On enforcement of corner conditions in triangular differential quadrature

Abstract

This paper is concerned with the enforcement of corner conditions in the recently proposed triangular differential quadrature method. The sensitivity of solution to some corner conditions is exemplified and a reduced quadrature technique is introduced to overcome the sensitivity. Numerical examples in the context of bending and vibration of Mindlin plates are studied to validate the proposed reduced quadrature technique. It is shown that the technique is effective to cope with sensitivity of solution to corner conditions. The effect of the order of the reduced quadrature on accuracy of solution is also studied. It is found that satisfactory convergence is usually achieved when the order of reduced quadrature employed at a corner is larger than one half of the order of the triangular differential quadrature approximation in the entire triangle but two orders less than the order of the triangular differential quadrature approximation.