ADVANCED ANALYTICAL TECHNIQUES - CERIC에...
Transcript of ADVANCED ANALYTICAL TECHNIQUES - CERIC에...
ADVANCEDANALYTICALTECHNIQUES
Dmitry Maslov & Roman GuzeevInstitute Giprostroymost Saint-Petersburg
Russian Federation
PART I
…finding a problem…
Issue:The program we use may seem incapable of solving a problem
Reasons:► Excessive demand► Lack of knowledge
Solutions:► Find a different program► Expand the limits of existing software
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All the commercial FE software is featured with non-linear analysis
Non-linear analysis is an iterative process involving the modelmodification according to immediate results
“Expand the limits” means a way of making any possible change in the model after results review
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Manual result handling requires “the art of mouse clicks” for large models
XXI century information technologies hint at some automation5
There is a variety of instruments for building an automation facility
► VBScript or JavaScript
► MatLab or MathCad
► General purpose programming languages
Result postprocessing and interaction with solver functionality are theonly two things to be developed
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Scripts:Easy to master but produce very slow code
Native code:Runs fast but requires programming skills to be developed
Engineers are not programmers, programmers are not familiar withStructural Mechanics
A balanced solution has to be found7
ORCODEN is the new name for Expression Converter program
New features :► Unicode text editor with syntax highlighting,
multiple undo, find and replace features,advanced clipboard facilities, popup hints,and context-sensitive help
► Script debug tools, breakpoints, watches, step-by-step tracing
► Resource-intensive GT STRUDL interaction is developed as built-infunctions which users treat as integral part of script language
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Composite cross-section bridges
One of the simplest concepts causesadditional problems in its analysis
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Construction Stages:
► Assembling of steel beams at construction site► Incremental launching using temporary and rolling piers► Deck concreting at bridge spans► Dismantling temporary piers► Deck concreting above piers► Making road surface
Service Actions: ► Carrying temporary loads► Suffering creep and shrinkage effects► Possible seismic events
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Analytical model for composite section
N M
Such modeling produces a slightly incorrect diagrams
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Construction steps for the analytical model:
► All deck members deactivated, pier joints declared supports, the structure carries the self weight of metal beam and the concreteof the first two divisions
Sq1Cq 2Cq
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Construction steps for the analytical model:
► Truss members of the first two concreting divisions activated,temporary support joints made free, the structure carries thethird concreting division weight
3Cq
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Construction steps for the analytical model:
► All members activated, the structure carries the remaining loads
IIq
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Are the final displacements correct?
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NO!
At the second stage we had to apply inverse joint reaction in the jointsmade free, which would make the concrete carry the self weight
1Cq
1R 2R 3R 4R16
Correct sequence
The joint reaction compensating for the stress can only be found afterthe first stage completed
Thus, the analysis after the first stage has to be suspended, reactionslisted and put into the model for stages 2 and 3
ORCODEN script performs the entire routine automatically from creating the model up to displaying the results
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Displacements doubled in the “correct” model
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So did stresses…
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A new LOADING command would be useful
L
L
i JOINTSCOMPENSATING (FOR STRESS) LOADING FACTOR v
'a ' MEMBERSlist...list
⎧ ⎫ ⎧ ⎫⎨ ⎬ ⎨ ⎬
⎩ ⎭⎩ ⎭
The command is supposed to calculate compensating joint forces beforethe user specifies STATUS FREE or INACTIVE MEMBERS/ELEMENTSfor the staged analysis
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Plate deactivation problem
Concrete structural elements do not work in tension areas due to cracks
Tension areas are dependent on loading
Each loading has to be applied twice: in the ‘whole’ model and afterdeck deactivation
ORCODEN script performs the entire routine automatically aftersome modification of the ‘correct’ model
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Displacement diagram after the deck deactivation
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Stress diagram after the deck deactivation
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According to our experience, it’s quite enough to find tension areas under dead load, deactivate the deck, and proceed with live loadanalysis…
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Incremental launching
Consequent analysis of many steps for a mechanical system withunilateral constraints with initial gaps
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Methods for finding solution:
► Disregarding “unilateracy” and/or gaps
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Methods for finding solution:
► Traditional Rabinovitch algorithm
At each iteration all supports with negative reaction are detached (declared free joints), and detached supports with negative displacementare attached (declared support joints)
This algorithm may enter an endless loop and collapse at an iteration,even though the solution definitely exists
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Methods for finding solution:
