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The dual reciprocity method applied to free vibrations of 2D structures using compact supported radial basis functions

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Abstract

This paper presents a new boundary element application for free vibration analysis of 2D elastic structures. The dual reciprocity method is applied using four compact supported radial basis functions for approximating the domain inertia terms. The eigen-problem of displacement is then solved considering the traction contribution by means of static condensation. The formulation is also extended to consider additional internal nodes to improve accuracy. Three numerical problems are studied to demonstrate the validity and accuracy of the developed formulation. The results are compared to those obtained from analytical and other numerical solutions. A parametric study is set up to demonstrate the effect of the compact support radius on the final results and on the sparsity of system matrices.

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Authors and Affiliations

  1. Civil Engineering Department, The Higher Technological Institute, Ramadan 10th city, Cairo, Egypt

    Morcos F. Samaan

  2. Structural Engineering Department, Cairo University, Giza, Egypt

    Youssef F. Rashed & Metwally A. Ahmed

  3. British University in Egypt, Postal No. 11837, P.O. Box 43, El-Sherouk City, Egypt

    Youssef F. Rashed

Authors
  1. Morcos F. Samaan
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  2. Youssef F. Rashed
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  3. Metwally A. Ahmed
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Correspondence to Youssef F. Rashed.

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Samaan, M.F., Rashed, Y.F. & Ahmed, M.A. The dual reciprocity method applied to free vibrations of 2D structures using compact supported radial basis functions. Comput Mech 41, 85–105 (2007). https://doi.org/10.1007/s00466-007-0171-0

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  • DOI: https://doi.org/10.1007/s00466-007-0171-0

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