CN108491591A - A kind of hot environment lower curve stiffened panel finite element method - Google Patents
A kind of hot environment lower curve stiffened panel finite element method Download PDFInfo
- Publication number
- CN108491591A CN108491591A CN201810182855.9A CN201810182855A CN108491591A CN 108491591 A CN108491591 A CN 108491591A CN 201810182855 A CN201810182855 A CN 201810182855A CN 108491591 A CN108491591 A CN 108491591A
- Authority
- CN
- China
- Prior art keywords
- matrix
- plate
- muscle
- displacement
- gusset
- 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
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Geometry (AREA)
- Theoretical Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Evolutionary Computation (AREA)
- Computer Hardware Design (AREA)
- General Engineering & Computer Science (AREA)
- Pure & Applied Mathematics (AREA)
- Mathematical Optimization (AREA)
- Mathematical Analysis (AREA)
- Computational Mathematics (AREA)
- Investigating Strength Of Materials By Application Of Mechanical Stress (AREA)
Abstract
The present invention discloses a kind of hot environment lower curve stiffened panel finite element method, includes the following steps：Consider that Effect of Materials, panel stiffness matrix is obtained in conjunction with DST BK plate unit theories for temperature change；The muscle element stiffness matrix after gusset displacement coordination and muscle element mass matrix are obtained according to gusset displacement coupling condition at gusset interface；Homogeneous temperature field is equivalent to thermal force, static analysis is onboard done in application, obtains the plate extra heat stress stiffness matrix for considering thermal stress, and derive muscle extra heat stress stiffness matrix；Overall structure stiffness matrix is subjected to Eigenvalues analysis with whole extra heat stress stiffness matrix and obtains buckling critical-temperature, overall structure stiffness matrix and extra heat stress stiffness matrix are superimposed to obtain the curve stiffened panel stiffness matrix for considering that temperature influences and consider that extra heat stress is influenced on material property, Eigenvalues analysis is carried out with total quality matrix, obtains dynamic characteristic of the curve stiffened panel under uniform temperature environment.
Description
Technical field
The present invention relates to a kind of hot environment lower curve stiffened panel finite element methods, belong to stiffened panel structure modeling point
Analysis field.
Background technology
Stiffened panel is a kind of the structure group being composed to be connected by certain paving mode with reinforcing rib by basal body structure
Part.Because it has many advantages, such as that handling ease, specific strength are big, bearing capacity is strong, and structure can be improved under the premise of equivalent weight and is bent
Song destroys critical pressure, and stiffened panel becomes one of the primary structure form of industrial pressure-resistance structure.Traditional stiffened panel generally use is straight
Line reinforcement form is laid with by lateral, longitudinal direction or according to a certain angle.Form of straight lines can not improve stock utilization, be not easy to
Optimization design.
Thermal environment can change material mechanical performance, while will produce extra heat stress.Business finite element software is to reinforcement
When harden structure carries out finite element analysis, it is necessary to assure gusset node overlaps modeling, when rib is laid with scheme in plate to be changed, needs
Again to plate unit grid division, therefore modeling efficiency is greatly reduced.In to stiffened panel Modelon Modeling, commonly use theoretical for warp
Allusion quotation plate theory and first order shear deformation theory can not construct a kind of modeling and analysis methods in face of reinforcement thin-thick plates.
Invention content
Goal of the invention：Cause modeling efficiency low and existing modeling for the coincidence of conventional finite element software requirement gusset node
Method cannot achieve the defect of thin-thick plates, and the present invention provides a kind of hot environment lower curve stiffened panel finite element analysis side
Method, this method may be implemented to analyze curve reinforcement thin-thick plates, and can realize arbitrary arrangement of the rib in plate, can pass through
Rib curvature and paving location are adjusted to improve structure overall stiffness.
