TABLE OF CONTENTS A person should always be flexible like a reed and not stiff like a cedar Talmud, Tractate Taanit 10a.
Flexible bodies like shells require a flexible approach W. T. Koiter.
Even with linear elastic problems, most stochastic analyses have not yet methodologically reached the present level already achieved by current deterministic methods T. Takada (1991b).
we realized that the available reliability methods failed to represent structures as realistically as possible. On the other hand, the deterministic finite element methods fails to consider uncertainty in the variables To capture the desirable features of those two approaches, they needed to be combined A. Haldar and S. Mahadevan (2000).
In Chapters 3 and 5 we proposed two non-perturbative FEMs for stochastic structures, namely the exact inverse based FEM for simple stochastic structures and the variational principle based FEM for stochastic beams. These two approaches encounter difficulties when they are generalized as a widely applicable tool for two-or three-dimensional structures. This chapter presents an element-level flexibility-based FEM for stochastic problems. The unconventional step in the new formulation is to divide the element-level finite element equilibrium equation by the element stiffness so that the reciprocal of the stiffness (the flexibility) appears on the right side of the equation, and thus becomes uncoupled from the unknown displacement. The mean and covariance of the displacement are then obtained in terms of the mean and covariance of the flexibility.
The concept and formulation of the element-level flexibility-based finite element for stochastic structures will...
