Static and stability analyses of arbitrary straight-sided quadrilateral thin plates by DQM

A differential quadrature (DQ) methodology is employed for the static and stability analysis of irregular quadrilateral straight-sided thin plates. A four-noded super element is used to map the irregular physical domain into a square computational domain. Second order transformation schemes with relative ease and low computational effort are employed to transform the fourth order governing equations of thin plates between the domains. Within the domain, the displacements are the only degrees of freedom whereas, along the boundaries, the displacements as well as the second order derivatives of the displacements with respect to the associated normal coordinate variables in the computational domain are the two sets of degrees of freedom. The implementation procedures for different boundary conditions including free-edge boundaries are formulated. To demonstrate the accuracy, convergency and stability of the methodology, detailed studies of skewed and trapezoidal plates for different geometries under different boundary and loading conditions are made. Good agreement is achieved between the results of the present methodology and those of other DQ methodologies or other comparable numerical algorithms