CN106960078B - It is a kind of for solving the efficient calculation method of local material nonlinear problem - Google Patents
It is a kind of for solving the efficient calculation method of local material nonlinear problem Download PDFInfo
- Publication number
- CN106960078B CN106960078B CN201710113194.XA CN201710113194A CN106960078B CN 106960078 B CN106960078 B CN 106960078B CN 201710113194 A CN201710113194 A CN 201710113194A CN 106960078 B CN106960078 B CN 106960078B
- Authority
- CN
- China
- Prior art keywords
- nonlinear
- node
- matrix
- increment
- deformation
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/17—Mechanical parametric or variational design
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Geometry (AREA)
- General Physics & Mathematics (AREA)
- Evolutionary Computation (AREA)
- General Engineering & Computer Science (AREA)
- Computer Hardware Design (AREA)
- Computational Mathematics (AREA)
- Mathematical Analysis (AREA)
- Mathematical Optimization (AREA)
- Pure & Applied Mathematics (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
Abstract
The invention discloses a kind of calculation methods of Efficient Solution local material nonlinear problem, belong to structural analysis technique field.Nonlinear deformation is changed into the virtual load acted on elastic construction by this method, so that stiffness matrix remains unchanged in nonlinear analysis, it is only necessary to once be decomposed；The partial structurtes information for entering nonlinear deformation state is only considered in equation building process, the small-scale matrix for representing local nonlinearity to one is then only needed to carry out decomposition operation during iterative solution, the real-time update and decomposition in conventional method to extensive Bulk stiffness matrix are avoided, the computational efficiency of local nonlinearity problem is effectively improved.In addition, the present invention is not limited to specific material constitutive relation and numerical model, may be used on it is numerous be related to the subject and research field of structural nonlinear calculating, there is stronger versatility and wide applicability.
Description
Technical field
The invention belongs to structural analysis technique fields, more specifically, being related to a kind of non-linear for solving local material
The efficient calculation method of problem.
Background technique
Non-linear behaviour of the structure under extreme environment load action is calculated in numerous researchs using technology of numerical simulation
Field is widely used.Due to structural load-deformation relationship non-linear attributes, step-type increment need to be usually used
Format is simultaneously solved in conjunction with iterative algorithm appropriate, and during this, the Bulk stiffness matrix of structure need to be in calculating process
It is constantly updated and decomposition operation, with the increase of computation model scale and fining degree, the scale of stiffness matrix is also fast
Speed increases, at this point, the real-time update of extensive stiffness matrix and the key for being decomposed into restriction nonlinear problem computational efficiency.It is right
In material non-linearity question, usually only nonlinear deformation occurs for structure partial, and remaining major part will be in initial elasticity always
Deformation state it is not intended that this feature in conventional method calculating process, thus can not achieve the difference of elasticity and non-linear partial
It Hua not treat, for this purpose, the local feature of nonlinear deformation how to be made full use of to realize such issues that efficient numerical solution becomes
Research emphasis.
Summary of the invention
In order to overcome the shortcomings of that above-mentioned existing method, the present invention utilize Woodbury formula, by considering material nonlinearity
The local feature of problem, proposes a kind of efficient calculation method for structure partial nonlinear problem, and calculating process only needs pair
One small-scale matrix for representing local nonlinearity deformation is updated and decomposition operation, avoids in conventional method to extensive
The corresponding operation that Bulk stiffness matrix carries out.Invention has relatively broad applicability, can be used for the non-linear of various fields
In structural analysis.
