Constitutive Relations of Stress and Strain in Stochastic Finite Element Method

摘要

The analysis and design in structural and geotechnical engineering problems requires the calculation of stress and strain which is generally a difficult task because of the uncertainty and spatial variability of the properties of soil materials. This paper presents a procedure of conducting Stochastic Finite Element Analysis using Polynomial Chaos in order to propagate the uncertainties of input to constitutive relation of stress and strain. The problem is dominated by highly non linearity. Among other methods the procedure leads to an efficient computational cost for real practical problems. This is achieved by polynomial chaos expansion displacement field, stress and strain also. An example of a plane-strain strip load on a semi-infinite elastic foundation is presented and the results of settlement are compared to those obtained from the closed form solution method. A close matching of the two is observed. The constitutive relation of stress and strain is presented as result of the Polynomial Chaos expansion and Monte Carlo method. A close matching of the two method is observed also.