Size-dependent axisymmetric bending analysis of modified gradient elastic Kirchhoff–Love plates

Abstract

The sixth-order basic differential equation of axisymmetric bending model for modified gradient elastic Kirchhoff–Love plates (MGEKLPs) subjected to both transverse and in-plane loads in cylindrical coordinate system is derived on the basis of the simplified deformation gradient theory and general MGEKLP model in Cartesian coordinates, which incorporates two length-scale parameters related to strain gradient and rotation gradient. Using the variational method, five distinct types of axisymmetric boundary conditions (BCs) corresponding to the basic equation are simultaneously obtained. Specifically, there are two modified classical BCs and one non-classical higher-order BC for each boundary. Applying the axisymmetric MGEKLP model, we present a general solution for size-dependent bending deflection and conduct a specific analysis of axisymmetric bending examples in circular and annular thin plates under transverse loads. The study presents two types of (i.e., singly and doubly) clamped and simply supported BCs and delves into the impact of two distinct higher-order BCs on axisymmetric deflection by examining clamped and simply supported circular thin plates. In addition, based on the axisymmetric bending of an annular thin plate with simply supported inner edge and free outer edge under the action of uniform bending moment, the special case of influence of strain gradient and rotation gradient parameters on axisymmetric deflection are discussed. This study enhances the comprehensiveness of axisymmetric bending deformation of gradient elastic thin plates and can offer theoretical guidance for the microstructure design of bending materials.