CN106777538A - A kind of bearing structure method of topological optimization design based on limited cellular description - Google Patents
A kind of bearing structure method of topological optimization design based on limited cellular description Download PDFInfo
- Publication number
- CN106777538A CN106777538A CN201611056819.5A CN201611056819A CN106777538A CN 106777538 A CN106777538 A CN 106777538A CN 201611056819 A CN201611056819 A CN 201611056819A CN 106777538 A CN106777538 A CN 106777538A
- Authority
- CN
- China
- Prior art keywords
- bearing structure
- growth
- grid
- reinforcement
- topological
- 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.)
- Pending
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
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
-
- 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
Abstract
The present invention provides a kind of bearing structure method of topological optimization design based on limited cellular description, and mentality of designing is will to equip the discrete accumulating growth course for turning to carrying reinforcement structure of bearing structure layout process, and its step is：Initial growth point is set on equipment bearing structure matrix；Based on limited cellular method, find and carry reinforcement structure optimal growth direction；One step growth is completed, growing point of the distal point that will be grown as next step；Iteration updates bearing structure layout；Judge whether to meet termination condition and terminate.Method different from the past, when carrying out equipment bearing structure design using this method, its position will not be fettered by fixed grid node, can obtain the equipment bearing structure design result of global optimum, quite convenient for engineering application, the method is largely effective to equipment reinforcement layout designs.
Description
Technical field
The invention belongs to industrial equipment bearing part Optimization Design field, and in particular to one kind is limited based on actual situation node
The equipment reinforcement layout intellectualized design method of meta analysis.
Background technology
In the design process of existing industrial equipment bearing structure, mostly using traditional reinforcement arrangement form, mainly
The combination of intersecting parallels, rice font etc. or above form is concentrated on, design form is excessively single, it is impossible to which obtaining has high specific stiffness
Design.At the same time, existing reinforcement layout design method depends on classical mechanics and designer's experience,
Verify that, to obtain final scheme, whole design process cannot realize intelligent and automation, cause by finite element analysis repeatedly
Design efficiency is low, it is impossible to meet the design requirement of industrial equipment.
When growth formula reinforcement layout is carried out using conventional finite element method, the growth end of its reinforcement fragment needs definition
On the grid node for being divided, the reinforcement fragment direction of growth resulting when grid is more sparse can not reach the overall situation most
Excellent solution；In order to improve the precision of solution, it is necessary to encrypt finite element grid, mesh generation is closeer, will directly result in calculating
Scale and memory space increase sharply, so as to substantially reduce computational efficiency, while such as fruit structure during grid division
Shape matching itself is complicated, then will be very easy to produce the i.e. lopsided grid of grid of poor quality, and calculating process will be unable to
Carry out.
The content of the invention
In order to overcome the shortcoming of above-mentioned prior art, the present invention to provide a kind of bearing structure based on limited cellular description and open up
Flutter Optimization Design.
To reach above-mentioned purpose, present invention employs following technical scheme：
The discrete accumulation for turning to some carrying reinforcement structures on bearing structure matrix of bearing structure layout process will be equipped
Formula growth course, the accumulating growth course for each carrying reinforcement structure carries out topological structure optimization, by topological structure
Optimization causes that the mechanical property of the bearing structure is optimal；The mechanical property of bearing structure is having in topological structure optimization
Calculating is analyzed based on limit cell description, the limited cellular description refers to with rule by the geometrical model of bearing structure
The grid cell that then structure but size have differences is divided, and makes the border of the geometrical model with the geometrical model
Corresponding grid cell be indicated.
The topological structure optimization specifically includes following steps：
1) setting carries reinforcement structure initial growth point；
2) based on limited cellular description, the optimal growth direction for carrying reinforcement structure is found；
3) complete to carry the one step growth of reinforcement structure according to optimal growth direction and growth step-length, knot is strengthened by carrying
Distal point after structure one step growth as next one-step growth growing point；
4) repeat step 2) and step 3), update the topological iteration of carrying reinforcement structure, until meet iteration terminating
Condition.
