Simple Test Functions in Meshless Local Petrov-Galerkin Methods

Two meshless local Petrov-Galerkin methods, based on two different trial functions but that use a simple linear test function, were developed for beam and column problems. These methods used generalized moving least squares and radial basis interpolation functions as trial functions. These two methods were tested on various patch-test problems. Both methods passed the patch tests successfully. Then the methods were applied to various beam vibration problems and problems involving Euler and Beck’s columns. Both methods yielded accurate solutions for all problems studied.