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Basis random variables in finite element analysis
Author(s) -
Lawrence Mark A.
Publication year - 1987
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620241004
Subject(s) - mathematics , finite element method , basis (linear algebra) , hilbert space , galerkin method , basis function , mathematical analysis , mixed finite element method , moment (physics) , operator (biology) , geometry , structural engineering , physics , biochemistry , chemistry , classical mechanics , repressor , transcription factor , engineering , gene
Galerkin's method is applied to random operator equations. Appropriate Hilbert spaces are defined for random functions and solutions are projected into these spaces, allowing the first‐ and second‐moment properties of the solution to be calculated. An equivalent energy‐based approach similar to the Rayleigh–Ritz method is developed, from which a stochastic finite element technique is derived. Several one‐ and two‐dimensional example problems are solved and the results discussed.