The step 2) specifically include following steps：Knot is strengthened in the carrying for growing regular length respectively to periphery from growing point
Structure, then calculate correspondence bearing structure mechanical property, by mechanical property it is optimal when it is corresponding growth angle-determining for carry plus
The direction of growth of strong structure.
The iteration termination condition refers to that the overall volume for carrying reinforcement structure reaches given volume upper limit.
The grid cell of the regular structure of apparatus carries out division and specifically includes following steps：By the geometry of bearing structure
Model insertion divides initial mesh in bounding box to the bounding box, and grid subdivision is carried out to initial mesh, thin by grid
Divide the border for recovering the geometrical model.
The grid subdivision is using quaternary tree or Octree refinement strategy.
The grid subdivision is comprised the following steps：
A) initial mesh is judged with the inclusion relation on the geometrical model border, for comprising geometrical model border
Initial mesh, then further decile；For the initial mesh not comprising geometrical model border, then do not continue to divide；
B) further after decile, the grid to still including geometrical model border proceeds decile；
C) repeat step b), until will finally divide grid that the grid cell for obtaining classified as in geometrical model with
Grid outside geometrical model.
The mechanical property is selected from strain energy.
The grid cell composes grid using rank.
The carrying reinforcement structure is selected from reinforcement.
Beneficial effects of the present invention are：
The geometrical model for equipping bearing structure is embedded into the present invention grid cell of rule, and then is retouched using limited cellular
State and treat the mechanical property of analytical structure and carry out high-precision analysis, it is to avoid conventional finite element method is in mesh generation when institute face
To lopsided grid problem, while generation bearing structure will not be fettered by existing grid, can freely arrange so that
Global optimum's result can be obtained；This method design output result become apparent from than traditional topological optimization result it is distinguishable, can be straight
It is connected in actual engineering design and scheme support is provided.The present invention is largely effective to equipment reinforcement layout designs.
Further, because the present invention completes bearing structure layout designs by calculating strain energy, it is possible to generation
Rigidity is substantially better than the result of Experience Design.
Brief description of the drawings
Fig. 1 is the generation schematic diagram of initial cell；
Fig. 2 is the schematic diagram of structural model boundary grid subdivision to be analyzed；
Fig. 3 is Gauss integration point schematic diagram；
Fig. 4 is the equipment model schematic (geological information and boundary condition) for importing；
Fig. 5 is setting growing point position and optimizing interval diagram；
Fig. 6 is the growth course and result schematic diagram of reinforcement.
Specific embodiment
The present invention is described in further details with reference to the accompanying drawings and examples.
Bearing structure method of topological optimization design based on limited cellular description of the present invention, comprises the following steps：
1) Geometric Modeling of structure to be analyzed：Simple geometric properties such as point, line, quadrangle, hexahedron etc. can be certainly
Row is set up, and the geometrical model of labyrinth can import the STL formatted files of CAD software generation.
2) material parameter of structure to be analyzed is set：Poisson's ratio, elastic modelling quantity, density.
3) mesh generation
Initially set up the bounding box (initial cell) of the geometrical model (structural model referred to as to be analyzed) of structure to be analyzed.It is right
Initial cell carries out an initial cut, forms initial cell (initial mesh), follow-up mesh generation and without the concern for treating
The detailed shape of analytical structure model, but carried out using regular quaternary tree/Octree, final grid (final cell) is formed,
It is embedded into the grid cell of rule (two dimension is quadrangle, three-dimensional is hexahedron) so as to be analysed to structural model.Final
Gauss integration point is generated in cell, the high-precision calculating of analytical structure model mechanics performance is treated in realization.
