Developing an element free method for higher order shear deformation analysis of plates

• An Element Free Galerkin method based on HSDT for the analysis of laminate plates is developed.
• Shear locking is avoided by considering integration points for shear and bending parts of stiffness matrix; and may be used for very thin plates.
• The method shows rapid convergence and larger displacements with respect to FEM based on HSDT.
• The method shows larger values of deflection for thicker plates when compared to EFG based on FSDT.

A procedure is presented to eliminate transverse shear locking in analysis of laminated composite plates using Element Free Galerkin (EFG) method based on higher-order transverse shear deformation theory (HSDT). In the procedure, derivatives of the transverse displacement are introduced as independent variables. Thus, a formulation requiring C0 continuity shape functions for approximation is proposed for higher-order transverse shear deformation analysis of plates. Shear locking is avoided considering reduced integration for shear stiffness matrix; a method which is implemented in FEM. Moving Least Squares (MLS) method is utilized for shape functions and the penalty method is implemented to impose approximate boundary conditions. The present solutions are verified with other higher-order shear deformable studies. Moreover, a comparison between the present solutions with those obtained by EFG procedure based on First-order transverse Shear Deformation Theory (FSDT) is performed.