Neumann Expansion for Stochastic Finite Element Analysis

With the aid of the finite element method, the present paper deals with the problem of structural response variability resulting from the spatial variability of material properties of structures, when they are subjected to static loads of a deterministic nature. The spatial variabilities are modeled as two‐dimensional stochastic fields. The finite element discretization is performed in such a way that the size of each element is sufficiently small. Then, the present paper takes advantage of the Neumann expansion technique in deriving the finite element solution for the response variability within the framework of the Monte Carlo method. The Neumann expansion technique permits more detailed comparison between the perturbation and Monte Carlo solutions for accuracy, convergence, and computational efficiency. The result from such a Monte Carlo method is also compared with that based on the commonly used perturbation method. The comparison shows that the validity of the perturbation method is limited to the c...

[1]  Masanobu Shinozuka,et al.  Stochastic Fields and their Digital Simulation , 1987 .

[2]  Masanobu Shinozuka,et al.  Parametric Study of Wind Loading on Structures , 1973 .

[3]  Masanobu Shinozuka,et al.  ARMA Model for Two‐Dimensional Processes , 1987 .

[4]  J. Lumley.  Stochastic tools in turbulence , 1970 .

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

[6]  M. Shinozuka,et al.  Digital simulation of random processes and its applications , 1972 .

[7]  Masanobu Shinozuka,et al.  Nonlinear Panel Response from a Turbulent Boundary Layer , 1972 .

[8]  Masanobu Shinozuka,et al.  PROBABILISTIC MODELING OF CONCRETE STRUCTURES , 1972 .

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

[10]  Masanobu Shinozuka,et al.  EFFECT OF SELF-WEIGHT AND VERTICAL ACCELERATION ON THE BEHAVIOUR OF TALL STRUCTURES DURING EARTHQUAKE* , 1972 .

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

[12]  R. A. Silverman,et al.  Wave Propagation in a Turbulent Medium , 1961 .

[13]  Armen Der Kiureghian,et al.  Finite Element Methods in Structural Safety Studies , 1985 .

[14]  Masanobu Shinozuka,et al.  Monte Carlo solution of structural dynamics , 1972 .

[15]  M. Shinozuka,et al.  Monte Carlo Solution of Nonlinear Vibrations , 1971 .

[16]  Masanobu Shinozuka,et al.  Random Eigenvalue Problems in Structural Analysis , 1971 .

[17]  R. Vaicaitis,et al.  Digital Generation of Random Forces for Large-Scale Experiments , 1976 .

[18]  A. S. Monin,et al.  Statistical Fluid Mechanics: The Mechanics of Turbulence , 1998 .

[19]  Masanobu Shinozuka,et al.  DYNAMIC ANALYSIS OF FIXED OFFSHORE STRUCTURES SUBJECTED TO WIND GENERATED WAVES , 1977 .

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