specific embodiment, and memory consumption is only
Only it is the 76% of ANSYS softwares.
Claims (1)
1. a kind of three-dimensional mechanical Modal Analysis analogy method based on three layers of pretreatment, includes the following steps：
A. target aircraft structure is subjected to finite element modeling, introduces displacement boundary conditions or stress boundary condition is established and corresponded to
Geometric model；
B. tetrahedron mesh generation is used to solve domain；
C. second order scalar hierarchical basis functions are selected, and target aircraft structure is obtained with the finite element Eigenanalysis method of standard
Finite element eigen[value；
D. use in ARPACK software packages implicit restart Arnoldi alternative manners to solve the finite element that step C is obtained intrinsic
Equation obtains eigenvalue λ and corresponding feature vector α, that is, amplitude vecotr, and Arnoldi alternative manners are often caused by single-step iteration
Linear equation uses the preconditioning conjugate gradient based on three layers of pretreatment to solve；
The specific configuration method of three layers of pretreatment is as follows：
It needs to solve following linear equation repeatedly during implicitly restarting Arnoldi iteration
Px=Myj (1)
Wherein matrix P is matrix to be pre-treated, and M is mass of system matrix, and x is intermediate vector to be asked, yjIt is iterative vectorized, adopts
(1) formula is solved with preconditioned conjugate gradient method, needs to solve following pretreatment system in preconditioning conjugate gradient
Nz=r (2)
Wherein N is pretreatment, and z waits seeking pretreatment vector, and r is residual vector；First matrix P according to x, tri- directions y, z
Block sorting obtains following matrix in block form form
Wherein PxxFor the matrix in the directions x, PyyFor the matrix in the directions y, PzzFor the matrix in the directions z, PxyAnd PyxFor the directions x and the directions y
Coupling matrix, PxzAnd PzxFor the coupling matrix in the directions x and the directions z, PyzAnd PzyFor the coupling matrix in the directions y and the directions z, take
First layer pre-processes sub form
To the block diagonal matrix P in (4) formulaxx, Pyy, PzzSecond layer pretreatment is constructed using the property based on hierarchical basis functions
Son；P is constructed firstxxThe second layer pretreatment son, according to single order basic function, the P that puts in order of second order basic functionxxWrite as
Lower block form
Wherein P11For the matrix that single order basic function is formed, P22For the matrix that second order basic function is formed, P12And P21For single order basic function
Coupling matrix between second order basic function, it is following form to take second layer pretreatment
Matrix Pyy, PzzThe building method and matrix P of corresponding second layer pretreatmentxxThe second layer pretreatment son construction
Method is the same, is named as N to the second layer pretreatment corresponding to them respectivelyy, Nz；
For the block diagonal matrix P in (6) formula11And P22It is decomposed using the incomplete cholesky of more wavefront and is located in advance to construct third layer
Reason, matrix P11And P22Corresponding third layer pretreatment is respectively NlAnd Nh, first to matrix P11It is endless to carry out more wavefront
Full cholesky is decomposed, and obtains the form of following third layer pretreatment
Wherein D0For diagonal matrix, P0Attach most importance to ordinal matrix, L is matrix P11Cholesky decompose lower triangular matrix, NhConstruction
Method and NlBuilding method it is the same, complete three layers pretreatment son constructions；
E. the characteristic value to the acquisition of D steps and character pair vector carry out post-processing acquisition vibration modal frequency and correspondence is shaken
Type.
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| CN111400820A (en) * | 2018-12-30 | 2020-07-10 | 长城汽车股份有限公司 | Method for determining connection point of non-bearing type electric automobile frame, non-bearing type electric automobile frame and electric automobile |
| CN111400940A (en) * | 2018-12-30 | 2020-07-10 | 长城汽车股份有限公司 | Method for determining connection point of rear end structure of vehicle frame |
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