Mesh generation is comprised the following steps that：
Step 3.1) consider the bounding box O of structural model to be analyzedeThe weak form balance side of the elastic problem in (Fig. 1) region
Cheng Wei：
U is motion vector, and v is test function, and L is standard strain deformation operator, and C is elastic matrix, and f is muscle power, and t is outer
Power, Γ is the border of model to be analyzed, ncIt is number of cells；α is the indicator function of definitionFor true
The profile of fixed structural model to be analyzed, it is 1 that the part in model takes α, and the part α not in model is 0；
By taking two-dimensional geometry model as an example, initial cell is split first, Nx, Ny that specific segmentation number is set by the user
Determine (the XY length according to initial cell proportionally determine, often short side is divided into 4 parts or more in practice).After segmentation,
Initial cell forms Nx*Ny daughter cell, and these daughter cells are referred to as initial cell, the section needed for for generating FEM calculation
Point.The subsequent divided of grid uses plane quadtree approach, and grid division step is：To initial cell and the bag on geometrical model border
Judged containing relation, for the initial cell comprising geometrical model border, by its further quartering；For not comprising geometry
The daughter cell of model boundary, then do not continue to divide.If initial cell continues to divide, the daughter cell of gained will be divided
Divide depth and add 1.For whole quaternary tree, it divides the division depth that depth is equal to most deep daughter cell.This process is not
Disconnected iteration is carried out, and (depth is often taken in practice for 5~8 to terminate bar until the division depth of quaternary tree is equal to set value
Part).Finally, classification is analyzed to final cell, the cell in geometrical model is defined as inner cell, otherwise is then defined as
Outer cell (Fig. 2)；
Step 3.2) conventional finite element Meshing Method be directly set up on geometrical model, needed for FEM calculation
The grid node of node and geometrical model unify, computational accuracy is strictly limited by mesh generation result with computation complexity.No
With the present invention is that necessary node in p-type FEM calculation is generated in initial cell, and grid subdivision is geometry mould
A kind of space lattice expression-form of type, its precision does not influence the calculating of finite element node, only influences next step Gauss integration
As a result；
After initial division grid, in addition to existing positioned at the physical node of unit angle point, also exist and be located in unit
Dummy node；Traditional c is used in the conventional finite element method0Type unit, and then compose unit using rank herein.Rank spectrum unit
Feature is collectively formed by dummy node and physical node, is referred to as generalized node, and c0Type unit is only made up of physical node.In rank spectrum
In unit, physical node is traditional c0Node in type unit, and dummy node includes rib node, face node and body node.P-type has
The raising of the first solving precision of limit is completed by rising rank to unit.During liter rank, generalized node gradually increases, but by
The characteristics of rank spectrum unit has adoption property, i.e., Low-Order Elements in FEM approximate spatial is a subset list of Element of High Order approximate spatial
Unit, it is on the basis of keeping original Low-Order Elements in FEM node constant, to increase new generalized node to rise rank；It is with hexahedral element
Example, detailed process is as follows：
(1) as p=1, rank spectrum unit only contains 8 physical nodes, with traditional c0Type unit is identical, and (p is composed for unit rank
Number)；
(2) as p=2,12 rib nodes are increased on the basis of 1 rank unit；
(3) as p=3,12 rib nodes are increased on the basis of 2 rank units；
(4) as p=4,12 rib nodes and 6 face nodes are increased on the basis of 3 rank units；
(5) as p=5,12 rib nodes and 6 face nodes are increased on the basis of 4 ranks；
(6) as p=6,12 rib nodes, 6 face nodes and 1 individual nodes are increased on the basis of 5 ranks.
Step 3.3) computing unit stiffness matrix is needed after grid division unit, from Gauss integration in unit
Numerical integration is carried out, the numerical solution of stiffness matrix is asked for；
Gauss integration needs to set Gauss integration point when numerical integration is carried out, if the exponent number for taking rank spectrum unit is p,
Then because the size of each level unit is different, on the first layer unit (initial cell) each orthogonal direction when being integrated
P+1 Gauss integration point is uniformly arranged, successively successively decreases 1 to point number afterwards, when each level unit sets Gauss integration point
Ignore Gauss integration point (Fig. 3) in outer cell；The numerical integration of element stiffness matrix is completed at each point, afterwards will be each
Element stiffness matrix is assembled into Bulk stiffness matrix, and the process for constructing Bulk stiffness matrix is identical with conventional finite element method.
