Abstract：Radial basis collocation method is introduced to analyze the bending problems of Timoshenko beam and Reissner-Mindlin plate. Radial basis functions are employed to be the approximation, collocation method is utilized for discretization, and least squares approach is adopted to solve the discretized equations. No mesh will be required in the discretization and resolution and so radial basis collocation method is a truly meshfree method. 1-D radial basis functions can represent all the 2-D or 3-D radial functions which greatly reduce the memory space.
No integration will be used in collocation method which improves the computational efficiency. For resolving the problems of thin Timoshenko beam and Reissner-Mindlin plate, analysis demonstrates that radial basis collocation method is free of locking since the shape functions with infinite continuity can satisfy the Kirchhoff constraint conditions, and no stress oscillation will be observed, while conventional finite element method and conventional meshfree methods suffer locking problems. The advantages of this approach include easy discretization and implementation, and possessing exponential convergence and high efficiency. Numerical examples validate the conclusions and the stability of this proposed method.
2012, Vol. 33 
