DOI QR코드

DOI QR Code

Added effect of uncertain geometrical parameter on the response variability of Mindlin plate

  • Noh, Hyuk Chun (Department of Civil Engineering and Engineering Mechanics, Columbia University) ;
  • Choi, Chang Koon (Department of Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology)
  • 투고 : 2005.02.16
  • 심사 : 2005.05.18
  • 발행 : 2005.07.10

초록

In case of Mindlin plate, not only the bending deformation but also the shear behavior is allowed. While the bending and shear stiffness are given in the same order in terms of elastic modulus, they are in different order in case of plate thickness. Accordingly, bending and shear contributions have to be dealt with independently if the stochastic finite element analysis is performed on the Mindlin plate taking into account of the uncertain plate thickness. In this study, a formulation is suggested to give the response variability of Mindlin plate taking into account of the uncertainties in elastic modulus as well as in the thickness of plate, a geometrical parameter, and their correlation. The cubic function of thickness and the correlation between elastic modulus and thickness are incorporated into the formulation by means of the modified auto- and cross-correlation functions, which are constructed based on the general formula for n-th joint moment of random variables. To demonstrate the adequacy of the proposed formulation, a plate with various boundary conditions is taken as an example and the results are compared with those obtained by means of classical Monte Carlo simulation.

키워드

참고문헌

  1. Babuska, I. and Chatzipantelidis, P. (2002), 'On solving elliptic stochastic partial differential equations', Comput. Meth. Appl. Mech. Engrg., 191(37-38), 4039-4122
  2. Choi, C.K. and Noh, H.C. (1993), 'Stochastic finite element analysis by using quadrilateral elements', J. of the KSCE, 13(5), 29-37
  3. Choi, C.K. and Noh, H.C. (1996a), 'Stochastic finite element analysis of plate structures by weighted integral method', Struct. Eng. Mech., 4(6), 703-715 https://doi.org/10.12989/sem.1996.4.6.703
  4. Choi, C.K. and Noh, H.C. (1996b), 'Stochastic finite element analysis with direct integration method', 4th Int. Conf. on Civil Eng., Manila, Philippines, Nov. 6-8, 522-531
  5. Choi, C.K. and Noh, H.C. (2000), 'Weighted integral SFEM including higher order terms', J. Engrg. Mech., ASCE, 126(8), 859-866 https://doi.org/10.1061/(ASCE)0733-9399(2000)126:8(859)
  6. Deodatis, G and Shinozuka, M. (1989), 'Bounds on response variability of stochastic systems', J. Engrg. Mech., ASCE, 115(11),2543-2563 https://doi.org/10.1061/(ASCE)0733-9399(1989)115:11(2543)
  7. 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
  8. Deodatis, G. (1996), 'Non-stationary stochastic vector processes: seismic ground motion applications', Probab. Engrg. Mech., 11, 149-168 https://doi.org/10.1016/0266-8920(96)00007-0
  9. Deodatis, G, Graham-Brady, L. and Micaletti, R. (2003), 'A hierarchy of upper bounds on the response of stochastic systems with large variation of their properties: random variable case', Probab. Engrg. Mech., 18, 349-363 https://doi.org/10.1016/j.probengmech.2003.08.001
  10. Deodatis, G., Graham-Brady, L. and Micaletti, R. (2003), 'A hierarchy of upper bounds on the response of stochastic systems with large variation of their properties: random field case', Probab. Engrg. Mech., 18, 365-375 https://doi.org/10.1016/j.probengmech.2003.08.002
  11. Falsone, G. and Impollonia, N. (2002), 'A new approach for the stochastic analysis of finite element modeled structures with uncertain parameters', Comput. Meth. Appl. Mech. Engrg., 191,5067-5085 https://doi.org/10.1016/S0045-7825(02)00437-1
