Elastic Stress Predictor for Stochastic Finite Element Problems

Abstract

The paper presents a new algorithm of elastic stress predictor in non linear stochastic finite element method using the Generalized Polynomial Chaos. The statistical moments of strains calculated based on the displacement Polynomial Chaos expansion. To descretise the stochastic process of material the Karhunen-Loeve Expansion was used and it is presented. Using the strains and the material Karhunen-Loeve Expansion the stress components are calculated. A numerical example of shallow foundation was carried out and the results of stress and strain of the new algorithm were compared with those raised from Monte Carlo method which is treated as the exact solution. A great accuracy was presented.

Uncertain Volatility Derivative Model Based on the Polynomial Chaos

“…Assuming that the volatility of stock The author has presented a stochastic finite element procedure to solve boundary problems using polynomial chaos [5]- [9]. The outcome derivative price of the problem is given by the polynomial chaos expansion as:…”