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Meshless Local Petrov-Galerkin Method for Rotating Timoshenko Beam: a Locking-Free Shape Function Formulation

V. Panchore1, R. Ganguli2, S. N. Omkar3

Ph.D. Student, Department of Aerospace Engineering, Indian Institute of Science, Bangalore, India, Email: vijaypanchore@aero.iisc.ernet.in
Professor, Department of Aerospace Engineering, Indian Institute of Science, Bangalore, India, Email: ganguli@aero.iisc.ernet.in
Chief Research Scientist, Department of Aerospace Engineering, Indian Institute of Science, Bangalore, India, Email: omkar@aero.iisc.ernet.in

Computer Modeling in Engineering & Sciences 2015, 108(4), 215-237. https://doi.org/10.3970/cmes.2015.108.215

Abstract

A rotating Timoshenko beam free vibration problem is solved using the meshless local Petrov-Galerkin method. A locking-free shape function formulation is introduced with an improved radial basis function interpolation and the governing differential equations of the Timoshenko beam are used instead of the alternative formulation used by Cho and Atluri (2001). The locking-free approximation overcomes the problem of ill conditioning associated with the normal approximation. The radial basis functions satisfy the Kronercker delta property and make it easier to apply the essential boundary conditions. The mass matrix and the stiffness matrix are derived for the meshless local Petrov-Galerkin method. Results are validated for the fixed-free boundary condition with published literature.

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APA Style
Panchore, V., Ganguli, R., Omkar, S.N. (2015). Meshless local petrov-galerkin method for rotating timoshenko beam: a locking-free shape function formulation. Computer Modeling in Engineering & Sciences, 108(4), 215-237. https://doi.org/10.3970/cmes.2015.108.215
Vancouver Style
Panchore V, Ganguli R, Omkar SN. Meshless local petrov-galerkin method for rotating timoshenko beam: a locking-free shape function formulation. Comput Model Eng Sci. 2015;108(4):215-237 https://doi.org/10.3970/cmes.2015.108.215
IEEE Style
V. Panchore, R. Ganguli, and S.N. Omkar, “Meshless Local Petrov-Galerkin Method for Rotating Timoshenko Beam: a Locking-Free Shape Function Formulation,” Comput. Model. Eng. Sci., vol. 108, no. 4, pp. 215-237, 2015. https://doi.org/10.3970/cmes.2015.108.215



cc Copyright © 2015 The Author(s). Published by Tech Science Press.
This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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