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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.

Keywords

Meshless local petrov-galerkin method, Radial basis function, Rotating timoshenko beam, Finite element method, Free vibration.

Cite This Article

Panchore, V., Ganguli, R., Omkar, S. N. (2015). Meshless Local Petrov-Galerkin Method for Rotating Timoshenko Beam: a Locking-Free Shape Function Formulation. CMES-Computer Modeling in Engineering & Sciences, 108(4), 215–237.



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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