On optimal selection of interior points for applying discretized boundary conditions in DQ vibration analysis of beams and plates

The direct implementation of derivative boundary conditions at edge points was demonstrated to be simple, flexible and computationally efficient in th e vibration analysis of beams and plates by using the differential quadratu re (DQ) method. In the approach, the discretized governing equations at cer tain interior points need to be replaced by the discretized boundary condit ions. Naturally, one may have questions as to whether the replacement point s can be selected arbitrarily, and how to choose the optimal replacement po ints. This paper tries to answer these questions, and its focus is to inves tigate systematically the effect of the replacement location on the accurac y of the numerical solution. From the error distribution analysis of deriva tive approximation, it is found that the optimal position for the replaceme nt is the interior point just adjacent to the boundary. This conclusion is confirmed by the numerical experiments of free vibration analysis for beams and plates with various boundary conditions. (C) 1999 Academic Press