Size-dependent bending behaviors of orthotropic function allygraded microplates

Based on the new modified couple stress theory and Kirchhoff elastic plate theory, the size-dependent bending behaviors of orthotropic functionally graded microplates with material parameters varying continuously along the thickness direction were studied. The basic variables of orthotropic functionally graded microplates, such as stress, couple stress, strain and curvature, were described as the function of partial derivative of displacement component by introducing different material length-scale parameters in two orthogonal directions. The equilibrium equation and boundary conditions of the microplate were derived according to the principle of minimum potential energy. Employing the presented model, the bending behavior of a four-sided simply supported microplate under bidirectional sinusoidal distributed loads with the materials parameters was studied, such as elastic modulus, shear modulus and material length-scale parameters, varying with the thickness in a sinusoidal gradient function. The effects of the ratio of length scale parameters to the plate thickness, material anisotropy and functional graded parameters on the size effects of deflection, normal stress and couple stress were analyzed. The critical geometric dimension parameters of orthotropic functionally graded microplates with consideration of the size effect were quantitatively calibrated. The results show that the solutions of the deflection and normal stress of the microplates are always smaller than those of the classical elastic Kirchhoff plate model. The smaller the ratio of plate thickness to material length scale parameters, the more obvious the size effects of the deflection and normal stress. The size effects of deflection, normal stress and couple stress of the microplate are influenced by the functionally graded parameter. The length-scale parameters in two orthogonal directions have different effects on the scale effects of deflection, normal stress and couple stress of the microplate. © 2020, Central South University Press. All right reserved.