Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Non-Linear Finite Element Analysis of Solids and Structures: Essentials
Non-Linear Finite Element Analysis of Solids and Structures: Essentials
Generalized perturbation-based stochastic finite element method in elastostatics
Computers and Structures
Generalized stochastic perturbation technique in engineering computations
Mathematical and Computer Modelling: An International Journal
Global structural optimization considering expected consequences of failure and using ANN surrogates
Computers and Structures
Nonlinear MDOF system stochastic response determination via a dimension reduction approach
Computers and Structures
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A very efficient and straightforward numerical procedure for the computation of statistical second moment characteristics of large, non-linear finite element systems under stochastic loading is presented. For the modeling of both the loading and the response of the system an orthogonal series expansion of the corresponding covariance matrix, the so-called Karhunen-Loeve expansion is applied, allowing to incorporate potentially available statistical data of an excitation process directly into the analysis. The non-linear equation of motion is linearized by the method of equivalent statistical linearization. According to the present capabilities of this linearization technique, one-dimensional hysteretic elements are used for modeling the non-linear system behavior. The mode acceleration method is applied in order to reduce significantly the size of the system equation and thus increasing the computational efficiency of the proposed procedure. Contrary to methodologies based on state space formulations, this procedure relies on deterministic step by step integration, implying that the dimension of the system equation is the same as in a purely deterministic analysis.