SOME CRITICAL OBSERVATIONS AND ATTENDANT NEW RESULTS IN THE FINITE-ELEMENT METHOD FOR STOCHASTIC PROBLEMS

Extensive motivation to do additional work in the finite element metho d in stochastic problems (FEMSP) is discussed. The qualitative compari son of FEMSP with the state of the art of the deterministic FEM is giv en. These critical observations and thoughts are then realized in seve ral manners. We first present the exact inverse FEMSP, which however c annot serve as a general tool for stochastic analysis of complex struc tures. Therefore, an improved FEMSP is presented. Finally, the variati onal principles for stochastic beams, for the mean response function, as well as the response's auto-correlation function are formulated for the first time in the literature. It is concluded that much work need s to be done in order for FEMSP to be at the level compared to that of the deterministic FEM. The advantage of the main methods presented he re over the conventional ones lies in their non-perturbational nature. Numerical examples are presented to illustrate the superiority (if no t yet universality) of the presented methods over the conventional one s.