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Keywords: finite element method, model reduction, orthogonal vectors set, Rayleigh-Ritz, 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 Rayleigh-Ritz 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

1: R.J. Guyan, "Reduction of stiffness and mass matrices", AIAA Journal, 280 (3), 171-175, 1965
2: Y.T. Leung, "An accurate method of dynamic condensation in structural vibration analysis", International Journal for Numerical Method in Engineering, 12, 1705-1715, 1978. doi:10.1002/nme.1620121108

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 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. Alkhoury¹, M.H. Chikhalsouk¹, R.B. Bhat¹ and K.D.P. Nigam² ¹Department of Mechanical and Industrial Engineering, Concordia University, Montreal, Quebec, Canada ²Department of Chemical Engineering, Indian Institute of Technology, Hauz Khas, New Delhi, India doi:10.4203/ccp.88.185 purchase the full-text of this paper Full Bibliographic Reference for this paper 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", Civil-Comp Press, Stirlingshire, UK, Paper 185, 2008. doi:10.4203/ccp.88.185 Keywords: finite element method, model reduction, orthogonal vectors set, Rayleigh-Ritz, 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 Rayleigh-Ritz 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 1 R.J. Guyan, "Reduction of stiffness and mass matrices", AIAA Journal, 280 (3), 171-175, 1965 2 Y.T. Leung, "An accurate method of dynamic condensation in structural vibration analysis", International Journal for Numerical Method in Engineering, 12, 1705-1715, 1978. doi:10.1002/nme.1620121108 purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £145 +P&P)
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