Three versions of the finite element method based on concepts of either stochasticity, fuzziness, or anti-optimization

Author Type

Faculty

Co-Author Type 1

Outside Researcher

Co-Author Type 2

Outside Researcher

Co-Author Type 3

Outside Researcher

College

Engineering and Computer Science

Department

Ocean and Mechanical Engineering

Document Type

Article

Publication/Event/Conference Title

Applied Mechanics Reviews

Publication Status

Version of Record

Abstract

In this review article, we describe in some detail three versions of the FEM pertinent to the uncertainty triangle, introduced by the present writer; in particular, to describe various types of uncertainties in the structure, namely a) non-perturbational finite element method for stochastic structures, b) finite element method associated with determination of least favorable responses through the method of anti-optimization in interval setting of parameters, and c) finite element method based on the fuzzy sets. The comparison between the probabilistic and convex modeling of uncertainty is conducted. The combined optimization and anti-optimization due to presence uncertainty is advocated. The author trusts that hybrid approaches, rather than a) genuine probabilistic treatment, b) anti-optimization, or c) fuzzy-sets-based modeling are called for to rigorously treat the realistic structures. In the end, the issue of relative robustness of these approaches is discussed. This review should be viewed as a continuation of our previous essays about non-probabilistic modeling of uncertainty, random vibrations, and introduction of initial imperfection-sensitivity concept into design, respectively (Comput Struct, 1995; Appl Mech Rev, 1995; NASA SP, 1998; Comput Meth in Appl Mech Eng, with Ren Y J, 1998), devoted to various aspects of uncertainty modeling in engineering. As its predecessors, it contains personal perspectives on the subject. It is envisioned, that at a later stage, these reviews, combined, will be published as a book, Thoughts on Uncertainty. © 1998 American Society of Mechanical Engineers.

First Page

209

Last Page

218

DOI

10.1115/1.3098998

Publication Date

1-1-1998

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