The bird's eye view on finite element method for structures with large stochastic variations

Extensive motivation to do an additional work in the finite element method in stochastic problems (FEMSP) is discussed. The qualitative comparison of FEMSP with the state of the art of the deterministic FEM is given. These ob servations and thoughts are then realized in several manners. We first pres ent the exact inverse FEMSP, which however cannot serve as a general tool f or stochastic analysis of complex structures. The new variational principle s for stochastic beams, for the mean response function, as well as response 's auto-correlation function are formulated and the FEM based on the variat ional principles is presented. Finally, a general non-perturbative FEM for stochastic problems with large Variations is developed, based on the elemen t-level flexibility. It is concluded that much work needs to be done in ord er FEMSP to be at the level compared to that of the deterministic FEM. The advantage of the main methods presented here over the conventional ones lie s in their non-perturbational nature. Numerical examples are presented. (C) 1999 Elsevier Science S.A. All rights reserved.