Technical solution of the present invention:
It is a kind of for solving the efficient calculation method of local material nonlinear problem, steps are as follows:
(1) numerical model for being used for structural analysis is established, and presets several nonlinear nodes in the structure；
(2) integrally-built initial elasticity stiffness matrix K is calculatedeAnd triangle decomposition is carried out to it, if structure total displacement is certainly
It is n by degree, then matrix KeScale be n × n；
(3) any non-linear incremental computations are walked, under increment load Δ F effect, only considers to enter nonlinear deformation
Nonlinear node in state regional area and the nonlinear deformation vector for establishing corresponding incremental form:
ΔΕ″p=[Δ ε "1 Δε″2 ... Δε″m]T (1)
In formula, m is the nonlinear node number entered in nonlinear deformation state regional area in the incremental step；Δε″i
The increment nonlinear deformation for representing wherein i-th of nonlinear node, wherein 1≤i≤m；If each nonlinear node is non-linear
Deformation is made of p component, then Δ Ε "pFor a pm rank vector, wherein each element represents a Nonlinear Free degree；
(4) the displacement structure increment under increment load Δ F effect is solved, it may be assumed that
In formula, Δ X represents displacement increment；ΔFp=K 'rΔΕ″p, it is the nonlinear additional virtual load of representative structure,
Middle matrix K 'rFor nonlinear deformation vector Δ Ε "pWith additional virtual load Δ FpThe stiffness matrix of relationship, order are between
n×pm.Nonlinear deformation vector Δ Ε " under given load increment Δ F effectpFollowing formula can be used to solve:
In formula,It is K 'rTransposition, be pm × n rank matrix, represent in the elasticity at displacement of joint and nonlinear node
Relationship between power, elastic internal force refer to the structure with initial elasticity attribute be subjected to displacement change non-linear hour node at generate answer
Power；K″prThe relationship between the nonlinear deformation and elastic internal force at nonlinear node is represented, is pm × pm rank matrix, needs basis
Material constitutive relation at nonlinear node determines.
In step 1, nonlinear node position and quantity in structure need to be determined according to the required precision of particular problem, non-thread
Property deformation field can be obtained by interpolation method.
In step 3, the nonlinear deformation under free position is equal to according to the remaining change after the unloading of material initial elasticity rigidity
Shape；Vector Δ Ε "pIn deformed comprising all nonlinear nodes into nonlinear deformation state in current delta step flowering structure,
It but does not include that the nonlinear node in initial elasticity deformation state deforms.
In step 3, matrix K 'rAndOccur that position is related with non-linear in numerical model, and it is non-with material
Linear degree is unrelated, and each element in matrix only needs to calculate once, without computing repeatedly during nonlinear iteration.
In step 3 and step 4, stiffness matrix KeInverse matrix and vector or multiplication of matrices operation can be by KeThree
Angle decompose and back substitution calculate complete, since the matrix remains unchanged in the analysis process, triangle decomposition only need before analysis into
Row is primary.
In step 4, the displacement increment accounting equation and Woodbury formula of any non-linear incremental computations step are of equal value, writeable
For the mathematic(al) representation of following form:
In the present invention, each calculating step is to matrixCalculation amount needed for decomposing becomes using solution
When main calculating consumption, the scale of the matrix is pm × pm (suitable with Nonlinear Free degree mesh), represent enter it is non-linear
The regional area of deformation state.When only small part enters non-linear to structure, there is pm < < n, at this time to matrixTo far smaller than Bulk stiffness matrix be carried out in conventional method by decompose consumed calculation amount
Calculation amount needed for decomposing, so as to be obviously improved the computational efficiency of nonlinear problem.
Beneficial effects of the present invention:
1. efficient NONLINEAR CALCULATION.For the non-linear material non-linearity question for only resulting from structure partial, the present invention
The small-scale carry out decomposition operation for representing local nonlinearity to one is only needed when solving, is avoided in existing method to larger
Entire the stiffness matrix real-time update and decomposition operation that carry out, can effectively be promoted under the premise of guaranteeing necessary computational accuracy non-
The solution efficiency of linear problem.
2. the extensive scope of application.The present invention is not limited to specific material constitutive relation and numerical model, may be used on
It is numerous to be related to the subject and research field of structural nonlinear calculating, thus there is wide applicability.
Detailed description of the invention
Fig. 1 is the analysis model figure of embodiment.
Fig. 2 is calculation flow chart of the invention.
Specific embodiment
The present invention provides a kind of for solving the efficient numerical calculation method of local material nonlinear problem, below in conjunction with
Attached Example and technical solution further illustrate a specific embodiment of the invention.Drawings and examples are only to illustrate the invention
Embodiment, do not constitute any limitation of the invention.
