A new hybrid meshless-differential order reduction ( hM-DOR) method with applications to shape control of smart structures via distributed sensors/actuators

Abstract

This paper presents the development of a new hybrid numerical method, the hM-DOR method, which is based on an order-reduction technique for partial differential equations, and combines the true-meshless collocation technique with a fixed reproducing kernel approximation. The proposed method is able to directly impose overlapping boundary conditions, a procedure difficult to accomplish with existing collocation-based meshless methods. The present method is applied to examine thin-plate bending for plates of various geometries and different boundary conditions. Its efficiency and accuracy are validated by numerical comparisons with finite element results. Furthermore, it is also used to simulate the deformation shape control of the uniformly loaded smart beams and plates integrated with piezoelectric sensors/actuators. The numerical results here again verify the efficiency of this newly developed method.