Summary
The new approach for application of boundary conditions in the differential quadrature (DQ) method, proposed earlier by the present authors, is extended to generalized force boundary conditions in two dimensions. A variety of problems is then analyzed by theDQ method with the new approach for application of boundary conditions, such as deflections of beams and circular and rectangular plates under nonuniformly distributed loadings, deflection of a rectangular plate on a Winkler foundation, and buckling and free vibrational analyses of circular plates. It is found that the present method gives good accuracy and is computationally efficient. Exact solutions can be obtained by theDQ method if analytical solutions are polynomials and the method is insensitive to the spacing of grid points for the cases considered.
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Bert, C.W., Wang, X. & Striz, A.G. Static and free vibrational analysis of beams and plates by differential quadrature method. Acta Mechanica 102, 11–24 (1994). https://doi.org/10.1007/BF01178514
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DOI: https://doi.org/10.1007/BF01178514