4) boundary condition is applied
According to actual condition, using Newman boundary condition (Neuman conditions) or Dirichlet boundary conditions
(Dirichletcondtions) corresponding boundary condition is applied；
When force boundary condition is applied, selection is using Newman boundary condition (Neuman conditions), Newman perimeter strip
Part is a kind of " zero tractive force condition ", in the case that this " zero tractive force " is equivalent to assume that the material in extension field is zero stiffness
Carry out；Uneven Newman boundary condition can directly be integrated by corresponding curve and surface and obtained；
Selection Dirichlet boundary conditions (Dirichletcondtions), Di Li Crays when displacement boundary conditions are applied
Boundary condition can be realized approximately by assuming the method for " rigid strip " at displacement constraint in extension field internal memory；It is this
Assuming that the method for " rigidity band " meets the physical model that finite element applies displacement boundary conditions in principle.
5) strain energy is calculated
In each inner cell, motion vector u can be estimated as：
U=NU
Wherein N is form function matrix, and U is unknown vector.Step 3.1 is substituted the above to based on Galerkin method) described in it is weak
In situation equilibrium equation, the formulation statement of global cell is can obtain：
KU=F
Wherein K is Bulk stiffness matrix, and F is global load vectors.The two overall situation amounts are by the group of limited cellular matrix
What dress was obtained：
Wherein Kc is that c-th element stiffness matrix of cell, Fc are that c-th the unit stress of cell, A are assembling matrix.
The boundary condition in step is introduced into, the strain energy J of structural model to be analyzed is calculated：
6) thin plate reinforcing rib structure layout optimization design
By taking the design of thin plate reinforcing rib structure as an example, the structural model of its reinforcement layout optimization problem includes substrate and rib
Two parts, substrate and rib are expressed using solid element.By base plan U (X, Y) as reinforcement layout optimization design
Space, the X of initial cell, Y-direction size is determined that the Z-direction size of initial cell is by substrate height and rib by base plan
Maximum height (maximum height is generally equal to substrate height) sum is determined.Rib in base plan arranged direction θ (xi、yiIt is the rib starting point coordinate under each growth step-length, xj、yjIt is the muscle under each growth step-length
Bar terminates point coordinates), rib height h, width b be set to fixed value, the rib under each growth step-length is defined as muscle
Bar section.The position of initial growth point is generally determined as the position of obligatory point or the position of stress point, if multiple obligatory points
Or stress point, then define multiple initial growth points.
The target of reinforcement layout optimization is to obtain an ordered set P being made up of rib section arranged direction.Rib section
Layout according to the geometrical topology as reinforcement of the composition that puts in order of element in ordered set P is distributed.Thin plate reinforcement
The layout optimization problem of structure can be described as ensureing that material consumption, no more than on the premise of a certain upper limit, is found and arranges reinforcement
Optimal path so that certain mechanical property (such as strain energy, minimal deformation) of reinforcement thin plate is optimal, its Mathematical Modeling
Can be expressed as follows：
Find:
Min:f(P)
Subject to:W(P)≤W0
P is the ordered set of rib section arranged direction composition；F (P) is design object, and W (P) is reinforcement material requested body
Product；W0It is the material volume upper limit set in advance；U refers to base plan scope.
