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CivilComp Proceedings
ISSN 17593433 CCP: 88
PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping and M. Papadrakakis
Paper 185
Model Reduction in Finite Element Analysis for a Fluid Filled Pipe Using an Orthogonal Vector Set R.J. Alkhoury^{1}, M.H. Chikhalsouk^{1}, R.B. Bhat^{1} and K.D.P. Nigam^{2}
^{1}Department of Mechanical and Industrial Engineering, Concordia University, Montreal, Quebec, Canada
R.J. Alkhoury, M.H. Chikhalsouk, R.B. Bhat, K.D.P. Nigam, "Model Reduction in Finite Element Analysis for a Fluid Filled Pipe Using an Orthogonal Vector Set", in B.H.V. Topping, M. Papadrakakis, (Editors), "Proceedings of the Ninth International Conference on Computational Structures Technology", CivilComp Press, Stirlingshire, UK, Paper 185, 2008. doi:10.4203/ccp.88.185
Keywords: finite element method, model reduction, orthogonal vectors set, RayleighRitz, pipes, Eigenvalue.
Summary
The finite element analysis of three dimensional structures is often computationally
intensive in view of the large number of degrees of freedom. A model reduction
approach is beneficial especially when only the first few modes of vibration are required.
There have been many studies of the reduction of large eigenvalue problems, for
example, the static condensation or Guyan reduction [1] which implies the selection of
master and slave degrees of freedom. This method is very sensitive to the correct
selection of the categories of the degrees of freedom. Another example is the dynamic
condensation [2] which, beside the slave and master, requires inverting the stiffness
dynamic matrix which is frequency dependant. Some more major studies on reduction
methods are listed in a brief literature review in the introduction. In the present study a
coiled heat exchanger filled with water is studied. The coordinates of the elements were
obtained using MATLAB with a three dimensional curve representing the geometry of
the coil. These coordinates were the input to ANSYS to build the geometry. The mass and
stiffness matrices of the finite element model were extracted from ANSYS and
transferred to MATLAB. A model reduction technique using a set of characteristic
orthogonal vectors was used to reduce the size of the problem. In this method, the
RayleighRitz analysis is employed to obtain the reduced mass and stiffness matrices.
This method takes a set of vectors that are used as transformation matrix to a
generalized coordinates system, which will reduce the model down to the same number
of generalized coordinates. The method of generation of those vectors is presented.
Results were obtained for two models, one with 10 generalized coordinates, resulting in
10x10 reduced matrices and the second with 20 generalized coordinates resulting in
20x20 reduced matrices. Tables containing the proprieties of the materials as well as the
eigenvalues of the reduced and complete models are presented. It is concluded that this
technique is able to predict up to 50% of the natural frequencies with negligible
deviation from the finite element results without the need to supply either the coordinates
or to choose any slave or master degrees of freedom.
References
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