Reliability study of uncertain structures using stochastic finite elements
A stochastic finite element method is developed to study the reliability of structures such as beams, columns, plates, and shells with structural uncertainties due to variabilities occurred during fabricating process. The three failure criteria considered are static displacement, buckling, an supersonic flutter. The structural uncertainties include modulus of elasticity, mass density, thickness, fiber orientation, geometric imperfection of the structure, in-plane load, mass density of air, and modulus of elastic foundation. The stochastic finite elements formulated include a six degree-of-freedom two dimensional beam-column element and a 48 degree-of-freedom doubly-curved quadrilateral laminated thin shell element. The formulations for the deterministic 6-DOF beam-column element and the 48-DOF shell element are based on the Euler-Bernoulli beam theory and Kirchhoff-Love thin shell theory, respectively. The stochastic element formulations are accomplished by including the effects of structural uncertainties and other uncertain parameters. The stochastic solution procedure is developed based on a mean-centered second-moment perturbation technique. The element formulations and the state-of-the-art solution procedure for the stochastic structural analysis and reliability study are coded into a computer program. To evaluate the validity and to demonstrate the applicability of the present developments, a series of statics, buckling, vibration, and supersonic flutter analyses of beams, columns, plates, shells with structural uncertainties are performed and compared with existing alternative solutions whenever available. Whenever alternative solutions are not available, representative results are verified by Monte-Carlo simulation solutions. The results quantify the effects of these uncertain parameters on the reduction of the structural reliability and stability boundaries of the uncertain structures. The results also provide physical insight into such practical design and fabrication problems.
Yang, Purdue University.
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