| Abstract: |
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 |
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