The step of reinforcement intelligentized design is：
Step 1) setting reinforcement growing point position, so-called reinforcement growing point is exactly the position of reinforcement initial growth,
Reinforcement will at the growing point accumulating segmentation growth；
Step 2) determine the direction of growth of reinforcement：With direction of growth θ as two points of variable uses at each growing point
Method finds optimal strain energy direction.Specific method is to grow one section of reinforcement of regular length, Ran Houji to periphery θ degree direction
The lower structural strain energy of reinforcement effect is calculated, the size according to strain energy under different angles carries out optimizing, and most strain energy is obtained at last
Direction during minimum value is defined as the final direction of growth of reinforcement；
Step 3) terminating point of the new reinforcement for growing is updated to the starting point of next secondary growth；
Step 4) iteration renewal：Repeat step 2)-step 3), given until the overall volume of the reinforcement for growing meets
Volume upper limit untill.
Applicating example
The reinforcement intellectualized design method of certain industrial equipment curved surface shell, comprises the following steps：
1) three-dimensional CAD model of curved surface shell, is set up in 3 d modeling software, the derivation of STL forms is saved as；
2) stl file in upper step, is imported into program, cast material parameter is set：Poisson's ratio, elastic modelling quantity, density, and set
Put boundary condition (Fig. 4)；
3) mesh generation, is carried out to model；
4), setting growing point position and optimizing are interval：Obligatory point (shown in Fig. 4) in selection this example is used as growing point position
Put, it is growth optimizing interval (Fig. 5) to select the projection circular arc of 20 millimeters of the growing point distance on Cylinder Surface in cylinder；
5) the reinforcement direction of growth, is determined：
With step 4) in the growing point that sets be starting point, it is 20 millimeters to grow length to periphery θ degree direction respectively
One section of reinforcement, then calculates structural strain energy when reinforcement is arranged in different directions, and strain energy is obtained into minimum value Jmin
When direction be defined as the final direction of growth of reinforcement；Next reinforcement is grown from the last time according to identical method
Terminal starts next section of reinforcement of continued growth；Iteration updates, (the figure untill whole reinforcement volume meets constraints
6).A-h represents 1-8 one-step growth results respectively in Fig. 6, as seen from the figure, with the growth of reinforcement, can intuitively observe the mould
The maximum deformation value of type has been reduced to 1.58 μm from 6.33 μm.
Claims (10)
1. it is a kind of based on limited cellular description bearing structure method of topological optimization design, it is characterised in that：Comprise the following steps：
The discrete accumulating life for turning to some carrying reinforcement structures on bearing structure matrix of bearing structure layout process will be equipped
Growth process, the accumulating growth course for each carrying reinforcement structure carries out topological structure optimization, by topological structure optimization
So that the mechanical property of the bearing structure is optimal；The mechanical property of bearing structure is with limited thin in topological structure optimization
Calculating is analyzed based on born of the same parents' description, the limited cellular description refers to by the regular knot of geometrical model apparatus of bearing structure
The grid cell that structure but size have differences is divided, and makes the border of the geometrical model with the phase in the geometrical model
Grid cell is answered to be indicated.
2. the bearing structure method of topological optimization design for being described based on limited cellular according to claim 1, it is characterised in that：
The topological structure optimization specifically includes following steps：
1) setting carries reinforcement structure initial growth point；
2) based on limited cellular description, the optimal growth direction for carrying reinforcement structure is found；
3) complete to carry the one step growth of reinforcement structure according to optimal growth direction and growth step-length, reinforcement structure one will be carried
Distal point after one-step growth as next one-step growth growing point；
4) repeat step 2) and step 3), update the topological iteration of carrying reinforcement structure, until meeting iteration termination condition.
3. the bearing structure method of topological optimization design for being described based on limited cellular according to claim 2, it is characterised in that：
The step 2) specifically include following steps：Grow the carrying reinforcement structure of regular length respectively to periphery from growing point, then
Calculate correspondence bearing structure mechanical property, by mechanical property it is optimal when it is corresponding growth angle-determining be carry reinforcement structure
The direction of growth.
4. the bearing structure method of topological optimization design for being described based on limited cellular according to claim 2, it is characterised in that：
The iteration termination condition refers to that the overall volume for carrying reinforcement structure reaches given volume upper limit.
