Multi‐patch variational differential quadrature method for shear‐deformable strain gradient plates

The integration of generalized differential quadrature techniques and finite element (FE) methods has been developed during the past decade for engineering problems within classical continuum theories. Hence, the main objective of the present study is to propose a novel numerical strategy called the multi-patch variational differential quadrature (VDQ) method to model the structural behavior of plate structures obeying the shear deformation plate theory within the strain gradient elasticity theory. The idea is to divide the two-dimensional solution domain of the plate model into sub-domains, called patches, and then to apply the VDQ method along with the FE mapping technique for each patch. The formulation is presented in a weak form and due to the C1-continuity requirements the corresponding compatibility conditions are applied through the patch interfaces. The Lagrange multiplier technique and the penalty method are implemented to apply the higher-order compatibility conditions and boundary conditions, respectively. To show the efficiency of the proposed method, numerical results are provided for plate structures with both regular and irregular solution domains. The provided numerical examples demonstrate the applicability and accuracy of the method in predicting the bending and vibration behavior of plate structures following the higher-order plate model.