Integrated Local Petrov-Galerkin Sinc Method for Structural Mechanics Problems
An integrated, local Petrov-Galerkin Sinc method is introduced and applied to static structural mechanics problems. The method approximates the highest derivative in the local weak form of the governing equation on a rectangular grid, and the lower derivatives and unknown function are found by numerical indenite integration. We suggest that the essential boundary conditions may be applied by the traditional penalty method or by a method in which the stiness matrix is reduced to eliminate dependent degrees of freedom. We propose and compare the performance of three basis functions in terms of their accuracy and convergence properties for two problems: a one-dimensional tapered bar and a two-dimensional plane-stress elasticity problem. Our results indicate that the present method can provide greater accuracy than the Sinc method based on Interpolation of Highest-Derivative, an integration based collocation method suggested by Li and Wu [Li, C. and Wu, X., Numerical solution of dierential equations using Sinc method based on