5. the bearing structure method of topological optimization design for being described based on limited cellular according to claim 1, it is characterised in that：
The grid cell of the regular structure of apparatus carries out division and specifically includes following steps：The geometrical model of bearing structure is embedded in
To in bounding box, initial mesh is divided to the bounding box, grid subdivision is carried out to initial mesh, institute is recovered by grid subdivision
State the border of geometrical model.
6. the bearing structure method of topological optimization design for being described based on limited cellular according to claim 5, it is characterised in that：
The grid subdivision is using quaternary tree or Octree refinement strategy.
7. the bearing structure method of topological optimization design for being described based on limited cellular according to claim 5, it is characterised in that：
The grid subdivision is comprised the following steps：
A) initial mesh is judged with the inclusion relation on the geometrical model border, for first comprising geometrical model border
Beginning grid, then further decile；For the initial mesh not comprising geometrical model border, then do not continue to divide；
B) further after decile, the grid to still including geometrical model border proceeds decile；
C) repeat step b), until will finally divide the grid cell for obtaining and classifying as the grid in geometrical model and being located at
Grid outside geometrical model.
8. the bearing structure method of topological optimization design for being described based on limited cellular according to claim 1, it is characterised in that：
The mechanical property is selected from strain energy.
9. the bearing structure method of topological optimization design for being described based on limited cellular according to claim 1, it is characterised in that：
The grid cell composes grid using rank.
10. the bearing structure method of topological optimization design for being described based on limited cellular according to claim 1, its feature is existed
In：The carrying reinforcement structure is selected from reinforcement.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201611056819.5A CN106777538A (en) | 2016-11-25 | 2016-11-25 | A kind of bearing structure method of topological optimization design based on limited cellular description |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201611056819.5A CN106777538A (en) | 2016-11-25 | 2016-11-25 | A kind of bearing structure method of topological optimization design based on limited cellular description |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN106777538A true CN106777538A (en) | 2017-05-31 |
Family
ID=58913187
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201611056819.5A Pending CN106777538A (en) | 2016-11-25 | 2016-11-25 | A kind of bearing structure method of topological optimization design based on limited cellular description |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN106777538A (en) |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109344524A (en) * | 2018-10-18 | 2019-02-15 | 燕山大学 | A kind of thin-slab structure reinforced bag sand well optimization method |
| CN109408939A (en) * | 2018-10-18 | 2019-03-01 | 燕山大学 | A kind of improved method for the thin-slab structure reinforced bag sand well optimization taking into account stress and displacement constraint |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2005044146A (en) * | 2003-07-22 | 2005-02-17 | National Institute Of Advanced Industrial & Technology | Finite element analysis method, program and device |
| CN105354388A (en) * | 2015-11-27 | 2016-02-24 | 西安交通大学 | Growth type topological optimization design method of reinforcing rib |
-
2016
- 2016-11-25 CN CN201611056819.5A patent/CN106777538A/en active Pending
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2005044146A (en) * | 2003-07-22 | 2005-02-17 | National Institute Of Advanced Industrial & Technology | Finite element analysis method, program and device |
| CN105354388A (en) * | 2015-11-27 | 2016-02-24 | 西安交通大学 | Growth type topological optimization design method of reinforcing rib |
Non-Patent Citations (8)
| Title |
|---|
| ALEXANDER DUSTER: "The Finite Cell Method for the J2 flow theory of plasticity", 《FINITE ELEMENTS IN ANALYSIS AND DESIGN》 * |
| ALEXANDER DUSTER: "The finite cell method for three-dimensional problems of solid mechanics", 《COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING》 * |
