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

The direct implementation of derivative boundary conditions at edge points was demonstrated to be simple, flexible and computationally ecient in the vibration analysis of beams and plates by using the dierential quadrature (DQ) method. In the approach, the discretized governing equations at certain interior points need to be replaced by the discretized boundary conditions. Naturally, one may have questions as to whether the replacement points can be selected arbitrarily, and how to choose the optimal replacement points. This paper tries to answer these questions, and its focus is to investigate systematically the eect of the replacement location on the accuracy of the numerical solution. From the error distribution analysis of derivative approximation, it is found that the optimal position for the replacement 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. # 1999 Academic Pres