Embodiment:
1. illustrating side proposed by the invention for numerical value that some is made of two node truss elements shown in Fig. 1 calculates
Embodiment of the method in NONLINEAR CALCULATION.For plane stress element, consider that its section axial direction strain stress and axle power N's is non-thread
A nonlinear node is arranged in unit and it is enabled to be located among unit for sexual intercourse, as shown in Figure 1, point of its section deformation
Solve expression formula are as follows:
ε=ε '+ε " (1)
In formula, ε ' represents section line elastic strain, i.e., section when being loaded onto axle power N using section initial elasticity rigidity is become
Shape；ε " represents section nonlinear strain.
2. synthesizing integrally-built initial elasticity stiffness matrix KeAnd triangle decomposition is carried out to it, it may be assumed that
Ke=LDLT (2)
In formula, L is unit lower triangular matrix, and D is diagonal matrix.
3. in conjunction with the iterative calculation process of the invention in nonlinear solution processes that Fig. 2 is provided, any iteration incremental step
Calculating can carry out as follows:
Step 1: carrying out the determination of location mode, for calculating under the conditions of current displacement nonlinear node in each unit
The materials behavior at place, including force on cross-section N and material tangent modulus Et, and further whether judging unit enters nonlinear deformation
State, if having E at certain unit nonlinear nodet≠Ee, then determine that the unit enters nonlinear deformation state, wherein EeFor the list
The initial elastic modulus of material at first nonlinear node.
Step 2: according to the materials behavior by nonlinear node in the resulting each unit of step 1, update matrix K 'rWithAnd calculating matrix K "prIf shared m unit enters nonlinear deformation state (in this example, there is m≤4), then matrix
K″prIt is represented by
Wherein, A is area of section；L is element length；(.)iRepresent material properties relevant to i-th of nonlinear node.
Step 3: the displacement increment Δ X under structure increment load Δ F effect is calculated using Woodbury formula, it may be assumed that
The matrix K provided using formula (2)eTriangle decomposition form, then above formula be related to and matrixRelated multiplication
Operation can be calculated by back substitution and be completed.
Step 4: convergence judges and updates for next load increment for calculating step.It needs to check that gained calculates knot at this time
Whether fruit reaches within defined error range, if convergence, carries out the calculating of next incremental step, if not restraining, continue
It is iterated.
Claims (1)
1. a kind of for solving the efficient calculation method of local material nonlinear problem, which is characterized in that steps are as follows:
(1) numerical model for being used for structural analysis is established, and presets several nonlinear nodes in the structure；
(2) integrally-built initial elasticity stiffness matrix K is calculatedeAnd triangle decomposition is carried out to it, if structure total displacement number of degrees of freedom,
It is n, then matrix KeScale be n × n；
(3) any non-linear incremental computations are walked, under increment load Δ F effect, only considers to enter nonlinear deformation state
Nonlinear node in regional area and the nonlinear deformation vector for establishing corresponding incremental form:
ΔΕ″p=[Δ ε "1 Δε″2 ... Δε″m]T (1)
In formula, m is the nonlinear node number entered in nonlinear deformation state regional area in the incremental step；Δε″iRepresent it
In i-th of nonlinear node increment nonlinear deformation, wherein 1≤i≤m；If the nonlinear deformation of each nonlinear node is by p
A component forms, then Δ Ε "pFor a pm rank vector, wherein each element represents a Nonlinear Free degree；
(4) the displacement structure increment under increment load Δ F effect is solved, it may be assumed that
In formula, Δ X represents displacement increment；ΔFp=K 'rΔΕ″p, it is the nonlinear additional virtual load of representative structure, wherein square
Battle array K 'rFor nonlinear deformation vector Δ Ε "pWith additional virtual load Δ FpThe stiffness matrix of relationship between, order be n ×
pm；Nonlinear deformation vector Δ Ε " under given load increment Δ F effectpFollowing formula can be used to solve:
In formula,It is K 'rTransposition, be pm × n rank matrix, represent elastic internal force at displacement of joint and nonlinear node it
