钢筋混凝土结构的随机场非线性有限元分析.pdf

1、Contents Introduction Application of Random Fields Examples of Random Fields in DIANA Conclusions Questions 2/39 Engineerings perspective Probability of failure Introduction|Application of RF|Examples|Conclusions 3/39 Uncertainty Loading Weight of the car Capacity Material properties Geometry proper

2、ties Introduction|Application of RF|Examples|Conclusions 4/39 Spatial variability Introduction|Application of RF|Examples|Conclusions 5/39 Random variable Correlated random variables Correlation function Lag distance Correlation function Introduction|Application of RF|Examples|Conclusions 6/39 Corre

3、lation length Introduction|Application of RF|Examples|Conclusions 7/39 Threshold value Introduction|Application of RF|Examples|Conclusions 8/39 Application of Random fields Introduction|Application of RF|Examples|Conclusions 9/39 1.Statistical characteristics of reinforced concrete 2.Assessment of R

4、andom Field(RF)generators 1.Statistical characteristics Introduction|Application of RF(1)|Examples|Conclusions 10/39 Steel Small variation in space Concrete Large variation in space Scholars use different values Lc 0.5 5 m Exponential&Squared exponential Normal&log-normal COV 0.1 0.3 JCSS probabilis

5、tic model code Introduction|Application of RF(1)|Examples|Conclusions 11/39 Lc=5 m C1=0.5 m and COV depends on concrete class All material properties are linked to basic random field 2.Assessment of RF generators Introduction|Application of RF(2)|Examples|Conclusions 12/39 Categorized the methods Im

6、plemented some of the methods Compared these methods Methods for RF generation Introduction|Application of RF(2)|Examples|Conclusions 13/39 Covariance Matrix Decomposition(CMD)Introduction|Application of RF(2)|Examples|Conclusions 14/39 H(x)=+L Where L is the decomposed covariance matrix using:Chole

7、sky decomposition Eigen decomposition Discrete Fourier Transform(DFT)Introduction|Application of RF(2)|Examples|Conclusions 15/39 Random field is represented by a sum of sinusoids Covariance function One sided SDF Random field FT Inv.FT Fast Fourier Transform(FFT)Introduction|Application of RF(2)|Ex

8、amples|Conclusions 16/39 The DFT is improved by applying a Fast Fourier algorithm Random field mesh and discritization of SDF are coupled Random field is periodic symmetric covariance structure Local Average Subdivision(LAS)Random field is obtained by a subdivision algorithm Start with coarse random

9、 field applying CMD Repeatedly subdivide cells Locally the statistical properties have to match with the previous stage Variance function Introduction|Application of RF(2)|Examples|Conclusions 17/39 Process of RF generation Introduction|Application of RF(2)|Examples|Conclusions 18/39 Correlation str

10、ucture(1)1D 2000 fields Sexp Normal C1=0 Lc=5 m Introduction|Application of RF(2)|Examples|Conclusions 19/39 Correlation structure(2)Introduction|Application of RF(2)|Examples|Conclusions 20/39 2D 200 fields Sexp Log-normal C1=0.5 Lc=5 m Outcome of RF assessment Introduction|Application of RF(2)|Exa

11、mples|Conclusions 21/39 All methods are appropriate CMD-small models only FFT-accurate and fast LAS-performs slightly less All methods are implemented Examples of RF in DIANA Introduction|Application of RF|Examples|Conclusions 22/39 Analysis 1:shrinkage of concrete floor First without RF Thereafter

12、RF according JCSS Analysis 2:4-point bending beam Input in DIANA IE Introduction|Application of RF|Examples|Conclusions 23/39 Input in dat/dcf-file DAT-File MATERI 1 NAME Membrane YOUNG 1.00000E+03 POISON 2.00000E-01 DCF-File *FILOS INITIA*INPUT*RANFLD BEGIN FIELD FLDTYP=COVARI BEGIN COVARI NX=40 NY

13、=20 END COVARI COVTYP=EXPONE CORLEN=5 STDDEV=20 MATIDX 1 MATPAR YOUNG END FIELD*LINSTA.24/39 Introduction|Application of RF|Examples|Conclusions Analysis of concrete floor Introduction|Application of RF|Examples(1)|Conclusions 25/39 =24 =510 Mechanical scheme Introduction|Application of RF|Examples(

14、1)|Conclusions 26/39 Crack growth-no RF Introduction|Application of RF|Examples(1)|Conclusions 27/39 Compressive strength Introduction|Application of RF|Examples(1)|Conclusions 28/39 Tensile strength Introduction|Application of RF|Examples(1)|Conclusions 29/39 Youngs modulus Introduction|Application

15、 of RF|Examples(1)|Conclusions 30/39 Crack growth with RF Introduction|Application of RF|Examples(1)|Conclusions 31/39 Number of cracks Introduction|Application of RF|Examples(1)|Conclusions 32/39 Influence of correlation length Introduction|Application of RF|Examples(1)|Conclusions 33/39 4-point be

16、nding beam Introduction|Application of RF|Examples(2)|Conclusions 34/39 Introduction|Application of RF|Examples(2)|Conclusions 4-point bending beam results(1)Trekstrerkte 3.24-3.38 MPa 35/39 Introduction|Application of RF|Examples(2)|Conclusions 4-point bending beam results(2)Trekstrerkte 3.04-3.07

17、MPa 36/39 Introduction|Application of RF|Examples(2)|Conclusions 4-point bending beam results(3)Trekstrerkte 2.67-2.98 MPa 37/39 Introduction|Application of RF|Examples(2)|Conclusions 4-point bending beam results(4)Trekstrerkte 3.49-3.67 MPa 38/39 Conclusies Random field function is presented and can now be used JCSS probabilistic model code is implemented Random fields for any other property An integrated calculation,of the probability of failure under investigation,may be expected in next version.39/39 Thank you for listening!