Structural Engineering and Mechanics

  • 제4권6호
  • /
  • Pages.703-715
  • /
  • 1996
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Stochastic finite element analysis of plate structures by weighted integral method

  • Choi, Chang-Koon (Department of Civil Engineering, Korea Advanced Institute of Science & Technology) ;
  • Noh, Hyuk-Chun (Department of Civil Engineering, Korea Advanced Institute of Science & Technology)
  • 발행 : 1996.11.25
⟨ 이전 논문 다음 논문 ⟩

초록

In stochastic analysis, the randomness of the structural parameters is taken into consideration and the response variability is obtained in addition to the conventional (mean) response. In the present paper the structural response variability of plate structure is calculated using the weighted integral method and is compared with the results obtained by different methods. The stochastic field is assumed to be normally distributed and to have the homogeneity. The decomposition of strain-displacement matrix enabled us to extend the formulation to the stochastic analysis with the quadratic elements in the weighted integral method. A new auto-correlation function is derived considering the uncertainty of plate thickness. The results obtained in the numerical examples by two different methods, i.e., weighted integral method and Monte Carlo simulation, are in a close agreement. In the case of the variable plate thickness, the obtained results are in good agreement with those of Lawrence and Monte Carlo simulation.

키워드

참고문헌

  1. Choi, C.K. and Kim, S.H. (1988), "Reduced integration nonconforming modes, and their coupling in thin plate elements", Computers and Structures, 29, 57-62. https://doi.org/10.1016/0045-7949(88)90171-X
  2. Choi, C.K. and Kim, S.H. (1989), "Coupled use of reduced integration and non-conforming modes in quadratic Mindlin plate element", International Journal for Numerical Methods in Engineering, 28, 1909-1928. https://doi.org/10.1002/nme.1620280814
  3. Choi, C.K. and Noh, H.C. (1993), "Stochastic finite element analysis by using quadrilateral elements", Journal of the KSCE, 13(5), 29-37.
  4. Deodatis, G. and Shinozuka, M. (1989), "Bounds on response variability of stochastic system", Journal of Engineering Mechanics, ASCE, 115(11), 2543-2563. https://doi.org/10.1061/(ASCE)0733-9399(1989)115:11(2543)
  5. Deodatis, G., Wall, W. and Shinozuka, M. (1991), "Analysis of two-dimensional stochastic systems by the weighted integral method", In Spanos, P.D. and Brebbia, C.A. editors, Computational Stochastic Mechanics, 395-406.
  6. Kleiber, M. and Hein, T.D. (1992), "The stochastic finite element method", John Wiley & Sons.
  7. Lawrence, M.A. (1987), "Basis random variables in finite element analysis", International Journal for Numerical Methods in Engineering, 24, 1849-1863. https://doi.org/10.1002/nme.1620241004
  8. Liu, W.K., Belytschko, T. and Mani, A. (1986), "Probabilistic finite elements for nonlinear structural dynamic", Computer Methods in Applied Mechanics and Engineering, 56, 91-81. https://doi.org/10.1016/0045-7825(86)90138-6
  9. Shinozuka, M. (1987), "Structural response variability", Journal of Engineering Mechanics, ASCE, 113(6), 825-842. https://doi.org/10.1061/(ASCE)0733-9399(1987)113:6(825)
  10. Shinozuka, M. and Deodatis, G. (1988), "Response variability of stochastic finite element systems", Journal of Engineering Mechanics, ASCE, 114(3), 499-519. https://doi.org/10.1061/(ASCE)0733-9399(1988)114:3(499)
  11. Thomas, J.R., Hughes and Martin Cohen (1978), "The' Heterosis' finite element for plate bending", Computers and Structures, 9(5), 445-450. https://doi.org/10.1016/0045-7949(78)90041-X
  12. Yamazaki, F. and Shinozuka, M. (1990), "Simulation of stochastic fields by statistical preconditioning", Journal of engineering Mechanics, ASCE, 116(2), 268-287. https://doi.org/10.1061/(ASCE)0733-9399(1990)116:2(268)
  13. Yamazaki, F. and Shinozuka, M. and Dasgupta, G. (1988), "Neumann expansion for stochastic finite element analysis", Journal of Engineering Mechanics, ASCE, 114(8), 1335-1355. https://doi.org/10.1061/(ASCE)0733-9399(1988)114:8(1335)

