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

Abstract 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 observations and thoughts are then realized in several manners. We first present the exact inverse FEMSP, which however cannot serve as a general tool for stochastic analysis of complex structures. The new variational principles for stochastic beams, for the mean response function, as well as response's auto-correlation function are formulated and the FEM based on the variational principles is presented. Finally, a general non-perturbative FEM for stochastic problems with large variations is developed, based on the element-level flexibility. It is concluded that much work needs to be done in order 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 lies in their non-perturbational nature. Numerical examples are presented.

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