Stochastic second-order perturbation approach to the stress-based finite element method. (English) Zbl 0981.74066

Kaminski, Marcin

Int. J. Solids Struct. 38, No. 21, 3831-3852 (2001).

From the summary: The paper is devoted to the application of the second-order perturbation second probabilistic moment method to the stress-based finite element method. The approach is introduced for the linear elastic heterogeneous medium – up to the second-order, and variational equations of complementary energy principle are presented together with an additional stochastic finite element discretization based on Airy and Prandtl stress functions. Numerical examples illustrate probabilistic stress and strain tensors in a cantilever beam under shear loading, and in a torsioned square beam with randomly defined material and geometrical parameters.

MSC:

74S05	Finite element methods applied to problems in solid mechanics
74A40	Random materials and composite materials
74K10	Rods (beams, columns, shafts, arches, rings, etc.)

Keywords:

Airy function; Prandtl function; Monte Carlo simulation; random material; second-order perturbation second probabilistic moment method; stress-based finite element method; linear elastic heterogeneous medium; variational equations; complementary energy principle; cantilever beam; shear loading; torsioned square beam