COBEM99

S25 Métodos Numéricos

Title:

ON MULTIDIMENSIONAL NON-GAUSSIAN RANDOM FIELDS GENERATION FOR FINITE ELEMENT STRUCTURAL ANALYSIS. KEYWORDS:RANDOM FIELDS GENERATION, STOCHASTIC FINITE ELEMENT ANALYSIS.

Summary :

ABSTRACT. RANDOM FIELDS GENERATION IS A VERY IMPORTANT SUBJECT RELATED WITH STOCHASTIC FINITE ELEMENT STRUCTURAL ANALYSIS AND STRUCTURAL RELIABILITY. IN THESE CASES, DESPITE OF THE INHERENT RANDOMNESS OF THE DIFFERENT VARIABLES, THE DESIGNER IS CONCERNED WITH THE SPATIAL RANDOMNESS OF MATERIAL PROPERTIES, GEOMETRY, APPLIED EXTERNAL LOADS AND BOUNDARY CONDITIONS IN ORDER TO IMPROVE THE REPRESENTATION OF THE SYSTEM CHARACTERISTICS. IN THIS WAY, THE MULTIDIMENSIONAL NON-GAUSSIAN STOCHASTIC FIELD GENERATION BECOMES, IN MANY CASES, AN APPROPRIATED TOOL TO OBTAIN RELIABLE RESULTS. A BRIEF REVIEW OF THREE MODELS FOR RANDOM FIELDS GENERATION IS PRESENTED IN THIS WORK. IN THE THREE MODELS THE INVERSE MAPPING TECHNIQUE IS USED TO OBTAIN A NON-GAUSSIAN FIELD. THE CHOLESKY DECOMPOSITION METHOD HAS BEEN USED INTENSIVELY FOR ANY FIELD CORRELATION. HOWEVER, THROUGH THE MODAL DECOMPOSITION METHOD, THE DECREASING CHARACTERISTICS OF THE COVARIANCE MATRIX EIGENVALUES IS USED, REDUCING SIGNIFICANTLY THE COMPUTATIONAL EFFORT AND COST TO GENERATE RANDOM FIELDS. FINALLY, THE SPECTRAL REPRESENTATION METHOD, EMPLOYING COSINE SERIES, IS VERY USEFUL TO OBTAIN ACCURATE GENERATIONS OF RANDOM FIELDS DUE TO ORTHOGONALITY AND PERIODICITY OF THE ADOPTED TRIGONOMETRIC FUNCTIONS. A NUMERICAL EXAMPLE FOR RANDOM FIELD GENERATION IS PRESENTED FOR A QUANTITATIVE AND QUALITATIVE EVALUATION OF THESE METHODS, HAVING IN SIGHT FUTURE APPLICATIONS IN THE RELIABILITY ANALYSIS OF STRUCTURAL SYSTEMS.

Author :

Awruch, Armando Miguel
Gomes, Herbert Martins

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