Technical solution：A kind of hot environment lower curve stiffened panel finite element method of the present invention, including it is as follows
Step：
Step 1, the deflection field combination DST-BK units indicated using linear interpolation obtain only considering temperature change to material
The plate unit stiffness matrix K of influencepAnd plate unit mass matrix Mp；
Step 2, muscles and joints-vital links in a speech point displacement is expressed using plate node displacement according to gusset displacement coupling condition at gusset interface,
Obtain the muscle element stiffness matrix K after gusset displacement coordinationsWith muscle element mass matrix Ms；
Step 3, homogeneous temperature field is equivalent to thermal force, static analysis is onboard done in application, calculates thermal stress, and derive
Obtain the plate extra heat stress stiffness matrix K for considering thermal stressTp；
Step 4, using gusset element stress relationship, muscle extra heat stress stiffness matrix K is obtainedTs；
Step 5, by curve stiffened panel structure stiffness matrix Kp+KsWith extra heat stress stiffness matrix KTp+KTsCarry out feature
Value analysis obtains buckling critical-temperature, by curve stiffened panel structure stiffness matrix Kp+KsWith extra heat stress stiffness matrix Kp+Ks
Superposition obtains considering the curve stiffened panel stiffness matrix K that temperature influences and consider that extra heat stress is influenced on material propertyp+Ks+
KTp+KTs, with curve stiffened panel mass matrix Mp+MsEigenvalues analysis is carried out, obtains curve stiffened panel under uniform temperature environment
Dynamic characteristic.
In above-mentioned steps 2, it includes following to express muscles and joints-vital links in a speech point displacement using plate node displacement according to gusset displacement coupling condition
Step：
Step 21, using Distmesh dividing plate unit grids, plate unit entirety coordinate and natural coordinates are obtained；Using 3
Rank B-spline curves divide muscle unit grid, obtain the natural coordinates of muscles and joints-vital links in a speech point under local coordinate system and are converted to whole coordinate；
Step 22, by the whole coordinate of muscles and joints-vital links in a speech point and the whole coordinate of plate node, the plate corresponding to each muscles and joints-vital links in a speech point is found out
Unit, and the muscles and joints-vital links in a speech point is calculated by the shape function of corresponding plate unit and corresponds to the natural coordinates in plate unit；
Step 23, muscles and joints-vital links in a speech point is corresponded into the natural coordinates in plate unit, in conjunction with the shape function of plate unit, interpolation is somebody's turn to do
Place's plate unit displacement is fallen using muscle unit shape function by plate unit modal displacement interpolation according to gusset displacement coupling condition
In the muscle modal displacement of plate unit, and obtain gusset displacement coupling shape function.
The muscle modal displacement such as following formula (4) for using plate node displacement to express as a result,：
In formula (4), us、υsAnd wsRespectively curve muscle corresponds to x, the displacement of the lines in tri- directions y, z, βsxAnd βsyFor curve
The corner of muscle；Ns,iFor muscle unit shape function, Ns,1=1- ξs-ηs,Ns,2=ξs,Ns,3=ηs, ξsAnd ηsFor the natural seat of muscles and joints-vital links in a speech point
Mark；Np,jFor plate unit shape function, Np,1=1- ξp-ηp,Np,2=ξp,Np,3=ηp, ξpAnd ηpFor the natural coordinates of plate node；up,j、
υp,jAnd wp,jRespectively plate unit corner node corresponds to x, the displacement of the lines in tri- directions y, z, βpx,jAnd βpy,jFor plate unit corner node
Corner；αkFor the corner at side midpoint, PkIndicate one group of higher-order function, P4=4 ξp(1-ξp-ηp)+4ηp/ 3-1/2, P5=4 ξpηp+
4(1-ξp-ηp)/3-1/2, P6=4 (1- ξp-ηp)ηp+4ξp/ 3-1/2, CkAnd SkRespectively triangle edges and x-axis angulation
Cosine and sine value.
Formula (4) is abbreviated as formula (5), obtains gusset displacement coupling shape function Nsp, displacement relation and coordinate between gusset
Relationship is represented by：
dsg=Nspdp,rs=Nsprp(5),
In formula (5), dsgIndicate the displacement of muscle unit under global coordinate system, dpIndicate the position of global coordinate system lower plate unit
It moves, rsIndicate the coordinate of muscle unit under global coordinate system, rpIndicate the coordinate of global coordinate system lower plate unit.
According to gusset displacement coupling shape function Nsp, obtain the muscle element stiffness matrix K after gusset displacement coordinationsFor：
In formula (6), TsFor muscle unit coordinate conversion matrix, BsFor muscle element strain matrix, DsFor muscle unitary elasticity matrix,
JsFor the Jacobian matrix of muscle unit.
Muscle element mass matrix M after gusset displacement coordinationsFor：
In formula (7), TsFor muscle unit coordinate conversion matrix, msFor the mass matrix of rib in local coordinate system, JsFor muscle list
The Jacobian matrix of member.
