The application of special matrix product to dierential quadrature solution of geometrically nonlinear bending of orthotropic rectangular plates

The Hadamard and SJT product of matrices are two types of special matrix product. The latter was ®rst de®ned by Chen. In this study, they are applied to the di€erential quadrature (DQ) solution of geometrically nonlinear bending of isotropic and orthotropic rectangular plates. By using the Hadamard product, the nonlinear formulations are greatly simpli®ed, while the SJT product approach minimizes the e€ort to evaluate the Jacobian derivative matrix in the Newton±Raphson method for solving the resultant nonlinear formulations. In addition, the coupled nonlinear formulations for the present problems can easily be decoupled by means of the Hadamard and SJT product. Therefore, the size of the simultaneous nonlinear algebraic equations is reduced by two-thirds and the computing e€ort and storage requirements are greatly alleviated. Two recent approaches applying the multiple boundary conditions are employed in the present DQ nonlinear computations. The solution accuracies are signi®cantly improved in comparison to the previously given by Bert et al. The numerical results and detailed solution procedures are provided to demonstrate the superb eciency, accuracy and simplicity of the new approaches in applying DQ method for nonlinear computations. # 1999 Elsevier Science Ltd. All rights reserved.