MCCEFF swMATH ID: 6179 Software Authors: Kamiński, Marcin Description: On semi-analytical probabilistic finite element method for homogenization of the periodic fiber-reinforced composites. The main aim of this paper is a development of the semi-analytical probabilistic version of the finite element method (FEM) related to the homogenization problem. This approach is based on the global version of the response function method and symbolic integral calculation of basic probabilistic moments of the homogenized tensor and is applied in conjunction with the effective modules method. It originates from the generalized stochastic perturbation-based FEM, where Taylor expansion with random parameters is not necessary now and is simply replaced with the integration of the response functions. The hybrid computational implementation of the system MAPLE with homogenization-oriented FEM code MCCEFF is invented to provide probabilistic analysis of the homogenized elasticity tensor for the periodic fiber-reinforced composites. Although numerical illustration deals with a homogenization of a composite with material properties defined as Gaussian random variables, other composite parameters as well as other probabilistic distributions may be taken into account. The methodology is independent of the boundary value problem considered and may be useful for general numerical solutions using finite or boundary elements, finite differences or volumes as well as for meshless numerical strategies. Homepage: http://www.sciencedirect.com/science/article/pii/S0045782599004247 Keywords: finite element method; homogenization method; Gaussian random variables; non linear least squares method; probabilistic moments Related Software: Maple Cited in: 5 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year On semi-analytical probabilistic finite element method for homogenization of the periodic fiber-reinforced composites. Zbl 1235.74290Kamiński, Marcin 2011 Cited by 4 Authors 4 Kamiński, Marcin Marek 1 Lauke, Bernd 1 Wu, Yuching 1 Xiao, Jianzhuang Cited in 3 Serials 2 International Journal for Numerical Methods in Engineering 1 CMES. Computer Modeling in Engineering & Sciences 1 International Journal of Computational Methods all top 5 Cited in 6 Fields 3 Mechanics of deformable solids (74-XX) 1 Partial differential equations (35-XX) 1 Probability theory and stochastic processes (60-XX) 1 Numerical analysis (65-XX) 1 Fluid mechanics (76-XX) 1 Statistical mechanics, structure of matter (82-XX) Citations by Year