In above-mentioned steps 3, plate extra heat stress stiffness matrix KTpIt is determined by following step：
Step 31, Δ T is risen by the temperature of the linear expansion coefficient α of plate material and structure, obtained hardened in homogeneous temperature field
Structure initial strain ε caused by thermal deformation0：
Step 32, pass through printed line strain matrix BcTransposed matrix, plate elastic matrix DPWith harden structure initial strain ε0Three
Integral, thermal force is equivalent to by the homogeneous temperature field being applied in plate in angular plate unit region A：
Step 33, static analysis is carried out to plate according to thermal force, obtains the overall strain ε and thermal stress σ of plate：
Step 34, pass through plate nonlinear strain matrixTransposed matrix and plate stress matrix σpIn TRIANGULAR PLATE ELEMENTS BASED
Region A inner products get plate extra heat stress stiffness matrix KTp：
In above-mentioned steps 4, muscle extra heat stress stiffness matrix KTsFor：
In formula (12), TsFor muscle unit coordinate conversion matrix,For reinforcing rib nonlinear strain matrix, σsIt is answered for reinforcing rib
Torque battle array.
In above-mentioned steps 5, (13)~(14) carry out Eigenvalues analysis according to the following formula, obtain hot environment lower curve stiffened panel
Buckling critical-temperature and dynamic characteristic：
[(Kp+Ks)-λ(KTp+KTs)] d=0 (13),
In above formula, λ is the buckling factor, and d is the buckling mode vibration shape, and ω is intrinsic frequency,For hot Mode Shape.
Advantageous effect：Compared with the prior art, the advantages of the present invention are as follows：(1) hot environment lower curve of the invention adds
Gusset finite element method obtains muscle element stiffness matrix, gusset cell node using plate unit node coordinate with positional displacement interpolation
Without overlapping, the modeling efficiency of curve stiffened panel is substantially increased；(2) utilize the analysis method of thin-thick plates to curve reinforcement
Plate carries out modeling analysis under hot environment, and avoiding first order shear deformation theory can encounter when analyzing curve stiffened panel structure
Shear locking problem.
Description of the drawings
Fig. 1 is a kind of hot environment lower curve stiffened panel finite element method flow diagram of the present invention；
Fig. 2 is the geometrical model of four muscle symmetrical curve stiffened panels in embodiment；
Fig. 3 is the finite element model of curve stiffened panel in embodiment；
Fig. 4 is the 1st first order mode cloud atlas of hot environment lower curve stiffened panel obtained in embodiment；
Fig. 5 is the 2nd first order mode cloud atlas of hot environment lower curve stiffened panel obtained in embodiment；
Fig. 6 is the 3rd first order mode cloud atlas of hot environment lower curve stiffened panel obtained in embodiment.
Specific implementation mode
Technical scheme of the present invention is described further below in conjunction with the accompanying drawings.
Such as Fig. 1, a kind of hot environment lower curve stiffened panel finite element method of the invention, main includes following step
Suddenly：
Step 1, the deflection field combination DST-BK units indicated using linear interpolation obtain only considering temperature change to material
The plate unit stiffness matrix K of influencepAnd plate unit mass matrix Mp；
Step 2, muscles and joints-vital links in a speech point displacement is expressed using plate node displacement according to gusset displacement coupling condition at gusset interface,
Obtain the muscle element stiffness matrix K after gusset displacement coordinationsWith muscle element mass matrix Ms；
Step 3, homogeneous temperature field is equivalent to thermal force, static analysis is onboard done in application, calculates thermal stress, and derive
Obtain the plate extra heat stress stiffness matrix K for considering thermal stressTp；
Step 4, using gusset element stress relationship, muscle extra heat stress stiffness matrix K is obtainedTs；
Step 5, by curve stiffened panel structure stiffness matrix Kp+KsWith extra heat stress stiffness matrix KTp+KTsCarry out feature
Value analysis obtains buckling critical-temperature, by curve stiffened panel structure stiffness matrix Kp+KsWith extra heat stress stiffness matrix Kp+Ks
Superposition obtains considering the curve stiffened panel stiffness matrix K that temperature influences and consider that extra heat stress is influenced on material propertyp+Ks+
KTp+KTs, with curve stiffened panel mass matrix Mp+MsEigenvalues analysis is carried out, obtains curve stiffened panel under uniform temperature environment
Dynamic characteristic.
This method may be implemented to analyze curve reinforcement thin-thick plates, and can realize arbitrary arrangement of the rib in plate,
Structure overall stiffness can be improved by adjusting rib curvature and paving location.
