ABSTRACT
To numerically model a finite body continuous random medium, classical deterministic finite element method has been extended to stochastic finite element method (SFEM). This chapter presents a unifying framework of variational formulation to cover both classical displacement-based SFEM and multiscale SFEM (MSFEM). The formulation shows that Monte Carlo SFEM, perturbation-type SFEM, and weighted integral SFEM belong to the quasiweak form, while the weak form yields spectral SFEM, pseudospectral SFEM, and MSFEM. A perturbation-type MSFEM is specifically formulated to solve continuous random media problems efficiently, especially soils in geotechnical engineering. A concluding remark is that in a scale-coupling problem, when the domain size is finite, the modified Green function and the potential energy demand finite element computation, which is exactly the application of the multiscale stochastic FEM in a random media problem. In predicting settlement of a geotechnical foundation, random variation of the Young's modulus is a major factor to be considered in geotechnical design.
