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

Abstract

The Hadamard and SJT product of matrices are two types of special matrix product. The latter was first defined by Chen. In this study, they are applied to the differential quadrature (DQ) solution of geometrically nonlinear bending of isotropic and orthotropic rectangular plates. By using the Hadamard product, the nonlinear formulations are greatly simplified, while the SJT product approach minimizes the effort 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 effort 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 significantly improved in comparison to the previously given by Bert et al. The numerical results and detailed solution procedures are provided to demonstrate the superb efficiency, accuracy and simplicity of the new approaches in applying DQ method for nonlinear computations.