By taking the curve stiffened panel of a symmetrical reinforcement as an example, geometrical model such as Fig. 2 utilizes song under the hot environment of the present invention
Line stiffened panel finite element method analyzes the dynamic characteristic of the structure, specifically includes following steps：
1, the deflection field combination DST-BK units indicated using linear interpolation obtain only considering temperature change to Effect of Materials
Plate unit stiffness matrix KpAnd plate unit mass matrix Mp
2, plate unit mesh generation is carried out using Distmesh, divides muscle unit grid using 3 rank B-spline curves, obtains
The finite element model of curve stiffened panel, such as Fig. 3, while muscles and joints-vital links in a speech point natural coordinates is obtained, it calculates muscles and joints-vital links in a speech point and corresponds in plate unit
Natural coordinates, calculate gusset displacement coupling shape function, indicate muscle displacement field with plate node displacement；
Specifically, first grid Core Generator Distmesh is used to generate 3 node TRIANGULAR PLATE ELEMENTS BASED grids, plate list is obtained
First entirety coordinate and natural coordinates, and 3 node muscle unit grids are generated using 3 rank B-spline curves, obtain muscle under local coordinate system
The natural coordinates of node is simultaneously converted to whole coordinate；Then it by the whole coordinate of muscles and joints-vital links in a speech point and the whole coordinate of plate node, finds out
Plate unit corresponding to each muscles and joints-vital links in a speech point, and the muscles and joints-vital links in a speech point is calculated by 3 points in corresponding plate unit of shape function and is corresponded to
Natural coordinates in plate unit；Natural coordinates corresponding to the muscles and joints-vital links in a speech point obtained by previous step in plate unit, and combine 3 gusset plates
The shape function of unit, interpolation obtain plate unit displacement at this, according to gusset intersection displacement coordination condition, it is believed that gusset position at this
Phase shift is same, therefore using the gusset junction displacement at 3 points, arbitrary point in rib is obtained using muscle unit shape function interpolation
Displacement field.
Theoretical using Timoshenko beam elements for rib, any point displacement field and coordinate in rib can
By in unit 3 displacements and interpolation of coordinate obtain：
In formula (1), usg,vsg,wsgRespectively muscle unit any point under global coordinate system along x, tri- directions y, z
Displacement of the lines, βxsg,βysgFor corner displacement of the muscle unit any point under global coordinate system；usg,i,vsg,i,wsg,iFor muscle unit three
A node is under global coordinate system along x, the displacement of the lines in tri- directions y, z, βxsg,iAnd βysg,iIt is three nodes of muscle unit whole
Corner displacement under body coordinate system；Ns,iIndicate muscle unit shape function, wherein Ns,1=1- ξs-ηs,Ns,2=ξs,Ns,3=ηs, ξsWith
ηsFor the natural coordinates of muscles and joints-vital links in a speech point.
Any point displacement can be obtained by modal displacement interpolation in 3 node, 9 degree of freedom DST-BK units：
In formula (2), up,vp,wpRespectively global coordinate system lower plate unit any point is along x, y, the displacement of the lines in the directions z,
βpx,βpyFor the corner displacement of global coordinate system lower plate unit any point；Np,jIndicate plate unit shape function, wherein Np,1=1- ξp-
ηp,Np,2=ξp,Np,3=ηp, ξpAnd ηpFor the natural coordinates of plate node.
up,j, υp,jAnd wp,jRespectively plate unit corner node corresponds to x, the displacement of the lines in tri- directions y, z；βpx,jAnd βpy,jFor
The corner of plate unit corner node, αkIt is the corner at side midpoint, PkIndicate one group of higher-order function, P4=4 ξp(1-ξp-ηp)+4ηp/3-
1/2, P5=4 ξpηp+4(1-ξp-ηp)/3-1/2, P6=4 (1- ξp-ηp)ηp+4ξp/ 3-1/2, CkAnd SkRespectively triangle edges and x
The cosine and sine value of axis angulation.
In gusset intersection, according to gusset displacement coordination condition, it is believed that gusset displacement is identical, then falls the muscles and joints-vital links in a speech in plate unit
Point displacement can be obtained by corresponding plate unit modal displacement interpolation：
In formula (3), us,i,υs,i,ws,iExpression falls the muscles and joints-vital links in a speech point displacement of the lines in a certain plate unit, βsx,i,βsy,iExpression is fallen
Muscle node rotation in a certain plate unit.