► Modified Rabinovitch algorithm
At each iteration only the support joint with maximal negative reactionis detached and the joint with maximal negative displacement isattached
The chance of looping and collapsing for this approach is way less thanfor traditional method
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Methods for finding solution:
► Optimization problem
Quadratic programming approach: in the case of incremental launching,the cost function definition involves positive semi-definite matrix, thus not every algorithm is suitable
General optimization approach turns to either Rabinovitch algorithms
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Methods for finding solution:
► Compression-only non-linear springs
Exact values for their stiffness have to be found. These cannot be orderslarger than the beam stiffness or the results will be absolutelyincorrect
We choose the modified Rabinovitch algorithm
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Straight and plain models can be drawn in AutoCAD using annotativeblocks, then processed in Orcoden, which runs GT STRUDL and results inDXF file with force, moment, reaction, and stress diagrams
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Curved and sophisticated models with thousands of joints and finiteelements still need GT STRUDL meshing facilities to be created
Joints: 17000Elements: 18500Steps: 200
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PART II
…offering some science…
Creep and shrinkage basic assumptions
Concrete creep:
► Creep deformation is proportional to elastic deformation (linear creep)
► The ratio between creep and elastic deformation is a creep coefficient function
0( , )cr t tε
00
( , ) ( , )( )
cr
el
t t t tt
ε= ϕ
ε
( )el tε► creep deformation
► elastic deformation
► creep coefficient function
► concrete age at loading application moment
0( , )t tϕ
0t
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Creep and shrinkage basic assumptions
Concrete shrinkage:
► Shrinkage deformation is time dependent function
( ) ( ) ( )sh sht f tε = ε ∞
► shrinkage deformation
► final shrinkage deformation
► shrinkage function
( )sh tε
( )shε ∞( )f t
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Creep coefficient and shrinkage functionsfor composite bridges
(1 )( ) tkt e −αϕ = ϕ
( )1( ) ( ) tsh sht e −βε = ε ∞
1.6 1.8kϕ ≈ −final creep coefficient at t →∞
4( ) 2 10sh−ε ∞ = ×
final shrinkage deformation at t →∞36
Elastic deformation obtaining at moment t0
,0 0 / ( )el b bF E Aε =
t=t1…tn
► Incremental initial deformation calculation
► Member distortion calculation
► Bridge analysis on action of external loading and member distortion obtained
► Obtaining elastic deformation for the next step
Post-processing
, , , 1 ,i cr i sh i i el i sh i−∆ε = ∆ε + ∆ ε = ∆ϕ ε + ∆ ε
1 0i i id d l−= + ∆ε
, / ( )el i i b bF E Aε =
Step-by-step algorithm for creep and shrinkage problem
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Seismic isolation and energy dissipation
Hydraulic damper Friction pendulumbearing
Anti-seismic devicesfor seismic isolation and energy
dissipation
►Rubber bearings with lead core
► Friction pendulum bearings
► Hydraulic dampers
► Steel hysteretic dampers
Main objectives of anti-seismic devices
►Increasing effective natural period
► Energy dissipation
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Seismic isolation analysis
Direct approach
► Artificial accelerogramgeneration
► Nonlinear time history analysis
Simplified approach
► Response spectrum and damping scale factors are specified by code
► Response spectrum analysis .
0 1 2 3 4 5 60
0.5
1
1.5
2
2.5
3
Natural Period T, sec
β
Ground type II
Ground type I
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Bridge analytical model with anti-seismic devices
ξeff(d)Κeff(d)
ξeff(d)Κeff(d)
ξeff(d)Κeff(d)
d
► The problem is that neither secant stiffness nor damping ratio which are dependent on amplitude can be determined in advance. ► We need an iterative process for determination of required parameters.
2
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Deff
eff
EK d⎡ ⎤
ξ = ⎢ ⎥π ⎢ ⎥⎣ ⎦
- energy dissipated during vibration cycle
DE
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Friction pendulum bearing Hydraulic damper
4D d sd bdE N d= µ
1 deff sd
bd
K NR d
⎛ ⎞µ= +⎜ ⎟
⎝ ⎠
max bdF C α= v0.15α ≈
max4D bdE F d≈
effbd
FKd
≈ max
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The analysis of seismically isolated structure comes down to finding the solutionof non-linear equation with unknown displacements
1. Setup initial value of horizontal displacement d.2. Initial secant stiffness and damping ratio computation
1. Eigenproblem analysis2. Response spectrum analysis
Obtaining displacement from DBX
Adjust stiffness and damping ratio
1 5%i i
i
d dd
−−>
Postprocessing 42
Example of seismic isolation analysis
Friction pendulum bearingEffective curvature radius R=3.2mDynamic friction coefficient µ=0.055
Hydraulic damperVelocity exponent 0.15Maximal damper force Fmax=50 mton
max1 1 abeff
V FKV R d d
µ⎡ ⎤= + +⎢ ⎥⎣ ⎦
[ ]max4D abE V F d= µ +
Abutment Middle pier1 1 m
effm
VKV R d
µ⎡ ⎤= +⎢ ⎥⎣ ⎦
4D mE V d= µ
2
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Deff
eff
EK d⎡ ⎤
ξ = ⎢ ⎥π ⎢ ⎥⎣ ⎦
Vab, Vm – support reaction caused by dead load 43
Response spectrum
10%ξ =
2%ξ =5%ξ =
10% 0.555%
η = ≥+ ξ
- damping scale factor
Peak ground acceleration 0.6g
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Results of seismic isolation analysis
Effective natural period T=1.8sDesign horizontal seismic displacement ±430mmAcceleration of the bridge girder 0.56g<PGA=0.6g
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Conclusions:
► No need to give up using the software if it seems incapable of something
► There is a way of going beyond the limits
Advice:
► Don’t trust the digit until it has been checked seven times
Questions:► ???
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THANK YOU FOR YOUR
ATTENTION