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, main objective present study is to propose a novel numerical strategy called multi-patch variational (VDQ) method model structural behavior plate structures obeying shear deformation theory strain gradient elasticity theory. idea divide two-dimensional solution domain into sub-domains, patches, then apply VDQ along with FE mapping technique each patch. formulation presented in weak form due C 1 -continuity requirements corresponding compatibility conditions are applied through patch interfaces. Lagrange multiplier penalty implemented higher-order boundary conditions, respectively. To show efficiency proposed method, results provided both regular irregular domains. examples demonstrate applicability accuracy predicting bending vibration following model.