On the direct approach in the theory of second gradient plates

Abstract

The aim of the paper is to formulate the two-dimensional governing equations in the theory of elastic second gradient plates, that is plates which constitutive equations include second gradients of strain and/or stress measures. Here we use socalled direct approach to modeling of plates and shells. According to the approach a plate is considered as a material deformed surface and all equations are written as for two-dimensional continuum. Here we use the six-parameter theory of shells.Within the framework of the six-parameter theory the kinematics of a shell is described by two independent fields of translations and rotations. We introduce the linear constitutive equations of six-parameter second gradient plates. Considering a deflection of a plate we discuss peculiarities of these models.