6th U.S. National Congress on Computational Mechanics
Proposed Standard for Verification and Validation
SUBSTITUTE ABSTRACTS (#9)
Filtering of the Numerical and Experimental Data at
Arbitrarily Located Points of Plates and Shells
Stanislaw Lukasiewicz and Rong Emily Qian
The University of Calgary
Calgary, 2500 University Dr. NW Alberta, Canada, T2N 1N4
sal@cadvision.com
The purpose of this work is to generalize the previously developed methods for filtering of the
experimental and numerical data [1, 2] to achieve their application for the cases when the data is obtained at
arbitrary points of the surface of the body. The data obtained from measurements or numerical analysis of
various technical problems always contain some errors caused by inaccuracies of measuring techniques and
instruments and also resulting from some imperfections of the numerical methods. The generalization
presented here has the objective to make filtering methods effective also in the cases when the data are
collected at arbitrary points in space or time, and are not necessary located on regular rectangular meshes.
It is assumed that the data have to satisfy certain constraints resulting from the nature of the analyzed
problem. For example, the stresses in the body have to satisfy the conditions of equilibrium and also
equations of continuity of the deformations. These equations can be used in this case as the constraint
equations that have to be imposed on the measured or calculated data. However, as the constraint equations
can be any of any nature, conditions of symmetry, additional boundary condition and even some
technological or manufacturing requirements can be used as constraint equations. The several examples of
the plate and shell problems are presented showing the effectiveness of the method.
The approach presented here can be also utilized in analyzing the data in thermal problems, dynamic
problems, in identification techniques and Finite Element applications. The most important advantage of the
matrix filter algorithm is that the correction of the data is a very fast operation and can be performed in real
time while measurements are performed.
The results obtained from the finite element (FEM) analysis are most often given at arbitrary nodal
points. Due to the fact that the FEM solutions are usually based on displacement method the boundary
conditions in terms of stresses are often not exactly satisfied. The filtering algorithm [1] offers a simple
and effective tool to correct quickly these errors. It is proved that this approach can give the correction also
in the case of the singularities of the stresses at the singular points and at the edges where the boundary
conditions are specified in terms of stresses. For example, the corrections can be done at the free edges of
the body where FEM calculation gives some unrealistic stresses.
References:
[1] S.A. Lukasiewicz, Matrix Filter for Correcting Experimental Data, Communications in Numerical
Methods in Engineering, Vol. 9, 1993, pp. 797-803.
[2] S.A. Lukasiewicz, M. Stanuszek, J. Czyz, Filtering of Experimental and FEM Data in Plain State of
Strain and Stress, Experimental Mechanics, 1993, pp. 139-147.
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