A Mesh-Free Method for Microplates with the Size Effect

This paper investigates the application of a mesh-free method in the numerical simulation of microplates with the size effect. Based on Kirchhoff's thin plate theory, the constitutive relationship of thin microplates is established in the context of strain gradient theory, in which the intrinsic material length parameter is introduced to capture the size effect. The moving least-square approximation is adopted to produce the shape function and its high-order derivatives, and a mesh-free computational scheme is developed to study the static bending behavior of the microplates. A distinguishing property associated with this method is that the first- to fourth-order derivatives of deflection are directly approximated with the nodal deflections by virtue of the higher-order continuum property of the shape function and that only nodal deflections are treated as unknowns. Numerical examples are presented to show the efficiency of the present method, and the effect of the scale parameter is studied numerically.