The purpose of this research is to model an‎d analyze bending, buckling an‎d free vibration of composite nanoplates using the equilibrated basis function method. The basic theory considered for the plate relationships is the classical plate theory (Kirchhoff’s deformation theory); of course, since the dimensions of the plates in the research are in the nanoscale, the classical elasticity theory cannot be used. Therefore, the theory considered must include the effect of size on the stress distribution. In this research, the nonlocal elasticity theory has been used in two forms: strain gradient for the bending problem an‎d nonlocal strain gradient for the buckling an‎d free vibration problems. After extracting the problem equations, the equilibrated basis functions method will be used to solve it. In this method, weighted integrals are used, an‎d the weight functions of these integrals are exponential functions in Gaussian coordinates. Also, the basis functions of these integrals are of Chebyshev polynomials of the first kind. These functions satisfy the homogeneous form of the differential equations of the problem an‎d therefore, it can be classified as Trefftz methods. Finally, the bending, buckling an‎d free vibration problems of multilayer an‎d FG nanoplates will be investigated, an‎d the method relations will be developed for them. In the first part of this research, the governing equilibrium equations for solving the bending, buckling, an‎d vibration problems of nanoplates, as well as the boundary conditions, are extracted based on the aforementioned theories. The idea an‎d innovation used in this research is in the boundary conditions section. In this section, twelve boundary conditions are extracted, but their use prolongs the problem-solving process an‎d creates complexity an‎d difficulty during problem-solving, so by using this idea, these conditions are reduced to seven. Then, in the next section, several examples from reputable references are presented an‎d examined to verify the validity of the proposed method. In the final section, the obtained results are compared with the results of the aforementioned references. It is observed that the answers obtained from the research method are in very good agreement with the aforementioned references.

بيژن برومند قهنويه , نيما نورمحمدي

نسرين جعفري , حسين عموشاهي