It brings (2) formula, (3) formula into (1) formula, can obtain：
In formula (4), us、υsAnd wsRespectively curve muscle corresponds to x, the displacement of the lines in tri- directions y, z, βsxAnd βsyFor curve
The corner of muscle.
Formula (4) is abbreviated as formula (5), obtains gusset displacement coupling shape function Nsp, displacement relation and coordinate between gusset
Relationship is represented by：
dsg=Nspdp,rs=Nsprp(5),
In formula (5), dsgIndicate the displacement of muscle unit under global coordinate system, dpIndicate the position of global coordinate system lower plate unit
It moves, rsIndicate the coordinate of muscle unit under global coordinate system, rpIndicate the coordinate of global coordinate system lower plate unit.
3, using above-mentioned gusset displacement coupling shape function Nsp, in conjunction with muscle unit coordinate conversion matrix Ts, muscle unit answer bending moment
Battle array BsWith muscle unitary elasticity matrix Ds, the muscle element stiffness matrix K after gusset displacement coordination is obtained by Gauss integrations：
In formula (6), JsFor the Jacobian matrix of muscle unit.
Using gusset displacement coupling shape function Nsp, in conjunction with muscle unit coordinate conversion matrix Ts, muscle is obtained by Gauss integration
Element mass matrix Ms：
In formula (7), msFor the mass matrix of rib in local coordinate system.
By plate unit stiffness matrix KpWith muscle element stiffness matrix KsSuperposition obtains considering that temperature adds the curve of Effect of Materials
Reinforcing plate structure Bulk stiffness matrix Kp+Ks, by plate unit mass matrix MpWith muscle element mass matrix MsSuperposition obtains curve reinforcement
Harden structure total quality matrix Mp+Ms。
4, by 300 DEG C of homogeneous temperature fields be equivalent to thermal force apply onboard, first pass through material linear expansion coefficient α and
The temperature of structure rises Δ T, calculates structure initial strain caused by thermal deformation in homogeneous temperature field：
Then pass through printed line strain matrix BcTransposed matrix, plate elastic matrix DpWith harden structure initial strain ε0, will apply
300 DEG C of homogeneous temperature fields in plate are equivalent to thermal force：
Static analysis is carried out to plate further according to thermal force, obtains overall strain ε and thermal stress σ：
Finally by plate nonlinear strain matrixTransposed matrix and plate stress matrix σpIt is rigid to obtain plate extra heat stress
Spend matrix KTp：
5, it is strengthened thermal stress and reinforcing rib thermal stress matrix σ in muscle using thermal stress in plates, pass through gusset displacement coupling
Close shape function Nsp, in conjunction with muscle unit coordinate conversion matrix TsWith reinforcing rib nonlinear strain matrixIt is obtained by Gauss integration
With the reinforcing rib extra heat stress stiffness matrix K of plate same orderTs；
By plate extra heat stress stiffness matrix KTpWith muscle extra heat stress stiffness matrix KTsThe two is superimposed to obtain curve reinforcement
The whole extra heat stress stiffness matrix K of plateTp+KTs。
6, in curve stiffened panel structure Bulk stiffness matrix Kp+KsThe middle influence for considering temperature to material, with whole additional heat
Stress stiffness matrix KTp+KTsEigenvalues analysis is done according to the following formula, obtains buckling critical-temperature：
[(Kp+Ks)-λ(KTp+KTs)] d=0 (13)；
In above formula, λ is the buckling factor, and d is the buckling mode vibration shape.
7, buckling critical-temperature uniform thermal environment below is selected, it will be considered that temperature is whole to the curve stiffened panel of Effect of Materials
Body structural stiffness matrix Kp+KsWith whole extra heat stress stiffness matrix KTp+KTsSuperposition, can be obtained thermal environment lower curve stiffened panel
Structural stiffness matrix Kp+Ks+KTp+KTs, with curve stiffened panel total quality matrix Mp+MsEigenvalues analysis is carried out according to the following formula：
In above formula, ω is intrinsic frequency,For hot Mode Shape.
Obtain the dynamic characteristic of thermal environment lower curve stiffened panel, i.e., frequency of the curve stiffened panel under uniform temperature environment and
Hot-die state, Fig. 4~6 be the free homogeneous material curve stiffened plate in the clamped one side in three sides 300 DEG C of uniform temperatures off field before 3
Rank hot-die state bending vibation mode picture.