| ALIREZA ABEDIAN: "Performance of different integration schemes in facing discontinuites in the finite cell method", 《INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS》 * |
| DOMINIK SCHILLINGER: "The Finite Cell Method: A Review in the Context of Higher-Order Structural Analysis of CAD and Image-Based Geometric Models", 《ARCH COMPUTAT METHODS》 * |
| MARK A. YERRY AND MARK S. SHEPHARD: "A Modified Quadtree Approach to Finite Element Mesh Generation", 《IEEE》 * |
| 孙丽萍主编: "《船舶结构有限元分析》", 31 January 2013 * |
| 张弢: "简单高效的复杂边界四叉树有限元网格生成技术", 《中国优秀博硕士学位论文全文数据库 (硕士)-信息科技辑》 * |
| 强晟等著: "《大体积混凝土施工期温度场和应力场的仿真算法研究》", 31 March 2013, 河海大学出版社 * |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109344524A (en) * | 2018-10-18 | 2019-02-15 | 燕山大学 | A kind of thin-slab structure reinforced bag sand well optimization method |
| CN109408939A (en) * | 2018-10-18 | 2019-03-01 | 燕山大学 | A kind of improved method for the thin-slab structure reinforced bag sand well optimization taking into account stress and displacement constraint |
| CN109408939B (en) * | 2018-10-18 | 2022-11-29 | 燕山大学 | Improvement method for optimizing distribution of reinforcing ribs of sheet structure considering both stress and displacement constraints |
| CN109344524B (en) * | 2018-10-18 | 2022-12-09 | 燕山大学 | Method for optimizing distribution of reinforcing ribs of thin plate structure |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN110110413B (en) | Structural topology optimization method based on material field reduction progression expansion | |
| CN102306396B (en) | Three-dimensional entity model surface finite element mesh automatic generation method | |
| CN106373184B (en) | A kind of 3 D-printing model puts required amount of support Method of fast estimating | |
| CN105313336B (en) | A kind of thin walled shell 3D printing optimization method | |
| CN110555263B (en) | Level set topology optimization method for curved shell structure optimization design | |
| CN104036095B (en) | Coupling high accuracy complex appearance flow field fast algorithm based on Region Decomposition | |
| CN106994483B (en) | A kind of method of the accurate type face processing of Automobile Cover Drawing Die | |
| CN102682172B (en) | Numerous-parameter optimization design method based on parameter classification for supercritical aerofoil | |
| CN116258042B (en) | Large-scale heat transfer heterogeneous parallel simulation method based on DDM | |
| CN106777538A (en) | A kind of bearing structure method of topological optimization design based on limited cellular description | |
| CN111079326B (en) | Two-dimensional anisotropic grid cell measurement tensor field smoothing method | |
| CN103065015B (en) | A kind of bearing structure low-carbon (LC) material-saving method for designing based on internal force path geometry form | |
| CN106682286A (en) | Geometric analysis method based functionally gradient material part modeling method | |
| CN104361625A (en) | Ray principle based cloud data compaction algorithm with boundary reservation | |
| CN115688276A (en) | Aircraft appearance automatic optimization method, system, equipment and medium based on discrete companion method | |
| Andrade et al. | A NURBS-discontinuous and enriched isogeometric boundary element formulation for two-dimensional fatigue crack growth | |
| CN102654923B (en) | Inside-to-outside hexahedron grid generation method | |
| CN113673186A (en) | Cartesian grid rapid generation method based on STL file | |
| CN108052778A (en) | For the proximate particle efficient double searching method of mesh free particle simulation technology | |
| CN110555267B (en) | Parameterized level set structure topology optimization method based on implicit B-spline | |
| CN110349265B (en) | Tetrahedral topological mesh generation method and electronic equipment | |
| US11340583B2 (en) | Data processing device for generating microstructures with orthotropic elastic properties | |
| CN106874611A (en) | A kind of interval analysis method of response containing Uncertain Structures with Interval Parameters based on hypervolume iterative strategy | |
| JP2017077773A (en) | Optimal tire cross-section shape preparing method and optimal tire cross-section shape preparing equipment | |
| CN109949420A (en) | Delaunay Triangulation mesh refinement method, GPU and system suitable for GPU |
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 |