피인용 문헌

  1. Stochastic behavior of Mindlin plate with uncertain geometric and material parameters vol.20, pp.4, 2005, https://doi.org/10.1016/j.probengmech.2005.06.001
  2. Response variability of cylindrical shells with stochastic non-Gaussian material and geometric properties vol.33, pp.9, 2011, https://doi.org/10.1016/j.engstruct.2011.05.009
  3. Extension of Weighted Integral Stochastic Finite Element Method to the Analysis of Semi-Infinite Domain vol.131, pp.5, 2005, https://doi.org/10.1061/(ASCE)0733-9399(2005)131:5(550)
  4. Inelastic deformation processes with random parameters––methods of analysis and design vol.192, pp.20-21, 2003, https://doi.org/10.1016/S0045-7825(03)00264-0
  5. Stochastic buckling behaviour of laminated composite structures with uncertain material properties vol.66, 2017, https://doi.org/10.1016/j.ast.2017.01.028
  6. Weighted Integral SFEM Including Higher Order Terms vol.126, pp.8, 2000, https://doi.org/10.1061/(ASCE)0733-9399(2000)126:8(859)
  7. Stochastic finite element method homogenization of heat conduction problem in fiber composites vol.11, pp.4, 2001, https://doi.org/10.12989/sem.2001.11.4.373
  8. Stochastic Analysis of Shape Imperfection in RC Cooling Tower Shells vol.126, pp.3, 2000, https://doi.org/10.1061/(ASCE)0733-9445(2000)126:3(417)
  9. A formulation for stochastic finite element analysis of plate structures with uncertain Poisson's ratio vol.193, pp.45-47, 2004, https://doi.org/10.1016/j.cma.2004.05.007
  10. Response variability due to randomness in Poisson’s ratio for plane-strain and plane-stress states vol.43, pp.5, 2006, https://doi.org/10.1016/j.ijsolstr.2005.03.072
  11. Plate response variability due to triple random parameters vol.15, pp.3, 2011, https://doi.org/10.1007/s12205-011-1081-4
  12. Higher order weighted integral stochastic finite element method and simplified first-order application vol.44, pp.11-12, 2007, https://doi.org/10.1016/j.ijsolstr.2006.11.013
  13. Variability of displacements and stresses at random variable state vol.31, pp.6, 2009, https://doi.org/10.12989/sem.2009.31.6.751
  14. Solution of randomly excited stochastic differential equations with stochastic operator using spectral stochastic finite element method (SSFEM) vol.28, pp.2, 2008, https://doi.org/10.12989/sem.2008.28.2.129
  15. Probabilistic optimal safety with minimum life-cycle cost based on stochastic finite element analysis of steel cable-stayed bridges vol.11, pp.3, 2011, https://doi.org/10.1007/s13296-011-3008-9
  16. Effect of multiple uncertain material properties on the response variability of in-plane and plate structures vol.195, pp.19-22, 2006, https://doi.org/10.1016/j.cma.2005.06.026
  17. Added effect of uncertain geometrical parameter on the response varibility of Mindlin plate vol.20, pp.4, 2005, https://doi.org/10.12989/sem.2005.20.4.477
  18. Finite element linear and nonlinear, static and dynamic analysis of structural elements – an addendum – A bibliography (1996‐1999) vol.17, pp.3, 2000, https://doi.org/10.1108/02644400010324893
  19. SOLVING (n×n) LINEAR EQUATIONS WITH PARAMETERS COVARIANCES vol.01, pp.03, 2004, https://doi.org/10.1142/S0219876204000289
  20. The stochastic finite element method: Past, present and future vol.198, pp.9-12, 2009, https://doi.org/10.1016/j.cma.2008.11.007
  21. Stochastic finite element analysis of shells with combined random material and geometric properties vol.193, pp.1-2, 2004, https://doi.org/10.1016/j.cma.2003.10.001
  22. Monte Carlo simulation-compatible stochastic field for application to expansion-based stochastic finite element method vol.84, pp.31-32, 2006, https://doi.org/10.1016/j.compstruc.2006.07.001
  23. Effect of Random Material Parameter in the Shell Structures vol.275-277, pp.1662-7482, 2013, https://doi.org/10.4028/www.scientific.net/AMM.275-277.1302
  24. Immune algorithm-embedded stochastic meshless method for structural reliability vol.226, pp.2, 2012, https://doi.org/10.1177/0954406211414522
  25. Probabilistic optimal safety valuation based on stochastic finite element analysis of steel cable-stayed bridges vol.10, pp.2, 1996, https://doi.org/10.12989/sss.2012.10.2.089
  26. 몬테카를로 해석 기반 확률적 위상최적화 vol.30, pp.2, 1996, https://doi.org/10.7734/coseik.2017.30.2.153
  27. Perturbation based stochastic isogeometric analysis for bending of functionally graded plates with the randomness of elastic modulus vol.17, pp.7, 1996, https://doi.org/10.1590/1679-78256066
  28. Inverse Estimation Method of Material Randomness Using Observation vol.10, pp.6, 1996, https://doi.org/10.3390/cryst10060512