Abstract
The paper is devoted to the application of the second-order perturbation second probabilistic moment method to the stress-based finite element method (FEM). The approach is introduced for the linear elastic heterogeneous medium – up to the second-order, variational equations of the complementary energy principle are presented together with an additional stochastic finite element discretization based on Airy and Prandtl stress functions. The numerical examples shown in this paper illustrate the probabilistic stress and strain tensors in the cantilever beam under shear loading and torsioned square beam with randomly defined material and geometrical parameters. The results obtained in the tests can be applied in probabilistic analyses of the boundary value problems having any closed form mathematical solutions as well as in the stress-based stochastic FEM analysis of solids and structures.
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