Claims (8)
1. a kind of hot environment lower curve stiffened panel finite element method, which is characterized in that include the following steps：
Step 1, the deflection field combination DST-BK units indicated using linear interpolation obtain only considering temperature change to Effect of Materials
Plate unit stiffness matrix KpAnd plate unit mass matrix Mp；
Step 2, muscles and joints-vital links in a speech point displacement is expressed using plate node displacement according to gusset displacement coupling condition at gusset interface, obtained
Muscle element stiffness matrix K after gusset displacement coordinationsWith muscle element mass matrix Ms；
Step 3, homogeneous temperature field is equivalent to thermal force, static analysis is onboard done in application, calculates thermal stress, and be derived from
Consider the plate extra heat stress stiffness matrix K of thermal stressTp；
Step 4, using gusset element stress relationship, muscle extra heat stress stiffness matrix K is obtainedTs；
Step 5, by curve stiffened panel structure stiffness matrix Kp+KsWith extra heat stress stiffness matrix KTp+KTsCarry out characteristic value point
Analysis obtains buckling critical-temperature, by curve stiffened panel structure stiffness matrix Kp+KsWith extra heat stress stiffness matrix Kp+KsSuperposition
It obtains considering the curve stiffened panel stiffness matrix K that temperature influences and consider that extra heat stress is influenced on material propertyp+Ks+KTp+
KTs, with curve stiffened panel mass matrix Mp+MsEigenvalues analysis is carried out, it is dynamic under uniform temperature environment to obtain curve stiffened panel
Step response.
2. hot environment lower curve stiffened panel finite element method according to claim 1, which is characterized in that step 2
In, it is described to be included the following steps using plate node displacement expression muscles and joints-vital links in a speech point displacement according to gusset displacement coupling condition：
Step 21, using Distmesh dividing plate unit grids, plate unit entirety coordinate and natural coordinates are obtained；Using 3 rank B samples
Curve divides muscle unit grid, obtains the natural coordinates of muscles and joints-vital links in a speech point under local coordinate system and is converted to whole coordinate；
Step 22, by the whole coordinate of muscles and joints-vital links in a speech point and the whole coordinate of plate node, the plate unit corresponding to each muscles and joints-vital links in a speech point is found out,
And the muscles and joints-vital links in a speech point is calculated by the shape function of corresponding plate unit and corresponds to the natural coordinates in plate unit；
Step 23, muscles and joints-vital links in a speech point is corresponded into the natural coordinates in plate unit, in conjunction with the shape function of plate unit, interpolation obtains plate at this
Element displacement is obtained falling in plate using muscle unit shape function according to gusset displacement coupling condition by plate unit modal displacement interpolation
The muscle modal displacement of unit, and obtain gusset displacement coupling shape function.
3. hot environment lower curve stiffened panel finite element method according to claim 2, which is characterized in that the use
The muscle modal displacement such as following formula (4) of plate node displacement expression：
In formula (4), us、υsAnd wsRespectively curve muscle corresponds to x, the displacement of the lines in tri- directions y, z, βsxAnd βsyFor curve muscle
Corner；Ns,iFor muscle unit shape function, Ns,1=1- ξs-ηs,Ns,2=ξs,Ns,3=ηs, ξsAnd ηsFor the natural coordinates of muscles and joints-vital links in a speech point；
Np,jFor plate unit shape function, Np,1=1- ξp-ηp,Np,2=ξp,Np,3=ηp, ξpAnd ηpFor the natural coordinates of plate node；up,j、υp,j
And wp,jRespectively plate unit corner node corresponds to x, the displacement of the lines in tri- directions y, z, βpx,jAnd βpy,jFor plate unit corner node
Corner；αkFor the corner at side midpoint, PkIndicate one group of higher-order function, P4=4 ξp(1-ξp-ηp)+4ηp/ 3-1/2, P5=4 ξpηp+4
(1-ξp-ηp)/3-1/2, P6=4 (1- ξp-ηp)ηp+4ξp/ 3-1/2, CkAnd SkRespectively triangle edges and x-axis angulation is remaining
String and sine value；
Formula (4) is abbreviated as formula (5), obtains gusset displacement coupling shape function Nsp, the displacement relation between gusset and coordinate relationship
For：
dsg=Nspdp,rs=Nsprp(5),
In formula (5), dsgIndicate the displacement of muscle unit under global coordinate system, dpIndicate the displacement of global coordinate system lower plate unit, rsTable
Show the coordinate of muscle unit under global coordinate system, rpIndicate the coordinate of global coordinate system lower plate unit.
