The Mathematica Journal
Departments
Feature Articles
Columns
New Products
New Publications
Classifieds
Calendar
News Bulletins
Mailbox
Letters
FAQ
Write Us
About the Journal
Staff and Contributors
Submissions
Subscriptions
Advertising
Back Issues
Home
Download this Issue

System Stochasticity: Discrete Formulation with Mathematica

Gautam Dasgupta
Professor, Civil Engineering and Engineering Mechanics
Columbia University
600 Seeley W. Mudd
New York, NY 10027, USA
gd18@columbia.edu

Material and geometrical randomness are depicted by the variability of numerical solutions. This second-order effect in response cannot be faithfully captured unless the equilibrium equation is exactly satisfied. Hence engineering approximations of system stochasticity demand higher accuracy than their deterministic counterparts.

Consequently, the contamination in numerical responses cannot be removed by selecting large Monte Carlo samples. Stochastic shape functions and stochastic Green's functions constitute the bases for finite and boundary elements, respectively. These fundamental solutions need to be modified distinctly for each Monte Carlo representative via symbolic manipulation of the governing algebraic equation. The subsequent closed-form analytical integration of the energy density function is illustrated here for a beam problem with geometrical stochasticity after zero shear locking is met in a patch test.

south.rotol.ramk.fi/~keranen/IMS99/paper56/ims99paper56.nb


Copyright © 2001 Wolfram Media, Inc. All rights reserved.

[Article Index][Prev Page][Next Page]