## 1 Introduction  
Nowadays, it is well established that the usual material properties at the nanoscale, such as Young's modulus, may significantly differ from what is observed at the macroscale. For example, Young's modulus becomes size-dependent; see, e.g., [1; 2; 3]. In other words, Young's modulus at the nanoscale depends on a specimen characteristic size. In fact, it describes the tensional stiffness of the considered specimen, which obviously can be size-dependent. In addition to tensional stiffness, there exist various other stiffness parameters such as bending and torsional stiffnesses, known from textbooks on the strength of materials. In particular, these parameters may characterize the behaviour of thin structures of nanometer size. For example, a bending stiffness can be directly measured using atomic force microscopy [4; 5; 6].  
The idea of the bending stiffness of a plate belongs to [PERSON], who defined it as follows [7; 8]  
\[D=\frac{Eh^{3}}{12(1-\
u^{2})},\quad M=D\kappa, \tag{1}\]  
where \(E\) and \(\
u\) are [PERSON]'s modulus and [PERSON]'s ratio, \(h\) is the plate thickness, \(M\) is a bending moment, and \(\kappa\) is the curvature of a bent plate. By considering the bending of plates only, we can restrict ourselves to two material parameters that are \(D\) and \(\
u\). So, in the \"world of plates\", \(D\) plays the role of an independent material parameter. In the literature, one can find various extensions of [PERSON]'s formula for more complex cases such as layered plates and plates with surface and interfacial stresses, etc.  
The aim of this paper is to discuss the bending stiffness of layered nanosized plates. To this end, we consider the classic linear elasticity as a model for material properties in the bulk and the Steigmann-Ogden surface elasticity [9; 10] for the modelling of plate faces and interfaces between layers. Let us note that surface elasticity models [9; 10; 11; 12] were used for the modelling of surface-related phenomena and of nanometer-sized solids; see, e.g., [13; 14; 15; 16; 17; 18; 19] and references therein. When considering thin-walled structures, it is worth mentioning nonlocal models, which can also describe size effects. For the derivation of the governing equations of plates and shells using [PERSON]'s type nonlocality, we refer to [20; 21] and the references therein. Let us note tat the surface elasticity models can be treated as a singular case of nonlocality related to the appearance of boundary layers near shell faces. Similarities between the linear Gurtin-Murdoch model and the Toupin-Mindlin strain gradient elasticity were discussed in [16], whereas, in [22], a comparison with lattice dynamics was provided.  
The paper is organized as follows. First, in Section 2, we briefly recall the basic governing equations of the Steigmann-Ogden surface elasticity. Here, we present the equilibrium equations in the bulk as well as the static boundary conditions derived through the Lagrange variational principle. In Section 3, we apply these equations to a laminate plate. By integrating trough-the-thickness, we obtain a layer-wise two-dimensional (2D) model of the plate. In order to find the bending stiffness of the whole plate, we consider a mean bending deflection in Section 4.