4. hot environment lower curve stiffened panel finite element method according to claim 3, which is characterized in that step 2
In, according to the gusset displacement coupling shape function Nsp, obtain the muscle element stiffness matrix K after gusset displacement coordinationsFor：
In formula (6), TsFor muscle unit coordinate conversion matrix, BsFor muscle element strain matrix, DsFor muscle unitary elasticity matrix, JsFor muscle
The Jacobian matrix of unit.
5. hot environment lower curve stiffened panel finite element method according to claim 3, which is characterized in that step 2
In, according to the gusset displacement coupling shape function Nsp, obtain the muscle element mass matrix M after gusset displacement coordinationsFor：
In formula (7), TsFor muscle unit coordinate conversion matrix, msFor the mass matrix of rib in local coordinate system, JsFor muscle unit
Jacobian matrix.
6. hot environment lower curve stiffened panel finite element method according to claim 3, which is characterized in that step 3
In, the plate extra heat stress stiffness matrix KTpIt is determined by following step：
Step 31, Δ T is risen by the temperature of the linear expansion coefficient α of plate material and structure, obtain in homogeneous temperature field harden structure by
Initial strain ε caused by thermal deformation0：
Step 32, pass through printed line strain matrix BcTransposed matrix, plate elastic matrix DPWith harden structure initial strain ε0In triangle
Integral, thermal force is equivalent to by the homogeneous temperature field being applied in plate in the A of plate unit region：
Step 33, static analysis is carried out to plate according to thermal force, obtains the overall strain ε and thermal stress σ of plate：
Step 34, pass through plate nonlinear strain matrixTransposed matrix and plate stress matrix σpIn TRIANGULAR PLATE ELEMENTS BASED region A
Inner product gets plate extra heat stress stiffness matrix KTp：
7. hot environment lower curve stiffened panel finite element method according to claim 6, which is characterized in that step 4
In, the muscle extra heat stress stiffness matrix KTsFor：
In formula (12), TsFor muscle unit coordinate conversion matrix,For reinforcing rib nonlinear strain matrix, σsTorque is answered for reinforcing rib
Battle array.
8. hot environment lower curve stiffened panel finite element method according to claim 7, which is characterized in that step 5
In, (13)~(14) carry out Eigenvalues analysis according to the following formula, obtain the reinforcement bucking of plate critical-temperature of hot environment lower curve and move
Step response：
[(Kp+Ks)-λ(KTp+KTs)] d=0 (13),
In above formula, λ is the buckling factor, and d is the buckling mode vibration shape, and ω is intrinsic frequency,For hot Mode Shape.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810182855.9A CN108491591A (en) | 2018-03-06 | 2018-03-06 | A kind of hot environment lower curve stiffened panel finite element method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810182855.9A CN108491591A (en) | 2018-03-06 | 2018-03-06 | A kind of hot environment lower curve stiffened panel finite element method |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN108491591A true CN108491591A (en) | 2018-09-04 |
Family
ID=63341415
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201810182855.9A Pending CN108491591A (en) | 2018-03-06 | 2018-03-06 | A kind of hot environment lower curve stiffened panel finite element method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN108491591A (en) |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| 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 |
| CN111339614A (en) * | 2020-02-26 | 2020-06-26 | 成都飞机工业（集团）有限责任公司 | Suspension structure rigidity estimation method |
| CN112836411A (en) * | 2021-02-09 | 2021-05-25 | 大连理工大学 | Method and device for optimizing structure of stiffened plate shell, computer equipment and storage medium |
| CN115081148A (en) * | 2022-07-20 | 2022-09-20 | 上海索辰信息科技股份有限公司 | Method for determining equivalent parameters of stiffened plate based on potential energy theory |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102063540A (en) * | 2010-12-30 | 2011-05-18 | 西安交通大学 | Method for optimally designing machine tool body structure |
| CN104133933A (en) * | 2014-05-29 | 2014-11-05 | 温州职业技术学院 | Pneumatic elastic mechanical characteristic analytical method of hypersonic speed aircraft in thermal environment |
| CN104239624A (en) * | 2014-09-05 | 2014-12-24 | 西安交通大学 | Optimal design method for internal structure of machine tool body |
-
2018
- 2018-03-06 CN CN201810182855.9A patent/CN108491591A/en active Pending
