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The Application of Spectral SFEM for 3D Systems with Stochastic Operator under Stochastic Excitation

O. M. Galal


This work considers a three-dimension stochastic structural system, discretized using 3D solid elements. This said type of elements is considered as the most generic one. On the other hand, Spectral Stochastic Finite Elements Method (SSFEM), utilized here, has its advantages in plotting the response probability distribution function (p.d.f.), consequently obtaining extreme values of stochastic system responses and any of its statistical moments. The system is assumed to have linear stochastic operator and submitted to stochastic excitations. Both the random operator and random excitation fields are considered to be modelled as second order stochastic processes, and the covariance functions for these processes are extended to 3D random fields. A bridge support system is introduced as an illustrative example considering three cases of stochasticity. These cases are: 1) stochastic operator with stochastic excitation, 2) stochastic operator with deterministic excitation and 3) deterministic operator with stochastic excitation.


3D stochastic solids, stochastic finite elements method (SFEM), stochastic excitation, stochastic operators, Neumann expansion, homogeneous chaos expansion.

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