PERTURBATION BASED STOCHASTIC ISOGEOMETRIC ANALYSIS FOR BENDING OF FUNCTIONALLY GRADED PLATES WITH THE RANDOMNESS OF ELASTIC MODULUS

Abstract

WE PROPOSE, IN THIS PAPER, STOCHASTIC ISOGEOMETRIC ANALYSIS (SIGA) IS A TYPE OF NON-STATISTIC APPROACH IN WHICH COMBINES THE PERTURBATION TECHNIQUE WITH THE STANDARD ISOGEOMETRIC ANALYSIS, IN PARTICULAR FOR STATIC BEHAVIOR OF FUNCTIONALLY GRADED PLATES WITH THE UNCERTAIN ELASTIC MODULUS. WE ASSUME THAT THE SPATIAL RANDOM VARIATION OF ELASTIC MODULUS CAN BE MODELED AS A TWO DIMENSIONAL GAUSSIAN RANDOM FIELD IN THE PLANE OF THE PLATE. THE RANDOM FIELD IS DISCRETIZED TO SET OF RANDOM VARIABLES USING THE INTEGRATION POINT METHOD. THE SYSTEM EQUATIONS OF SIGA ARE CREATED USING THE NURBS FUNCTIONS FOR APPROXIMATION DISPLACEMENT FIELDS IN CONJUNCTION WITH THE FIRST-ORDER AND SECOND-ORDER PERTURBATION EXPANSIONS OF RANDOM FIELDS, STIFFNESS MATRIX, DISPLACEMENT FIELDS. BESIDES THE NON-STATISTIC APPROACH, MONTE CARLO SIMULATION IS PRESENTED FOR VALIDATION. THE ACCURACY AND APPROPRIATENESS OF THE NON-STATISTIC APPROACH ARE DEMONSTRATED VIA COMPARISONS OF THE PRESENT RESULTS WITH THOSE GIVEN BY THE STOCHASTIC FINITE ELEMENT METHOD IN THE LITERATURE AND BY THE MONTE CARLO ANALYSIS AS WELL. THE NUMERICAL EXAMPLES ARE EMPLOYED TO INVESTIGATE THE EFFECT OF THE RANDOMNESS OF
ELASTIC MODULUS AND SYSTEM PARAMETERS ON THE FIRST AND SECOND STATISTICAL MOMENTS OF DISPLACEMENT.