Abstract
We present and analyze a new hybrid stochastic finite element method for solving eigenmodes of structures with random geometry and random elastic modulus. The fundamental assumption is that the smallest eigenpair is well defined over the whole stochastic parameter space. The geometric uncertainty is resolved using collocation and random material models using Galerkin method at each collocation point. The response statistics, expectation and variance of the smallest eigenmode, are computed in numerical experiments. The hybrid approach is superior to alternatives in practical cases where the number of random parameters used to describe geometric uncertainty is much smaller than that of the material models.
Highlights
In standard engineering models many physical quantities such as material parameters are taken to be constant, even though their statistical nature is well understood
We present and analyze a new hybrid stochastic finite element method for solving eigenmodes of structures with random geometry and random elastic modulus
We have demonstrated the practicality of the new hybrid algorithm in a practical, yet idealized, application
Summary
In standard engineering models many physical quantities such as material parameters are taken to be constant, even though their statistical nature is well understood. In a detailed report on a state-of-the-art verification and validation process comparing modern simulations with the set of experiments performed in the Oak Ridge National Laboratory in the early 70s, Szabo and Muntges report discrepancies of over 20% in some quantities of interest [1] These discrepancies are attributed to machining imperfections not accounted for in the computations. In important nonlinear problems such as buckling of a shell, it is known that variation between manufactured specimens has a profound effect in the actual performance [2] This suggests that a stochastic dimension should be added to the models.
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