TY - EJOU AU - Panchore, V. AU - Ganguli, R. AU - Omkar, S. N. TI - Meshless Local Petrov-Galerkin Method for Rotating Timoshenko Beam: a Locking-Free Shape Function Formulation T2 - Computer Modeling in Engineering \& Sciences PY - 2015 VL - 108 IS - 4 SN - 1526-1506 AB - 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. KW - Meshless local petrov-galerkin method KW - Radial basis function KW - Rotating timoshenko beam KW - Finite element method KW - Free vibration DO - 10.3970/cmes.2015.108.215