  12. Frauenfelder, P., Schwab, C. and Todor, R.A. (2005), 'Finite elements for elliptic problems with stochastic coefficients', Comput. Meth. Appl. Mech. Engrg., 194(2-5), 205-228 https://doi.org/10.1016/j.cma.2004.04.008
  13. Graham, L. and Deodatis, G (1998), 'Variability response functions for stochastic plate bending problems', Structural Safety, 20, 167-188 https://doi.org/10.1016/S0167-4730(98)00006-X
  14. Graham, L.L. and Deodatis, G. (2001), 'Response and eigenvalue analysis of stochastic finite element systems with multiple correlated material and geometric properties', Probab. Engrg. Mech., 16(1), 11-29 https://doi.org/10.1016/S0266-8920(00)00003-5
  15. Kaminski, M. (2001), 'Stochastic finite element method homogenization of heat conduction problem in fiber composites', Struct. Eng. Mech., 11(4), 373-392 https://doi.org/10.12989/sem.2001.11.4.373
  16. Liu, W'K., Belytschko, T. and Mani, A. (1986), 'Probabilistic finite elements for nonlinear structural dynamic', Comput. Meth. Appl. Mech. Engrg., 56, 91-81 https://doi.org/10.1016/0045-7825(86)90138-6
  17. Lin, Y.K. (1967), Probabilistic Theory of Structural Dynamics, McGraw-Hill, Inc., 68
  18. Manjuprasad, M., Gopalakrishnan, S. and Balaji Rao, K. (2003), 'Stochastic finite element based seismic analysis of framed structures with open-storey', Struct. Eng. Mech., 15(4),381-394 https://doi.org/10.12989/sem.2003.15.4.381
  19. Noh, H.C. (2004), 'A formulation for stochastic finite element analysis of plate structures with uncertain Poisson's ratio', Comput. Meth. Appl. Mech. Engrg., 193(45-47),4857-4873 https://doi.org/10.1016/j.cma.2004.05.007
  20. Papadopoulos, V., Deodatis, G. and Papadrakakis, M. (2005), 'Flexibility-based upper bounds on the response variability of simple beams', Comput. Meth. Appl. Meeh. Engrg., 194(12-16),1385-1404 https://doi.org/10.1016/j.cma.2004.06.040
  21. Popescu, R., Deodatis, G. and Prevost, J.H. (1998), 'Simulation of homogeneous nonGaussian stochastic vector fields', Probab. Engrg. Mech., 13(1), 1-13 https://doi.org/10.1016/S0266-8920(97)00001-5
  22. Sarkani, S., Lutes, L.D., Jin, S. and Chan, C. (1999), 'Stochastic analysis of seismic structural response with soil-structure interaction', Struet. Eng. Mech., 8(1), 53-72 https://doi.org/10.12989/sem.1999.8.1.053
  23. Shinozuka, M. (1972), 'Monte Carlo solution of structural dynamics', Comput. Struet., 2, 855-874 https://doi.org/10.1016/0045-7949(72)90043-0
  24. Shinozuka, M. and Deodatis, G. (1988), 'Response variability of stochastic finite element systems', J. Engrg. Mech., ASCE, 114(3),499-519 https://doi.org/10.1061/(ASCE)0733-9399(1988)114:3(499)
  25. Stefanou, G and Papadrakakis, M. (2004), 'Stochastic finite element analysis of shells with combined random material and geometric properties', Comput. Meth. Appl. Mech. Engrg., 193(1-2), 139-160 https://doi.org/10.1016/j.cma.2003.09.006
  26. Timoshenko, S.P. and Krieger, S.W. (1959), Theory of Plates and Shells, McGraw-Hili, Inc
  27. To, C.S.W (1986), 'The stochastic central difference method in structural dynamics', Comput. Struct., 23(6), 813-818 https://doi.org/10.1016/0045-7949(86)90250-6
  28. Yamazaki, F. and Shinozuka, M. (1990), 'Simulation of stochastic fields by statistical preconditioning', J. Engrg. Mech., ASCE, 116(2), 268-287 https://doi.org/10.1061/(ASCE)0733-9399(1990)116:2(268)
  29. Zhu, W.Q., Ren, Y.J. and Wu, W.Q. (1992), 'Stochastic FEM based on local averages of random vector fields', J. Engrg. Mech., ASCE, 118(3), 496-511 https://doi.org/10.1061/(ASCE)0733-9399(1992)118:3(496)

피인용 문헌

  1. 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
  2. Behavior of high-strength fiber reinforced concrete plates under in-plane and transverse loads vol.31, pp.4, 2009, https://doi.org/10.12989/sem.2009.31.4.371