Finite element analysis of nonlinear shell structures with uncertain material property

Abstract The statistical dynamic responses of geometrically nonlinear shell structures with stochastic Young's modulus of elasticity are investigated in this study. In general, large deformation of the shell structures must be considered when shell structures are under excessive loading, and then the governing equations of the shell structures become nonlinear since the stiffness matrix of the system is related to the deflection. In this paper, the stochastic finite element method along with the perturbation technique is used to deal with statistical responses of shell structures with structural randomness; in particular, the Newton–Raphson iteration procedure in conjunction with Newmark scheme is adopted to solve the nonlinearity of the dynamic governing equation of shell structures. Some results obtained by the perturbation technique and those from the Monte Carlo simulation approach show a good agreement. Finally, it should be emphasized that these statistically dynamic responses are very useful for estimating the reliability of structures.

[1]  Ahmed K. Noor,et al.  Nonlinear shell analysis via mixed isoparametric elements , 1977 .

[2]  C. Mei,et al.  A Finite Element Method for Nonlinear Forced Vibrations of Beams , 1985 .

[4]  T.-P. Chang,et al.  Stochastic dynamic finite element analysis of a nonuniform beam , 1994 .

[5]  Toshio Yoshimura,et al.  Vibration analysis of non-linear beams subjected to a moving load using the finite element method , 1985 .

[6]  Nicholas F. Morris,et al.  The use of modal superposition in nonlinear dynamics , 1977 .

[7]  K. Surana.  Geometrically nonlinear formulation for the curved shell elements , 1983 .

[8]  P. Bergan,et al.  A comparative study of different numerical solution techniques as applied to a nonlinear structural problem , 1973 .

[9]  Masanobu Shinozuka,et al.  Response Variability of Stochastic Finite Element Systems , 1988 .

[10]  Armen Der Kiureghian,et al.  The stochastic finite element method in structural reliability , 1988 .

[11]  Mircea Grigoriu,et al.  STOCHASTIC FINITE ELEMENT ANALYSIS OF SIMPLE BEAMS , 1983 .

[12]  Dipankar Chakravorty,et al.  Finite element free vibration analysis of conoidal shells , 1995 .

[13]  Gregory B. Beacher,et al.  Stochastic FEM In Settlement Predictions , 1981 .

[14]  Wing Kam Liu,et al.  Probabilistic finite elements for nonlinear structural dynamics , 1986 .

[15]  Q. Cheng,et al.  Geometrically non-linear analysis including shear deformation of composite laminates , 1999 .

[16]  Chih-Chen Chang,et al.  Reliability of uncertain flexible laminated skewed plates under random compressions , 1992 .

[17]  Masanobu Shinozuka,et al.  Stochastic Finite Element Methods in Dynamics , 1986 .

[18]  Toshiaki Hisada,et al.  研究速報 : A Note on Stochastic Finite Element Method（part 1） : Variation of Stress and Strain Caused by Shape Fluctuation , 1980 .

[19]  Hui-Shen Shen,et al.  Postbuckling analysis of stiffened cylindrical shells under combined external pressure and axial compression , 1993 .

[20]  Klaus-Jürgen Bathe,et al.  A geometric and material nonlinear plate and shell element , 1980 .

[21]  Klaus-Jürgen Bathe,et al.  Some practical procedures for the solution of nonlinear finite element equations , 1980 .

[22]  Masanobu Shinozuka,et al.  Impact Loading on Structures with Random Properties , 1972 .

[23]  R. D. Wood,et al.  GEOMETRICALLY NONLINEAR FINITE ELEMENT ANALYSIS OF BEAMS, FRAMES, ARCHES AND AXISYMMETRIC SHELLS , 1977 .

[24]  Su-huan Chen,et al.  Nonlinear frequency spectrum in nonlinear structural analysis , 1992 .

[25]  Su-huan Chen,et al.  Statistical properties of nonlinear mode spectrum for large amplitude forced vibration systems , 1995 .

[26]  Chih‐Ping Wu,et al.  Asymptotic solutions of axisymmetric laminated conical shells , 2005 .

[27]  Marcin Kamiński,et al.  Generalized perturbation-based stochastic finite element method in elastostatics , 2007 .

[28]  R. E. Nickell,et al.  Nonlinear dynamics by mode superposition , 1976 .

[29]  Masanobu Shinozuka,et al.  Neumann Expansion for Stochastic Finite Element Analysis , 1988 .

[30]  Masanobu Shinozuka,et al.  SAFETY ANALYSIS OF STOCHASTIC FINITE ELEMENT SYSTEMS BY MONTE CARLO SIMULATION , 1988 .

[31]  J. Z. Zhu,et al.  The finite element method , 1977 .

[32]  M. Shinozuka,et al.  Structural Response Variability III , 1987 .

[33]  P. G. Bergan,et al.  Nonlinear analysis of free-form shells by flat finite elements , 1978 .