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102063540A (en) * | 2010-12-30 | 2011-05-18 | 西安交通大学 | Method for optimally designing machine tool body structure |
| CN104133933A (en) * | 2014-05-29 | 2014-11-05 | 温州职业技术学院 | Pneumatic elastic mechanical characteristic analytical method of hypersonic speed aircraft in thermal environment |
| CN104239624A (en) * | 2014-09-05 | 2014-12-24 | 西安交通大学 | Optimal design method for internal structure of machine tool body |
Non-Patent Citations (3)
| Title |
|---|
| ZHAO W 等: "Buckling analysis of unitized curvilinearly stiffened composite panels", 《COMPOSITE STRUCTURES》 * |
| 刘璟泽 等: "曲线加筋Kirchhoff-Mindlin 板自由振动分析", 《力学学报》 * |
| 王斌等: "热载荷下结构动力特性的优化设计", 《中国计算力学大会\"2010（CCCM2010）暨第八届南方计算力学学术会议（SCCM8）论文集》 * |
Cited By (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| 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 |
| CN111339614A (en) * | 2020-02-26 | 2020-06-26 | 成都飞机工业（集团）有限责任公司 | Suspension structure rigidity estimation method |
| CN111339614B (en) * | 2020-02-26 | 2022-08-12 | 成都飞机工业（集团）有限责任公司 | Suspension structure rigidity estimation method |
| CN112836411A (en) * | 2021-02-09 | 2021-05-25 | 大连理工大学 | Method and device for optimizing structure of stiffened plate shell, computer equipment and storage medium |
| CN112836411B (en) * | 2021-02-09 | 2022-11-08 | 大连理工大学 | Method and device for optimizing structure of stiffened plate shell, computer equipment and storage medium |
| CN115081148A (en) * | 2022-07-20 | 2022-09-20 | 上海索辰信息科技股份有限公司 | Method for determining equivalent parameters of stiffened plate based on potential energy theory |
| CN115081148B (en) * | 2022-07-20 | 2022-11-15 | 上海索辰信息科技股份有限公司 | Method for determining equivalent parameters of stiffened plate based on potential energy theory |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN108491591A (en) | A kind of hot environment lower curve stiffened panel finite element method | |
| Caliri Jr et al. | A review on plate and shell theories for laminated and sandwich structures highlighting the Finite Element Method | |
| Kant | Numerical analysis of thick plates | |
| Kant et al. | Analytical solutions for free vibration of laminated composite and sandwich plates based on a higher-order refined theory | |
| Dokainish | A new approach for plate vibrations: combination of transfer matrix and finite-element technique | |
| Vinson | Plate and panel structures of isotropic, composite and piezoelectric materials, including sandwich construction | |
| CN107220461A (en) | A kind of variation rigidity composite panel shell structure effectively optimizing method | |
| Qin et al. | Static and dynamic analyses of isogeometric curvilinearly stiffened plates | |
| Bushnell | Analysis of buckling and vibration of ring-stiffened, segmented shells of revolution | |
| Katariya et al. | Geometrically nonlinear deflection and stress analysis of skew sandwich shell panel using higher-order theory | |
| Di Sciuva | A third‐order triangular multilayered plate finite element with continuous interlaminar stresses | |
| CN108197417A (en) | A kind of curve stiffened panel finite element method | |
| Ganapathi et al. | Large amplitude vibrations of circular cylindrical shells | |
| Dawe et al. | Spline finite strip analysis of the buckling and vibration of rectangular composite laminated plates | |
| CN109299540A (en) | Plane frame structure Static Non-linear Analyisis based on rigid body criterion | |
| CN110162826A (en) | Thin-wall construction thermographic curve dynamic response analysis method | |
| Lezgy-Nazargah | A generalized layered global-local beam theory for elasto-plastic analysis of thin-walled members | |
| Sapountzakis et al. | Nonlinear analysis of shear deformable beam-columns partially supported on tensionless three-parameter foundation | |
| CN106354954A (en) | Three-dimensional mechanical modal simulation method based on hierarchical basis function | |
| Dey et al. | An efficient plate element for the vibration of composite plates | |
| Erkmen et al. | Nonlinear elastic analysis of composite beams curved in-plan | |
| CN110020498A (en) | Curve steel-Combined concrete box beam One Dimensional Finite meta-model construction method | |
| Tan | Free vibration analysis of shells of revolution | |
| Toorani et al. | Free vibrations of non-uniform composite cylindrical shells | |
| CN110516404B (en) | Finite element analysis and coordinate conversion method for connecting rod of paddy field grader |
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 | ||
| RJ01 | Rejection of invention patent application after publication | ||
| RJ01 | Rejection of invention patent application after publication |
Application publication date: 20180904 |