An improved moving Kriging meshfree method for plate analysis using a refined plate theory. (November 2016) - Thai, Chien H.; Nguyen, Tan N.; Rabczuk, T.; Nguyen-Xuan, H.
Highlights: A correlation polynomial function for a moving Kriging interpolation-based meshfree method is exploited. A two-variable refined formulation is presented for plate analysis. A rotation-free technique based on isogeometric analysis is formulated for meshfree methods. The proposed method is insensitive to shear locking. The numerical results show excellent performance of the present method. Abstract: This paper proposes a simple and efficient approach based on a moving Kriging interpolation-based (MKI) meshfree method and a two-variable refined plate theory for static, free vibration and buckling analyses of isotropic plates. A generalized formulation through various higher-order distributed functions is presented. Shear correction factors are not required due to zero-shear stresses satisfied at the top and bottom surfaces of plates. The governing partial differential equations are discretized by a weak Galerkin form and numerically solved by using MKI basis functions. The present theory considers the transverse, shear deflections and their derivations while only the deflections are included in approximate solutions. A new correlation function is proposed to construct MKI shape functions so that the underlying solution becomes stable. In addition, a rotation-free technique based on isogeometric analysis is presented to enforce boundary conditions of normal slopes for clamped plate cases, which is simpler and more efficient than several existing approaches. Numerical results show excellent performance of the present method.