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

Panchore, V and Ganguli, R and Omkar, SN (2016) Meshless Local Petrov-Galerkin Method for Rotating Timoshenko Beam: a Locking-Free Shape Function Formulation. In: CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 108 (4). pp. 215-237.

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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.

Item Type: Journal Article
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Additional Information: Copy right for this article belongs to the TECH SCIENCE PRESS, 6825 JIMMY CARTER BLVD, STE 1850, NORCROSS, GA 30071 USA
Keywords: Meshless local petrov-galerkin method; Radial basis function; Rotating timoshenko beam; Finite element method; Free vibration
Department/Centre: Division of Mechanical Sciences > Aerospace Engineering (Formerly, Aeronautical Engineering)
Date Deposited: 15 Jun 2016 05:32
Last Modified: 15 Jun 2016 05:32
URI: http://eprints.iisc.ernet.in/id/eprint/53939

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