Differential quadrature finite difference method for structural mechanics problems

Abstract

AbstractThe differential quadrature finite difference method (DQFDM) has been proposed by the author. The finite difference operators are derived by the differential quadrature (DQ). They can be obtained by using the weighting coefficients for DQ discretizations. The derivation is straight and easy. By using different orders or the same order but different grid DQ discretizations for the same derivative or partial derivative, various finite difference operators for the same differential or partial differential operator can be obtained. Finite difference operators for unequally spaced and irregular grids can also be generated through the use of generic differential quadrature (GDQ). The derivation of higher‐order finite difference operators is also easy. By adopting the same order of approximation for all mathematical terms existing in the problem to be solved, excellent convergence can be obtained due to the consistent approximation.The DQFDM is effective for solving structural mechanics problems. The numerical simulations for solving anisotropic nonuniform plate problems and two‐dimensional plane elasticity problems are carried out. Numerical results are presented. They demonstrate the DQFDM. Copyright © 2001 John Wiley Sons, Ltd.