Between relationship, elastic internal force refer to the structure with initial elasticity attribute be subjected to displacement change non-linear hour node at generate stress；
K″prThe relationship between the nonlinear deformation and elastic internal force at nonlinear node is represented, is pm × pm rank matrix, it need to be according to non-thread
Property node at material constitutive relation determine.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710113194.XA CN106960078B (en) | 2017-03-01 | 2017-03-01 | It is a kind of for solving the efficient calculation method of local material nonlinear problem |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710113194.XA CN106960078B (en) | 2017-03-01 | 2017-03-01 | It is a kind of for solving the efficient calculation method of local material nonlinear problem |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN106960078A CN106960078A (en) | 2017-07-18 |
| CN106960078B true CN106960078B (en) | 2019-09-27 |
Family
ID=59470049
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201710113194.XA Active CN106960078B (en) | 2017-03-01 | 2017-03-01 | It is a kind of for solving the efficient calculation method of local material nonlinear problem |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN106960078B (en) |
Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106096257A (en) * | 2016-06-06 | 2016-11-09 | 武汉理工大学 | A kind of non-linear cable elements analyzes method and system |
-
2017
- 2017-03-01 CN CN201710113194.XA patent/CN106960078B/en active Active
Patent Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106096257A (en) * | 2016-06-06 | 2016-11-09 | 武汉理工大学 | A kind of non-linear cable elements analyzes method and system |
Also Published As
| Publication number | Publication date |
|---|---|
| CN106960078A (en) | 2017-07-18 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Angeli | A tutorial on Chemical Reaction Networks dynamics | |
| Liew et al. | Meshfree method for large deformation analysis–a reproducing kernel particle approach | |
| Duddu et al. | A combined extended finite element and level set method for biofilm growth | |
| Gholizadeh et al. | Design optimization of tall steel buildings by a modified particle swarm algorithm | |
| CN103324850B (en) | Twice polycondensation parallel method of finite element two-stage subregion based on multifile stream | |
| CN101887474B (en) | Structural vibration analysis method based on finite element method and generalized Fourier series method | |
| Zuo et al. | Sensitivity reanalysis of static displacement using Taylor series expansion and combined approximate method | |
| CN111125963B (en) | Numerical simulation system and method based on Lagrange integral point finite element | |
| Bilotta et al. | Three field finite elements for the elastoplastic analysis of 2D continua | |
| CN107368649A (en) | A kind of sequence optimisation test design method based on increment Kriging | |
| CN103942381B (en) | State near field dynamics method used for predicting airplane aluminum alloy structure performance | |
| Yu et al. | Time-variant reliability analysis via approximation of the first-crossing PDF | |
| CN110955941A (en) | Vector field-based composite material structure optimization design method and device | |
| Chakraborty et al. | An efficient algorithm for building locally refined hp–adaptive H-PCFE: Application to uncertainty quantification | |
| CN108491591A (en) | A kind of hot environment lower curve stiffened panel finite element method | |
| CN104504189A (en) | Large-scale structural design method under random excitation | |
| Wu et al. | Static reanalysis of structures with added degrees of freedom | |
| CN106960078B (en) | It is a kind of for solving the efficient calculation method of local material nonlinear problem | |
| CN116306178B (en) | Structural strain inversion method based on self-adaptive shape function and equivalent neutral layer | |
| CN112446071B (en) | Lattice type arch rigid frame optimization design method and device | |
| CN111930491A (en) | Global communication optimization acceleration method and device and computer equipment | |
| CN107562991B (en) | Structural nonlinear buckling equilibrium path tracking method completely based on reduced order model | |
| CN106021186B (en) | A kind of multiple dimensioned alternative manner of Efficient Solution large-scale nonlinear Random Structural Systems state | |
| CN106934133B (en) | The nonlinear finite element stiffness matrix update method decomposed based on elastoplasticity | |
| CN115659843A (en) | Method for constructing display dynamics model by using artificial intelligence technology |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |