Inverse differential quadrature method for structural analysis of composite plates

Abstract

A novel two-dimensional inverse differential quadrature method is proposed to approximate the solution of high-order system of differential equations. A critical aspect of the proposed scheme is to circumvent the error arising from high sensitivity to noise associated with high-order numerical differentiation operations during direct approximation. A general framework for approximating arbitrary functions from high-order partial derivatives is developed and a comprehensive insight for the implementation of different orders of the analysis within the context of first-order shear deformation theory kinematical assumptions governing laminated plates bending and buckling behaviours is presented. Concerning buckling analysis, a Moore–Penrose pseudo-inverse preconditioning procedure is further proposed to formulate the eigenvalue problem, since the developed algebraic expressions constitute an underdetermined system. According to the numerical tests for bending and buckling analyses of laminated plates under different loading and boundary conditions, the accuracy of current solutions compares satisfactorily with Navier’s solution, differential quadrature method and commercial finite element analysis models. Furthermore, the developed method demonstrates the potential for improved convergence in comparison with differential quadrature solutions highlighting its computational merits.