Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

A Design-of-Experiments Plug-In for Estimating Uncertainties in Finite Element Simulations



Jeffrey T. Fong, Roland deWit, Pedro V. Marcal, James J. Filliben, Nathanael A. Heckert


The objective of this paper is to introduce an economical and user-friendly technique for estimating a specific type of finite element simulation uncertainties, or, "error bars," for a class of mathematical models, of which no closed-form or approximate solution is known to exist. Using PYTHON, ABAQUS-PYTHON, and a public-domain statistical data analysis software package named DATAPLOT, we present a design-of-experiments-based PYTHON-DATAPLOT-Uncertainty Plug-In (PD-UP) to estimate the finite element simulation uncertainties in a mathematical model due to variability in modeling parameters such as material property constants, geometric parameters, loading rates, etc. Examples of finite element simulations of the free vibrations of a single-crystal silicon cantilever beam in an atomic force microscope with an estimation of the uncertainties of one of the simulation results, namely, the first bending mode resonance frequency of the beam, are included
Proceedings Title
2009 Simulia Customer Conference
Conference Dates
May 18-21, 2009
Conference Location


ABAQUS, ANSYS, Atomic Force Microscope, DATAPLOT, Design of Experiments, Finite Element Method, Mechanics, Nanotechnology, Plug-In, PYTHON, Simulation, Single Crystal Silicon, Statistical Data Analysis, Uncertainty Analysis, Verification, Vibration.


Fong, J. , deWit, R. , Marcal, P. , Filliben, J. and Heckert, N. (2009), A Design-of-Experiments Plug-In for Estimating Uncertainties in Finite Element Simulations, 2009 Simulia Customer Conference, London, -1, [online], (Accessed June 24, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created May 18, 2009, Updated February 19, 2017