@article{34877ec50436479baa347e0a7e36c777,
title = "Advances and trends in computational structural mechanics",
author = "Noor, {Ahmed K.} and Atluri, {Satya N.}",
note = "Funding Information: In probabilistic finite-element methods, the response quantities (stresses, strains, and displacements) are expressed as random variables governed by probability density functions. This allows the uncertainties associated with these response quantities to be treated in a quantitative but realistic manner. Probabilistic finite-element methods were recently formulated for linear and nonlinear continua with inhomogeneous random fields. The random field is discretized in a manner analogous to the discretization of the displacement field in single-field finite-element models111'112 or the displacement and stress fields in multifield finite-element models.70 New approaches are currently being developed to introduce probabilistic aspects of geometry, boundary conditions, material properties, loading conditions, and operational environment directly into the structural analysis formulation for realistic turbine blade models. This work is supported by NASA Lewis and is described in Ref. 51. Also, a state-of-the-art review of probabilistic methods for engineering analysis is given in Ref. 180. Funding Information: The work of A. K. Noor was supported by NASA Langley Research Center, and the work of S. N. Atluri was supported by both the Air Force Office of Scientific Research and the Office of Naval Research. The authors wish to acknowledge useful discussions and suggestions by many of their colleagues, including H. Armen, J. K. Bathe, T. Belytschko, L. Berke, C. C. Chamis, T. A. Cruse, C. A. Felippa, R. T. Haftka, T. J. R. Hughes, W. K. Liu, J. T. Oden, J. Padovan, K. C. Park, L. A. Schmit, J. Sobieski, J. Starnes, O. O. Storaasli, V. B. Venkayya, and K. J. Willam. The constructive comments of the reviewers are also appreciated.",
year = "1987",
month = jul,
doi = "10.2514/3.9731",
language = "English",
volume = "25",
pages = "977--995",
journal = "AIAA Journal",
issn = "0001-1452",
number = "7",
}